From 4e70fbe95cb7a00fa52f64d15a3800a8896a402a Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Tue, 9 Sep 2025 20:10:00 -0700 Subject: [PATCH 01/29] Minor format change --- flystar/tests/test_startable.py | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 9962c05..cf3be71 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -554,9 +554,15 @@ def make_star_table(): starlist_names = np.array(['file1', 'file2', 'file3', 'file4', 'file5', 'file6', 'file7', 'file8']) # Generate the startable - startable = StarTable(name=name_in, x=x_in, y=y_in, m=m_in, xe=xe_in, ye=ye_in, me=me_in, n=n_in, - ref_list=1, - list_times=starlist_times, list_names=starlist_names) + startable = StarTable( + name=name_in, + x=x_in, y=y_in, m=m_in, + xe=xe_in, ye=ye_in, me=me_in, + n=n_in, + ref_list=1, + list_times=starlist_times, + list_names=starlist_names + ) return startable From 243b56f675d0757623861ec4d270b311691153a9 Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Wed, 17 Sep 2025 00:00:27 -0700 Subject: [PATCH 02/29] Remove 2-epoch linear fitting as scipy/matrix already handles it; Fixed absolute sigma in Linear model --- flystar/motion_model.py | 117 ++++++++++++++++++++-------------------- 1 file changed, 59 insertions(+), 58 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index ebf4c46..39e2573 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -3,7 +3,7 @@ import pdb from flystar import parallax from astropy.time import Time -from scipy.optimize import curve_fit +from scipy.optimize import curve_fit, OptimizeWarning import warnings class MotionModel(ABC): @@ -207,64 +207,65 @@ def run_fit(self, t, x, y, xe, ye, t0, weighting='var', params_guess=None, if params_guess is None: params_guess = [x.mean(),0.0,y.mean(),0.0] - # Handle 2-data point case - if len(np.unique(dt))==2: - if len(x)>2: # Catch case where bootstrap sends only 2 unique epochs - _,idx=np.unique(dt, return_index=True) - dt = dt[idx] - x = x[idx] - y = y[idx] - xe = xe[idx] - ye = ye[idx] - dx = np.diff(x)[0] - dy = np.diff(y)[0] - dt_diff = np.diff(dt)[0] - vx = dx / dt_diff - vy = dy / dt_diff - # TODO: still not sure about the error handling here - x0 = x[0] - dt[0]*vx # np.average(x, weights=x_wt) # - y0 = y[0] - dt[0]*vy # np.average(y, weights=y_wt) # - x0e = np.abs(dx) / 2**0.5 # np.sqrt(np.sum(xe**2)/2) # - y0e = np.abs(dy) / 2**0.5 # np.sqrt(np.sum(ye**2)/2) # - vxe = 0.0 #np.abs(vx) * np.sqrt(np.sum(xe**2/x**2)) - vye = 0.0 #np.abs(vy) * np.sqrt(np.sum(ye**2/y**2)) - + if use_scipy: + def linear(t, c0, c1): + return c0 + c1*t + x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) + x0, vx = x_opt + y0, vy = y_opt + x0e, vxe = np.sqrt(x_cov.diagonal()) + y0e, vye = np.sqrt(y_cov.diagonal()) + x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) else: - if use_scipy: - def linear(t, c0, c1): - return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) - x0, vx = x_opt - y0, vy = y_opt - x0e, vxe = np.sqrt(x_cov.diagonal()) - y0e, vye = np.sqrt(y_cov.diagonal()) - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) - else: - # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme - x = np.array(x) - y = np.array(y) - dt = np.array(dt) - X_mat_t = np.vander(dt, 2) - # x calculation - W_mat_x = np.diag(x_wt) - XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t - pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix - popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution - perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution - # y calculation - W_mat_y = np.diag(y_wt) - XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t - pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix - popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution - perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution - # prepare values to return - x0, vx = popt_x[1], popt_x[0] - y0, vy = popt_y[1], popt_y[0] - x0e, vxe = perr_x[1], perr_x[0] - y0e, vye = perr_y[1], perr_y[0] - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) - + # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme + x = np.array(x) + y = np.array(y) + dt = np.array(dt) + X_mat_t = np.vander(dt, 2) + # x calculation + W_mat_x = np.diag(x_wt) + XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t + pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix + popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution + perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution + # y calculation + W_mat_y = np.diag(y_wt) + XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t + pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix + popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution + perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution + # prepare values to return + vx, x0 = popt_x + vy, y0 = popt_y + vxe, x0e = perr_x + vye, y0e = perr_y + x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) + + residual_x = x - X_mat_t @ popt_x + residual_y = y - X_mat_t @ popt_y + + chi2_x = residual_x.T @ W_mat_x @ residual_x + chi2_y = residual_y.T @ W_mat_y @ residual_y + + if not absolute_sigma: + degree_of_freedom = len(x) - 2 + if degree_of_freedom > 0: + reduced_chi2_x = chi2_x/(len(x) - 2) + reduced_chi2_y = chi2_y/(len(x) - 2) + x0e *= reduced_chi2_x**0.5 + y0e *= reduced_chi2_y**0.5 + vxe *= reduced_chi2_x**0.5 + vye *= reduced_chi2_y**0.5 + else: + warnings.warn( + "Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to infinity.", + OptimizeWarning, stacklevel=2 + ) + x0e *= np.inf + y0e *= np.inf + vxe *= np.inf + vye *= np.inf params = [x0, vx, y0, vy] param_errors = [x0e, vxe, y0e, vye] return params, param_errors From 138546437d9a8adf352d15b7e2f4800c181c0c6c Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Wed, 17 Sep 2025 00:13:30 -0700 Subject: [PATCH 03/29] Add testing function for both absolute_sigma True and False --- flystar/tests/test_motion_model.py | 219 +++++++++++++++++++++++++++++ 1 file changed, 219 insertions(+) diff --git a/flystar/tests/test_motion_model.py b/flystar/tests/test_motion_model.py index a5d8fdb..2fa1b57 100755 --- a/flystar/tests/test_motion_model.py +++ b/flystar/tests/test_motion_model.py @@ -1,6 +1,8 @@ from flystar import motion_model import numpy as np import pytest +import matplotlib.pyplot as plt +from scipy.optimize import curve_fit def within_error(true_val, fit_val, fit_err, n_sigma=3): #print('True', true_val, 'Fit', fit_val, 'Fit err', fit_err) @@ -278,3 +280,220 @@ def test_Parallax_PA(): dat_pa90 = mod_pa90.get_pos_at_time([y0,vy,-x0,-vx,pi],[2020.0],t_set) assert (np.abs(dat_pa0[0]-(-dat_pa90[1]))<1e-10).all() assert (np.abs(dat_pa0[1]-(dat_pa90[0]))<1e-10).all() + + +def test_Linear_fit_vs_scipy(): + # Compare Linear fit results to scipy curve_fit results + t = np.array([0, 1., 2.2, 3.5, 5.]) + + x = np.array([ + [0., 0.5, 2.1, 3.2, 6.0], # Increasing 5 Epochs + [10.0, 8.9, 9.2, 7.4, 7.0], # Decreasing 5 Epochs + [2.5, np.nan, 5.2, np.nan, 5.0], # 3 Epochs + [np.nan, 6.2, np.nan, np.nan, 9.2], # 2 Epochs + # [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch + # [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs + ]) + + y = np.array([ + [10.2, 8.5, 9.1, 12.2, 13.0], # Increasing 5 Epochs + [8.0, 9.9, 8.2, 7.4, 7.0], # Decreasing 5 Epochs + [5.2, np.nan, 4.7, np.nan, 6.0], # 3 Epochs + [np.nan, 1.2, np.nan, np.nan, 3.2], # 2 Epochs + # [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch + # [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs + ]) + + xe = np.array([ + [0.2, 0.5, 0.3, 0.4, 0.6], + [0.5, 0.2, 0.7, 0.3, 0.2], + [0.5, np.nan, 0.6, np.nan, 0.3], + [np.nan, 0.6, np.nan, np.nan, 0.3], + # [np.nan, 0.4, np.nan, np.nan, np.nan], + # [np.nan, np.nan, np.nan, np.nan, np.nan] + ]) + + ye = np.array([ + [0.3, 0.2, 0.5, 0.2, 0.4], + [0.2, 0.5, 0.6, 0.4, 0.2], + [0.7, np.nan, 0.5, np.nan, 0.2], + [np.nan, 0.4, np.nan, np.nan, 0.5], + # [np.nan, 0.5, np.nan, np.nan, np.nan], + # [np.nan, np.nan, np.nan, np.nan, np.nan] + ]) + + x = np.ma.masked_invalid(x) + y = np.ma.masked_invalid(y) + xe = np.ma.masked_invalid(xe) + ye = np.ma.masked_invalid(ye) + mask = np.ma.getmaskarray(x) | np.ma.getmaskarray(y) | np.ma.getmaskarray(xe) | np.ma.getmaskarray(ye) + + # tab = StarTable({ + # 'x': x, + # 'y': y, + # 'xe': xe, + # 'ye': ye + # }) + # tab.meta['LIST_TIMES'] = t + # tab.fit_velocities(use_scipy=True, absolute_sigma=True) + + # Plot data + N = x.shape[0] + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6)) + for i in range(N): + line_mask = ~np.isnan(x[i]) & ~mask[i] + ax1.errorbar(t[line_mask], x[i][line_mask], yerr=xe[i][line_mask], fmt='o-', label=f'Line {i}') + ax2.errorbar(t[line_mask], y[i][line_mask], yerr=ye[i][line_mask], fmt='o-', label=f'Line {i}') + ax1.set_xlabel('Time') + ax1.set_ylabel('Position') + ax1.legend() + ax1.set_title('X vs Time') + ax2.set_xlabel('Time') + ax2.set_ylabel('Position') + ax2.legend() + ax2.set_title('Y vs Time') + plt.show() + + N = len(x) + t0 = np.average(np.broadcast_to(t, x.shape), weights=1./np.hypot(xe, ye), axis=1) + dt = np.zeros_like(x) + + # velfit + # vx_velfit = np.zeros(N) + # vxe_velfit = np.zeros(N) + # vy_velfit = np.zeros(N) + # vye_velfit = np.zeros(N) + # x0_velfit = np.zeros(N) + # x0e_velfit = np.zeros(N) + # y0_velfit = np.zeros(N) + # y0e_velfit = np.zeros(N) + + # scipy + vx_scipy = np.zeros(N) + vxe_scipy = np.zeros(N) + vy_scipy = np.zeros(N) + vye_scipy = np.zeros(N) + x0_scipy = np.zeros(N) + x0e_scipy = np.zeros(N) + y0_scipy = np.zeros(N) + y0e_scipy = np.zeros(N) + + # motion_model + mm = motion_model.Linear() + + vx_mm_scipy = np.zeros(N) + vxe_mm_scipy = np.zeros(N) + vy_mm_scipy = np.zeros(N) + vye_mm_scipy = np.zeros(N) + x0_mm_scipy = np.zeros(N) + x0e_mm_scipy = np.zeros(N) + y0_mm_scipy = np.zeros(N) + y0e_mm_scipy = np.zeros(N) + + vx_mm = np.zeros(N) + vxe_mm = np.zeros(N) + vy_mm = np.zeros(N) + vye_mm = np.zeros(N) + x0_mm = np.zeros(N) + x0e_mm = np.zeros(N) + y0_mm = np.zeros(N) + y0e_mm = np.zeros(N) + + def linear(t, c0, c1): + return c0 + c1*t + + # Absolute sigma + for absolute_sigma in [True, False]: + for i in range(N): + dt[i] = t - t0[i] + + # # velfit.linear_fit + # vx_velfit_results = linear_fit(dt[i][~mask[i]], x[i][~mask[i]], sigma=xe[i][~mask[i]], absolute_sigma=absolute_sigma) + # vy_velfit_results = linear_fit(dt[i][~mask[i]], y[i][~mask[i]], sigma=ye[i][~mask[i]], absolute_sigma=absolute_sigma) + + # vx_velfit[i] = vx_velfit_results['slope'] + # vxe_velfit[i] = vx_velfit_results['e_slope'] + # vy_velfit[i] = vy_velfit_results['slope'] + # vye_velfit[i] = vy_velfit_results['e_slope'] + # x0_velfit[i] = vx_velfit_results['intercept'] + # x0e_velfit[i] = vx_velfit_results['e_intercept'] + # y0_velfit[i] = vy_velfit_results['intercept'] + # y0e_velfit[i] = vy_velfit_results['e_intercept'] + + # scipy.curve_fit + p0x = np.array([0., x[i][~mask[i]].mean()]) + p0y = np.array([0., y[i][~mask[i]].mean()]) + popt_x, pcov_x = curve_fit(linear, dt[i][~mask[i]], x[i][~mask[i]], p0=p0x, sigma=xe[i][~mask[i]], absolute_sigma=absolute_sigma) + vx_scipy[i], vxe_scipy[i] = popt_x[1], np.sqrt(pcov_x[1, 1]) + x0_scipy[i], x0e_scipy[i] = popt_x[0], np.sqrt(pcov_x[0, 0]) + popt_y, pcov_y = curve_fit(linear, dt[i][~mask[i]], y[i][~mask[i]], p0=p0y, sigma=ye[i][~mask[i]], absolute_sigma=absolute_sigma) + vy_scipy[i], vye_scipy[i] = popt_y[1], np.sqrt(pcov_y[1, 1]) + y0_scipy[i], y0e_scipy[i] = popt_y[0], np.sqrt(pcov_y[0, 0]) + + # motion_model without scipy + params, param_errs = mm.fit_motion_model( + t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], + xe[i][~mask[i]], ye[i][~mask[i]], t0[i], + weighting='var', + use_scipy=False, + absolute_sigma=absolute_sigma + ) + vx_mm[i] = params[mm.fitter_param_names.index('vx')] + vy_mm[i] = params[mm.fitter_param_names.index('vy')] + vxe_mm[i] = param_errs[mm.fitter_param_names.index('vx')] + vye_mm[i] = param_errs[mm.fitter_param_names.index('vy')] + x0_mm[i] = params[mm.fitter_param_names.index('x0')] + y0_mm[i] = params[mm.fitter_param_names.index('y0')] + x0e_mm[i] = param_errs[mm.fitter_param_names.index('x0')] + y0e_mm[i] = param_errs[mm.fitter_param_names.index('y0')] + + # motion_model with scipy + params, param_errs = mm.fit_motion_model( + t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], + xe[i][~mask[i]], ye[i][~mask[i]], t0[i], + weighting='var', + use_scipy=True, + absolute_sigma=absolute_sigma + ) + vx_mm_scipy[i] = params[mm.fitter_param_names.index('vx')] + vy_mm_scipy[i] = params[mm.fitter_param_names.index('vy')] + vxe_mm_scipy[i] = param_errs[mm.fitter_param_names.index('vx')] + vye_mm_scipy[i] = param_errs[mm.fitter_param_names.index('vy')] + x0_mm_scipy[i] = params[mm.fitter_param_names.index('x0')] + y0_mm_scipy[i] = params[mm.fitter_param_names.index('y0')] + x0e_mm_scipy[i] = param_errs[mm.fitter_param_names.index('x0')] + y0e_mm_scipy[i] = param_errs[mm.fitter_param_names.index('y0')] + + rtol = 1e-5 + # np.testing.assert_allclose(vx_velfit, vx_scipy, rtol=rtol) + # np.testing.assert_allclose(vxe_velfit, vxe_scipy, rtol=rtol) + # np.testing.assert_allclose(vy_velfit, vy_scipy, rtol=rtol) + # np.testing.assert_allclose(vye_velfit, vye_scipy, rtol=rtol) + # np.testing.assert_allclose(x0_velfit, x0_scipy, rtol=rtol) + # np.testing.assert_allclose(x0e_velfit, x0e_scipy, rtol=rtol) + # np.testing.assert_allclose(y0_velfit, y0_scipy, rtol=rtol) + # np.testing.assert_allclose(y0e_velfit, y0e_scipy, rtol=rtol) + # np.testing.assert_allclose(vx_velfit, vx_mm, rtol=rtol) + # np.testing.assert_allclose(vxe_velfit, vxe_mm, rtol=rtol) + # np.testing.assert_allclose(vy_velfit, vy_mm, rtol=rtol) + # np.testing.assert_allclose(vye_velfit, vye_mm, rtol=rtol) + # np.testing.assert_allclose(x0_velfit, x0_mm, rtol=rtol) + # np.testing.assert_allclose(x0e_velfit, x0e_mm, rtol=rtol) + # np.testing.assert_allclose(y0_velfit, y0_mm, rtol=rtol) + # np.testing.assert_allclose(y0e_velfit, y0e_mm, rtol=rtol) + np.testing.assert_allclose(vx_scipy, vx_mm, rtol=rtol) + np.testing.assert_allclose(vxe_scipy, vxe_mm, rtol=rtol) + np.testing.assert_allclose(vy_scipy, vy_mm, rtol=rtol) + np.testing.assert_allclose(vye_scipy, vye_mm, rtol=rtol) + np.testing.assert_allclose(x0_scipy, x0_mm, rtol=rtol) + np.testing.assert_allclose(x0e_scipy, x0e_mm, rtol=rtol) + np.testing.assert_allclose(y0_scipy, y0_mm, rtol=rtol) + np.testing.assert_allclose(y0e_scipy, y0e_mm, rtol=rtol) + np.testing.assert_allclose(vx_scipy, vx_mm_scipy, rtol=rtol) + np.testing.assert_allclose(vxe_scipy, vxe_mm_scipy, rtol=rtol) + np.testing.assert_allclose(vy_scipy, vy_mm_scipy, rtol=rtol) + np.testing.assert_allclose(vye_scipy, vye_mm_scipy, rtol=rtol) + np.testing.assert_allclose(x0_scipy, x0_mm_scipy, rtol=rtol) + np.testing.assert_allclose(x0e_scipy, x0e_mm_scipy, rtol=rtol) + np.testing.assert_allclose(y0_scipy, y0_mm_scipy, rtol=rtol) + np.testing.assert_allclose(y0e_scipy, y0e_mm_scipy, rtol=rtol) From d7884e85dc250e44bc2394f732c21d53a9e22e3a Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Wed, 17 Sep 2025 00:14:14 -0700 Subject: [PATCH 04/29] Simple cleanup --- flystar/startables.py | 13 +++---------- 1 file changed, 3 insertions(+), 10 deletions(-) diff --git a/flystar/startables.py b/flystar/startables.py index a0bf3e3..422f9a7 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -828,7 +828,7 @@ def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scip # If the points do not cover multiple times, go to a fixed model if (t == t[0]).all(): motion_model_use = 'Fixed' - + self['motion_model_used'][ss] = motion_model_use # # Get the motion model object. @@ -960,15 +960,8 @@ def fit_velocities_all_detected(self, motion_model_to_fit, weighting='var', use_ valid_ye = np.all(self['ye'][select_stars, :][:, epoch_cols]!=0, axis=1) & np.all(np.isfinite(self['ye'][select_stars, :][:, epoch_cols]), axis=1) if mask_val: - x = np.ma.masked_values(self['x'][select_stars, :][:, epoch_cols], mask_val) - y = np.ma.masked_values(self['y'][select_stars, :][:, epoch_cols], mask_val) - - # If no mask, convert x.mask to list - if not np.ma.is_masked(x): - x.mask = np.zeros_like(self['x'][select_stars, :][:, epoch_cols].data, dtype=bool) - if not np.ma.is_masked(y): - y.mask = np.zeros_like(self['y'][select_stars, :][:, epoch_cols].data, dtype=bool) - + x = np.ma.masked_values(self['x'][select_stars, :][:, epoch_cols], mask_val, shrink=False) + y = np.ma.masked_values(self['y'][select_stars, :][:, epoch_cols], mask_val, shrink=False) valid_x = ~np.any(x.mask, axis=1) valid_y = ~np.any(y.mask, axis=1) detected_in_all_epochs = np.logical_and.reduce(( From 200d7e70653702411533cce2bc1ed50006eaa8bb Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Wed, 17 Sep 2025 10:09:56 -0700 Subject: [PATCH 05/29] Revert 2 epoch case changes --- flystar/motion_model.py | 138 +++++++++++++++++++++++----------------- 1 file changed, 80 insertions(+), 58 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 549b46a..c5642d6 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -207,65 +207,87 @@ def run_fit(self, t, x, y, xe, ye, t0, weighting='var', params_guess=None, if params_guess is None: params_guess = [x.mean(),0.0,y.mean(),0.0] - if use_scipy: - def linear(t, c0, c1): - return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) - x0, vx = x_opt - y0, vy = y_opt - x0e, vxe = np.sqrt(x_cov.diagonal()) - y0e, vye = np.sqrt(y_cov.diagonal()) - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) + # Handle 2-data point case + if len(np.unique(dt))==2: + if len(x)>2: # Catch case where bootstrap sends only 2 unique epochs + _,idx=np.unique(dt, return_index=True) + dt = dt[idx] + x = x[idx] + y = y[idx] + xe = xe[idx] + ye = ye[idx] + dx = np.diff(x)[0] + dy = np.diff(y)[0] + dt_diff = np.diff(dt)[0] + vx = dx / dt_diff + vy = dy / dt_diff + # TODO: still not sure about the error handling here + x0 = x[0] - dt[0]*vx # np.average(x, weights=x_wt) # + y0 = y[0] - dt[0]*vy # np.average(y, weights=y_wt) # + x0e = np.abs(dx) / 2**0.5 # np.sqrt(np.sum(xe**2)/2) # + y0e = np.abs(dy) / 2**0.5 # np.sqrt(np.sum(ye**2)/2) # + vxe = 0.0 #np.abs(vx) * np.sqrt(np.sum(xe**2/x**2)) + vye = 0.0 #np.abs(vy) * np.sqrt(np.sum(ye**2/y**2)) else: - # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme - x = np.array(x) - y = np.array(y) - dt = np.array(dt) - X_mat_t = np.vander(dt, 2) - # x calculation - W_mat_x = np.diag(x_wt) - XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t - pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix - popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution - perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution - # y calculation - W_mat_y = np.diag(y_wt) - XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t - pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix - popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution - perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution - # prepare values to return - vx, x0 = popt_x - vy, y0 = popt_y - vxe, x0e = perr_x - vye, y0e = perr_y - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) - - residual_x = x - X_mat_t @ popt_x - residual_y = y - X_mat_t @ popt_y - - chi2_x = residual_x.T @ W_mat_x @ residual_x - chi2_y = residual_y.T @ W_mat_y @ residual_y - - if not absolute_sigma: - degree_of_freedom = len(x) - 2 - if degree_of_freedom > 0: - reduced_chi2_x = chi2_x/(len(x) - 2) - reduced_chi2_y = chi2_y/(len(x) - 2) - x0e *= reduced_chi2_x**0.5 - y0e *= reduced_chi2_y**0.5 - vxe *= reduced_chi2_x**0.5 - vye *= reduced_chi2_y**0.5 - else: - warnings.warn( - "Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to infinity.", - OptimizeWarning, stacklevel=2 - ) - x0e *= np.inf - y0e *= np.inf - vxe *= np.inf - vye *= np.inf + if use_scipy: + def linear(t, c0, c1): + return c0 + c1*t + x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) + x0, vx = x_opt + y0, vy = y_opt + x0e, vxe = np.sqrt(x_cov.diagonal()) + y0e, vye = np.sqrt(y_cov.diagonal()) + x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) + else: + # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme + x = np.array(x) + y = np.array(y) + dt = np.array(dt) + X_mat_t = np.vander(dt, 2) + # x calculation + W_mat_x = np.diag(x_wt) + XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t + pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix + popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution + perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution + # y calculation + W_mat_y = np.diag(y_wt) + XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t + pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix + popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution + perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution + # prepare values to return + vx, x0 = popt_x + vy, y0 = popt_y + vxe, x0e = perr_x + vye, y0e = perr_y + x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) + + residual_x = x - X_mat_t @ popt_x + residual_y = y - X_mat_t @ popt_y + + chi2_x = residual_x.T @ W_mat_x @ residual_x + chi2_y = residual_y.T @ W_mat_y @ residual_y + + if not absolute_sigma: + degree_of_freedom = len(x) - 2 + if degree_of_freedom > 0: + reduced_chi2_x = chi2_x/(len(x) - 2) + reduced_chi2_y = chi2_y/(len(x) - 2) + x0e *= reduced_chi2_x**0.5 + y0e *= reduced_chi2_y**0.5 + vxe *= reduced_chi2_x**0.5 + vye *= reduced_chi2_y**0.5 + else: + warnings.warn( + "Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to infinity.", + OptimizeWarning, stacklevel=2 + ) + x0e *= np.inf + y0e *= np.inf + vxe *= np.inf + vye *= np.inf params = [x0, vx, y0, vy] param_errors = [x0e, vxe, y0e, vye] return params, param_errors From 5a859dbeefbe43427cb7026a1bd49816b89fe1aa Mon Sep 17 00:00:00 2001 From: Lingfeng Wei Date: Wed, 24 Sep 2025 18:17:01 -0700 Subject: [PATCH 06/29] Fix r string import warning --- flystar/plots.py | 12 ++++++------ flystar/starlists.py | 4 ++-- 2 files changed, 8 insertions(+), 8 deletions(-) diff --git a/flystar/plots.py b/flystar/plots.py index be6f0fe..d6a8d40 100755 --- a/flystar/plots.py +++ b/flystar/plots.py @@ -262,7 +262,7 @@ def pos_diff_err_hist(ref_mat, starlist_mat, transform, nbins=25, bin_width=None py.plot(x, norm.pdf(x,mean,sigma), 'g-', linewidth=2) # Annotate reduced chi-sqared values in plot: with outliers - xstr = '$\chi^2_r$ = {0}'.format(np.round(chi_sq_red, decimals=3)) + xstr = r'$\chi^2_r$ = {0}'.format(np.round(chi_sq_red, decimals=3)) py.annotate(xstr, xy=(0.3, 0.77), xycoords='figure fraction', color='black') txt = r'$\nu$ = 2*{0} - {1} = {2}'.format(len(diff_x), num_mod_params, deg_freedom) @@ -273,7 +273,7 @@ def pos_diff_err_hist(ref_mat, starlist_mat, transform, nbins=25, bin_width=None py.annotate(xstr3, xy=(0.25, 0.80), xycoords='figure fraction', color='black') # Annotate reduced chi-sqared values in plot: without outliers - xstr = '$\chi^2_r$ = {0}'.format(np.round(chi_sq_red_good, decimals=3)) + xstr = r'$\chi^2_r$ = {0}'.format(np.round(chi_sq_red_good, decimals=3)) py.annotate(xstr, xy=(0.7, 0.8), xycoords='figure fraction', color='black') txt = r'$\nu$ = 2*{0} - {1} = {2}'.format(len(good[0]), num_mod_params, deg_freedom_good) @@ -2221,7 +2221,7 @@ def plot_chi2_dist(tab, Ndetect, motion_model_dict={}, xlim=40, n_bins=50, boot_ plt.hist(x[idx], bins=chi2_bins, histtype='step', label='X', density=True) plt.hist(y[idx], bins=chi2_bins, histtype='step', label='Y', density=True) plt.plot(chi2_xaxis, chi2.pdf(chi2_xaxis, Ndof), 'r-', alpha=0.6, - label='$\chi^2$ ' + str(Ndof) + ' dof') + label=r'$\chi^2$ ' + str(Ndof) + ' dof') plt.title('$N_{epoch} = $' + str(Ndetect) + ', $N_{dof} = $' + str(Ndof)) plt.xlim(0, xlim) plt.legend() @@ -2306,7 +2306,7 @@ def plot_chi2_dist_per_filter(tab, Ndetect, motion_model_dict={}, xlim=40, n_bin plt.hist(x[idx], bins=chi2_bins, histtype='stepfilled', label='RA', density=True, color='skyblue', alpha=0.8, edgecolor='k') plt.hist(y[idx], bins=chi2_bins, histtype='stepfilled', label='DEC', density=True, color='orange', alpha=0.8, edgecolor='k') plt.plot(chi2_xaxis, chi2.pdf(chi2_xaxis, Ndof), 'r-', alpha=0.6, - label='$\chi^2$ ' + str(Ndof) + ' dof') + label=r'$\chi^2$ ' + str(Ndof) + ' dof') #plt.title('$N_{epoch} = $' + str(Ndetect) + ', $N_{dof} = $' + str(Ndof)) plt.title(str(filter)+' (N = '+str(len(chi2_x_list))+')', fontsize=22) plt.xlim(0, xlim) @@ -2593,7 +2593,7 @@ def plot_chi2_dist_mag(tab, Ndetect, xlim=40, n_bins=30, boot_err=False): plt.clf() plt.hist(chi2_m[idx], bins=np.arange(xlim*10), histtype='step', density=True) plt.plot(chi2_maxis, chi2.pdf(chi2_maxis, Ndof), 'r-', alpha=0.6, - label='$\chi^2$ ' + str(Ndof) + ' dof') + label=r'$\chi^2$ ' + str(Ndof) + ' dof') plt.title('$N_{epoch} = $' + str(Ndetect) + ', $N_{dof} = $' + str(Ndof)) plt.xlim(0, xlim) plt.legend() @@ -2642,7 +2642,7 @@ def plot_chi2_dist_mag_per_filter(tab, Ndetect, mlim=40, n_bins=30, xlim=40, fil plt.clf() plt.hist(chi2_m[idx], bins=np.arange(xlim*10), label='mag', histtype='stepfilled', density=True, color='green', alpha=0.7, edgecolor='k') plt.plot(chi2_maxis, chi2.pdf(chi2_maxis, Ndof), 'r-', alpha=0.6, - label='$\chi^2$ ' + str(Ndof) + ' dof') + label=r'$\chi^2$ ' + str(Ndof) + ' dof') #plt.title('$N_{epoch} = $' + str(Ndetect) + ', $N_{dof} = $' + str(Ndof)) plt.xlim(0, xlim) plt.xlabel(r'$\chi^{2}$', fontsize=28) diff --git a/flystar/starlists.py b/flystar/starlists.py index 23df44f..f1f3278 100644 --- a/flystar/starlists.py +++ b/flystar/starlists.py @@ -421,7 +421,7 @@ def read_starlist(starlistFile, error=True): starlist astropy table. containing: name, m, x, y, xe, ye, t """ - t_ref = Table.read(starlistFile, format='ascii', delimiter='\s') + t_ref = Table.read(starlistFile, format='ascii', delimiter=r'\s') # Check if this already has column names: cols = t_ref.colnames @@ -624,7 +624,7 @@ def from_lis_file(cls, filename, error=True, fvu_file=None): ------ starlists.StarList() object (subclass of Astropy Table). """ - t_ref = Table.read(filename, format='ascii', delimiter='\s') + t_ref = Table.read(filename, format='ascii', delimiter=r'\s') # Check if this already has column names: cols = t_ref.colnames From 253c52db5b0337944237a490a4850a67aa1b950e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Fri, 7 Nov 2025 12:42:39 -0800 Subject: [PATCH 07/29] Clean up: Remove scale_errors; Update init functions; Update Linear model error calculations --- flystar/motion_model.py | 370 +++++++++++++++++++++------------------- 1 file changed, 199 insertions(+), 171 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index c5642d6..3c5069c 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -41,8 +41,13 @@ def get_batch_pos_at_time(self, t): #return x, y, x_err, y_err pass - def run_fit(self, t, x, y, xe, ye, t0, weighting='var', - use_scipy=True, absolute_sigma=True): + def run_fit( + self, t, x, y, xe, ye, t0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + fill_value=np.inf + ): # Run a single fit (used both for overall fit + bootstrap iterations) pass @@ -54,37 +59,43 @@ def get_weights(self, xe, ye, weighting='var'): else: warnings.warn("Invalid weighting, using default weighting scheme var.", UserWarning) return 1./xe**2, 1./ye**2 - - def scale_errors(self, errs, weighting='var'): - if weighting=='std': - return np.array(errs)**2 - elif weighting=='var': - return errs - else: - warnings.warn("Invalid weighting, using default weighting scheme var.", UserWarning) - return errs - def fit_motion_model(self, t, x, y, xe, ye, t0, bootstrap=0, weighting='var', - use_scipy=True, absolute_sigma=True): + def fit_motion_model( + self, t, x, y, xe, ye, t0, + bootstrap=0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + fill_value=np.inf, + rng=None + ): """ Fit the input positions on the sky and errors to determine new parameters for this motion model (MM). Best-fit parameters will be returned along with uncertainties. """ - params, param_errs = self.run_fit(t, x, y, xe, ye, t0=t0, weighting=weighting, - use_scipy=use_scipy, absolute_sigma=absolute_sigma) - - if bootstrap>0 and len(x)>(self.n_pts_req): + params, param_errs, chi2x, chi2y = self.run_fit( + t, x, y, xe, ye, t0=t0, + weighting=weighting, + use_scipy=use_scipy, + absolute_sigma=absolute_sigma, + fill_value=fill_value + ) + + if bootstrap > 0 and len(x) > (self.n_pts_req): edx = np.arange(len(x), dtype=int) bb_params = [] bb_params_errs = [] for bb in range(bootstrap): - bdx = np.random.choice(edx, len(x)) - while len(np.unique(bdx)) 0: + reduced_chi2x = chi2x / degree_of_freedom + reduced_chi2y = chi2y / degree_of_freedom + + param_errors[0] *= reduced_chi2x**0.5 + param_errors[1] *= reduced_chi2y**0.5 + else: + warnings.warn( + f'Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value {fill_value}.', + OptimizeWarning, stacklevel=2 + ) + param_errors = np.full_like(param_errors, fill_value) + + return params, param_errors, chi2x, chi2y + class Linear(MotionModel): """ A 2D linear motion model for a star on the sky. """ - n_pts_req = 2 - n_params=2 - fitter_param_names = ['x0', 'vx', 'y0', 'vy'] - fixed_param_names = ['t0'] - def __init__(self, **kwargs): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() + self.n_pts_req = 2 + self.n_params = 2 + self.fitter_param_names = ['x0', 'vx', 'y0', 'vy'] + self.fixed_param_names = ['t0'] return def get_pos_at_time(self, fit_params, fixed_params, t): @@ -183,7 +216,7 @@ def get_pos_at_time(self, fit_params, fixed_params, t): fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) dt = t-fixed_params_dict['t0'] return fit_params_dict['x0'] + fit_params_dict['vx']*dt, fit_params_dict['y0'] + fit_params_dict['vy']*dt - + def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], x0_err=[],vx_err=[], y0_err=[],vy_err=[], **kwargs): if hasattr(t, "__len__"): @@ -200,113 +233,98 @@ def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], y_err = np.hypot(y0_err, vy_err*dt) return x,y,x_err,y_err - def run_fit(self, t, x, y, xe, ye, t0, weighting='var', params_guess=None, - use_scipy=True, absolute_sigma=True): - dt = t-t0 - x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) + def run_fit( + self, t, x, y, xe, ye, t0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + params_guess=None, + fill_value=np.inf + ): + dt = t - t0 + x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) if params_guess is None: - params_guess = [x.mean(),0.0,y.mean(),0.0] - - # Handle 2-data point case - if len(np.unique(dt))==2: - if len(x)>2: # Catch case where bootstrap sends only 2 unique epochs - _,idx=np.unique(dt, return_index=True) - dt = dt[idx] - x = x[idx] - y = y[idx] - xe = xe[idx] - ye = ye[idx] - dx = np.diff(x)[0] - dy = np.diff(y)[0] - dt_diff = np.diff(dt)[0] - vx = dx / dt_diff - vy = dy / dt_diff - # TODO: still not sure about the error handling here - x0 = x[0] - dt[0]*vx # np.average(x, weights=x_wt) # - y0 = y[0] - dt[0]*vy # np.average(y, weights=y_wt) # - x0e = np.abs(dx) / 2**0.5 # np.sqrt(np.sum(xe**2)/2) # - y0e = np.abs(dy) / 2**0.5 # np.sqrt(np.sum(ye**2)/2) # - vxe = 0.0 #np.abs(vx) * np.sqrt(np.sum(xe**2/x**2)) - vye = 0.0 #np.abs(vy) * np.sqrt(np.sum(ye**2/y**2)) + params_guess = [x.mean(), 0., y.mean(), 0.] + + if use_scipy: + def linear(t, c0, c1): + return c0 + c1*t + x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) + x0, vx = x_opt + y0, vy = y_opt + x0e, vxe = np.sqrt(x_cov.diagonal()) + y0e, vye = np.sqrt(y_cov.diagonal()) + params = np.array([x0, vx, y0, vy]) + param_errors = np.array([x0e, vxe, y0e, vye]) + chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) + else: - if use_scipy: - def linear(t, c0, c1): - return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) - x0, vx = x_opt - y0, vy = y_opt - x0e, vxe = np.sqrt(x_cov.diagonal()) - y0e, vye = np.sqrt(y_cov.diagonal()) - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) - else: - # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme - x = np.array(x) - y = np.array(y) - dt = np.array(dt) - X_mat_t = np.vander(dt, 2) - # x calculation - W_mat_x = np.diag(x_wt) - XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t - pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix - popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution - perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution - # y calculation - W_mat_y = np.diag(y_wt) - XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t - pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix - popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution - perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution - # prepare values to return - vx, x0 = popt_x - vy, y0 = popt_y - vxe, x0e = perr_x - vye, y0e = perr_y - x0e, vxe, y0e, vye = self.scale_errors([x0e, vxe, y0e, vye], weighting=weighting) - - residual_x = x - X_mat_t @ popt_x - residual_y = y - X_mat_t @ popt_y - - chi2_x = residual_x.T @ W_mat_x @ residual_x - chi2_y = residual_y.T @ W_mat_y @ residual_y - - if not absolute_sigma: - degree_of_freedom = len(x) - 2 - if degree_of_freedom > 0: - reduced_chi2_x = chi2_x/(len(x) - 2) - reduced_chi2_y = chi2_y/(len(x) - 2) - x0e *= reduced_chi2_x**0.5 - y0e *= reduced_chi2_y**0.5 - vxe *= reduced_chi2_x**0.5 - vye *= reduced_chi2_y**0.5 - else: - warnings.warn( - "Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to infinity.", - OptimizeWarning, stacklevel=2 - ) - x0e *= np.inf - y0e *= np.inf - vxe *= np.inf - vye *= np.inf - params = [x0, vx, y0, vy] - param_errors = [x0e, vxe, y0e, vye] - return params, param_errors - - + # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme + x = np.array(x) + y = np.array(y) + dt = np.array(dt) + X_mat_t = np.vander(dt, 2) + # x calculation + W_mat_x = np.diag(x_wt) + XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t + pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix + popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution + perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution + # y calculation + W_mat_y = np.diag(y_wt) + XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t + pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix + popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution + perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution + # prepare values to return + vx, x0 = popt_x + vy, y0 = popt_y + vxe, x0e = perr_x + vye, y0e = perr_y + + # Does not use get_chi2 to accelerate calculation + residual_x = x - X_mat_t @ popt_x + residual_y = y - X_mat_t @ popt_y + + + chi2_x = residual_x.T @ W_mat_x @ residual_x + chi2_y = residual_y.T @ W_mat_y @ residual_y + + params = np.array([x0, vx, y0, vy]) + param_errors = np.array([x0e, vxe, y0e, vye]) + + if not absolute_sigma: + degree_of_freedom = len(x) - 2 + if degree_of_freedom > 0: + reduced_chi2_x = chi2_x/(len(x) - 2) + reduced_chi2_y = chi2_y/(len(x) - 2) + + param_errors[0:2] *= reduced_chi2_x**0.5 + param_errors[2:4] *= reduced_chi2_y**0.5 + + else: + warnings.warn( + f'Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value {fill_value}.', + OptimizeWarning, stacklevel=2 + ) + param_errors = np.full_like(param_errors, fill_value) + + return params, param_errors, chi2_x, chi2_y + class Acceleration(MotionModel): """ A 2D accelerating motion model for a star on the sky. """ - n_pts_req = 4 # TODO: consider special case for 3 pts - n_params=3 - fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] - fixed_param_names = ['t0'] - def __init__(self, x0=0, vx0=0, ax=0, y0=0, vy0=0, ay=0, t0=None, x0_err=0, vx0_err=0, ax_err=0, y0_err=0, vy0_err=0, ay_err=0, **kwargs): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() + self.n_pts_req = 4 # TODO: consider special case for 3 pts + self.n_params = 3 + self.fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] + self.fixed_param_names = ['t0'] return def get_pos_at_time(self, fit_params, fixed_params, t): @@ -334,18 +352,24 @@ def get_batch_pos_at_time(self,t, y_err = np.sqrt(y0_err**2 + (vy0_err*dt)**2 + (0.5*ay_err*dt**2)**2) return x,y,x_err,y_err - def run_fit(self, t, x, y, xe, ye, t0, weighting='var', params_guess=None, - use_scipy=True, absolute_sigma=True): + def run_fit( + self, t, x, y, xe, ye, t0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + params_guess=None, + fill_value=np.inf + ): if not use_scipy: Warning("Acceleration model has no non-scipy fitter option. Running with scipy.") - dt = t-t0 + dt = t - t0 x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) if params_guess is None: - params_guess = [x.mean(),0.0,0.0,y.mean(),0.0,0.0] - - def accel(t, c0,c1,c2): + params_guess = [x.mean(), 0., 0., y.mean(), 0., 0.] + + def accel(t, c0, c1, c2): return c0 + c1*t + 0.5*c2*t**2 - + x_opt, x_cov = curve_fit(accel, dt, x, p0=np.array(params_guess[:3]), sigma=1/x_wt**0.5, absolute_sigma=True) y_opt, y_cov = curve_fit(accel, dt, y, p0=np.array(params_guess[3:]), sigma=1/y_wt**0.5, absolute_sigma=True) x0 = x_opt[0] @@ -354,14 +378,13 @@ def accel(t, c0,c1,c2): vy0 = y_opt[1] ax = x_opt[2] ay = y_opt[2] - + x0e, vx0e, axe = np.sqrt(x_cov.diagonal()) y0e, vy0e, aye = np.sqrt(y_cov.diagonal()) - x0e, vx0e, axe, y0e, vy0e, aye = self.scale_errors([x0e, vx0e, axe, y0e, vy0e, aye], weighting=weighting) params = [x0, vx0, ax, y0, vy0, ay] param_errors = [x0e, vx0e, axe, y0e, vy0e, aye] - + return params, param_errors class Parallax(MotionModel): @@ -373,18 +396,17 @@ class Parallax(MotionModel): Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ - n_pts_req = 4 - n_params=3 - fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] - fixed_param_names = ['t0'] - fixed_meta_data = ['RA','Dec','PA','obs'] - def __init__(self, RA, Dec, PA=0.0, obs='earth', **kwargs): self.RA = RA self.Dec = Dec self.PA = PA self.obs = obs self.plx_vector_cached = None + self.n_pts_req = 4 + self.n_params = 3 + self.fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] + self.fixed_param_names = ['t0'] + self.fixed_meta_data = ['RA','Dec','PA','obs'] return def get_parallax_vector(self, t_mjd): @@ -411,7 +433,7 @@ def get_parallax_vector(self, t_mjd): def get_pos_at_time(self, fit_params, fixed_params, t): fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t-fixed_params_dict['t0'] + dt = t - fixed_params_dict['t0'] t_mjd = Time(t, format='decimalyear', scale='utc').mjd pvec = self.get_parallax_vector(t_mjd) @@ -420,7 +442,7 @@ def get_pos_at_time(self, fit_params, fixed_params, t): x = fit_params_dict['x0'] + fit_params_dict['vx']*dt + fit_params_dict['pi']*pvec_x y = fit_params_dict['y0'] + fit_params_dict['vy']*dt + fit_params_dict['pi']*pvec_y return x, y - + def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], pi=[], t0=[], x0_err=[],vx_err=[], y0_err=[],vy_err=[], pi_err=[], **kwargs): @@ -446,8 +468,14 @@ def get_batch_pos_at_time(self, t, x_err,y_err = [],[] return x,y,x_err,y_err - def run_fit(self, t, x, y, xe, ye, t0, weighting='var', params_guess=None, - use_scipy=True, absolute_sigma=True): + def run_fit( + self, t, x, y, xe, ye, t0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + params_guess=None, + fill_value=np.inf + ): if not use_scipy: Warning("Parallax model has no non-scipy fitter option. Running with scipy.") t_mjd = Time(t, format='decimalyear', scale='utc').mjd @@ -467,8 +495,8 @@ def fit_func(t, x0,vx, y0,vy, pi): y.mean(),(y[idx_last]-y[idx_first])/(t[idx_last]-t[idx_first]), 1] res = curve_fit(fit_func, np.append(t,t), np.append(x,y), p0=params_guess, sigma = 1.0/np.append(x_wt,y_wt)) - x0,vx,y0,vy,pi = res[0] - x0_err,vx_err,y0_err,vy_err,pi_err = self.scale_errors(np.sqrt(np.diag(res[1])), weighting=weighting) + x0, vx, y0, vy, pi = res[0] + x0_err, vx_err, y0_err, vy_err, pi_err = np.sqrt(np.diag(res[1])) params = [x0, vx, y0, vy, pi] param_errors = [x0_err, vx_err, y0_err, vy_err, pi_err] @@ -498,7 +526,7 @@ def validate_motion_model_dict(motion_model_dict, startable, default_motion_mode raise ValueError(f"Cannot use {mm} motion model without required metadata. Please initialize with required metadata and provide in motion_model_dict.") else: motion_model_dict[mm] = mm_obj() - warnings.warn(f"Using default model/fitter for {mm}.", UserWarning) + # warnings.warn(f"Using default model/fitter for {mm}.", UserWarning) return motion_model_dict From 0ba32c91bb052d2f6fa924e4c10c936962aa2220 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Fri, 7 Nov 2025 12:47:53 -0800 Subject: [PATCH 08/29] Rename py to plt; Add save path; Fix unclosed figure --- flystar/plots.py | 531 ++++++++++++++++++++++++----------------------- 1 file changed, 268 insertions(+), 263 deletions(-) diff --git a/flystar/plots.py b/flystar/plots.py index d6a8d40..d2dea16 100755 --- a/flystar/plots.py +++ b/flystar/plots.py @@ -1,9 +1,8 @@ from flystar import analysis, motion_model, startables -import pylab as py -import pylab as plt import numpy as np import matplotlib.mlab as mlab import matplotlib +import matplotlib.pyplot as plt from matplotlib import colors import matplotlib.cm as cm from scipy.stats import chi2 @@ -23,8 +22,8 @@ #################################################### -def trans_positions(ref, ref_mat, starlist, starlist_mat, xlim=None, ylim=None, fileName=None, - equal_axis=True, root='./'): +def trans_positions(ref, ref_mat, starlist, starlist_mat, xlim=None, ylim=None, + equal_axis=True, save_path=None, show_plot=True): """ Plot positions of stars in reference list and the transformed starlist, in reference list coordinates. Stars used in the transformation are @@ -55,31 +54,37 @@ def trans_positions(ref, ref_mat, starlist, starlist_mat, xlim=None, ylim=None, equal_axis: boolean If true, make axes equal. True by default + + save_path: string + Path to save the figure to. Default is None + show_plot: boolean + If true, show the plot. Default is True + """ - py.figure(figsize=(10,10)) - py.clf() - py.plot(ref['x'], ref['y'], 'g+', ms=5, label='Reference') - py.plot(starlist['x'], starlist['y'], 'rx', ms=5, label='starlist') - py.plot(ref_mat['x'], ref_mat['y'], color='skyblue', marker='s', ms=10, alpha=0.3, + plt.figure(figsize=(10,10)) + plt.clf() + plt.plot(ref['x'], ref['y'], 'g+', ms=5, label='Reference') + plt.plot(starlist['x'], starlist['y'], 'rx', ms=5, label='starlist') + plt.plot(ref_mat['x'], ref_mat['y'], color='skyblue', marker='s', ms=10, alpha=0.3, linestyle='None', label='Matched Reference') - py.plot(starlist_mat['x'], starlist_mat['y'], color='darkblue', marker='s', ms=5, alpha=0.3, + plt.plot(starlist_mat['x'], starlist_mat['y'], color='darkblue', marker='s', ms=5, alpha=0.3, linestyle='None', label='Matched starlist') - py.xlabel('X position (Reference Coords)') - py.ylabel('Y position (Reference Coords)') - py.legend(numpoints=1) - py.title('Label.dat Positions After Transformation') + plt.xlabel('X position (Reference Coords)') + plt.ylabel('Y position (Reference Coords)') + plt.legend(numpoints=1) + plt.title('Label.dat Positions After Transformation') if xlim != None: - py.axis([xlim[0], xlim[1], ylim[0], ylim[1]]) + plt.axis([xlim[0], xlim[1], ylim[0], ylim[1]]) if equal_axis: - py.axis('equal') - if fileName!=None: - #py.savefig(root + fileName[3:8] + 'Transformed_positions_' + '.png') - py.savefig(root + 'Transformed_positions_{0}'.format(fileName) + '.png') - else: - py.savefig(root + 'Transformed_positions.png') + plt.axis('equal') + + if save_path: + plt.savefig(save_path) + if show_plot: + plt.show() - py.close() + plt.close() return @@ -121,22 +126,22 @@ def pos_diff_hist(ref_mat, starlist_mat, nbins=25, bin_width=None, xlim=None, fi bins = np.arange(min_range, max_range+bin_width, bin_width) - py.figure(figsize=(10,10)) - py.clf() - py.hist(diff_x, histtype='step', bins=bins, color='blue', label='X') - py.hist(diff_y, histtype='step', bins=bins, color='red', label='Y') - py.xlabel('Reference Position - starlist Position') - py.ylabel('N stars') - py.title('Position Differences for matched stars') + plt.figure(figsize=(10,10)) + plt.clf() + plt.hist(diff_x, histtype='step', bins=bins, color='blue', label='X') + plt.hist(diff_y, histtype='step', bins=bins, color='red', label='Y') + plt.xlabel('Reference Position - starlist Position') + plt.ylabel('N stars') + plt.title('Position Differences for matched stars') if xlim != None: - py.xlim([xlim[0], xlim[1]]) - py.legend() + plt.xlim([xlim[0], xlim[1]]) + plt.legend() if fileName != None: - py.savefig(root + fileName[3:8] + 'Positions_hist_' + '.png') + plt.savefig(root + fileName[3:8] + 'Positions_hist_' + '.png') else: - py.savefig(root + 'Positions_hist.png') + plt.savefig(root + 'Positions_hist.png') - py.close() + plt.close() return def pos_diff_err_hist(ref_mat, starlist_mat, transform, nbins=25, bin_width=None, errs='both', xlim=None, @@ -248,51 +253,51 @@ def pos_diff_err_hist(ref_mat, starlist_mat, transform, nbins=25, bin_width=None bins = np.arange(min_range, max_range+bin_width, bin_width) - py.figure(figsize=(10,10)) - py.clf() - n_x, bins_x, p = py.hist(ratio_x, histtype='step', bins=bins, color='blue', + plt.figure(figsize=(10,10)) + plt.clf() + n_x, bins_x, p = plt.hist(ratio_x, histtype='step', bins=bins, color='blue', label='X', density=True, linewidth=2) - n_y, bins_y, p = py.hist(ratio_y, histtype='step', bins=bins, color='red', + n_y, bins_y, p = plt.hist(ratio_y, histtype='step', bins=bins, color='red', label='Y', density=True, linewidth=2) # Overplot a Gaussian, as well mean = 0 sigma = 1 x = np.arange(-6, 6, 0.1) - py.plot(x, norm.pdf(x,mean,sigma), 'g-', linewidth=2) + plt.plot(x, norm.pdf(x,mean,sigma), 'g-', linewidth=2) # Annotate reduced chi-sqared values in plot: with outliers xstr = r'$\chi^2_r$ = {0}'.format(np.round(chi_sq_red, decimals=3)) - py.annotate(xstr, xy=(0.3, 0.77), xycoords='figure fraction', color='black') + plt.annotate(xstr, xy=(0.3, 0.77), xycoords='figure fraction', color='black') txt = r'$\nu$ = 2*{0} - {1} = {2}'.format(len(diff_x), num_mod_params, deg_freedom) - py.annotate(txt, xy=(0.25,0.74), xycoords='figure fraction', color='black') + plt.annotate(txt, xy=(0.25,0.74), xycoords='figure fraction', color='black') xstr2 = 'With Outliers' xstr3 = '{0} with +/- {1}+ sigma'.format(len(ratio_x) - len(good[0]), outlier) - py.annotate(xstr2, xy=(0.29, 0.83), xycoords='figure fraction', color='black') - py.annotate(xstr3, xy=(0.25, 0.80), xycoords='figure fraction', color='black') + plt.annotate(xstr2, xy=(0.29, 0.83), xycoords='figure fraction', color='black') + plt.annotate(xstr3, xy=(0.25, 0.80), xycoords='figure fraction', color='black') # Annotate reduced chi-sqared values in plot: without outliers xstr = r'$\chi^2_r$ = {0}'.format(np.round(chi_sq_red_good, decimals=3)) - py.annotate(xstr, xy=(0.7, 0.8), xycoords='figure fraction', color='black') + plt.annotate(xstr, xy=(0.7, 0.8), xycoords='figure fraction', color='black') txt = r'$\nu$ = 2*{0} - {1} = {2}'.format(len(good[0]), num_mod_params, deg_freedom_good) - py.annotate(txt, xy=(0.65,0.77), xycoords='figure fraction', color='black') + plt.annotate(txt, xy=(0.65,0.77), xycoords='figure fraction', color='black') xstr2 = 'Without Outliers' - py.annotate(xstr2, xy=(0.67, 0.83), xycoords='figure fraction', color='black') + plt.annotate(xstr2, xy=(0.67, 0.83), xycoords='figure fraction', color='black') - py.xlabel('(Ref Pos - TransStarlist Pos) / Ast. Error') - py.ylabel('N stars (normalized)') - py.title('Position Residuals for Matched Stars') + plt.xlabel('(Ref Pos - TransStarlist Pos) / Ast. Error') + plt.ylabel('N stars (normalized)') + plt.title('Position Residuals for Matched Stars') if xlim != None: - py.xlim([xlim[0], xlim[1]]) - py.legend() + plt.xlim([xlim[0], xlim[1]]) + plt.legend() if fileName != None: - py.savefig(root + fileName[3:8] + 'Positions_err_ratio_hist_' + '.png') + plt.savefig(root + fileName[3:8] + 'Positions_err_ratio_hist_' + '.png') else: - py.savefig(root + 'Positions_err_ratio_hist.png') + plt.savefig(root + 'Positions_err_ratio_hist.png') - py.close() + plt.close() return @@ -319,18 +324,18 @@ def mag_diff_hist(ref_mat, starlist_mat, bins=25, fileName=None, root='./'): bad2 = np.where(bad == True) diff_m = np.delete(diff_m, bad2) - py.figure(figsize=(10,10)) - py.clf() - py.hist(diff_m, bins=bins) - py.xlabel('Reference Mag - TransStarlist Mag') - py.ylabel('N stars') - py.title('Magnitude Difference for matched stars') + plt.figure(figsize=(10,10)) + plt.clf() + plt.hist(diff_m, bins=bins) + plt.xlabel('Reference Mag - TransStarlist Mag') + plt.ylabel('N stars') + plt.title('Magnitude Difference for matched stars') if fileName != None: - py.savefig(root + fileName[3:8] + 'Magnitude_hist_' + '.png') + plt.savefig(root + fileName[3:8] + 'Magnitude_hist_' + '.png') else: - py.savefig(root + 'Magnitude_hist.png') + plt.savefig(root + 'Magnitude_hist.png') - py.close() + plt.close() return def pos_diff_quiver(ref_mat, starlist_mat, qscale=10, keyLength=0.2, xlim=None, ylim=None, @@ -411,35 +416,35 @@ def pos_diff_quiver(ref_mat, starlist_mat, qscale=10, keyLength=0.2, xlim=None, s = len(xpos) - py.figure(figsize=(10,10)) - py.clf() - q = py.quiver(xpos, ypos, diff_x, diff_y, scale=qscale) + plt.figure(figsize=(10,10)) + plt.clf() + q = plt.quiver(xpos, ypos, diff_x, diff_y, scale=qscale) fmt = '{0} ref units'.format(keyLength) - #py.quiverkey(q, 0.2, 0.92, keyLength, fmt, coordinates='figure', color='black') + #plt.quiverkey(q, 0.2, 0.92, keyLength, fmt, coordinates='figure', color='black') # Make our reference arrow a different color - q2 = py.quiver(xpos[s-2:s], ypos[s-2:s], diff_x[s-2:s], diff_y[s-2:s], scale=qscale, color='red') + q2 = plt.quiver(xpos[s-2:s], ypos[s-2:s], diff_x[s-2:s], diff_y[s-2:s], scale=qscale, color='red') # Annotate our reference quiver arrow - py.annotate(fmt, xy=(xpos[-1]-2, ypos[-1]+0.5), color='red') - py.xlabel('X Position (Reference coords)') - py.ylabel('Y Position (Reference coords)') + plt.annotate(fmt, xy=(xpos[-1]-2, ypos[-1]+0.5), color='red') + plt.xlabel('X Position (Reference coords)') + plt.ylabel('Y Position (Reference coords)') if xlim != None: - py.axis([xlim[0], ylim[1], ylim[0], ylim[1]]) + plt.axis([xlim[0], ylim[1], ylim[0], ylim[1]]) if sigma: if fileName != None: - py.title('(Reference - Transformed Starlist positions) / sigma') - py.savefig(root + fileName[3:8] + 'Positions_quiver_sigma_' + '.png') + plt.title('(Reference - Transformed Starlist positions) / sigma') + plt.savefig(root + fileName[3:8] + 'Positions_quiver_sigma_' + '.png') else: - py.title('(Reference - Transformed Starlist positions) / sigma') - py.savefig(root + 'Positions_quiver_sigma.png') + plt.title('(Reference - Transformed Starlist positions) / sigma') + plt.savefig(root + 'Positions_quiver_sigma.png') else: if fileName != None: - py.title('Reference - Transformed Starlist positions') - py.savefig(root + fileName[3:8] + 'Positions_quiver_' + '.png') + plt.title('Reference - Transformed Starlist positions') + plt.savefig(root + fileName[3:8] + 'Positions_quiver_' + '.png') else: - py.title('Reference - Transformed Starlist positions') - py.savefig(root + 'Positions_quiver.png') + plt.title('Reference - Transformed Starlist positions') + plt.savefig(root + 'Positions_quiver.png') - py.close() + plt.close() return def vpd(ref, starlist_trans, vxlim, vylim): @@ -472,17 +477,17 @@ def vpd(ref, starlist_trans, vxlim, vylim): trans_vx = starlist_trans['vx'] trans_vy = starlist_trans['vy'] - py.figure(figsize=(10,10)) - py.clf() - py.plot(trans_vx, trans_vy, 'k.', ms=8, label='Transformed', alpha=0.4) - py.plot(ref_vx, ref_vy, 'r.', ms=8, label='Reference', alpha=0.4) - py.xlabel('Vx (Reference units)') - py.ylabel('Vy (Reference units)') + plt.figure(figsize=(10,10)) + plt.clf() + plt.plot(trans_vx, trans_vy, 'k.', ms=8, label='Transformed', alpha=0.4) + plt.plot(ref_vx, ref_vy, 'r.', ms=8, label='Reference', alpha=0.4) + plt.xlabel('Vx (Reference units)') + plt.ylabel('Vy (Reference units)') if vxlim != None: - py.axis([vxlim[0], vylim[1], vylim[0], vylim[1]]) - py.title('Reference and Transformed Proper Motions') - py.legend() - py.savefig('Transformed_velocities.png') + plt.axis([vxlim[0], vylim[1], vylim[0], vylim[1]]) + plt.title('Reference and Transformed Proper Motions') + plt.legend() + plt.savefig('Transformed_velocities.png') return @@ -538,27 +543,27 @@ def vel_diff_err_hist(ref_mat, starlist_mat, nbins=25, bin_width=None, vxlim=Non sigma = 1 x = np.arange(-6, 6, 0.1) - py.figure(figsize=(20,10)) - py.subplot(121) - py.subplots_adjust(left=0.1) - py.hist(ratio_vx, bins=xbins, histtype='step', color='black', density=True, + plt.figure(figsize=(20,10)) + plt.subplot(121) + plt.subplots_adjust(left=0.1) + plt.hist(ratio_vx, bins=xbins, histtype='step', color='black', density=True, linewidth=2) - py.plot(x, norm.pdf(x,mean,sigma), 'r-', linewidth=2) - py.xlabel('(Ref Vx - Trans Vx) / Vxe') - py.ylabel('N_stars') - py.title('Vx Residuals, Matched') + plt.plot(x, norm.pdf(x,mean,sigma), 'r-', linewidth=2) + plt.xlabel('(Ref Vx - Trans Vx) / Vxe') + plt.ylabel('N_stars') + plt.title('Vx Residuals, Matched') if vxlim != None: - py.xlim([vxlim[0], vxlim[1]]) - py.subplot(122) - py.hist(ratio_vy, bins=ybins, histtype='step', color='black', density=True, + plt.xlim([vxlim[0], vxlim[1]]) + plt.subplot(122) + plt.hist(ratio_vy, bins=ybins, histtype='step', color='black', density=True, linewidth=2) - py.plot(x, norm.pdf(x,mean,sigma), 'r-', linewidth=2) - py.xlabel('(Ref Vy - Trans Vy) / Vye') - py.ylabel('N_stars') - py.title('Vy Residuals, Matched') + plt.plot(x, norm.pdf(x,mean,sigma), 'r-', linewidth=2) + plt.xlabel('(Ref Vy - Trans Vy) / Vye') + plt.ylabel('N_stars') + plt.title('Vy Residuals, Matched') if vylim != None: - py.xlim([vylim[0], vylim[1]]) - py.savefig('Vel_err_ratio_dist.png') + plt.xlim([vylim[0], vylim[1]]) + plt.savefig('Vel_err_ratio_dist.png') return @@ -606,17 +611,17 @@ def residual_vpd(ref_mat, starlist_trans_mat, pscale=None): yerr = np.hypot(ref_mat['vy_err'], starlist_trans_mat['vy_err']) # Plotting - py.figure(figsize=(10,10)) - py.clf() - py.errorbar(diff_x, diff_y, xerr=xerr, yerr=yerr, fmt='k.', ms=8, alpha=0.5) + plt.figure(figsize=(10,10)) + plt.clf() + plt.errorbar(diff_x, diff_y, xerr=xerr, yerr=yerr, fmt='k.', ms=8, alpha=0.5) if pscale != None: - py.xlabel('Reference_vx - Transformed_vx (mas/yr)') - py.ylabel('Reference_vy - Transformed_vy (mas/yr)') + plt.xlabel('Reference_vx - Transformed_vx (mas/yr)') + plt.ylabel('Reference_vy - Transformed_vy (mas/yr)') else: - py.xlabel('Reference_vx - Transformed_vx (reference coords)') - py.ylabel('Reference_vy - Transformed_vy (reference coords)') - py.title('Proper Motion Residuals') - py.savefig('resid_vpd.png') + plt.xlabel('Reference_vx - Transformed_vx (reference coords)') + plt.ylabel('Reference_vy - Transformed_vy (reference coords)') + plt.title('Proper Motion Residuals') + plt.savefig('resid_vpd.png') return @@ -636,8 +641,8 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', else: Nrows = math.ceil(Nstars / (Ncols / 2)) * 3 - py.close('all') - py.figure(2, figsize=figsize) + plt.close('all') + plt.figure(2, figsize=figsize) names = s.getArray('name') mag = s.getArray('mag') x = s.getArray('x') @@ -746,7 +751,7 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', t0 = int(np.floor(np.min(time))) tO = int(np.ceil(np.max(time))) - dateTicLoc = py.MultipleLocator(3) + dateTicLoc = plt.MultipleLocator(3) dateTicRng = [t0-1, tO+1] dateTics = np.arange(t0, tO+1) DateTicsLabel = dateTics-2000 @@ -754,7 +759,7 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', # See if we are using MJD instead. if time[0] > 50000: print('MJD') - dateTicLoc = py.MultipleLocator(1000) + dateTicLoc = plt.MultipleLocator(1000) t0 = int(np.round(np.min(time), 50)) tO = int(np.round(np.max(time), 50)) dateTicRng = [t0-200, tO+200] @@ -779,121 +784,121 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', ind = (row-1)*Ncols + col - paxes = py.subplot(Nrows, Ncols, ind) - py.plot(time, fitLineX, 'b-') - py.plot(time, fitLineX + fitSigX, 'b--') - py.plot(time, fitLineX - fitSigX, 'b--') - py.errorbar(time, x, yerr=xerr, fmt='k.') - rng = py.axis() - py.ylim(np.min(x-xerr-0.1),np.max(x+xerr+0.1)) - py.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) + paxes = plt.subplot(Nrows, Ncols, ind) + plt.plot(time, fitLineX, 'b-') + plt.plot(time, fitLineX + fitSigX, 'b--') + plt.plot(time, fitLineX - fitSigX, 'b--') + plt.errorbar(time, x, yerr=xerr, fmt='k.') + rng = plt.axis() + plt.ylim(np.min(x-xerr-0.1),np.max(x+xerr+0.1)) + plt.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) if time[0] > 50000: - py.xlabel('Date (MJD)', fontsize=fontsize1) - py.ylabel('X (pix)', fontsize=fontsize1) + plt.xlabel('Date (MJD)', fontsize=fontsize1) + plt.ylabel('X (pix)', fontsize=fontsize1) paxes.xaxis.set_major_formatter(fmtX) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.yaxis.set_major_formatter(fmtY) paxes.tick_params(axis='both', which='major', labelsize=fontsize1) - py.yticks(np.arange(np.min(x-xerr-0.1), np.max(x+xerr+0.1), 0.2)) - py.xticks(dateTics, DateTicsLabel) - py.xlim(np.min(dateTics), np.max(dateTics)) - py.annotate(starName,xy=(1.0,1.1), xycoords='axes fraction', fontsize=12, color='red') + plt.yticks(np.arange(np.min(x-xerr-0.1), np.max(x+xerr+0.1), 0.2)) + plt.xticks(dateTics, DateTicsLabel) + plt.xlim(np.min(dateTics), np.max(dateTics)) + plt.annotate(starName,xy=(1.0,1.1), xycoords='axes fraction', fontsize=12, color='red') col = col + 1 ind = (row-1)*Ncols + col - paxes = py.subplot(Nrows, Ncols, ind) - py.plot(time, fitLineY, 'b-') - py.plot(time, fitLineY + fitSigY, 'b--') - py.plot(time, fitLineY - fitSigY, 'b--') - py.errorbar(time, y, yerr=yerr, fmt='k.') - rng = py.axis() - py.axis(dateTicRng + [rng[2], rng[3]], fontsize=fontsize1) - py.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) + paxes = plt.subplot(Nrows, Ncols, ind) + plt.plot(time, fitLineY, 'b-') + plt.plot(time, fitLineY + fitSigY, 'b--') + plt.plot(time, fitLineY - fitSigY, 'b--') + plt.errorbar(time, y, yerr=yerr, fmt='k.') + rng = plt.axis() + plt.axis(dateTicRng + [rng[2], rng[3]], fontsize=fontsize1) + plt.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) if time[0] > 50000: - py.xlabel('Date (MJD)', fontsize=fontsize1) - py.ylabel('Y (pix)', fontsize=fontsize1) + plt.xlabel('Date (MJD)', fontsize=fontsize1) + plt.ylabel('Y (pix)', fontsize=fontsize1) #paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.xaxis.set_major_formatter(fmtX) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.yaxis.set_major_formatter(fmtY) paxes.tick_params(axis='both', which='major', labelsize=12) - py.ylim(np.min(y-yerr-0.1),np.max(y+yerr+0.1)) - py.yticks(np.arange(np.min(y-yerr-0.1), np.max(y+yerr+0.1), 0.2)) - py.xticks(dateTics, DateTicsLabel) - py.xlim(np.min(dateTics), np.max(dateTics)) + plt.ylim(np.min(y-yerr-0.1),np.max(y+yerr+0.1)) + plt.yticks(np.arange(np.min(y-yerr-0.1), np.max(y+yerr+0.1), 0.2)) + plt.xticks(dateTics, DateTicsLabel) + plt.xlim(np.min(dateTics), np.max(dateTics)) row = row + 1 col = col - 1 ind = (row-1)*Ncols + col - paxes = py.subplot(Nrows, Ncols, ind) - py.plot(time, np.zeros(len(time)), 'b-') - py.plot(time, fitSigX, 'b--') - py.plot(time, -fitSigX, 'b--') - py.errorbar(time, x - fitLineX, yerr=xerr, fmt='k.') - py.axis(dateTicRng + resTicRng, fontsize=fontsize1) - py.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) + paxes = plt.subplot(Nrows, Ncols, ind) + plt.plot(time, np.zeros(len(time)), 'b-') + plt.plot(time, fitSigX, 'b--') + plt.plot(time, -fitSigX, 'b--') + plt.errorbar(time, x - fitLineX, yerr=xerr, fmt='k.') + plt.axis(dateTicRng + resTicRng, fontsize=fontsize1) + plt.xlabel('Date - 2000 (yrs)', fontsize=fontsize1) if time[0] > 50000: - py.xlabel('Date (MJD)', fontsize=fontsize1) - py.ylabel('X Residuals (pix)', fontsize=fontsize1) + plt.xlabel('Date (MJD)', fontsize=fontsize1) + plt.ylabel('X Residuals (pix)', fontsize=fontsize1) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.xaxis.set_major_formatter(fmtX) paxes.tick_params(axis='both', which='major', labelsize=fontsize1) - py.xticks(dateTics, DateTicsLabel) - py.xlim(np.min(dateTics), np.max(dateTics)) + plt.xticks(dateTics, DateTicsLabel) + plt.xlim(np.min(dateTics), np.max(dateTics)) col = col + 1 ind = (row-1)*Ncols + col - paxes = py.subplot(Nrows, Ncols, ind) - py.plot(time, np.zeros(len(time)), 'b-') - py.plot(time, fitSigY, 'b--') - py.plot(time, -fitSigY, 'b--') - py.errorbar(time, y - fitLineY, yerr=yerr, fmt='k.') - py.axis(dateTicRng + resTicRng, fontsize=fontsize1) - py.xlabel('Date -2000 (yrs)', fontsize=fontsize1) + paxes = plt.subplot(Nrows, Ncols, ind) + plt.plot(time, np.zeros(len(time)), 'b-') + plt.plot(time, fitSigY, 'b--') + plt.plot(time, -fitSigY, 'b--') + plt.errorbar(time, y - fitLineY, yerr=yerr, fmt='k.') + plt.axis(dateTicRng + resTicRng, fontsize=fontsize1) + plt.xlabel('Date -2000 (yrs)', fontsize=fontsize1) if time[0] > 50000: - py.xlabel('Date (MJD)', fontsize=fontsize1) - py.ylabel('Y Residuals (pix)', fontsize=fontsize1) + plt.xlabel('Date (MJD)', fontsize=fontsize1) + plt.ylabel('Y Residuals (pix)', fontsize=fontsize1) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.xaxis.set_major_formatter(fmtX) paxes.tick_params(axis='both', which='major', labelsize=fontsize1) - py.xticks(dateTics, DateTicsLabel) - py.xlim(np.min(dateTics), np.max(dateTics)) + plt.xticks(dateTics, DateTicsLabel) + plt.xlim(np.min(dateTics), np.max(dateTics)) row = row + 1 col = col - 1 ind = (row-1)*Ncols + col - paxes = py.subplot(Nrows, Ncols, ind) - py.errorbar(x,y, xerr=xerr, yerr=yerr, fmt='k.') - py.yticks(np.arange(np.min(y-yerr-0.1), np.max(y+yerr+0.1), 0.2)) - py.xticks(np.arange(np.min(x-xerr-0.1), np.max(x+xerr+0.1), 0.2), rotation = 270) - py.axis('equal') + paxes = plt.subplot(Nrows, Ncols, ind) + plt.errorbar(x,y, xerr=xerr, yerr=yerr, fmt='k.') + plt.yticks(np.arange(np.min(y-yerr-0.1), np.max(y+yerr+0.1), 0.2)) + plt.xticks(np.arange(np.min(x-xerr-0.1), np.max(x+xerr+0.1), 0.2), rotation = 270) + plt.axis('equal') paxes.tick_params(axis='both', which='major', labelsize=fontsize1) paxes.yaxis.set_major_formatter(FormatStrFormatter('%.2f')) paxes.xaxis.set_major_formatter(FormatStrFormatter('%.2f')) - py.xlabel('X (pix)', fontsize=fontsize1) - py.ylabel('Y (pix)', fontsize=fontsize1) - py.plot(fitLineX, fitLineY, 'b-') + plt.xlabel('X (pix)', fontsize=fontsize1) + plt.ylabel('Y (pix)', fontsize=fontsize1) + plt.plot(fitLineX, fitLineY, 'b-') col = col + 1 ind = (row-1)*Ncols + col bins = np.arange(-7.5, 7.5, 1) - paxes = py.subplot(Nrows, Ncols, ind) + paxes = plt.subplot(Nrows, Ncols, ind) id = np.where(diffY < 0)[0] sig[id] = -1.*sig[id] - (n, b, p) = py.hist(sigX, bins, histtype='stepfilled', color='b', label='X') - py.setp(p, 'facecolor', 'b') - (n, b, p) = py.hist(sigY, bins, histtype='step', color='r', label='Y') - py.axis([-7, 7, 0, 8], fontsize=10) - py.legend() - py.xlabel('Residuals (sigma)', fontsize=fontsize1) - py.ylabel('Number of Epochs', fontsize=fontsize1) + (n, b, p) = plt.hist(sigX, bins, histtype='stepfilled', color='b', label='X') + plt.setp(p, 'facecolor', 'b') + (n, b, p) = plt.hist(sigY, bins, histtype='step', color='r', label='Y') + plt.axis([-7, 7, 0, 8], fontsize=10) + plt.legend() + plt.xlabel('Residuals (sigma)', fontsize=fontsize1) + plt.ylabel('Number of Epochs', fontsize=fontsize1) ########## # @@ -901,9 +906,9 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', # ########## if (radial == True): - py.clf() + plt.clf() - dateTicLoc = py.MultipleLocator(3) + dateTicLoc = plt.MultipleLocator(3) maxErr = np.array([rerr, terr]).max() resTicRng = [-3*maxErr, 3*maxErr] @@ -912,83 +917,83 @@ def plotStar(starNames, rootDir='./', align='align/align_d_rms_1000_abs_t', fmtX = FormatStrFormatter('%5i') fmtY = FormatStrFormatter('%6.2f') - paxes = py.subplot(3,2,1) - py.plot(time, fitLineR, 'b-') - py.plot(time, fitLineR + fitSigR, 'b--') - py.plot(time, fitLineR - fitSigR, 'b--') - py.errorbar(time, r, yerr=rerr, fmt='k.') - rng = py.axis() - py.axis(dateTicRng + [rng[2], rng[3]]) - py.xlabel('Date (yrs)') - py.ylabel('R (pix)') + paxes = plt.subplot(3,2,1) + plt.plot(time, fitLineR, 'b-') + plt.plot(time, fitLineR + fitSigR, 'b--') + plt.plot(time, fitLineR - fitSigR, 'b--') + plt.errorbar(time, r, yerr=rerr, fmt='k.') + rng = plt.axis() + plt.axis(dateTicRng + [rng[2], rng[3]]) + plt.xlabel('Date (yrs)') + plt.ylabel('R (pix)') paxes.xaxis.set_major_formatter(fmtX) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.yaxis.set_major_formatter(fmtY) - paxes = py.subplot(3, 2, 2) - py.plot(time, fitLineT, 'b-') - py.plot(time, fitLineT + fitSigT, 'b--') - py.plot(time, fitLineT - fitSigT, 'b--') - py.errorbar(time, t, yerr=terr, fmt='k.') - rng = py.axis() - py.axis(dateTicRng + [rng[2], rng[3]]) - py.xlabel('Date (yrs)') - py.ylabel('T (pix)') + paxes = plt.subplot(3, 2, 2) + plt.plot(time, fitLineT, 'b-') + plt.plot(time, fitLineT + fitSigT, 'b--') + plt.plot(time, fitLineT - fitSigT, 'b--') + plt.errorbar(time, t, yerr=terr, fmt='k.') + rng = plt.axis() + plt.axis(dateTicRng + [rng[2], rng[3]]) + plt.xlabel('Date (yrs)') + plt.ylabel('T (pix)') paxes.xaxis.set_major_formatter(fmtX) paxes.get_xaxis().set_major_locator(dateTicLoc) paxes.yaxis.set_major_formatter(fmtY) - paxes = py.subplot(3, 2, 3) - py.plot(time, np.zeros(len(time)), 'b-') - py.plot(time, fitSigR, 'b--') - py.plot(time, -fitSigR, 'b--') - py.errorbar(time, r - fitLineR, yerr=rerr, fmt='k.') - py.axis(dateTicRng + resTicRng) - py.xlabel('Date (yrs)') - py.ylabel('R Residuals (pix)') + paxes = plt.subplot(3, 2, 3) + plt.plot(time, np.zeros(len(time)), 'b-') + plt.plot(time, fitSigR, 'b--') + plt.plot(time, -fitSigR, 'b--') + plt.errorbar(time, r - fitLineR, yerr=rerr, fmt='k.') + plt.axis(dateTicRng + resTicRng) + plt.xlabel('Date (yrs)') + plt.ylabel('R Residuals (pix)') paxes.get_xaxis().set_major_locator(dateTicLoc) - paxes = py.subplot(3, 2, 4) - py.plot(time, np.zeros(len(time)), 'b-') - py.plot(time, fitSigT, 'b--') - py.plot(time, -fitSigT, 'b--') - py.errorbar(time, t - fitLineT, yerr=terr, fmt='k.') - py.axis(dateTicRng + resTicRng) - py.xlabel('Date (yrs)') - py.ylabel('T Residuals (pix)') + paxes = plt.subplot(3, 2, 4) + plt.plot(time, np.zeros(len(time)), 'b-') + plt.plot(time, fitSigT, 'b--') + plt.plot(time, -fitSigT, 'b--') + plt.errorbar(time, t - fitLineT, yerr=terr, fmt='k.') + plt.axis(dateTicRng + resTicRng) + plt.xlabel('Date (yrs)') + plt.ylabel('T Residuals (pix)') paxes.get_xaxis().set_major_locator(dateTicLoc) bins = np.arange(-7, 7, 1) - py.subplot(3, 2, 5) - (n, b, p) = py.hist(sigR, bins) - py.setp(p, 'facecolor', 'k') - py.axis([-5, 5, 0, 20]) - py.xlabel('T Residuals (sigma)') - py.ylabel('Number of Epochs') - - py.subplot(3, 2, 6) - (n, b, p) = py.hist(sigT, bins) - py.axis([-5, 5, 0, 20]) - py.setp(p, 'facecolor', 'k') - py.xlabel('Y Residuals (sigma)') - py.ylabel('Number of Epochs') - - py.subplots_adjust(wspace=0.4, hspace=0.4, right=0.95, top=0.95) - py.savefig(rootDir+'plots/plotStarRadial_' + starName + '.png') - py.show() + plt.subplot(3, 2, 5) + (n, b, p) = plt.hist(sigR, bins) + plt.setp(p, 'facecolor', 'k') + plt.axis([-5, 5, 0, 20]) + plt.xlabel('T Residuals (sigma)') + plt.ylabel('Number of Epochs') + + plt.subplot(3, 2, 6) + (n, b, p) = plt.hist(sigT, bins) + plt.axis([-5, 5, 0, 20]) + plt.setp(p, 'facecolor', 'k') + plt.xlabel('Y Residuals (sigma)') + plt.ylabel('Number of Epochs') + + plt.subplots_adjust(wspace=0.4, hspace=0.4, right=0.95, top=0.95) + plt.savefig(rootDir+'plots/plotStarRadial_' + starName + '.png') + plt.show() title = rootDir.split('/')[-2] - py.suptitle(title, x=0.5, y=0.97) + plt.suptitle(title, x=0.5, y=0.97) if Nstars == 1: - py.subplots_adjust(wspace=0.4, hspace=0.4, left = 0.15, bottom = 0.1, right=0.9, top=0.9) - py.savefig(rootDir+'plots/plotStar_' + starName + '.png') + plt.subplots_adjust(wspace=0.4, hspace=0.4, left = 0.15, bottom = 0.1, right=0.9, top=0.9) + plt.savefig(rootDir+'plots/plotStar_' + starName + '.png') else: - py.subplots_adjust(wspace=0.6, hspace=0.6, left = 0.08, bottom = 0.05, right=0.95, top=0.90) - py.savefig(rootDir+'plots/plotStar_all.png') - py.show() + plt.subplots_adjust(wspace=0.6, hspace=0.6, left = 0.08, bottom = 0.05, right=0.95, top=0.90) + plt.savefig(rootDir+'plots/plotStar_all.png') + plt.show() - py.show() + plt.show() print('Fubar') @@ -1051,7 +1056,7 @@ def plot_pm_error(tab): plt.legend() plt.xlabel('Mag') plt.ylabel('PM Error (mas/yr)') - + plt.show() return def plot_mag_error(tab): @@ -3607,8 +3612,8 @@ def plot_sky(stars_tab, foo = cnorm(yearsInt[ee]) colorList.append( cmap(cnorm(yearsInt[ee])) ) - py.close(2) - fig = py.figure(2, figsize=(13,10)) + plt.close(2) + fig = plt.figure(2, figsize=(13,10)) previousYear = 0.0 @@ -3646,13 +3651,13 @@ def plot_sky(stars_tab, label = '_nolegend_' if plot_errors: - (line, foo1, foo2) = py.errorbar(x, y, xerr=xe, yerr=ye, + (line, foo1, foo2) = plt.errorbar(x, y, xerr=xe, yerr=ye, color=colorList[ee], fmt='^', markeredgecolor=colorList[ee], markerfacecolor=colorList[ee], label=label, picker=4) else: - (line, foo1, foo2) = py.errorbar(x, y, xerr=None, yerr=None, + (line, foo1, foo2) = plt.errorbar(x, y, xerr=None, yerr=None, color=colorList[ee], fmt='^', markeredgecolor=colorList[ee], markerfacecolor=colorList[ee], @@ -3670,19 +3675,19 @@ def plot_sky(stars_tab, point_labels[line] = points_info foo = PrintSelected(point_labels, fig, stars_tab, mag_range, manual_print=manual_print) - py.connect('pick_event', foo) + plt.connect('pick_event', foo) xlo = xcenter + (range) xhi = xcenter - (range) ylo = ycenter - (range) yhi = ycenter + (range) - py.axis('equal') - py.axis([xlo, xhi, ylo, yhi]) - py.xlabel('R.A. Offset from Sgr A* (arcsec)') - py.ylabel('Dec. Offset from Sgr A* (arcsec)') + plt.axis('equal') + plt.axis([xlo, xhi, ylo, yhi]) + plt.xlabel('R.A. Offset from Sgr A* (arcsec)') + plt.ylabel('Dec. Offset from Sgr A* (arcsec)') - py.legend(handles=epochs_legend, numpoints=1, loc='lower left', fontsize=12) + plt.legend(handles=epochs_legend, numpoints=1, loc='lower left', fontsize=12) if show_names: xpos = stars_tab['x0'] @@ -3690,16 +3695,16 @@ def plot_sky(stars_tab, goodind = np.where((xpos <= xlo) & (xpos >= xhi) & (ypos >= ylo) & (ypos <= yhi))[0] for ind in goodind: - py.text(xpos[ind], ypos[ind], stars_tab['name'][ind], size=10) + plt.text(xpos[ind], ypos[ind], stars_tab['name'][ind], size=10) if saveplot: - py.show(block=0) + plt.show(block=0) if (center_star != None): - py.savefig('plot_sky_' + center_star + '.png') + plt.savefig('plot_sky_' + center_star + '.png') else: - py.savefig('plot_sky.png') + plt.savefig('plot_sky.png') else: - py.show() + plt.show() return From f0e478cf0b0396f850e694771e3af6a969c2c1dc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Fri, 7 Nov 2025 12:51:14 -0800 Subject: [PATCH 09/29] Minor fix: Add assertion message; Add times into ref_table meta data; Update trans_positions --- flystar/align.py | 19 ++++++++++++------- 1 file changed, 12 insertions(+), 7 deletions(-) diff --git a/flystar/align.py b/flystar/align.py index 7b00ba0..152ceac 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -241,15 +241,15 @@ def = None. If not None, then this should contain an array or list of transform def fix_iterable_conditions(self): if not np.iterable(self.dr_tol): self.dr_tol = np.repeat(self.dr_tol, self.iters) - assert len(self.dr_tol) == self.iters + assert len(self.dr_tol) == self.iters, f'len(dr_tol)={len(self.dr_tol)} != iters={self.iters}' if not np.iterable(self.dm_tol): self.dm_tol = np.repeat(self.dm_tol, self.iters) - assert len(self.dm_tol) == self.iters + assert len(self.dm_tol) == self.iters, f'len(dm_tol)={len(self.dm_tol)} != iters={self.iters}' if not np.iterable(self.outlier_tol): self.outlier_tol = np.repeat(self.outlier_tol, self.iters) - assert len(self.outlier_tol) == self.iters + assert len(self.outlier_tol) == self.iters, f'len(outlier_tol)={len(self.outlier_tol)} != iters={self.iters}' if self.mag_lim is None: self.mag_lim = np.repeat([[None, None]], len(self.star_lists), axis=0) @@ -367,6 +367,10 @@ def fit(self): if self.iter_callback != None: self.iter_callback(self.ref_table, nn) + # Add times into ref_table meta data + complete_times = np.array([np.unique(col[~np.isnan(col)])[0] for col in self.ref_table['t'].T]) + self.ref_table.meta['LIST_TIMES'] = complete_times + if self.save_path: with open(self.save_path, 'wb') as file: pickle.dump(self, file) @@ -504,7 +508,7 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar dy=(star_t['y'] - star_r['y']) * 1e3, dm=(star_t['m'] - star_r['m']), xo=star_s['x'], yo=star_s['y'], mo=star_s['m'])) - + idx_lis, idx_ref, dr, dm = match.match(star_list_T['x'], star_list_T['y'], star_list_T['m'], ref_list['x'], ref_list['y'], ref_list['m'], dr_tol=dr_tol, dm_tol=dm_tol, verbose=self.verbose) @@ -515,7 +519,8 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar ## Make plot, if desired plots.trans_positions(ref_list, ref_list[idx_ref], star_list_T, star_list_T[idx_lis], - fileName='{0}'.format(star_list_T['t'][0])) + save_path=f"{self.save_path}/Transformed_Positions_{star_list_T['t'][0]}.png" if self.save_path else None, + show_plot=False) ### Update the observed (but transformed) values in the reference table. self.update_ref_table_from_list(star_list, star_list_T, ii, idx_ref, idx_lis, idx2) @@ -1424,7 +1429,7 @@ def __init__(self, ref_list, list_of_starlists, iters=2, If different from None, it indicates the minimum and maximum magnitude on the catalogs for finding the transformations. Note, if you want specify the mag_lim separately for each list and each iteration, you need to pass in a 2D array that - has shape (N_lists, 2). + has shape (N_lists, N_iters). ref_mag_lim : array If different from None, it indicates the minimum and maximum magnitude @@ -2485,7 +2490,7 @@ def transform_from_object(starlist, transform): keys = list(starlist.keys()) # Check to see if velocities or motion_model are present in starlist. - vel = ('vx' in keys)and ~("motion_model_input" in keys) + vel = ('vx' in keys) and ("motion_model_input" not in keys) mot = ("motion_model_input" in keys) # If the only motion models used are Fixed and Linear, we can still transform velocities. if mot: From 7b010034e7257ed3c6e64599c687e376ad7c92a0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Fri, 7 Nov 2025 12:52:02 -0800 Subject: [PATCH 10/29] Minor fix: Update startables accordingly with motion model --- flystar/startables.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/flystar/startables.py b/flystar/startables.py index 422f9a7..8f7a397 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -845,13 +845,13 @@ def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scip fixed_params = [self[par][ss] for par in mod.fixed_param_names] # Fit for the best parameters - params, param_errs = mod.fit_motion_model(t, x, y, xe, ye, t0, bootstrap=bootstrap, + params, param_errs, chi2_x, chi2_y = mod.fit_motion_model(t, x, y, xe, ye, t0, bootstrap=bootstrap, weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma) - chi2_x,chi2_y = mod.get_chi2(params,fixed_params, t,x,y,xe,ye) + # chi2_x,chi2_y = mod.get_chi2(params,fixed_params, t,x,y,xe,ye) self['chi2_x'][ss]=chi2_x self['chi2_y'][ss]=chi2_y self['n_params'][ss] = mod.n_params - + # Save parameters and errors to table. for pp in range(len(mod.fitter_param_names)): par = mod.fitter_param_names[pp] From 289150ddf5b054e539e8e56df0b2de16d1092730 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Fri, 7 Nov 2025 13:48:53 -0800 Subject: [PATCH 11/29] Revert class meta definitions --- flystar/motion_model.py | 58 +++++++++++++++++++++++++---------------- 1 file changed, 36 insertions(+), 22 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 3c5069c..27d84af 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -129,14 +129,15 @@ class Fixed(MotionModel): A non-moving motion model for a star on the sky. """ + n_pts_req = 1 + n_params = 1 + fitter_param_names = ['x0','y0'] + fixed_param_names = [] + def __init__(self, **kwargs): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() - self.n_pts_req = 1 - self.n_params = 1 - self.fitter_param_names = ['x0','y0'] - self.fixed_param_names = [] return def get_pos_at_time(self, fit_params, fixed_params, t): @@ -200,17 +201,19 @@ class Linear(MotionModel): """ A 2D linear motion model for a star on the sky. """ + + n_pts_req = 2 + n_params = 2 + fitter_param_names = ['x0', 'vx', 'y0', 'vy'] + fixed_param_names = ['t0'] + def __init__(self, **kwargs): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() - self.n_pts_req = 2 - self.n_params = 2 - self.fitter_param_names = ['x0', 'vx', 'y0', 'vy'] - self.fixed_param_names = ['t0'] return - + def get_pos_at_time(self, fit_params, fixed_params, t): fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) @@ -316,15 +319,16 @@ class Acceleration(MotionModel): """ A 2D accelerating motion model for a star on the sky. """ + n_pts_req = 4 # TODO: consider special case for 3 pts + n_params = 3 + fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] + fixed_param_names = ['t0'] + def __init__(self, x0=0, vx0=0, ax=0, y0=0, vy0=0, ay=0, t0=None, x0_err=0, vx0_err=0, ax_err=0, y0_err=0, vy0_err=0, ay_err=0, **kwargs): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() - self.n_pts_req = 4 # TODO: consider special case for 3 pts - self.n_params = 3 - self.fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] - self.fixed_param_names = ['t0'] return def get_pos_at_time(self, fit_params, fixed_params, t): @@ -396,17 +400,19 @@ class Parallax(MotionModel): Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ + + n_pts_req = 4 + n_params = 3 + fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] + fixed_param_names = ['t0'] + fixed_meta_data = ['RA','Dec','PA','obs'] + def __init__(self, RA, Dec, PA=0.0, obs='earth', **kwargs): self.RA = RA self.Dec = Dec self.PA = PA self.obs = obs self.plx_vector_cached = None - self.n_pts_req = 4 - self.n_params = 3 - self.fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] - self.fixed_param_names = ['t0'] - self.fixed_meta_data = ['RA','Dec','PA','obs'] return def get_parallax_vector(self, t_mjd): @@ -549,11 +555,19 @@ def get_one_motion_model_param_names(motion_model_name, with_errors=True, with_f Optionally, include fixed and error parameters (included by default). """ def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_fixed=True): + motion_model_map = { + 'Fixed': Fixed, + 'Linear': Linear, + 'Acceleration': Acceleration, + 'Parallax': Parallax + } + list_of_parameters = [] - all_motion_models = [eval(mm) for mm in np.unique(motion_model_list).tolist()] - for aa in range(len(all_motion_models)): - param_names = getattr(all_motion_models[aa], 'fitter_param_names') - param_fixed_names = getattr(all_motion_models[aa], 'fixed_param_names') + # all_motion_models = [eval(mm) for mm in np.unique(motion_model_list).tolist()] + for mm in range(len(motion_model_list)): + motion_model = motion_model_map[motion_model_list[mm]] + param_names = motion_model.fitter_param_names + param_fixed_names = motion_model.fixed_param_names param_err_names = [par+'_err' for par in param_names] list_of_parameters += param_names From 443c4bdff1ddbe09f980acc7a8d563d69998a178 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Tue, 11 Nov 2025 20:03:44 -0800 Subject: [PATCH 12/29] Add get_sigma --- flystar/motion_model.py | 32 +++++++++++++++++++++----------- 1 file changed, 21 insertions(+), 11 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index fd9f0cd..e38d6df 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -50,7 +50,16 @@ def run_fit( ): # Run a single fit (used both for overall fit + bootstrap iterations) pass - + + def get_sigma(self, xe, ye, weighting='var'): + if weighting=='std': + return xe**0.5, ye**0.5 + elif weighting=='var': + return xe, ye + else: + warnings.warn("Invalid weighting, using default weighting scheme var.", UserWarning) + return xe, ye + def get_weights(self, xe, ye, weighting='var'): if weighting=='std': return 1./xe, 1./ye @@ -74,7 +83,7 @@ def fit_motion_model( to determine new parameters for this motion model (MM). Best-fit parameters will be returned along with uncertainties. """ - params, param_errs, chi2x, chi2y = self.run_fit( + params, param_errs, chi2_x, chi2_y = self.run_fit( t, x, y, xe, ye, t0=t0, weighting=weighting, use_scipy=use_scipy, @@ -82,6 +91,7 @@ def fit_motion_model( fill_value=fill_value ) + # Bootstrap errors if bootstrap > 0 and len(x) > (self.n_pts_req): edx = np.arange(len(x), dtype=int) bb_params = [] @@ -101,12 +111,12 @@ def fit_motion_model( # Save the errors from the bootstrap param_errs = np.std(bb_params, axis=0) - + # Account for odd case inf_errs = [np.all(arr==np.inf) for arr in np.transpose(np.array(bb_params_errs))] param_errs[inf_errs] = 0.0 - return params, param_errs, chi2x, chi2y + return params, param_errs, chi2_x, chi2_y def get_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): """ @@ -217,7 +227,7 @@ def __init__(self, **kwargs): def get_pos_at_time(self, fit_params, fixed_params, t): fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t-fixed_params_dict['t0'] + dt = t - fixed_params_dict['t0'] return fit_params_dict['x0'] + fit_params_dict['vx']*dt, fit_params_dict['y0'] + fit_params_dict['vy']*dt def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], @@ -234,7 +244,7 @@ def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], y = y0 + dt*vy x_err = np.hypot(x0_err, vx_err*dt) y_err = np.hypot(y0_err, vy_err*dt) - return x,y,x_err,y_err + return x, y, x_err, y_err def run_fit( self, t, x, y, xe, ye, t0, @@ -245,15 +255,15 @@ def run_fit( fill_value=np.inf ): dt = t - t0 - x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) + sigma_x, sigma_y = self.get_sigma(xe, ye, weighting=weighting) if params_guess is None: params_guess = [x.mean(), 0., y.mean(), 0.] if use_scipy: def linear(t, c0, c1): return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/np.sqrt(x_wt), absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/np.sqrt(y_wt), absolute_sigma=absolute_sigma) + x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=sigma_x, absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=sigma_y, absolute_sigma=absolute_sigma) x0, vx = x_opt y0, vy = y_opt x0e, vxe = np.sqrt(x_cov.diagonal()) @@ -269,13 +279,13 @@ def linear(t, c0, c1): dt = np.array(dt) X_mat_t = np.vander(dt, 2) # x calculation - W_mat_x = np.diag(x_wt) + W_mat_x = np.diag(1 / sigma_x**2) XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution # y calculation - W_mat_y = np.diag(y_wt) + W_mat_y = np.diag(1 / sigma_y**2) XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution From a1ef471d1339816be94876531af6c4a88d1f04c1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Tue, 11 Nov 2025 20:15:31 -0800 Subject: [PATCH 13/29] Revert back to get_weight --- flystar/motion_model.py | 21 ++++++--------------- 1 file changed, 6 insertions(+), 15 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index e38d6df..90d1442 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -50,16 +50,7 @@ def run_fit( ): # Run a single fit (used both for overall fit + bootstrap iterations) pass - - def get_sigma(self, xe, ye, weighting='var'): - if weighting=='std': - return xe**0.5, ye**0.5 - elif weighting=='var': - return xe, ye - else: - warnings.warn("Invalid weighting, using default weighting scheme var.", UserWarning) - return xe, ye - + def get_weights(self, xe, ye, weighting='var'): if weighting=='std': return 1./xe, 1./ye @@ -255,15 +246,15 @@ def run_fit( fill_value=np.inf ): dt = t - t0 - sigma_x, sigma_y = self.get_sigma(xe, ye, weighting=weighting) + x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) if params_guess is None: params_guess = [x.mean(), 0., y.mean(), 0.] if use_scipy: def linear(t, c0, c1): return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=sigma_x, absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=sigma_y, absolute_sigma=absolute_sigma) + x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) x0, vx = x_opt y0, vy = y_opt x0e, vxe = np.sqrt(x_cov.diagonal()) @@ -279,13 +270,13 @@ def linear(t, c0, c1): dt = np.array(dt) X_mat_t = np.vander(dt, 2) # x calculation - W_mat_x = np.diag(1 / sigma_x**2) + W_mat_x = np.diag(x_wt) XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution # y calculation - W_mat_y = np.diag(1 / sigma_y**2) + W_mat_y = np.diag(y_wt) XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution From 1a7481d45e3ad44035c4bf2a8ca7dafaac5c9ba8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Wed, 12 Nov 2025 23:34:02 -0800 Subject: [PATCH 14/29] Major Update: Update data fitting logic: Compare observed data points with model parameters. If n_obs < n_params, return fill value for the parameters and infinity for the uncertainties; Otherwise, calculate parameters normally. If n_obs = n_params and absolute_sigma=False, return infinity for uncertainties (Same behavior as scipy curve fit). --- flystar/motion_model.py | 506 +++++++++++++++++++++++++++------------- 1 file changed, 343 insertions(+), 163 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 90d1442..939cd0b 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -7,8 +7,6 @@ import warnings class MotionModel(ABC): - # Number of data points required to fit model - n_pts_req = 0 # Degrees of freedom for model n_params = 0 @@ -33,7 +31,7 @@ def __init__(self, *args, **kwargs): setattr(self, param, np.array([param_var]))''' return - def get_pos_at_time(self, params, t): + def get_pos_at_time(self, fit_params, fixed_params, t): #return x, y pass @@ -46,10 +44,11 @@ def run_fit( weighting='var', use_scipy=True, absolute_sigma=True, - fill_value=np.inf + fill_value=np.nan, + verbose=True ): # Run a single fit (used both for overall fit + bootstrap iterations) - pass + return np.full(self.n_params, fill_value), np.full(self.n_params, np.inf), np.nan, np.nan def get_weights(self, xe, ye, weighting='var'): if weighting=='std': @@ -66,36 +65,74 @@ def fit_motion_model( weighting='var', use_scipy=True, absolute_sigma=True, - fill_value=np.inf, - rng=None + fill_value=np.nan, + verbose=True, + seed=None ): - """ - Fit the input positions on the sky and errors - to determine new parameters for this motion model (MM). - Best-fit parameters will be returned along with uncertainties. + """Fit stellar motion parameters + + Parameters + ---------- + t : array-like + Times of measurements + x : array-like + x-coordinates + y : array-like + y-coordinates + xe : array-like + Uncertainty of x + ye : array-like + Uncertainty of y + t0 : array-like + Reference time for fitting, i.e. dt = t - t0 will be used in fitting + bootstrap : int, optional + Bootstrapping uncertainties, by default 0 + weighting : str, optional + Use standard error weighting ('std': w=1/xe, 1/ye) or variance weighting ('var': w=1/xe**2, 1/ye**2), by default 'var' + use_scipy : bool, optional + Use scipy for optmization. Otherwise, use linear algebraic solution (Linear model only), which is faster for < 300 epochs, by default True + absolute_sigma : bool, optional + Absolute sigma. See scipy.optimize.curve_fit for details, by default True + fill_value : float, optional + Fill value for parameters when not enough data points to fit model, by default np.nan + verbose : bool, optional + Print warning messages, by default True + seed : int, optional + Seed for the random number generator, by default None + Returns + ------- + params, params_err, chi2_x, chi2_y + Parameters, uncertainties, and chi squares. The corresponding parameter names are in self.fitter_param_names. """ params, param_errs, chi2_x, chi2_y = self.run_fit( t, x, y, xe, ye, t0=t0, weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma, - fill_value=fill_value + fill_value=fill_value, + verbose=verbose ) - + if seed is not None: + rng = np.random.default_rng(seed) + else: + rng = np.random.default_rng() + # Bootstrap errors - if bootstrap > 0 and len(x) > (self.n_pts_req): - edx = np.arange(len(x), dtype=int) + n_obs = len(t) + if bootstrap > 0 and n_obs > (self.n_params): + edx = np.arange(n_obs, dtype=int) bb_params = [] bb_params_errs = [] for bb in range(bootstrap): - bdx = np.random.choice(edx, len(x), replace=False) + bdx = rng.choice(edx, n_obs, replace=False) params_bdx, param_errs_bdx, chi2x_bdx, chi2y_bdx = self.run_fit( t[bdx], x[bdx], y[bdx], xe[bdx], ye[bdx], t0=t0, weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma, params_guess=params, - fill_value=fill_value + fill_value=fill_value, + verbose=verbose ) bb_params.append(params_bdx) bb_params_errs.append(param_errs_bdx) @@ -125,12 +162,51 @@ def get_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): chi2x, chi2y = chi2x / dof, chi2y / dof return chi2x, chi2y +class Empty(MotionModel): + n_params = 0 + fitter_param_names = [] + fixed_param_names = [] + + def __init__(self, **kwargs): + """Empty motion model, returns nan for values and inf for uncertainties. + """ + super().__init__() + return + + def get_pos_at_time(self, fit_params, fixed_params, t): + if hasattr(t, "__len__"): + return np.full(len(t), np.nan), np.full(len(t), np.nan) + else: + return np.nan, np.nan + + def get_batch_pos_at_time(self,t, + x0=[],y0=[],t0=[], + x0_err=[], y0_err=[]): + if hasattr(t, "__len__"): + return np.full((len(x0), len(t)), np.nan), np.full((len(y0), len(t)), np.nan), np.full((len(x0), len(t)), np.nan), np.full((len(y0), len(t)), np.nan) + else: + return np.nan, np.nan, np.nan, np.nan + + def run_fit( + self, t, x, y, xe, ye, t0, + weighting='var', + use_scipy=True, + absolute_sigma=True, + fill_value=np.nan, + verbose=True + ): + if verbose: + warnings.warn(f"Empty data cannot be fit. Setting parameters to {fill_value} and uncertainties to np.inf.", OptimizeWarning, stacklevel=2) + params = np.full(self.n_params, fill_value) + param_errors = np.full(self.n_params, np.inf) + return params, param_errors, np.nan, np.nan + + class Fixed(MotionModel): """ A non-moving motion model for a star on the sky. """ - n_pts_req = 1 n_params = 1 fitter_param_names = ['x0','y0'] fixed_param_names = [] @@ -154,7 +230,7 @@ def get_batch_pos_at_time(self,t, if hasattr(t, "__len__"): return np.repeat(x0[:,np.newaxis],len(t),axis=1), np.repeat(y0[:,np.newaxis],len(t),axis=1), np.repeat(x0_err[:,np.newaxis],len(t),axis=1), np.repeat(y0_err[:,np.newaxis],len(t),axis=1) else: - return x0,y0,x0_err,y0_err + return x0, y0, x0_err, y0_err def run_fit( self, t, x, y, xe, ye, t0, @@ -162,26 +238,40 @@ def run_fit( use_scipy=True, absolute_sigma=True, params_guess=None, - fill_value=np.inf + fill_value=np.nan, + verbose=True ): - if not use_scipy: - Warning("Fixed model has no non-scipy fitter option. Running with scipy.") - # Handle single data point case - if len(x)==1: - x0, y0, x0e, y0e = x[0], y[0], xe[0], ye[0] - - else: - x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) - x0 = np.average(x, weights=x_wt) - x0e = np.sqrt(np.average((x - x0)**2, weights=x_wt)) - y0 = np.average(y, weights=y_wt) - y0e = np.sqrt(np.average((y - y0)**2, weights=y_wt)) + if verbose and (not use_scipy): + warnings.warn("Fixed model has no non-scipy fitter option. Running with scipy.") + + n_obs = len(t) + degree_of_freedom = n_obs - self.n_params + # Not enough data points to fit model + if degree_of_freedom < 0: + if verbose: + warnings.warn( + f'Not enough data points to fit model. Setting parameters to {fill_value} and uncertainties to np.inf.', + OptimizeWarning, stacklevel=2 + ) + params = np.full(self.n_params, fill_value) + param_errors = np.full(self.n_params, np.inf) + return params, param_errors, np.nan, np.nan + + # degree_of_freedom >= 0 + # Calculate weighted average position + x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) + x_wt_norm = x_wt / np.sum(x_wt) + y_wt_norm = y_wt / np.sum(y_wt) + x0 = np.average(x, weights=x_wt) + x0e = (np.sum(x_wt_norm**2 * xe**2))**0.5 / n_obs # Error propagation + y0 = np.average(y, weights=y_wt) + y0e = (np.sum(y_wt_norm**2 * ye**2))**0.5 / n_obs # Error propagation params = np.array([x0, y0]) param_errors = np.array([x0e, y0e]) chi2x, chi2y = self.get_chi2(params, [], t, x, y, xe, ye) - degree_of_freedom = len(x) - 1 + if not absolute_sigma: if degree_of_freedom > 0: reduced_chi2x = chi2x / degree_of_freedom @@ -190,11 +280,13 @@ def run_fit( param_errors[0] *= reduced_chi2x**0.5 param_errors[1] *= reduced_chi2y**0.5 else: + # degree_of_freedom == 0, as < 0 case already handled above warnings.warn( - f'Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value {fill_value}.', + f'Degree of freedom < 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value np.inf.', OptimizeWarning, stacklevel=2 ) - param_errors = np.full_like(param_errors, fill_value) + # Set parameter uncertainties to np.inf, same behavior as scipy.optimize.curve_fit + param_errors = np.full_like(param_errors, np.inf) return params, param_errors, chi2x, chi2y @@ -202,8 +294,6 @@ class Linear(MotionModel): """ A 2D linear motion model for a star on the sky. """ - - n_pts_req = 2 n_params = 2 fitter_param_names = ['x0', 'vx', 'y0', 'vy'] fixed_param_names = ['t0'] @@ -224,13 +314,13 @@ def get_pos_at_time(self, fit_params, fixed_params, t): def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], x0_err=[],vx_err=[], y0_err=[],vy_err=[], **kwargs): if hasattr(t, "__len__"): - dt = t-t0[:,np.newaxis] + dt = t - t0[:,np.newaxis] x = x0[:,np.newaxis] + dt*vx[:,np.newaxis] y = y0[:,np.newaxis] + dt*vy[:,np.newaxis] x_err = np.hypot(x0_err[:,np.newaxis], vx_err[:,np.newaxis]*dt) y_err = np.hypot(y0_err[:,np.newaxis], vy_err[:,np.newaxis]*dt) else: - dt = t-t0 + dt = t - t0 x = x0 + dt*vx y = y0 + dt*vy x_err = np.hypot(x0_err, vx_err*dt) @@ -243,8 +333,23 @@ def run_fit( use_scipy=True, absolute_sigma=True, params_guess=None, - fill_value=np.inf + fill_value=np.nan, + verbose=True ): + n_obs = len(t) + degree_of_freedom = n_obs - self.n_params + # Not enough data points to fit model + if degree_of_freedom < 0: + if verbose: + warnings.warn( + f'Not enough data points to fit model. Setting parameters to {fill_value} and uncertainties to np.inf.', + OptimizeWarning, stacklevel=2 + ) + params = np.full(self.n_params, fill_value) + param_errors = np.full(self.n_params, np.inf) + return params, param_errors, np.nan, np.nan + + # degree_of_freedom >= 0 dt = t - t0 x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) if params_guess is None: @@ -290,8 +395,7 @@ def linear(t, c0, c1): # Does not use get_chi2 to accelerate calculation residual_x = x - X_mat_t @ popt_x residual_y = y - X_mat_t @ popt_y - - + chi2_x = residual_x.T @ W_mat_x @ residual_x chi2_y = residual_y.T @ W_mat_y @ residual_y @@ -299,20 +403,21 @@ def linear(t, c0, c1): param_errors = np.array([x0e, vxe, y0e, vye]) if not absolute_sigma: - degree_of_freedom = len(x) - 2 if degree_of_freedom > 0: - reduced_chi2_x = chi2_x/(len(x) - 2) - reduced_chi2_y = chi2_y/(len(x) - 2) + reduced_chi2_x = chi2_x / degree_of_freedom + reduced_chi2_y = chi2_y / degree_of_freedom param_errors[0:2] *= reduced_chi2_x**0.5 param_errors[2:4] *= reduced_chi2_y**0.5 else: + # degree_of_freedom == 0, as < 0 case already handled above warnings.warn( - f'Degree of freedom <= 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value {fill_value}.', + f'Degree of freedom < 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value np.inf.', OptimizeWarning, stacklevel=2 ) - param_errors = np.full_like(param_errors, fill_value) + # Set parameter uncertainties to np.inf, same behavior as scipy.optimize.curve_fit + param_errors = np.full_like(param_errors, np.inf) return params, param_errors, chi2_x, chi2_y @@ -320,7 +425,6 @@ class Acceleration(MotionModel): """ A 2D accelerating motion model for a star on the sky. """ - n_pts_req = 4 # TODO: consider special case for 3 pts n_params = 3 fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] fixed_param_names = ['t0'] @@ -335,7 +439,7 @@ def __init__(self, x0=0, vx0=0, ax=0, y0=0, vy0=0, ay=0, t0=None, def get_pos_at_time(self, fit_params, fixed_params, t): fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t-fixed_params_dict['t0'] + dt = t - fixed_params_dict['t0'] x = fit_params_dict['x0'] + fit_params_dict['vx0']*dt + 0.5*fit_params_dict['ax']*dt**2 y = fit_params_dict['y0'] + fit_params_dict['vy0']*dt + 0.5*fit_params_dict['ay']*dt**2 return x, y @@ -344,18 +448,18 @@ def get_batch_pos_at_time(self,t, x0=[],vx0=[],ax=[], y0=[],vy0=[],ay=[], t0=[], x0_err=[],vx0_err=[],ax_err=[], y0_err=[],vy0_err=[],ay_err=[], **kwargs): if hasattr(t, "__len__"): - dt = t-t0[:,np.newaxis] - x = x0[:,np.newaxis] + dt*vx0[:,np.newaxis] + 0.5*dt**2*ax[:,np.newaxis] - y = y0[:,np.newaxis] + dt*vy0[:,np.newaxis] + 0.5*dt**2*ay[:,np.newaxis] - x_err = np.sqrt(x0_err[:,np.newaxis]**2 + (vx0_err[:,np.newaxis]*dt)**2 + (0.5*ax_err[:,np.newaxis]*dt**2)**2) - y_err = np.sqrt(y0_err[:,np.newaxis]**2 + (vy0_err[:,np.newaxis]*dt)**2 + (0.5*ay_err[:,np.newaxis]*dt**2)**2) + dt = t - t0[:,np.newaxis] + x = x0[:, np.newaxis] + dt * vx0[:, np.newaxis] + 0.5 * ax[:, np.newaxis] * dt**2 + y = y0[:, np.newaxis] + dt * vy0[:, np.newaxis] + 0.5 * ay[:, np.newaxis] * dt**2 + x_err = np.sqrt(x0_err[:, np.newaxis]**2 + (vx0_err[:, np.newaxis]*dt)**2 + (0.5*ax_err[:, np.newaxis]*dt**2)**2) + y_err = np.sqrt(y0_err[:, np.newaxis]**2 + (vy0_err[:, np.newaxis]*dt)**2 + (0.5*ay_err[:, np.newaxis]*dt**2)**2) else: - dt = t-t0 - x = x0 + dt*vx0 + 0.5*dt**2*ax - y = y0 + dt*vy0 + 0.5*dt**2*ay - x_err = np.sqrt(x0_err**2 + (vx0_err*dt)**2 + (0.5*ax_err*dt**2)**2) - y_err = np.sqrt(y0_err**2 + (vy0_err*dt)**2 + (0.5*ay_err*dt**2)**2) - return x,y,x_err,y_err + dt = t - t0 + x = x0 + dt * vx0 + 0.5 * ax * dt**2 + y = y0 + dt * vy0 + 0.5 * ay * dt**2 + x_err = np.sqrt(x0_err**2 + (vx0_err * dt)**2 + (0.5 * ax_err * dt**2)**2) + y_err = np.sqrt(y0_err**2 + (vy0_err * dt)**2 + (0.5 * ay_err * dt**2)**2) + return x, y, x_err, y_err def run_fit( self, t, x, y, xe, ye, t0, @@ -363,34 +467,50 @@ def run_fit( use_scipy=True, absolute_sigma=True, params_guess=None, - fill_value=np.inf + fill_value=np.nan, + verbose=True ): if not use_scipy: - Warning("Acceleration model has no non-scipy fitter option. Running with scipy.") + if verbose: + warnings.warn("Acceleration model has no non-scipy fitter option. Running with scipy.") + + n_obs = len(t) + degree_of_freedom = n_obs - self.n_params + # Not enough data points to fit model + if degree_of_freedom < 0: + if verbose: + warnings.warn( + f'Not enough data points to fit model. Setting parameters to {fill_value} and uncertainties to np.inf.', + OptimizeWarning, stacklevel=2 + ) + params = np.full(self.n_params, fill_value) + param_errors = np.full(self.n_params, np.inf) + return params, param_errors, np.nan, np.nan + + # degree_of_freedom >= 0 dt = t - t0 x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) if params_guess is None: - params_guess = [x.mean(), 0., 0., y.mean(), 0., 0.] + # Initial guess for velocity: + idx_first, idx_last = np.argmin(t), np.argmax(t) + t_span = t[idx_last] - t[idx_first] + params_guess = [x.mean(), (x[idx_last] - x[idx_first]) / t_span, 0., y.mean(), (y[idx_last] - y[idx_first]) / t_span, 0.] def accel(t, c0, c1, c2): return c0 + c1*t + 0.5*c2*t**2 - x_opt, x_cov = curve_fit(accel, dt, x, p0=np.array(params_guess[:3]), sigma=1/x_wt**0.5, absolute_sigma=True) - y_opt, y_cov = curve_fit(accel, dt, y, p0=np.array(params_guess[3:]), sigma=1/y_wt**0.5, absolute_sigma=True) - x0 = x_opt[0] - y0 = y_opt[0] - vx0 = x_opt[1] - vy0 = y_opt[1] - ax = x_opt[2] - ay = y_opt[2] - + x_opt, x_cov = curve_fit(accel, dt, x, p0=np.array(params_guess[:3]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(accel, dt, y, p0=np.array(params_guess[3:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) + x0, vx0, ax = x_opt + y0, vy0, ay = y_opt x0e, vx0e, axe = np.sqrt(x_cov.diagonal()) y0e, vy0e, aye = np.sqrt(y_cov.diagonal()) - params = [x0, vx0, ax, y0, vy0, ay] - param_errors = [x0e, vx0e, axe, y0e, vy0e, aye] + params = np.array([x0, vx0, ax, y0, vy0, ay]) + param_errors = np.array([x0e, vx0e, axe, y0e, vy0e, aye]) + chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) - return params, param_errors + return params, param_errors, chi2_x, chi2_y class Parallax(MotionModel): """ @@ -401,8 +521,6 @@ class Parallax(MotionModel): Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ - - n_pts_req = 4 n_params = 3 fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] fixed_param_names = ['t0'] @@ -473,7 +591,7 @@ def get_batch_pos_at_time(self, t, y_err = np.sqrt(y0_err**2 + (vy_err*dt)**2 + (pi_err*pvec[1])**2) except: x_err,y_err = [],[] - return x,y,x_err,y_err + return x, y, x_err, y_err def run_fit( self, t, x, y, xe, ye, t0, @@ -481,10 +599,27 @@ def run_fit( use_scipy=True, absolute_sigma=True, params_guess=None, - fill_value=np.inf + fill_value=np.nan, + verbose=True ): if not use_scipy: - Warning("Parallax model has no non-scipy fitter option. Running with scipy.") + if verbose: + warnings.warn("Parallax model has no non-scipy fitter option. Running with scipy.", UserWarning) + + n_obs = len(t) + degree_of_freedom = n_obs - self.n_params + # Not enough data points to fit model + if degree_of_freedom < 0: + if verbose: + warnings.warn( + f'Not enough data points to fit model. Setting parameters to {fill_value} and uncertainties to np.inf.', + OptimizeWarning, stacklevel=2 + ) + params = np.full(self.n_params, fill_value) + param_errors = np.full(self.n_params, np.inf) + return params, param_errors + + # degree_of_freedom >= 0 t_mjd = Time(t, format='decimalyear', scale='utc').mjd pvec = self.get_parallax_vector(t_mjd) x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) @@ -494,107 +629,152 @@ def fit_func(use_t, x0,vx, y0,vy, pi): return np.hstack([x_res, y_res]) # Initial guesses, x0,y0 as x,y averages; # vx,vy as average velocity if first and last points are perfectly measured; - # pi for 10 pc disance + # pi for 10 pc distance if params_guess is None: idx_first, idx_last = np.argmin(t), np.argmax(t) - params_guess = [x.mean(),(x[idx_last]-x[idx_first])/(t[idx_last]-t[idx_first]), - y.mean(),(y[idx_last]-y[idx_first])/(t[idx_last]-t[idx_first]), 0.1] - res = curve_fit(fit_func, t, np.hstack([x,y]), - p0=params_guess, sigma = 1.0/np.hstack([x_wt,y_wt])) + t_span = t[idx_last] - t[idx_first] + params_guess = [ + x.mean(), (x[idx_last] - x[idx_first]) / t_span, + y.mean(), (y[idx_last] - y[idx_first]) / t_span, + 0.1 + ] + res = curve_fit( + fit_func, t, np.hstack([x,y]), + p0=params_guess, sigma = 1.0/np.hstack([x_wt,y_wt]), + absolute_sigma=absolute_sigma + ) x0, vx, y0, vy, pi = res[0] x0_err, vx_err, y0_err, vy_err, pi_err = np.sqrt(np.diag(res[1])) - params = [x0, vx, y0, vy, pi] - param_errors = [x0_err, vx_err, y0_err, vy_err, pi_err] - return params, param_errors + params = np.array([x0, vx, y0, vy, pi]) + param_errors = np.array([x0_err, vx_err, y0_err, vy_err, pi_err]) + chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) -""" -Check that everything is set up properly for motion models to run and their -required metadata. -""" -def validate_motion_model_dict(motion_model_dict, startable, default_motion_model): - # Collect names of all motion models that might get used. - all_motion_model_names = ['Fixed'] - if default_motion_model is not None: - all_motion_model_names.append(default_motion_model) - if 'motion_model_input' in startable.columns: - all_motion_model_names += np.unique(startable['motion_model_input']).tolist() - if 'motion_model_used' in startable.columns: - all_motion_model_names += np.unique(startable['motion_model_used']).tolist() - all_motion_model_names = np.unique(all_motion_model_names) - - # Check whether all motion models are in the dict, and if not, try to add them - # here or raise an error. - for mm in all_motion_model_names: - if mm not in motion_model_dict: - mm_obj = eval(mm) - if len(mm_obj.fixed_meta_data)>0: - raise ValueError(f"Cannot use {mm} motion model without required metadata. Please initialize with required metadata and provide in motion_model_dict.") - else: - motion_model_dict[mm] = mm_obj() - # warnings.warn(f"Using default model/fitter for {mm}.", UserWarning) + return params, param_errors, chi2_x, chi2_y - return motion_model_dict - -""" -Get all the motion model parameters for a given motion_model_name. -Optionally, include fixed and error parameters (included by default). -""" -def get_one_motion_model_param_names(motion_model_name, with_errors=True, with_fixed=True): - mod = eval(motion_model_name) - list_of_parameters = [] - list_of_parameters += getattr(mod, 'fitter_param_names') - if with_fixed: - list_of_parameters += getattr(mod, 'fixed_param_names') - if with_errors: - list_of_parameters += [par+'_err' for par in getattr(mod, 'fitter_param_names')] - return list_of_parameters -""" -Get all the motion model parameters for all models given in motion_model_list. -Optionally, include fixed and error parameters (included by default). -""" -def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_fixed=True): +def validate_motion_models(motion_models, startable, default_motion_model): + """Validate that all the unique motion models in startable and default_motion_model are in the motion_models. If not, add available models to the list. + + Parameters + ---------- + motion_models : list of MotionModels + List of MotionModels that are expected to encompass all the motion models + startable : StarTable + Star table that possibly contains 'motion_model_input' and 'motion_model_used' + default_motion_model : MotionModel + Default MotionModel + """ motion_model_map = { 'Fixed': Fixed, 'Linear': Linear, 'Acceleration': Acceleration, 'Parallax': Parallax } + # Collect names of all motion models that might get used. + all_motion_model_names = set() + all_motion_model_names.add('Fixed') + if default_motion_model is not None: + all_motion_model_names.add(default_motion_model.__name__) + if 'motion_model_input' in startable.colnames: + all_motion_model_names.update(startable['motion_model_input'].tolist()) + if 'motion_model_used' in startable.colnames: + all_motion_model_names.update(startable['motion_model_used'].tolist()) + + # Check whether all motion models are in the list, and if not, raise an error. + all_motion_models = [motion_model_map[mm] for mm in all_motion_model_names] + for mm in all_motion_models: + if mm not in motion_models: + if len(mm.fixed_meta_data) > 0: + raise ValueError(f"Cannot use {mm} motion model without required metadata. Please initialize with required metadata and provide in motion_models.") + else: + motion_models.append(mm) + warnings.warn(f"{mm} not found in motion_models list. Added default instance.", UserWarning) + + return motion_models + + +def get_one_motion_model_param_names(motion_model, with_errors=True, with_fixed=True): + """Get all the motion model parameters + + Parameters + ---------- + motion_model : MotionModel + MotionModel instance + with_errors : bool, optional + Add uncertainty names with '_err' suffix or not, by default True + with_fixed : bool, optional + Add fixed param names with '_fixed' suffix or not, by default True + Returns + ------- + list + List of all parameter names for the motion model + """ list_of_parameters = [] - # all_motion_models = [eval(mm) for mm in np.unique(motion_model_list).tolist()] - for mm in range(len(motion_model_list)): - motion_model = motion_model_map[motion_model_list[mm]] - param_names = motion_model.fitter_param_names - param_fixed_names = motion_model.fixed_param_names - param_err_names = [par+'_err' for par in param_names] - - list_of_parameters += param_names - if with_fixed: - list_of_parameters += param_fixed_names - if with_errors: - list_of_parameters += param_err_names - return np.unique(list_of_parameters).tolist() + def list_add(name): + if name not in list_of_parameters: + list_of_parameters.append(name) + + for param in motion_model.fitter_param_names: + # Fitter params + list_add(param) + # Error params + if with_errors: + list_add(param + '_err') + # Fixed params + if with_fixed: + for param in motion_model.fixed_param_names: + list_add(param) + return list_of_parameters + -""" -Get all the motion model parameters for all models defined in this module. -Optionally, include fixed and error parameters (included by default). -""" -def get_all_motion_model_param_names(with_errors=True, with_fixed=True): +def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_fixed=True): + """Get all the motion model parameters + + Parameters + ---------- + motion_model_list : list + List of MotionModels + with_errors : bool, optional + Add uncertainty names with '_err' suffix or not, by default True + with_fixed : bool, optional + Add fixed param names with '_fixed' suffix or not, by default True + + Returns + ------- + list + List of all unique parameter names across all motion models + """ list_of_parameters = [] - all_motion_models = MotionModel.__subclasses__() - for aa in range(len(all_motion_models)): - param_names = getattr(all_motion_models[aa], 'fitter_param_names') - param_fixed_names = getattr(all_motion_models[aa], 'fixed_param_names') - param_err_names = [par+'_err' for par in param_names] - list_of_parameters += param_names + def list_add(name): + if name not in list_of_parameters: + list_of_parameters.append(name) + + for mm in motion_model_list: + for param in mm.fitter_param_names: + # Fitter params + list_add(param) + # Error params + if with_errors: + list_add(param + '_err') + # Fixed params if with_fixed: - list_of_parameters += param_fixed_names - if with_errors: - list_of_parameters += param_err_names - - return np.unique(list_of_parameters).tolist() - + for param in mm.fixed_param_names: + list_add(param) + return list(list_of_parameters) + + +def get_all_motion_model_names(with_errors=True, with_fixed=True): + return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) + +def motion_model_map(): + return { + 'Empty': Empty, + 'Fixed': Fixed, + 'Linear': Linear, + 'Acceleration': Acceleration, + 'Parallax': Parallax + } \ No newline at end of file From 77820b2ab6d28cbe519bfb7edd90a9473c6514ca Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Wed, 12 Nov 2025 23:37:32 -0800 Subject: [PATCH 15/29] Rewrite startable fit velocity function for acceleration and the new motion models. Update fitting logic: Provide multiple motion models, use the available model with the most number of parameters to fit according to the observed data points (i.e., choose the model with n_obs >= n_params). Removed motion_model_input and default_motion_model for clarity. --- flystar/startables.py | 296 ++++++++++++++++++++++++++++++++++-------- 1 file changed, 243 insertions(+), 53 deletions(-) diff --git a/flystar/startables.py b/flystar/startables.py index 8f7a397..60b8310 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -11,78 +11,74 @@ import copy from flystar import motion_model import pandas as pd +from flystar.motion_model import Empty, Fixed, Linear class StarTable(Table): - """ - A StarTable is an astropy.Table with stars matched from multiple starlists. + def __init__(self, *args, ref_list=0, **kwargs): + """ + A StarTable is an astropy.Table with stars matched from multiple starlists. - Required table columns (input as keywords): - ------------------------- - name : 1D numpy.array with shape = N_stars - List of unique names for each of the stars in the table. + Required table columns (input as keywords): + ------------------------- + name : 1D numpy.array with shape = N_stars + List of unique names for each of the stars in the table. - x : 2D numpy.array with shape = (N_stars, N_lists) - Positions of N_stars in each of N_lists in the x dimension. + x : 2D numpy.array with shape = (N_stars, N_lists) + Positions of N_stars in each of N_lists in the x dimension. - y : 2D numpy.array with shape = (N_stars, N_lists) - Positions of N_stars in each of N_lists in the y dimension. + y : 2D numpy.array with shape = (N_stars, N_lists) + Positions of N_stars in each of N_lists in the y dimension. - m : 2D numpy.array with shape = (N_stars, N_lists) - Magnitudes of N_stars in each of N_lists. + m : 2D numpy.array with shape = (N_stars, N_lists) + Magnitudes of N_stars in each of N_lists. - Optional table columns (input as keywords): - ------------------------- - motion_model : 1D numpy.array with shape = N_stars - string indicating motion model type for each star - - xe : 2D numpy.array with shape = (N_stars, N_lists) - Position uncertainties of N_stars in each of N_lists in the x dimension. + Optional table columns (input as keywords): + ------------------------- + motion_model : 1D numpy.array with shape = N_stars + string indicating motion model type for each star + + xe : 2D numpy.array with shape = (N_stars, N_lists) + Position uncertainties of N_stars in each of N_lists in the x dimension. - ye : 2D numpy.array with shape = (N_stars, N_lists) - Position uncertainties of N_stars in each of N_lists in the y dimension. + ye : 2D numpy.array with shape = (N_stars, N_lists) + Position uncertainties of N_stars in each of N_lists in the y dimension. - me : 2D numpy.array with shape = (N_stars, N_lists) - Magnitude uncertainties of N_stars in each of N_lists. + me : 2D numpy.array with shape = (N_stars, N_lists) + Magnitude uncertainties of N_stars in each of N_lists. - ep_name : 2D numpy.array with shape = (N_stars, N_lists) - Names in each epoch for each of N_stars in each of N_lists. This is - useful for tracking purposes. - - corr : 2D numpy.array with shape = (N_stars, N_lists) - Fitting correlation for each of N_stars in each of N_lists. + ep_name : 2D numpy.array with shape = (N_stars, N_lists) + Names in each epoch for each of N_stars in each of N_lists. This is + useful for tracking purposes. + + corr : 2D numpy.array with shape = (N_stars, N_lists) + Fitting correlation for each of N_stars in each of N_lists. - Optional table meta data - ------------------------- - list_names : list of strings - List of names, one for each of the starlists. + Optional table meta data + ------------------------- + list_names : list of strings + List of names, one for each of the starlists. - list_times : list of integers or floats - List of times/dates for each starlist. + list_times : list of integers or floats + List of times/dates for each starlist. - ref_list : int - Specify which list is the reference list (if any). + ref_list : int + Specify which list is the reference list (if any). - Examples - -------------------------- + Examples + -------------------------- - t = startables.StarTable(name=name, x=x, y=y, m=m) + t = startables.StarTable(name=name, x=x, y=y, m=m) - # Access the data: - print(t) - print(t['name'][0:10]) # print the first 10 star names - print(t['x'][0:10, 0]) # print x from the first epoch/list/column for the first 10 stars - """ - def __init__(self, *args, ref_list=0, **kwargs): - """ + # Access the data: + print(t) + print(t['name'][0:10]) # print the first 10 star names + print(t['x'][0:10, 0]) # print x from the first epoch/list/column for the first 10 stars """ # Check if the required arguments are present arg_req = ('name', 'x', 'y', 'm') - - found_all_required = True - for arg_test in arg_req: - if arg_test not in kwargs: - found_all_required = False + + found_all_required = all(arg in kwargs for arg in arg_req) if not found_all_required: if len(args) > 1: # If there are no arguments, it's because the @@ -151,7 +147,7 @@ def __init__(self, *args, ref_list=0, **kwargs): names=('name', 'x', 'y', 'm')) self['name'] = self['name'].astype('U20') self.meta = {'n_stars': n_stars, 'n_lists': n_lists, 'ref_list': ref_list} - + for meta_arg in meta_tab: if meta_arg in kwargs: self.meta[meta_arg] = kwargs[meta_arg] @@ -536,6 +532,200 @@ def detections(self): return + def fit_velocities_new( + self, + motion_models=['Empty', 'Fixed', 'Linear'], + weighting='var', + use_scipy=False, + absolute_sigma=True, + bootstrap=0, + fixed_t0=False, + verbose=True, + mask_value=None, + fill_value=np.nan, + show_progress=True + ): + """Fit velocity for star table + + Parameters + ---------- + motion_models : list, optional + Motion models name to use. + If multiple models are supplied, prioritize the model with the most parameters to fit. + If multiple models have the same number of parameters, raise AssertionError: not sure which to use. + When not enough data points, use the model with just enough parameters to fit, by default ['Empty, 'Fixed', 'Linear'] + weighting : str, optional + Uncertainty weighting, 'std' for weight=1/xe(ye) or 'var' for weight=1/xe(ye)**2, by default 'var' + use_scipy : bool, optional + Use scipy.optimize.curve_fit or algebraic solution (for Linear model only), by default False + absolute_sigma : bool, optional + Use absolute sigma or not, see scipy curve_fit for details, by default True + bootstrap : int, optional + Number of bootstrap for uncertainty resampling, by default 0 + fixed_t0 : bool or float, optional + If provided, use the fixed t0. Otherwise, use average t weighted by 1/np.hypot(xe, ye), by default False + verbose : bool, optional + Print verbose messages or not, by default True + mask_value : float, optional + Values to mask in data, by default None + fill_value : float, optional + Fill value when there is not enough data points to fit, by default np.nan + show_progress : bool, optional + Show progress bar or not, by default True + + Raises + ------ + ValueError + If weighting is not 'var' or 'std'. + KeyError + If time values are not found in the table or meta. + KeyError + If required columns 'x' and 'y' are missing in the table. + """ + ########################### + ####### Check Params ###### + ########################### + if weighting not in ['var', 'std']: + raise ValueError(f"fit_velocities: Weighting must either be 'var' or 'std', not {weighting}!") + + if ('t' not in self.colnames) and ('LIST_TIMES' not in self.meta): + raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'LIST_TIMES' in meta.") + + # Check if we have the required columns + if not all([_ in self.colnames for _ in ['x', 'y']]): + raise KeyError(f"fit_velocities: Missing required columns in the table: {', '.join(['x', 'y'])}!") + + # Convert motion models from strings to classes + motion_model_map = motion_model.motion_model_map() + if 'Empty' not in motion_models: + motion_models.insert(0, 'Empty') # Ensure Empty model is always included + motion_models = [motion_model_map[mm] for mm in motion_models] + + ########################### + ####### Prepare Data ###### + ########################### + # Prepare data for fitting + N_stars = len(self) + x_data = np.ma.masked_invalid(self['x'].data, copy=True) + y_data = np.ma.masked_invalid(self['y'].data, copy=True) + xe_data = np.ma.masked_invalid(self['xe'].data, copy=True) if 'xe' in self.colnames else None + ye_data = np.ma.masked_invalid(self['ye'].data, copy=True) if 'ye' in self.colnames else None + # t_data: 2d array with shape (N_stars, N_epochs) + # t0: 1d array with shape (N_stars,) + if 't' in self.colnames: + t_data = copy.deepcopy(self['t'].data) + t0 = np.average(t_data, axis=1, weights=1/np.hypot(xe_data, ye_data)) if not fixed_t0 else np.ones(N_stars)*fixed_t0 + else: + t_data = copy.deepcopy(np.array(self.meta['LIST_TIMES'])) + t_data = np.broadcast_to(t_data, x_data.shape) + t0 = np.average(t_data, axis=1, weights=1/np.hypot(xe_data, ye_data)) if not fixed_t0 else np.ones(N_stars)*fixed_t0 + if mask_value: + x_data = np.ma.masked_values(x_data, mask_value) + y_data = np.ma.masked_values(y_data, mask_value) + if xe_data is not None: + xe_data = np.ma.masked_values(xe_data, mask_value) + if ye_data is not None: + ye_data = np.ma.masked_values(ye_data, mask_value) + + # Calculate mask array + xy_mask = (~x_data.mask) & (~y_data.mask) + self['n_obs'] = xy_mask.sum(axis=1) + + # Convert to lists of arrays for faster access during fitting + t_stars = [np.array(t_data[i][xy_mask[i]]) for i in range(N_stars)] + x_stars = [np.array(x_data[i][xy_mask[i]]) for i in range(N_stars)] + y_stars = [np.array(y_data[i][xy_mask[i]]) for i in range(N_stars)] + xe_stars = [np.array(xe_data[i][xy_mask[i]]) if xe_data is not None else None for i in range(N_stars)] + ye_stars = [np.array(ye_data[i][xy_mask[i]]) if ye_data is not None else None for i in range(N_stars)] + + + ########################### + ####### Determine MM ###### + ########################### + mm_n_params = np.sort([mm.n_params for mm in motion_models]) + # Assert that motion model n_params are unique and sorted + assert len(mm_n_params) == len(set(mm_n_params)), "fit_velocities: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs." + + # Select motion model based on n_obs + mm_digitized = np.digitize( + x=self['n_obs'], + bins=mm_n_params + ) - 1 # -1 to convert to 0-based index + self['motion_model'] = np.array([motion_models[d].__name__ for d in mm_digitized]) + + # Fill table with all possible motion model parameter names as new columns. + new_col_list = motion_model.get_list_motion_model_param_names(motion_models, with_errors=True) + new_col_list += ['chi2_x', 'chi2_y', 'n_params'] + if 't0' not in new_col_list: + new_col_list.append('t0') + + # Replace old columns if they exist + for col in new_col_list: + if col.endswith('_err'): + self.add_column( + Column(data=np.full(N_stars, np.inf, dtype=float), name=col), + rename_duplicate=True + ) + else: + self.add_column( + Column(data=np.full(N_stars, np.nan, dtype=float), name=col), + rename_duplicate=True + ) + + # Add a column to keep track of the number of points used in a fit and number of bootstrap used. + self['n_bootstrap'] = bootstrap + + ########################### + ######### FITTING ######### + ########################### + unique_motion_models, unique_inv_indices = np.unique(self['motion_model'], return_inverse=True) + indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} + + for unique_motion_model, unique_index in indices_by_motion_model.items(): + # Create motion model instance + motion_model_instance = motion_model_map[unique_motion_model]() + # Initialize arrays to store results + n_stars_this_model = len(unique_index) + n_params = len(motion_model_instance.fitter_param_names) + + params_array = np.full((n_stars_this_model, n_params), fill_value, dtype=float) + param_errs_array = np.full((n_stars_this_model, n_params), np.inf, dtype=float) + chi2_x_array = np.full(n_stars_this_model, np.nan, dtype=float) + chi2_y_array = np.full(n_stars_this_model, np.nan, dtype=float) + + for idx, i_star in enumerate(tqdm(unique_index, disable=not show_progress, desc=f"Fitting motion model {unique_motion_model}")): + # Fit the star + params, param_errs, chi2_x, chi2_y = motion_model_instance.fit_motion_model( + t=t_stars[i_star], + x=x_stars[i_star], + y=y_stars[i_star], + xe=xe_stars[i_star], + ye=ye_stars[i_star], + t0=t0[i_star], + weighting=weighting, + use_scipy=use_scipy, + absolute_sigma=absolute_sigma, + bootstrap=bootstrap, + fill_value=fill_value, + verbose=verbose + ) + # Store results to arrays + params_array[idx] = params + param_errs_array[idx] = param_errs + chi2_x_array[idx] = chi2_x + chi2_y_array[idx] = chi2_y + + # Store results back to the table + param_names = motion_model_instance.fitter_param_names + for j, param_name in enumerate(param_names): + self[param_name][unique_index] = params_array[:, j] + self[param_name + '_err'][unique_index] = param_errs_array[:, j] + self['chi2_x'][unique_index] = chi2_x_array + self['chi2_y'][unique_index] = chi2_y_array + self['n_params'][unique_index] = n_params + self['t0'][unique_index] = t0[unique_index] + return + def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, bootstrap=0, fixed_t0=False, verbose=False, mask_val=None, mask_lists=False, show_progress=True, default_motion_model='Linear', reassign_motion_model=False, select_stars=None, motion_model_dict={}): From 043cdf1386c90320fa1b29f9b50ec8d23778630b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Sun, 16 Nov 2025 20:22:18 -0800 Subject: [PATCH 16/29] Add support for motion_model_input --- flystar/motion_model.py | 44 +++++++++++----- flystar/startables.py | 113 +++++++++++++++++++++++++++++----------- 2 files changed, 114 insertions(+), 43 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 939cd0b..4849214 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -7,12 +7,12 @@ import warnings class MotionModel(ABC): - # Degrees of freedom for model - n_params = 0 - # Fit paramters: Shared fit parameters fitter_param_names = [] + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) + # Fixed parameters: These are parameters that are required for the model, but are not # fit quantities. For example, RA and Dec in a parallax model. fixed_param_names = [] @@ -22,6 +22,7 @@ class MotionModel(ABC): # These parameters should be derived from the fit parameters and # they must exist as a variable on the model object optional_param_names = [] + name = "MotionModel" def __init__(self, *args, **kwargs): # TODO: do we need this? @@ -59,7 +60,7 @@ def get_weights(self, xe, ye, weighting='var'): warnings.warn("Invalid weighting, using default weighting scheme var.", UserWarning) return 1./xe**2, 1./ye**2 - def fit_motion_model( + def fit( self, t, x, y, xe, ye, t0, bootstrap=0, weighting='var', @@ -163,9 +164,11 @@ def get_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): return chi2x, chi2y class Empty(MotionModel): - n_params = 0 fitter_param_names = [] fixed_param_names = [] + name = "Empty" + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) def __init__(self, **kwargs): """Empty motion model, returns nan for values and inf for uncertainties. @@ -207,9 +210,12 @@ class Fixed(MotionModel): A non-moving motion model for a star on the sky. """ - n_params = 1 fitter_param_names = ['x0','y0'] fixed_param_names = [] + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) + + name = "Fixed" def __init__(self, **kwargs): # Must call after setting parameters. @@ -294,10 +300,14 @@ class Linear(MotionModel): """ A 2D linear motion model for a star on the sky. """ - n_params = 2 fitter_param_names = ['x0', 'vx', 'y0', 'vy'] fixed_param_names = ['t0'] + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) + + name = "Linear" + def __init__(self, **kwargs): # Must call after setting parameters. @@ -348,7 +358,7 @@ def run_fit( params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) return params, param_errors, np.nan, np.nan - + # degree_of_freedom >= 0 dt = t - t0 x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) @@ -425,9 +435,12 @@ class Acceleration(MotionModel): """ A 2D accelerating motion model for a star on the sky. """ - n_params = 3 fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] fixed_param_names = ['t0'] + name = "Acceleration" + + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) def __init__(self, x0=0, vx0=0, ax=0, y0=0, vy0=0, ay=0, t0=None, x0_err=0, vx0_err=0, ax_err=0, y0_err=0, vy0_err=0, ay_err=0, **kwargs): @@ -521,10 +534,13 @@ class Parallax(MotionModel): Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ - n_params = 3 fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] fixed_param_names = ['t0'] fixed_meta_data = ['RA','Dec','PA','obs'] + name = "Parallax" + + # Number of fit parameters/required observations in each direction + n_params = int(np.ceil(len(fitter_param_names) / 2)) def __init__(self, RA, Dec, PA=0.0, obs='earth', **kwargs): self.RA = RA @@ -771,10 +787,14 @@ def get_all_motion_model_names(with_errors=True, with_fixed=True): return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) def motion_model_map(): - return { + mm_map = { 'Empty': Empty, 'Fixed': Fixed, 'Linear': Linear, 'Acceleration': Acceleration, 'Parallax': Parallax - } \ No newline at end of file + } + + # Sort by n_params + mm_map = dict(sorted(mm_map.items(), key=lambda item: item[1].n_params)) + return mm_map \ No newline at end of file diff --git a/flystar/startables.py b/flystar/startables.py index 60b8310..08461a1 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -532,9 +532,9 @@ def detections(self): return - def fit_velocities_new( + def fit_motion_model( self, - motion_models=['Empty', 'Fixed', 'Linear'], + motion_models=[Empty(), Fixed(), Linear()], weighting='var', use_scipy=False, absolute_sigma=True, @@ -549,11 +549,19 @@ def fit_velocities_new( Parameters ---------- - motion_models : list, optional - Motion models name to use. - If multiple models are supplied, prioritize the model with the most parameters to fit. - If multiple models have the same number of parameters, raise AssertionError: not sure which to use. - When not enough data points, use the model with just enough parameters to fit, by default ['Empty, 'Fixed', 'Linear'] + motion_models : list of MotionModel, optional + Motion models to use. + Empty() and Fixed() models are always added automatically for stars with n_fit = 0 or 1. + The behavior is as follows: + 1. If 'motion_model_input' column is NOT in table: + - Use the most complex model that has enough parameters to fit the data (n_fit >= n_params). + - If multiple models are supplied, prioritize the model with the most parameters to fit. + - If multiple models have the same number of parameters, raise AssertionError: not sure which to use. + 2. If 'motion_model_input' column is in table: + - Use the model specified in the 'motion_model_input' column. + - If motion model requires initialization parameters, an instance of the motion model must be provided in motion_models list, i.e., motion_models=[Parallax(RA=0, DEC=0)]. + - If not enough data points to fit the specified model, use the most complex model that has enough parameters to fit the data (n_fit >= n_params) among the provided motion_models and 'motion_model_input'. + The actual used motion model is stored in the 'motion_model_used' column. The default motion_models are [Empty(), Fixed(), Linear()]. weighting : str, optional Uncertainty weighting, 'std' for weight=1/xe(ye) or 'var' for weight=1/xe(ye)**2, by default 'var' use_scipy : bool, optional @@ -595,11 +603,38 @@ def fit_velocities_new( if not all([_ in self.colnames for _ in ['x', 'y']]): raise KeyError(f"fit_velocities: Missing required columns in the table: {', '.join(['x', 'y'])}!") - # Convert motion models from strings to classes - motion_model_map = motion_model.motion_model_map() - if 'Empty' not in motion_models: - motion_models.insert(0, 'Empty') # Ensure Empty model is always included - motion_models = [motion_model_map[mm] for mm in motion_models] + # Always add Empty and Fixed in motion models + mm_names = [mm.name for mm in motion_models] + if 'Fixed' not in mm_names: + motion_models.insert(0, Fixed()) + if 'Empty' not in mm_names: + motion_models.insert(0, Empty()) + mm_names = [mm.name for mm in motion_models] + + # Construct motion models if motion_model_input column exists + all_mm_map = motion_model.motion_model_map() + if 'motion_model_input' in self.colnames: + input_mm_names = np.unique(self['motion_model_input']) + assert all([name in all_mm_map.keys() for name in input_mm_names]), \ + f"fit_velocities: Unknown motion model name(s) in 'motion_model_input' column. Available motion models are: {', '.join(all_mm_map.keys())}." + for mm_name in input_mm_names: + if mm_name not in mm_names: + try: + motion_models.append(all_mm_map[mm_name]()) + except Exception as e: + raise ValueError(f"fit_velocities: An instance of motion model {mm_name} with initialization parameters is missing in motion_models: {e}") + + # Sort motion models by n_params + motion_models = sorted(motion_models, key=lambda mm: mm.n_params) + + input_mm_map = {mm.name: mm for mm in motion_models} + + mm_n_params = np.sort([mm.n_params for mm in motion_models]) + if 'motion_model_input' not in self.colnames: + # If motion_model_input column is not provided, assert that motion model n_params are unique and sorted + # Otherwise the fitter does not know which motion model to use based on n_obs + assert len(mm_n_params) == len(set(mm_n_params)), "fit_velocities: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs. Please provide unique motion_models or a 'motion_model_input' column." + ########################### ####### Prepare Data ###### @@ -610,6 +645,7 @@ def fit_velocities_new( y_data = np.ma.masked_invalid(self['y'].data, copy=True) xe_data = np.ma.masked_invalid(self['xe'].data, copy=True) if 'xe' in self.colnames else None ye_data = np.ma.masked_invalid(self['ye'].data, copy=True) if 'ye' in self.colnames else None + # t_data: 2d array with shape (N_stars, N_epochs) # t0: 1d array with shape (N_stars,) if 't' in self.colnames: @@ -619,6 +655,7 @@ def fit_velocities_new( t_data = copy.deepcopy(np.array(self.meta['LIST_TIMES'])) t_data = np.broadcast_to(t_data, x_data.shape) t0 = np.average(t_data, axis=1, weights=1/np.hypot(xe_data, ye_data)) if not fixed_t0 else np.ones(N_stars)*fixed_t0 + if mask_value: x_data = np.ma.masked_values(x_data, mask_value) y_data = np.ma.masked_values(y_data, mask_value) @@ -629,7 +666,7 @@ def fit_velocities_new( # Calculate mask array xy_mask = (~x_data.mask) & (~y_data.mask) - self['n_obs'] = xy_mask.sum(axis=1) + self['n_fit'] = xy_mask.sum(axis=1) # Convert to lists of arrays for faster access during fitting t_stars = [np.array(t_data[i][xy_mask[i]]) for i in range(N_stars)] @@ -642,19 +679,31 @@ def fit_velocities_new( ########################### ####### Determine MM ###### ########################### - mm_n_params = np.sort([mm.n_params for mm in motion_models]) - # Assert that motion model n_params are unique and sorted - assert len(mm_n_params) == len(set(mm_n_params)), "fit_velocities: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs." + if 'motion_model_input' in self.colnames: + # Determine which motion model to use based on motion_model_input column + # If n_fit < required n_params for the input motion model, use the most complicated motion model with n_fit >= n_params + motion_model_names = np.unique(self['motion_model_input']) + required_params = [all_mm_map[mm_name].n_params for mm_name in self['motion_model_input']] + mm_digitized = np.digitize( + x=np.minimum(np.array(self['n_fit']), required_params), + bins=mm_n_params + ) - 1 # Convert to 0-based index + + else: + mm_digitized = np.digitize( + x=np.array(self['n_fit']), + bins=mm_n_params + ) - 1 # Convert to 0-based index + + self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized]) - # Select motion model based on n_obs - mm_digitized = np.digitize( - x=self['n_obs'], - bins=mm_n_params - ) - 1 # -1 to convert to 0-based index - self['motion_model'] = np.array([motion_models[d].__name__ for d in mm_digitized]) + ############################ + ####### Prepare Table ###### + ############################ # Fill table with all possible motion model parameter names as new columns. - new_col_list = motion_model.get_list_motion_model_param_names(motion_models, with_errors=True) + motion_model_used = [all_mm_map[name] for name in np.unique(self['motion_model_used'])] + new_col_list = motion_model.get_list_motion_model_param_names(motion_model_used, with_errors=True) new_col_list += ['chi2_x', 'chi2_y', 'n_params'] if 't0' not in new_col_list: new_col_list.append('t0') @@ -668,7 +717,7 @@ def fit_velocities_new( ) else: self.add_column( - Column(data=np.full(N_stars, np.nan, dtype=float), name=col), + Column(data=np.full(N_stars, fill_value, dtype=float), name=col), rename_duplicate=True ) @@ -678,12 +727,13 @@ def fit_velocities_new( ########################### ######### FITTING ######### ########################### - unique_motion_models, unique_inv_indices = np.unique(self['motion_model'], return_inverse=True) + unique_motion_models, unique_inv_indices = np.unique(self['motion_model_used'], return_inverse=True) indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} - + + start_time = time.time() for unique_motion_model, unique_index in indices_by_motion_model.items(): # Create motion model instance - motion_model_instance = motion_model_map[unique_motion_model]() + motion_model_instance = input_mm_map[unique_motion_model] # Initialize arrays to store results n_stars_this_model = len(unique_index) n_params = len(motion_model_instance.fitter_param_names) @@ -695,7 +745,7 @@ def fit_velocities_new( for idx, i_star in enumerate(tqdm(unique_index, disable=not show_progress, desc=f"Fitting motion model {unique_motion_model}")): # Fit the star - params, param_errs, chi2_x, chi2_y = motion_model_instance.fit_motion_model( + params, param_errs, chi2_x, chi2_y = motion_model_instance.fit( t=t_stars[i_star], x=x_stars[i_star], y=y_stars[i_star], @@ -709,7 +759,7 @@ def fit_velocities_new( fill_value=fill_value, verbose=verbose ) - # Store results to arrays + # print(f'{params_array.shape=}, {idx=}, {params=}') params_array[idx] = params param_errs_array[idx] = param_errs chi2_x_array[idx] = chi2_x @@ -722,10 +772,11 @@ def fit_velocities_new( self[param_name + '_err'][unique_index] = param_errs_array[:, j] self['chi2_x'][unique_index] = chi2_x_array self['chi2_y'][unique_index] = chi2_y_array - self['n_params'][unique_index] = n_params + self['n_params'][unique_index] = motion_model_instance.n_params self['t0'][unique_index] = t0[unique_index] return + def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, bootstrap=0, fixed_t0=False, verbose=False, mask_val=None, mask_lists=False, show_progress=True, default_motion_model='Linear', reassign_motion_model=False, select_stars=None, motion_model_dict={}): @@ -1100,7 +1151,7 @@ def get_star_positions_at_time(self, t, motion_model_dict, allow_alt_models=True param_dict[par] = self[par][idx] x[idx],y[idx],xe[idx],ye[idx] = mod.get_batch_pos_at_time(t,**param_dict) - return x,y,xe,ye + return x, y, xe, ye def fit_velocities_all_detected(self, motion_model_to_fit, weighting='var', use_scipy=True, absolute_sigma=True, times=None, From 5ec18cb6847b97562f8936c33890cf3b3bb7e8f5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Thu, 20 Nov 2025 19:05:15 -0800 Subject: [PATCH 17/29] Passed testing for fit_motion_model. Merged get_pos_at_time and get_batch_pos at_time into model; Renamed get_ functions into calc_ functions --- flystar/motion_model.py | 568 +++++++++++++++++++---------- flystar/parallax.py | 43 ++- flystar/startables.py | 17 +- flystar/tests/test_align.py | 2 +- flystar/tests/test_motion_model.py | 288 +++++++++------ flystar/tests/test_startable.py | 12 +- 6 files changed, 599 insertions(+), 331 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 4849214..5a542e0 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -8,10 +8,10 @@ class MotionModel(ABC): # Fit paramters: Shared fit parameters - fitter_param_names = [] + fit_param_names = [] # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) + n_params = int(np.ceil(len(fit_param_names) / 2)) # Fixed parameters: These are parameters that are required for the model, but are not # fit quantities. For example, RA and Dec in a parallax model. @@ -25,21 +25,16 @@ class MotionModel(ABC): name = "MotionModel" def __init__(self, *args, **kwargs): - # TODO: do we need this? - '''for param in self.fitter_param_names: - param_var = getattr(self, param) - if not isinstance(param_var, (list, np.ndarray)): - setattr(self, param, np.array([param_var]))''' return + + def model_fit(self, dt): + return np.full_like(dt, np.nan) + + def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): + if fit_param_errs is None: + return np.full_like(t, np.nan), np.full_like(t, np.nan) + return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) - def get_pos_at_time(self, fit_params, fixed_params, t): - #return x, y - pass - - def get_batch_pos_at_time(self, t): - #return x, y, x_err, y_err - pass - def run_fit( self, t, x, y, xe, ye, t0, weighting='var', @@ -103,7 +98,7 @@ def fit( Returns ------- params, params_err, chi2_x, chi2_y - Parameters, uncertainties, and chi squares. The corresponding parameter names are in self.fitter_param_names. + Parameters, uncertainties, and chi squares. The corresponding parameter names are in self.fit_param_names. """ params, param_errs, chi2_x, chi2_y = self.run_fit( t, x, y, xe, ye, t0=t0, @@ -147,48 +142,41 @@ def fit( return params, param_errs, chi2_x, chi2_y - def get_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): + def calc_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): """ Get the chi^2 value for the current MM and the input data. """ - x_pred, y_pred = self.get_pos_at_time(fit_params, fixed_params, t) + x_pred, y_pred = self.model(t, fit_params, fixed_params) chi2x = np.sum((x - x_pred)**2 / xe**2) chi2y = np.sum((y - y_pred)**2 / ye**2) if reduced: if len(t) == self.n_params: - chi2x, chi2y = 0, 0 + return np.inf, np.inf else: - dof = len(x) - self.n_params - chi2x, chi2y = chi2x / dof, chi2y / dof + degree_of_freedom = len(x) - self.n_params + chi2x, chi2y = chi2x / degree_of_freedom, chi2y / degree_of_freedom return chi2x, chi2y class Empty(MotionModel): - fitter_param_names = [] + fit_param_names = [] fixed_param_names = [] name = "Empty" # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) + n_params = int(np.ceil(len(fit_param_names) / 2)) def __init__(self, **kwargs): """Empty motion model, returns nan for values and inf for uncertainties. """ super().__init__() return - - def get_pos_at_time(self, fit_params, fixed_params, t): - if hasattr(t, "__len__"): - return np.full(len(t), np.nan), np.full(len(t), np.nan) - else: - return np.nan, np.nan + + def model_fit(self, dt): + return np.full_like(dt, np.nan) - def get_batch_pos_at_time(self,t, - x0=[],y0=[],t0=[], - x0_err=[], y0_err=[]): - if hasattr(t, "__len__"): - return np.full((len(x0), len(t)), np.nan), np.full((len(y0), len(t)), np.nan), np.full((len(x0), len(t)), np.nan), np.full((len(y0), len(t)), np.nan) - else: - return np.nan, np.nan, np.nan, np.nan + def model(self, t, fit_params, fixed_params, fixed_param_errs=None): + t = np.atleast_1d(t) + return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) def run_fit( self, t, x, y, xe, ye, t0, @@ -210,10 +198,10 @@ class Fixed(MotionModel): A non-moving motion model for a star on the sky. """ - fitter_param_names = ['x0','y0'] + fit_param_names = ['x0','y0'] fixed_param_names = [] # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) + n_params = int(np.ceil(len(fit_param_names) / 2)) name = "Fixed" @@ -222,22 +210,78 @@ def __init__(self, **kwargs): # This checks for proper parameter formatting. super().__init__() return + + def model_fit(self, dt, x0): + """Fit function for Fixed motion model + + Parameters + ---------- + dt : array-like + Time offset, shape (N_times,) + x0 : float or array-like + Average positions, scalar or shape (N_stars,) - def get_pos_at_time(self, fit_params, fixed_params, t): - fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) - if hasattr(t, "__len__"): - return np.repeat(fit_params_dict['x0'], len(t)), np.repeat(fit_params_dict['y0'], len(t)) - else: - return fit_params_dict['x0'], fit_params_dict['y0'] - - def get_batch_pos_at_time(self,t, - x0=[],y0=[],t0=[], - x0_err=[], y0_err=[]): - if hasattr(t, "__len__"): - return np.repeat(x0[:,np.newaxis],len(t),axis=1), np.repeat(y0[:,np.newaxis],len(t),axis=1), np.repeat(x0_err[:,np.newaxis],len(t),axis=1), np.repeat(y0_err[:,np.newaxis],len(t),axis=1) - else: - return x0, y0, x0_err, y0_err - + Returns + ------- + x : array-like + Predicted positions, shape (N_times,) if scalar x0, else (N_stars, N_times) + """ + dt = np.atleast_1d(dt) + x0 = np.asarray(x0) + return np.broadcast_to(x0[:, np.newaxis], (x0.shape[0], dt.shape[0])) if x0.ndim > 0 else np.full_like(dt, x0) + + def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): + """Predicted positions (and uncertainties, if fit_param_errs is provided) at time t of Fixed model. + + Parameters + ---------- + t : float or array-like + Time array, shape (N_times,) + fit_params : array-like + Fit parameters x0, y0 in shape (N_params,) or (N_stars, N_params) + fixed_params : array-like, optional + Not applicable for Fixed, by default None + fit_param_errs : array-like, optional + Uncertainties for x0, y0 in shape (N_params,) or (N_stars, N_params), by default None + + Returns + ------- + x, y (, xe, ye) + Predicted position (and uncertainties) of Fixed model, shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 + """ + t = np.atleast_1d(t) + fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) + + N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 + N_times = len(t) + x0, y0 = fit_params.T # Each shape (N_stars,) + + # Return results in (N_stars, N_times) shape + x = self.model_fit(t, x0) # Shape (N_stars, N_times) + y = self.model_fit(t, y0) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x = x.flatten() + y = y.flatten() + + if fit_param_errs is None: + return x, y + + fit_param_errs = np.atleast_2d(fit_param_errs) # (N_stars, N_params) + x0_err, y0_err = fit_param_errs.T + + # Return results in (N_stars, N_times) shape + x_err = np.broadcast_to(x0_err[:, np.newaxis], (N_stars, N_times)) + y_err = np.broadcast_to(y0_err[:, np.newaxis], (N_stars, N_times)) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x_err = x_err.flatten() + y_err = y_err.flatten() + + return x, y, x_err, y_err + def run_fit( self, t, x, y, xe, ye, t0, weighting='var', @@ -262,22 +306,22 @@ def run_fit( params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) return params, param_errors, np.nan, np.nan - + # degree_of_freedom >= 0 # Calculate weighted average position x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) x_wt_norm = x_wt / np.sum(x_wt) y_wt_norm = y_wt / np.sum(y_wt) x0 = np.average(x, weights=x_wt) - x0e = (np.sum(x_wt_norm**2 * xe**2))**0.5 / n_obs # Error propagation + x0e = (np.sum(x_wt_norm**2 * xe**2))**0.5 # Error propagation y0 = np.average(y, weights=y_wt) - y0e = (np.sum(y_wt_norm**2 * ye**2))**0.5 / n_obs # Error propagation + y0e = (np.sum(y_wt_norm**2 * ye**2))**0.5 # Error propagation params = np.array([x0, y0]) param_errors = np.array([x0e, y0e]) - - chi2x, chi2y = self.get_chi2(params, [], t, x, y, xe, ye) - + + chi2x, chi2y = self.calc_chi2(params, [], t, x, y, xe, ye) + if not absolute_sigma: if degree_of_freedom > 0: reduced_chi2x = chi2x / degree_of_freedom @@ -300,41 +344,89 @@ class Linear(MotionModel): """ A 2D linear motion model for a star on the sky. """ - fitter_param_names = ['x0', 'vx', 'y0', 'vy'] + fit_param_names = ['x0', 'vx', 'y0', 'vy'] fixed_param_names = ['t0'] # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) + n_params = int(np.ceil(len(fit_param_names) / 2)) name = "Linear" def __init__(self, **kwargs): - # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() return - def get_pos_at_time(self, fit_params, fixed_params, t): - fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) - fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t - fixed_params_dict['t0'] - return fit_params_dict['x0'] + fit_params_dict['vx']*dt, fit_params_dict['y0'] + fit_params_dict['vy']*dt - - def get_batch_pos_at_time(self, t, x0=[],vx=[], y0=[],vy=[], t0=[], - x0_err=[],vx_err=[], y0_err=[],vy_err=[], **kwargs): - if hasattr(t, "__len__"): - dt = t - t0[:,np.newaxis] - x = x0[:,np.newaxis] + dt*vx[:,np.newaxis] - y = y0[:,np.newaxis] + dt*vy[:,np.newaxis] - x_err = np.hypot(x0_err[:,np.newaxis], vx_err[:,np.newaxis]*dt) - y_err = np.hypot(y0_err[:,np.newaxis], vy_err[:,np.newaxis]*dt) - else: - dt = t - t0 - x = x0 + dt*vx - y = y0 + dt*vy - x_err = np.hypot(x0_err, vx_err*dt) - y_err = np.hypot(y0_err, vy_err*dt) + def model_fit(self, dt, x0, v): + """Linear motion model fit function + + Parameters + ---------- + dt : array-like + Time offset, shape (N_times,) + x0 : float or array-like + Initial position, shape (N_stars,) or scalar + v : float or array-like + Velocity, shape (N_stars,) or scalar + + Returns + ------- + x : array-like + Predicted position(s) + """ + return x0 + v * dt + + def model(self, t, fit_params, fixed_params, fit_param_errs=None): + """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Linear model. + + Parameters + ---------- + t : float or array-like + Time(s) at which to evaluate the model + fit_params : array-like + Fit parameters x0, vx, y0, vy in shape (N_params,) or (N_stars, N_params) + fixed_params : array-like + Fixed parameters t0 in shape (1,) or (N_stars, 1) + fit_param_errs : array-like, optional + Uncertainties of fit parameters in shape (N_params,) or (N_stars, N_params), by default None + + Returns + ------- + x, y (, xe, ye) + Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 + """ + t = np.atleast_1d(t) + fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) + + N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 + N_times = len(t) + + x0, vx, y0, vy = fit_params.T # Each shape (N_stars,) + t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) + + dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) + + x = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis]) # Shape (N_stars, N_times) + y = self.model_fit(dt, y0[:, np.newaxis], vy[:, np.newaxis]) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x = x.flatten() + y = y.flatten() + + if fit_param_errs is None: + return x, y + + fit_param_errs = np.atleast_2d(fit_param_errs) # (N_stars, N_params) + x0_err, vx_err, y0_err, vy_err = fit_param_errs.T # Each shape (N_stars,) + x_err = np.hypot(x0_err[:, np.newaxis], vx_err[:, np.newaxis] * dt) # Shape (N_stars, N_times) + y_err = np.hypot(y0_err[:, np.newaxis], vy_err[:, np.newaxis] * dt) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x_err = x_err.flatten() + y_err = y_err.flatten() return x, y, x_err, y_err def run_fit( @@ -366,17 +458,15 @@ def run_fit( params_guess = [x.mean(), 0., y.mean(), 0.] if use_scipy: - def linear(t, c0, c1): - return c0 + c1*t - x_opt, x_cov = curve_fit(linear, dt, x, p0=np.array(params_guess[:2]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(linear, dt, y, p0=np.array(params_guess[2:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) + x_opt, x_cov = curve_fit(self.model_fit, dt, x, p0=np.array(params_guess[:2]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(self.model_fit, dt, y, p0=np.array(params_guess[2:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) x0, vx = x_opt y0, vy = y_opt x0e, vxe = np.sqrt(x_cov.diagonal()) y0e, vye = np.sqrt(y_cov.diagonal()) params = np.array([x0, vx, y0, vy]) param_errors = np.array([x0e, vxe, y0e, vye]) - chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) + chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) else: # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme @@ -435,45 +525,94 @@ class Acceleration(MotionModel): """ A 2D accelerating motion model for a star on the sky. """ - fitter_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] + fit_param_names = ['x0', 'vx0', 'ax', 'y0', 'vy0', 'ay'] fixed_param_names = ['t0'] name = "Acceleration" # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) - - def __init__(self, x0=0, vx0=0, ax=0, y0=0, vy0=0, ay=0, t0=None, - x0_err=0, vx0_err=0, ax_err=0, y0_err=0, vy0_err=0, ay_err=0, **kwargs): + n_params = int(np.ceil(len(fit_param_names) / 2)) + + def __init__(self): # Must call after setting parameters. # This checks for proper parameter formatting. super().__init__() return + + def model_fit(self, t, x0, v0, a): + """Model positions at time t of Acceleration model. + + Parameters + ---------- + t : float or array-like + Time(s) at which to evaluate the model + x0 : float or array-like + Initial position(s) + v0 : float or array-like + Initial velocity(ies) + a : float or array-like + Acceleration(s) + + Returns + ------- + float or array-like + Model positions at time t of Acceleration model + """ + return x0 + v0*t + 0.5*a*t**2 + + def model(self, t, fit_params, fixed_params, fit_param_errs=None): + """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Acceleration model. + + Parameters + ---------- + t : float or array-like + Time(s) at which to evaluate the model + fit_params : array-like + Fit parameters with shape (N_stars, N_params) or (N_params,) + fixed_params : array-like + Fixed parameters with shape (N_stars, N_fixed_params) or (N_fixed_params,) + fit_param_errs : array-like, optional + Fit parameter uncertainties with shape (N_stars, N_params) or (N_params,), by default None + + Returns + ------- + x, y (, xe, ye) + Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 + """ + t = np.atleast_1d(t) + fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) + + N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 + N_times = len(t) - def get_pos_at_time(self, fit_params, fixed_params, t): - fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) - fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t - fixed_params_dict['t0'] - x = fit_params_dict['x0'] + fit_params_dict['vx0']*dt + 0.5*fit_params_dict['ax']*dt**2 - y = fit_params_dict['y0'] + fit_params_dict['vy0']*dt + 0.5*fit_params_dict['ay']*dt**2 - return x, y + x0, vx0, ax, y0, vy0, ay = fit_params.T # Each shape (N_stars,) + t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) - def get_batch_pos_at_time(self,t, - x0=[],vx0=[],ax=[], y0=[],vy0=[],ay=[], t0=[], - x0_err=[],vx0_err=[],ax_err=[], y0_err=[],vy0_err=[],ay_err=[], **kwargs): - if hasattr(t, "__len__"): - dt = t - t0[:,np.newaxis] - x = x0[:, np.newaxis] + dt * vx0[:, np.newaxis] + 0.5 * ax[:, np.newaxis] * dt**2 - y = y0[:, np.newaxis] + dt * vy0[:, np.newaxis] + 0.5 * ay[:, np.newaxis] * dt**2 - x_err = np.sqrt(x0_err[:, np.newaxis]**2 + (vx0_err[:, np.newaxis]*dt)**2 + (0.5*ax_err[:, np.newaxis]*dt**2)**2) - y_err = np.sqrt(y0_err[:, np.newaxis]**2 + (vy0_err[:, np.newaxis]*dt)**2 + (0.5*ay_err[:, np.newaxis]*dt**2)**2) - else: - dt = t - t0 - x = x0 + dt * vx0 + 0.5 * ax * dt**2 - y = y0 + dt * vy0 + 0.5 * ay * dt**2 - x_err = np.sqrt(x0_err**2 + (vx0_err * dt)**2 + (0.5 * ax_err * dt**2)**2) - y_err = np.sqrt(y0_err**2 + (vy0_err * dt)**2 + (0.5 * ay_err * dt**2)**2) + dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) + + x = self.model_fit(dt, x0[:, np.newaxis], vx0[:, np.newaxis], ax[:, np.newaxis]) # Shape (N_stars, N_times) + y = self.model_fit(dt, y0[:, np.newaxis], vy0[:, np.newaxis], ay[:, np.newaxis]) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x = x.flatten() + y = y.flatten() + + if fit_param_errs is None: + return x, y + + fit_param_errs = np.atleast_2d(fit_param_errs) # (N_stars, N_params) + x0_err, vx0_err, ax_err, y0_err, vy0_err, ay_err = fit_param_errs.T + x_err = np.sqrt(x0_err[:, np.newaxis]**2 + (vx0_err[:, np.newaxis] * dt)**2 + (0.5 * ax_err[:, np.newaxis] * dt**2)**2) # Shape (N_stars, N_times) + y_err = np.sqrt(y0_err[:, np.newaxis]**2 + (vy0_err[:, np.newaxis] * dt)**2 + (0.5 * ay_err[:, np.newaxis] * dt**2)**2) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x_err = x_err.flatten() + y_err = y_err.flatten() + return x, y, x_err, y_err + def run_fit( self, t, x, y, xe, ye, t0, weighting='var', @@ -509,11 +648,8 @@ def run_fit( t_span = t[idx_last] - t[idx_first] params_guess = [x.mean(), (x[idx_last] - x[idx_first]) / t_span, 0., y.mean(), (y[idx_last] - y[idx_first]) / t_span, 0.] - def accel(t, c0, c1, c2): - return c0 + c1*t + 0.5*c2*t**2 - - x_opt, x_cov = curve_fit(accel, dt, x, p0=np.array(params_guess[:3]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) - y_opt, y_cov = curve_fit(accel, dt, y, p0=np.array(params_guess[3:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) + x_opt, x_cov = curve_fit(self.model_fit, dt, x, p0=np.array(params_guess[:3]), sigma=1/x_wt**0.5, absolute_sigma=absolute_sigma) + y_opt, y_cov = curve_fit(self.model_fit, dt, y, p0=np.array(params_guess[3:]), sigma=1/y_wt**0.5, absolute_sigma=absolute_sigma) x0, vx0, ax = x_opt y0, vy0, ay = y_opt x0e, vx0e, axe = np.sqrt(x_cov.diagonal()) @@ -521,7 +657,7 @@ def accel(t, c0, c1, c2): params = np.array([x0, vx0, ax, y0, vy0, ay]) param_errors = np.array([x0e, vx0e, axe, y0e, vy0e, aye]) - chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) + chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) return params, param_errors, chi2_x, chi2_y @@ -534,81 +670,135 @@ class Parallax(MotionModel): Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ - fitter_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] + fit_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] fixed_param_names = ['t0'] fixed_meta_data = ['RA','Dec','PA','obs'] name = "Parallax" # Number of fit parameters/required observations in each direction - n_params = int(np.ceil(len(fitter_param_names) / 2)) - - def __init__(self, RA, Dec, PA=0.0, obs='earth', **kwargs): - self.RA = RA - self.Dec = Dec - self.PA = PA + n_params = int(np.ceil(len(fit_param_names) / 2)) + + def __init__(self, ra, dec, pa=0., obs='earth'): + super().__init__() + self.ra = ra + self.dec = dec + self.pa = pa self.obs = obs self.plx_vector_cached = None return - - def get_parallax_vector(self, t_mjd): - recalc_plx = True + + def calc_parallax_vector(self, t_mjd): + """Calculate parallax vector of shape (2, N_times) + + Parameters + ---------- + t_mjd : array-like + Time array in mjd + + Returns + ------- + pvec + Parallax vector of shape (2, N_times) + """ if self.plx_vector_cached is not None: - if hasattr(t_mjd, "__len__"): - if list(t_mjd) == list(self.plx_vector_cached[0]): - pvec = self.plx_vector_cached[1:] - recalc_plx = False - elif all([t_mjd_i in self.plx_vector_cached[0] for t_mjd_i in t_mjd]): - pvec_idxs = [np.argwhere(self.plx_vector_cached[0]==t_mjd_i)[0][0] for t_mjd_i in t_mjd] - pvec = [self.plx_vector_cached[1][pvec_idxs], self.plx_vector_cached[2][pvec_idxs]] - recalc_plx = False - elif t_mjd in self.plx_vector_cached[0]: - idx = np.where(t_mjd==self.plx_vector_cached[0])[0][0] - pvec = np.array([self.plx_vector_cached[1][idx], self.plx_vector_cached[2][idx]]) - recalc_plx = False - if recalc_plx: - pvec = parallax.parallax_in_direction(self.RA, self.Dec, t_mjd, obsLocation=self.obs, PA=self.PA).T - if hasattr(t_mjd, "__len__"): - self.plx_vector_cached = [t_mjd, pvec[0], pvec[1]] + t_mjd = np.atleast_1d(t_mjd) + t_mjd_cached = self.plx_vector_cached[0] + if np.allclose(t_mjd, t_mjd_cached): + # If cached values match input times, return cached values + return self.plx_vector_cached[1] + + elif all(np.isin(t_mjd, t_mjd_cached)): + # If all input times are in cached values, return those + # Calculate pvec_idxs such that t_mjd_cached[ pvec_idxs ] == t_mjd + pvec_idxs = np.array([np.where(t_mjd_cached==t_mjd_i)[0][0] for t_mjd_i in t_mjd]) + pvec = self.plx_vector_cached[1][:, pvec_idxs] + return pvec + + pvec = parallax.parallax_in_direction(self.ra, self.dec, t_mjd, obsLocation=self.obs, PA=self.pa).T + self.plx_vector_cached = [t_mjd, pvec] return pvec + + def model_fit(self, dt, x0, vx, y0, vy, pi): + """Model positions at time t of Parallax model. + + Parameters + ---------- + dt : float or array-like + Time(s) at which to evaluate the model + x0 : float or array-like + Initial position(s) + vx : float or array-like + Velocity(ies) + y0 : float or array-like + Initial position(s) + vy : float or array-like + Velocity(ies) + pi : float or array-like + Parallax factor(s) + + Returns + ------- + 2d array + Model positions at time t of Parallax model, shape (2, N_times) + """ + x_res = x0 + vx*dt + pi * self.pvec[0] + y_res = y0 + vy*dt + pi * self.pvec[1] + return np.vstack([x_res, y_res]) + + + def model(self, t, fit_params, fixed_params, fit_param_errs=None): + """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Parallax model. + + Parameters + ---------- + t : float or array-like + Times at which to evaluate the model + fit_params : array-like + Fit parameters for the model + fixed_params : array-like + Fixed parameters for the model + fit_param_errs : array-like, optional + Uncertainties in fit parameters, by default None + + Returns + ------- + x, y (, xe, ye) + Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 + """ + t = np.atleast_1d(t) + fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) - def get_pos_at_time(self, fit_params, fixed_params, t): - fit_params_dict = dict(zip(self.fitter_param_names, fit_params)) - fixed_params_dict = dict(zip(self.fixed_param_names, fixed_params)) - dt = t - fixed_params_dict['t0'] + N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 + N_times = len(t) + + x0, vx, y0, vy, pi = fit_params.T # Each shape (N_stars,) + t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) + + dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) + t_mjd = Time(t, format='decimalyear', scale='utc').mjd # Shape (N_times,) + self.pvec = self.calc_parallax_vector(t_mjd) # Shape (2, N_times) + x, y = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) + + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x = x.flatten() + y = y.flatten() + + if fit_param_errs is None: + return x, y + + fit_param_errs = np.atleast_2d(fit_param_errs) # (N_stars, N_params) + x0_err, vx_err, y0_err, vy_err, pi_err = fit_param_errs.T + x_err = np.sqrt(x0_err[:, np.newaxis]**2 + (vx_err[:, np.newaxis] * dt)**2 + (pi_err[:, np.newaxis] * self.pvec[0][np.newaxis, :])**2) # Shape (N_stars, N_times) + y_err = np.sqrt(y0_err[:, np.newaxis]**2 + (vy_err[:, np.newaxis] * dt)**2 + (pi_err[:, np.newaxis] * self.pvec[1][np.newaxis, :])**2) # Shape (N_stars, N_times) - t_mjd = Time(t, format='decimalyear', scale='utc').mjd - pvec = self.get_parallax_vector(t_mjd) - pvec_x = np.reshape(pvec[0], t.shape) - pvec_y = np.reshape(pvec[1], t.shape) - x = fit_params_dict['x0'] + fit_params_dict['vx']*dt + fit_params_dict['pi']*pvec_x - y = fit_params_dict['y0'] + fit_params_dict['vy']*dt + fit_params_dict['pi']*pvec_y - return x, y - - def get_batch_pos_at_time(self, t, - x0=[],vx=[], y0=[],vy=[], pi=[], t0=[], - x0_err=[],vx_err=[], y0_err=[],vy_err=[], pi_err=[], **kwargs): - t_mjd = Time(t, format='decimalyear', scale='utc').mjd - pvec = self.get_parallax_vector(t_mjd) - if hasattr(t, "__len__"): - dt = t-t0[:,np.newaxis] - x = x0[:,np.newaxis] + dt*vx[:,np.newaxis] + pi[:,np.newaxis]*pvec[0].T - y = y0[:,np.newaxis] + dt*vy[:,np.newaxis] + pi[:,np.newaxis]*pvec[1].T - try: - x_err = np.sqrt(x0_err[:,np.newaxis]**2 + (vx_err[:,np.newaxis]*dt)**2 + (pi_err[:,np.newaxis]*pvec[0].T)**2) - y_err = np.sqrt(y0_err[:,np.newaxis]**2 + (vy_err[:,np.newaxis]*dt)**2 + (pi_err[:,np.newaxis]*pvec[1].T)**2) - except: - x_err,y_err = [],[] - else: - dt = t-t0 - x = x0 + dt*vx + pi*pvec[0] - y = y0 + dt*vy + pi*pvec[1] - try: - x_err = np.sqrt(x0_err**2 + (vx_err*dt)**2 + (pi_err*pvec[0])**2) - y_err = np.sqrt(y0_err**2 + (vy_err*dt)**2 + (pi_err*pvec[1])**2) - except: - x_err,y_err = [],[] + if N_stars == 1 or N_times == 1: + # If only one star, return flattened arrays + x_err = x_err.flatten() + y_err = y_err.flatten() return x, y, x_err, y_err + def run_fit( self, t, x, y, xe, ye, t0, weighting='var', @@ -622,6 +812,7 @@ def run_fit( if verbose: warnings.warn("Parallax model has no non-scipy fitter option. Running with scipy.", UserWarning) + t = np.atleast_1d(t) n_obs = len(t) degree_of_freedom = n_obs - self.n_params # Not enough data points to fit model @@ -637,12 +828,9 @@ def run_fit( # degree_of_freedom >= 0 t_mjd = Time(t, format='decimalyear', scale='utc').mjd - pvec = self.get_parallax_vector(t_mjd) + self.pvec = self.get_parallax_vector(t_mjd) x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) - def fit_func(use_t, x0,vx, y0,vy, pi): - x_res = x0 + vx*(use_t-t0) + pi*pvec[0] - y_res = y0 + vy*(use_t-t0) + pi*pvec[1] - return np.hstack([x_res, y_res]) + # Initial guesses, x0,y0 as x,y averages; # vx,vy as average velocity if first and last points are perfectly measured; # pi for 10 pc distance @@ -655,7 +843,7 @@ def fit_func(use_t, x0,vx, y0,vy, pi): 0.1 ] res = curve_fit( - fit_func, t, np.hstack([x,y]), + self.model_fit, t - t0, np.vstack([x, y]), p0=params_guess, sigma = 1.0/np.hstack([x_wt,y_wt]), absolute_sigma=absolute_sigma ) @@ -664,7 +852,7 @@ def fit_func(use_t, x0,vx, y0,vy, pi): params = np.array([x0, vx, y0, vy, pi]) param_errors = np.array([x0_err, vx_err, y0_err, vy_err, pi_err]) - chi2_x, chi2_y = self.get_chi2(params, [t0], t, x, y, xe, ye) + chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) return params, param_errors, chi2_x, chi2_y @@ -733,7 +921,7 @@ def list_add(name): if name not in list_of_parameters: list_of_parameters.append(name) - for param in motion_model.fitter_param_names: + for param in motion_model.fit_param_names: # Fitter params list_add(param) # Error params @@ -770,7 +958,7 @@ def list_add(name): list_of_parameters.append(name) for mm in motion_model_list: - for param in mm.fitter_param_names: + for param in mm.fit_param_names: # Fitter params list_add(param) # Error params diff --git a/flystar/parallax.py b/flystar/parallax.py index b4b3a1b..3f7602b 100755 --- a/flystar/parallax.py +++ b/flystar/parallax.py @@ -24,20 +24,32 @@ cache_memory.reduce_size() @cache_memory.cache() -def parallax_in_direction(RA, Dec, mjd, obsLocation='earth', PA=0): +def parallax_in_direction(ra, dec, mjd, obsLocation='earth', PA=0.): """ - | R.A. in degrees. (J2000) - | Dec. in degrees. (J2000) - | MJD - | PA in degrees. (counterclockwise offset of the image y-axis from North) - - Equations following MulensModel. + Calculate the parallax vector in a given direction following MulensModel. + + Parameters + ---------- + RA : float + Right Ascension in degrees. (J2000) + Dec : float + Declination in degrees. (J2000) + mjd : float or array-like + Modified Julian Date. + obsLocation : str, optional + Observer location, by default 'earth'. + PA : float, optional + Position angle in degrees (counterclockwise offset of the image y-axis from North), by default 0. + + Returns + ------- + pvec : ndarray + Parallax vector components, shape of (N, 2), where N is the number of mjd entries. """ - #print('parallax_in_direction: len(t) = ', len(mjd)) - # Munge inputs into astropy format. - times = Time(mjd + 2400000.5, format='jd', scale='tdb') - coord = SkyCoord(RA, Dec, unit=(units.deg, units.deg)) + # times = Time(mjd + 2400000.5, format='jd', scale='tdb') + times = Time(mjd, format='mjd', scale='tdb') # convert to TDB + coord = SkyCoord(ra, dec, unit=(units.deg, units.deg)) direction = coord.cartesian.xyz.value north = np.array([0., 0., 1.]) @@ -58,13 +70,12 @@ def parallax_in_direction(RA, Dec, mjd, obsLocation='earth', PA=0): PA_rad = np.pi/180.0 * PA x = -e.value*np.cos(PA_rad) + n.value*np.sin(PA_rad) y = e.value*np.sin(PA_rad) + n.value*np.cos(PA_rad) - pvec = np.array([x, y]).T - + return pvec -def dparallax_dt_in_direction(RA, Dec, mjd, obsLocation='earth'): +def dparallax_dt_in_direction(ra, dec, mjd, obsLocation='earth'): """ R.A. in degrees. (J2000) Dec. in degrees. (J2000) @@ -76,8 +87,8 @@ def dparallax_dt_in_direction(RA, Dec, mjd, obsLocation='earth'): """ # print('parallax_in_direction: len(t) = ', len(mjd)) # Munge inputs into astropy format. - times = Time(mjd + 2400000.5, format='jd', scale='tdb') - coord = SkyCoord(RA, Dec, unit=(units.deg, units.deg)) + times = Time(mjd, format='mjd', scale='tdb') + coord = SkyCoord(ra, dec, unit=(units.deg, units.deg)) direction = coord.cartesian.xyz.value north = np.array([0., 0., 1.]) diff --git a/flystar/startables.py b/flystar/startables.py index 08461a1..661382f 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -730,19 +730,19 @@ def fit_motion_model( unique_motion_models, unique_inv_indices = np.unique(self['motion_model_used'], return_inverse=True) indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} - start_time = time.time() for unique_motion_model, unique_index in indices_by_motion_model.items(): # Create motion model instance motion_model_instance = input_mm_map[unique_motion_model] # Initialize arrays to store results n_stars_this_model = len(unique_index) - n_params = len(motion_model_instance.fitter_param_names) + n_params = len(motion_model_instance.fit_param_names) params_array = np.full((n_stars_this_model, n_params), fill_value, dtype=float) param_errs_array = np.full((n_stars_this_model, n_params), np.inf, dtype=float) chi2_x_array = np.full(n_stars_this_model, np.nan, dtype=float) chi2_y_array = np.full(n_stars_this_model, np.nan, dtype=float) + # Expensive for loop! Prepare everything beforehand to speed up. for idx, i_star in enumerate(tqdm(unique_index, disable=not show_progress, desc=f"Fitting motion model {unique_motion_model}")): # Fit the star params, param_errs, chi2_x, chi2_y = motion_model_instance.fit( @@ -759,14 +759,13 @@ def fit_motion_model( fill_value=fill_value, verbose=verbose ) - # print(f'{params_array.shape=}, {idx=}, {params=}') params_array[idx] = params param_errs_array[idx] = param_errs chi2_x_array[idx] = chi2_x chi2_y_array[idx] = chi2_y # Store results back to the table - param_names = motion_model_instance.fitter_param_names + param_names = motion_model_instance.fit_param_names for j, param_name in enumerate(param_names): self[param_name][unique_index] = params_array[:, j] self[param_name + '_err'][unique_index] = param_errs_array[:, j] @@ -1077,7 +1076,7 @@ def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scip # # # Load up any prior information on parameters for this model. # param_dict = {} -# for par in modClass.fitter_param_names+modClass.fixed_param_names: +# for par in modClass.fit_param_names+modClass.fixed_param_names: # if ~np.isnan(self[par][ss]): # param_dict[par] = self[par][ss] @@ -1094,8 +1093,8 @@ def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scip self['n_params'][ss] = mod.n_params # Save parameters and errors to table. - for pp in range(len(mod.fitter_param_names)): - par = mod.fitter_param_names[pp] + for pp in range(len(mod.fit_param_names)): + par = mod.fit_param_names[pp] par_err = par + '_err' self[par][ss] = params[pp] self[par_err][ss] = param_errs[pp] @@ -1131,7 +1130,7 @@ def get_star_positions_at_time(self, t, motion_model_dict, allow_alt_models=True mod = motion_model_dict[mm] # Set up parameters param_dict = {} - for par in mod.fitter_param_names + mod.fixed_param_names + [pm+'_err' for pm in mod.fitter_param_names]: + for par in mod.fit_param_names + mod.fixed_param_names + [pm+'_err' for pm in mod.fit_param_names]: param_dict[par] = self[par][idx] x[idx],y[idx],xe[idx],ye[idx] = mod.get_batch_pos_at_time(t,**param_dict) except: @@ -1211,7 +1210,7 @@ def fit_velocities_all_detected(self, motion_model_to_fit, weighting='var', use_ detected_in_all_epochs = np.logical_and(valid_xe, valid_ye) N = len(self['x'][select_stars, :]) - fit_params = motion_model_to_fit.fitter_param_names + fit_params = motion_model_to_fit.fit_param_names param_data = {p: np.zeros(N) for p in fit_params} param_data.update({p+'_err': np.zeros(N) for p in fit_params}) param_data.update({p: np.zeros(N) for p in motion_model_to_fit.fixed_param_names}) diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index 9b65eb6..195a67b 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -990,7 +990,7 @@ def make_fake_starlists_poly1_par(seed=-1): for ss in range(len(times)): dt = times[ss] - lis['t0'] - par_mod = motion_model.Parallax(PA=0,RA=18.0, Dec=-30.0) + par_mod = motion_model.Parallax(pa=0,ra=18.0, dec=-30.0) par_mod_dat = par_mod.get_batch_pos_at_time(dt+lis['t0'], x0=lis['x0'],vx=lis['vx']/1e3, pi=lis['pi'], y0=lis['y0'], vy=lis['vy']/1e3, t0=lis['t0']) x,y = par_mod_dat[0], par_mod_dat[1] diff --git a/flystar/tests/test_motion_model.py b/flystar/tests/test_motion_model.py index 2fa1b57..ccbba68 100755 --- a/flystar/tests/test_motion_model.py +++ b/flystar/tests/test_motion_model.py @@ -1,27 +1,35 @@ from flystar import motion_model import numpy as np -import pytest import matplotlib.pyplot as plt from scipy.optimize import curve_fit def within_error(true_val, fit_val, fit_err, n_sigma=3): #print('True', true_val, 'Fit', fit_val, 'Fit err', fit_err) - return (true_val < (fit_val+fit_err*n_sigma)) & (true_val> (fit_val-fit_err*n_sigma)) + # return (true_val < (fit_val + fit_err*n_sigma)) & (true_val > (fit_val - fit_err*n_sigma)) + return np.abs(true_val - fit_val) <= n_sigma*fit_err def test_Fixed(): # Test handling of a single star true_params = {'x0': 1.0, 'y0':0.5, 'x0_err':0.1, 'y0_err':0.1} mod = motion_model.Fixed() - param_list = mod.fitter_param_names + param_list = mod.fit_param_names fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t and array t - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], 0.0) + # x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], + # [true_params[p] for p in fixed_param_list], 0.0) + x_t, y_t = mod.model( + 0.0, + fit_params=np.array([true_params['x0'], true_params['y0']]).T + ) assert x_t==true_params['x0'] assert y_t==true_params['y0'] - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], - [0.0,2025.0,10000]) + # x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], + # [true_params[p] for p in fixed_param_list], + # [0.0,2025.0,10000]) + x_t, y_t = mod.model( + [0.0,2025.0,10000], + fit_params=np.array([true_params['x0'], true_params['y0']]).T + ) assert (x_t==true_params['x0']).all() assert (y_t==true_params['y0']).all() @@ -32,16 +40,26 @@ def test_Fixed(): y0_err_batch = np.repeat(0.1, 50) # Single epoch t_batch=2020.0 - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) + # x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, + # x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t_batch, + fit_params=np.array([x0_batch, y0_batch]).T, + fit_param_errs=np.array([x0_err_batch, y0_err_batch]).T + ) assert (x_t_batch==x0_batch).all() assert (y_t_batch==y0_batch).all() assert (x_err_t_batch==x0_err_batch).all() assert (y_err_t_batch==y0_err_batch).all() # Multiple times t_batch = np.arange(2015.0,2025.0, 0.5) - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) + # x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, + # x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t_batch, + fit_params=np.array([x0_batch, y0_batch]).T, + fit_param_errs=np.array([x0_err_batch, y0_err_batch]).T + ) assert (x_t_batch==np.array([np.repeat(x0_batch_i, len(t_batch)) for x0_batch_i in x0_batch])).all() assert (y_t_batch==np.array([np.repeat(y0_batch_i, len(t_batch)) for y0_batch_i in y0_batch])).all() assert (x_err_t_batch==np.array([np.repeat(x0_err_batch_i, len(t_batch)) for x0_err_batch_i in x0_err_batch])).all() @@ -50,15 +68,22 @@ def test_Fixed(): # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], t) + # x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], + # [true_params[p] for p in fixed_param_list], t) + x_true, y_true = mod.model( + t, + fit_params=np.array([true_params['x0'], true_params['y0']]) + ) x_sim = np.random.normal(x_true, true_params['x0_err']) y_sim = np.random.normal(y_true, true_params['y0_err']) # Run fit - params, param_errs = mod.fit_motion_model(t, x_sim,y_sim, - np.ones(len(t))*true_params['x0_err'], - np.ones(len(t))*true_params['y0_err'], - np.nan) + params, param_errs, _ , _ = mod.fit( + t, + x_sim,y_sim, + xe=np.ones(len(t))*true_params['x0_err'], + ye=np.ones(len(t))*true_params['y0_err'], + t0=np.nan + ) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) @@ -69,21 +94,25 @@ def test_Linear(): 'vx':0.2, 'vy':0.5, 'vx_err':0.05, 'vy_err':0.05, 't0':2025.0} mod = motion_model.Linear() - param_list = mod.fitter_param_names + param_list = mod.fit_param_names fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t=t0 and array t - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], - true_params['t0']) + x_t, y_t = mod.model( + t=true_params['t0'], + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) assert x_t==true_params['x0'] assert y_t==true_params['y0'] t_arr = np.array([2010.0,true_params['t0'],2030.0]) - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], - t_arr) + x_t, y_t = mod.model( + t=t_arr, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) assert (x_t==(true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx'])).all() assert (y_t==(true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy'])).all() - + # Check behavior of get_batch_pos_at_time x0_batch = np.random.uniform(-2.0,2.0, 50) y0_batch = np.random.uniform(-2.0,2.0, 50) @@ -96,20 +125,24 @@ def test_Linear(): t0_batch = np.repeat(2025.0,50) # Single epoch t_batch=2020.0 - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch, - vx=vx_batch, vy=vy_batch, vx_err=vx_err_batch, vy_err=vy_err_batch, - t0=t0_batch) + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t=t_batch, + fit_params=np.array([x0_batch, vx_batch, y0_batch, vy_batch]).T, + fit_param_errs=np.array([x0_err_batch, vx_err_batch, y0_err_batch, vy_err_batch]).T, + fixed_params=t0_batch + ) assert (x_t_batch==(x0_batch+(t_batch-t0_batch)*vx_batch)).all() assert (y_t_batch==(y0_batch+(t_batch-t0_batch)*vy_batch)).all() assert (x_err_t_batch==np.hypot(x0_err_batch, (t_batch-t0_batch)*vx_err_batch)).all() assert (y_err_t_batch==np.hypot(y0_err_batch, (t_batch-t0_batch)*vy_err_batch)).all() # Multiple times t_batch = np.arange(2015.0,2025.0, 0.5) - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch, - vx=vx_batch, vy=vy_batch, vx_err=vx_err_batch, vy_err=vy_err_batch, - t0=t0_batch) + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t=t_batch, + fit_params=np.array([x0_batch, vx_batch, y0_batch, vy_batch]).T, + fit_param_errs=np.array([x0_err_batch, vx_err_batch, y0_err_batch, vy_err_batch]).T, + fixed_params=t0_batch + ) assert (x_t_batch==np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx_batch[i] for i in range(len(x0_batch))])).all() assert (y_t_batch==np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy_batch[i] for i in range(len(x0_batch))])).all() assert (x_err_t_batch==np.array([np.hypot(x0_err_batch[i], (t_batch-t0_batch[i])*vx_err_batch[i]) for i in range(len(x0_batch))])).all() @@ -118,13 +151,24 @@ def test_Linear(): # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list],t) + # x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], + # [true_params[p] for p in fixed_param_list],t) + x_true, y_true = mod.model( + t=t, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) x_sim = np.random.normal(x_true, 0.05) y_sim = np.random.normal(y_true, 0.05) # Run fit - params, param_errs = mod.fit_motion_model(t, x_sim,y_sim, - np.repeat(0.05, len(t)), np.repeat(0.05,len(t)), true_params['t0']) + params, param_errs, _, _ = mod.fit( + t=t, + x=x_sim, + y=y_sim, + xe=np.repeat(0.05, len(t)), + ye=np.repeat(0.05,len(t)), + t0=true_params['t0'] + ) print(param_errs) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) @@ -138,11 +182,11 @@ def test_Linear(): x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - params, param_errs = mod.fit_motion_model(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0'],bootstrap=10) + params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0'],bootstrap=10) print(param_errs) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) - + # # Test fitter for 2 pts # t = np.array([2015.0,2025.0]) # # Get values from model and add scatter @@ -169,20 +213,24 @@ def test_Acceleration(): 'ax':0.1, 'ay':-0.1, 'ax_err':0.02, 'ay_err':0.02, 't0':2025.0} mod = motion_model.Acceleration() - param_list = mod.fitter_param_names + param_list = mod.fit_param_names fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t=t0 and array t - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], - true_params['t0']) - assert x_t==true_params['x0'] - assert y_t==true_params['y0'] - t_arr = np.array([2010.0,true_params['t0'],2030.0]) - x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list], - t_arr) - assert (x_t==(true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ax'])).all() - assert (y_t==(true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ay'])).all() + x_t, y_t = mod.model( + t=true_params['t0'], + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) + np.testing.assert_allclose(x_t, true_params['x0']) + np.testing.assert_allclose(y_t, true_params['y0']) + t_arr = np.array([2010.0, true_params['t0'], 2030.0]) + x_t, y_t = mod.model( + t=t_arr, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) + np.testing.assert_allclose(x_t, true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ax']) + np.testing.assert_allclose(y_t, true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ay']) # Check behavior of get_batch_pos_at_time x0_batch = np.random.uniform(-2.0,2.0, 50) @@ -200,43 +248,56 @@ def test_Acceleration(): t0_batch = np.repeat(2025.0,50) # Single epoch t_batch=2020.0 - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch, - vx0=vx0_batch, vy0=vy0_batch, vx0_err=vx0_err_batch, vy0_err=vy0_err_batch, - ax=ax_batch, ay=ay_batch, ax_err=ax_err_batch, ay_err=ay_err_batch, - t0=t0_batch) - assert (x_t_batch==(x0_batch + (t_batch-t0_batch)*vx0_batch + 0.5*(t_batch-t0_batch)**2*ax_batch)).all() - assert (y_t_batch==(y0_batch + (t_batch-t0_batch)*vy0_batch + 0.5*(t_batch-t0_batch)**2*ay_batch)).all() - assert (x_err_t_batch==np.sqrt(x0_err_batch**2 + ((t_batch-t0_batch)*vx0_err_batch)**2 + - (0.5*(t_batch-t0_batch)**2*ax_err_batch)**2)).all() - assert (y_err_t_batch==np.sqrt(y0_err_batch**2 + ((t_batch-t0_batch)*vy0_err_batch)**2 + - (0.5*(t_batch-t0_batch)**2*ay_err_batch)**2)).all() + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t=t_batch, + fit_params=np.array([x0_batch, vx0_batch, ax_batch, y0_batch, vy0_batch, ay_batch]).T, + fit_param_errs=np.array([x0_err_batch, vx0_err_batch, ax_err_batch, y0_err_batch, vy0_err_batch, ay_err_batch]).T, + fixed_params=t0_batch + ) + np.testing.assert_allclose(x_t_batch, x0_batch + (t_batch-t0_batch)*vx0_batch + 0.5*(t_batch-t0_batch)**2*ax_batch) + np.testing.assert_allclose(y_t_batch, y0_batch + (t_batch-t0_batch)*vy0_batch + 0.5*(t_batch-t0_batch)**2*ay_batch) + np.testing.assert_allclose(x_err_t_batch, np.sqrt(x0_err_batch**2 + ((t_batch-t0_batch)*vx0_err_batch)**2 + + (0.5*(t_batch-t0_batch)**2*ax_err_batch)**2)) + np.testing.assert_allclose(y_err_t_batch, np.sqrt(y0_err_batch**2 + ((t_batch-t0_batch)*vy0_err_batch)**2 + + (0.5*(t_batch-t0_batch)**2*ay_err_batch)**2)) + # Multiple times t_batch = np.arange(2015.0,2025.0, 0.5) - x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch, - vx0=vx0_batch, vy0=vy0_batch, vx0_err=vx0_err_batch, vy0_err=vy0_err_batch, - ax=ax_batch, ay=ay_batch, ax_err=ax_err_batch, ay_err=ay_err_batch, - t0=t0_batch) - assert (x_t_batch==np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ax_batch[i] for i in range(len(x0_batch))])).all() - assert (y_t_batch==np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ay_batch[i] for i in range(len(x0_batch))])).all() - assert (x_err_t_batch==np.array([np.sqrt(x0_err_batch[i]**2 + ((t_batch-t0_batch[i])*vx0_err_batch[i])**2 + (0.5*(t_batch-t0_batch[i])**2*ax_err_batch[i])**2) for i in range(len(x0_batch))])).all() - assert (y_err_t_batch==np.array([np.sqrt(y0_err_batch[i]**2 + ((t_batch-t0_batch[i])*vy0_err_batch[i])**2 + (0.5*(t_batch-t0_batch[i])**2*ay_err_batch[i])**2) for i in range(len(x0_batch))])).all() - + x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( + t=t_batch, + fit_params=np.array([x0_batch, vx0_batch, ax_batch, y0_batch, vy0_batch, ay_batch]).T, + fit_param_errs=np.array([x0_err_batch, vx0_err_batch, ax_err_batch, y0_err_batch, vy0_err_batch, ay_err_batch]).T, + fixed_params=t0_batch + ) + np.testing.assert_allclose(x_t_batch, np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ax_batch[i] for i in range(len(x0_batch))])) + np.testing.assert_allclose(y_t_batch, np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ay_batch[i] for i in range(len(x0_batch))])) + np.testing.assert_allclose(x_err_t_batch, np.array([np.sqrt(x0_err_batch[i]**2 + ((t_batch-t0_batch[i])*vx0_err_batch[i])**2 + (0.5*(t_batch-t0_batch[i])**2*ax_err_batch[i])**2) for i in range(len(x0_batch))])) + np.testing.assert_allclose(y_err_t_batch, np.array([np.sqrt(y0_err_batch[i]**2 + ((t_batch-t0_batch[i])*vy0_err_batch[i])**2 + (0.5*(t_batch-t0_batch[i])**2*ay_err_batch[i])**2) for i in range(len(x0_batch))])) + # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list],t) - x_true_err = np.sqrt(true_params['x0_err']**2 + ((t-true_params['t0'])*true_params['vx0_err'])**2 + - (0.5*(t-true_params['t0'])**2*true_params['ax_err'])**2) - y_true_err = np.sqrt(true_params['y0_err']**2 + ((t-true_params['t0'])*true_params['vy0_err'])**2 + - (0.5*(t-true_params['t0'])**2*true_params['ay_err'])**2) + x_true, y_true = mod.model( + t=t, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + ) + x_true_err = np.sqrt(true_params['x0_err']**2 + ((t - true_params['t0']) * true_params['vx0_err'])**2 + + (0.5*(t - true_params['t0'])**2 * true_params['ax_err'])**2) + y_true_err = np.sqrt(true_params['y0_err']**2 + ((t - true_params['t0']) * true_params['vy0_err'])**2 + + (0.5*(t - true_params['t0'])**2 * true_params['ay_err'])**2) x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - mod_fit = motion_model.Acceleration(t0=true_params['t0']) - params, param_errs = mod_fit.fit_motion_model(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0']) + mod_fit = motion_model.Acceleration() + params, param_errs, _, _ = mod_fit.fit( + t=t, + x=x_sim, + y=y_sim, + xe=x_true_err, + ye=y_true_err, + t0=true_params['t0'] + ) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) @@ -248,7 +309,7 @@ def test_Parallax(): 'pi':0.5, 'RA':17.76, 'Dec':-28.933, 'PA':0, 't0':2020.0} mod = motion_model.Parallax(**{'RA':17.76, 'Dec':-28.933, 'PA':0}) - param_list = mod.fitter_param_names + param_list = mod.fit_param_names fixed_param_list = mod.fixed_param_names print(param_list) @@ -261,7 +322,7 @@ def test_Parallax(): x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - params, param_errs = mod.fit_motion_model(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0']) + params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0']) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) @@ -270,16 +331,25 @@ def test_Parallax_PA(): # Set PA=0 model x0, y0 = 2.0, -1.0 vx, vy = 0.2, 0.5 - RA, Dec = 17.76, -28.933 + ra, dec = 17.76, -28.933 pi = 0.5 - mod_pa0 = motion_model.Parallax(RA=RA,Dec=Dec, PA=0) + mod_pa0 = motion_model.Parallax(ra=ra, dec=dec, pa=0) # Set PA=90 model with equivalent parameters in that frame - mod_pa90 = motion_model.Parallax(RA=RA,Dec=Dec,t0=2020.0, PA=90) - t_set = np.arange(2018,2024,0.01) - dat_pa0 = mod_pa0.get_pos_at_time([x0,vx,y0,vy,pi],[2020.0],t_set) - dat_pa90 = mod_pa90.get_pos_at_time([y0,vy,-x0,-vx,pi],[2020.0],t_set) - assert (np.abs(dat_pa0[0]-(-dat_pa90[1]))<1e-10).all() - assert (np.abs(dat_pa0[1]-(dat_pa90[0]))<1e-10).all() + mod_pa90 = motion_model.Parallax(ra=ra, dec=dec, pa=90) + + t_set = np.arange(2018, 2024, 0.01) + dat_pa0 = mod_pa0.model( + t = t_set, + fit_params = np.array([x0, vx, y0, vy, pi]).T, + fixed_params = [2020.0] + ) + dat_pa90 = mod_pa90.model( + t = t_set, + fit_params = np.array([y0, vy, -x0, -vx, pi]).T, + fixed_params = [2020.0] + ) + np.testing.assert_allclose(dat_pa0[0], -dat_pa90[1], atol=1e-10) + np.testing.assert_allclose(dat_pa0[1], dat_pa90[0], atol=1e-10) def test_Linear_fit_vs_scipy(): @@ -431,38 +501,38 @@ def linear(t, c0, c1): y0_scipy[i], y0e_scipy[i] = popt_y[0], np.sqrt(pcov_y[0, 0]) # motion_model without scipy - params, param_errs = mm.fit_motion_model( + params, param_errs = mm.fit( t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], xe[i][~mask[i]], ye[i][~mask[i]], t0[i], weighting='var', use_scipy=False, absolute_sigma=absolute_sigma ) - vx_mm[i] = params[mm.fitter_param_names.index('vx')] - vy_mm[i] = params[mm.fitter_param_names.index('vy')] - vxe_mm[i] = param_errs[mm.fitter_param_names.index('vx')] - vye_mm[i] = param_errs[mm.fitter_param_names.index('vy')] - x0_mm[i] = params[mm.fitter_param_names.index('x0')] - y0_mm[i] = params[mm.fitter_param_names.index('y0')] - x0e_mm[i] = param_errs[mm.fitter_param_names.index('x0')] - y0e_mm[i] = param_errs[mm.fitter_param_names.index('y0')] + vx_mm[i] = params[mm.fit_param_names.index('vx')] + vy_mm[i] = params[mm.fit_param_names.index('vy')] + vxe_mm[i] = param_errs[mm.fit_param_names.index('vx')] + vye_mm[i] = param_errs[mm.fit_param_names.index('vy')] + x0_mm[i] = params[mm.fit_param_names.index('x0')] + y0_mm[i] = params[mm.fit_param_names.index('y0')] + x0e_mm[i] = param_errs[mm.fit_param_names.index('x0')] + y0e_mm[i] = param_errs[mm.fit_param_names.index('y0')] # motion_model with scipy - params, param_errs = mm.fit_motion_model( + params, param_errs = mm.fit( t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], xe[i][~mask[i]], ye[i][~mask[i]], t0[i], weighting='var', use_scipy=True, absolute_sigma=absolute_sigma ) - vx_mm_scipy[i] = params[mm.fitter_param_names.index('vx')] - vy_mm_scipy[i] = params[mm.fitter_param_names.index('vy')] - vxe_mm_scipy[i] = param_errs[mm.fitter_param_names.index('vx')] - vye_mm_scipy[i] = param_errs[mm.fitter_param_names.index('vy')] - x0_mm_scipy[i] = params[mm.fitter_param_names.index('x0')] - y0_mm_scipy[i] = params[mm.fitter_param_names.index('y0')] - x0e_mm_scipy[i] = param_errs[mm.fitter_param_names.index('x0')] - y0e_mm_scipy[i] = param_errs[mm.fitter_param_names.index('y0')] + vx_mm_scipy[i] = params[mm.fit_param_names.index('vx')] + vy_mm_scipy[i] = params[mm.fit_param_names.index('vy')] + vxe_mm_scipy[i] = param_errs[mm.fit_param_names.index('vx')] + vye_mm_scipy[i] = param_errs[mm.fit_param_names.index('vy')] + x0_mm_scipy[i] = params[mm.fit_param_names.index('x0')] + y0_mm_scipy[i] = params[mm.fit_param_names.index('y0')] + x0e_mm_scipy[i] = param_errs[mm.fit_param_names.index('x0')] + y0e_mm_scipy[i] = param_errs[mm.fit_param_names.index('y0')] rtol = 1e-5 # np.testing.assert_allclose(vx_velfit, vx_scipy, rtol=rtol) diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index cf3be71..1b8e5cb 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -305,7 +305,7 @@ def test_fit_velocities(): tab = table.vstack((tab1, tab2, tab3)) tab.meta = tab1.meta - tab.fit_velocities(verbose=True) + tab.fit_motion_model(verbose=True) # Test creation of new variables assert len(tab['vx']) == len(tab) @@ -313,7 +313,7 @@ def test_fit_velocities(): assert len(tab['vx_err']) == len(tab) assert len(tab['vy_err']) == len(tab) assert len(tab['n_fit']) == len(tab) - assert tab.meta['n_fit_bootstrap'] == 0 + assert tab.meta['n_bootstrap'] == 0 # Test no-fit for stars with N<2 epochs. n_epochs = (tab['x'] >= 0).sum(axis=1) @@ -365,7 +365,7 @@ def test_fit_velocities(): tab_b.meta = tab1.meta tab_b.fit_velocities(verbose=True, bootstrap=50) - assert tab_b.meta['n_fit_bootstrap'] == 50 + assert tab_b.meta['n_bootstrap'] == 50 assert tab_b['x0_err'][0] > tab['x0_err'][0] assert tab_b['vx_err'][0] > tab['vx_err'][0] assert tab_b['y0_err'][0] > tab['y0_err'][0] @@ -559,10 +559,10 @@ def make_star_table(): x=x_in, y=y_in, m=m_in, xe=xe_in, ye=ye_in, me=me_in, n=n_in, - ref_list=1, - list_times=starlist_times, - list_names=starlist_names + ref_list=1 ) + startable.meta['LIST_TIMES'] = starlist_times + startable.meta['LIST_NAMES'] = starlist_names return startable From e0e0c2c13573ba5d199aa3019a0df2d14fa67b4e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Tue, 25 Nov 2025 15:54:47 -0800 Subject: [PATCH 18/29] MotionModel acceleration with passed testings. Merged get_pos_at_time and get_batch_pos_at_time into model; Replaced MotionModel.fit_motion_model with MotionModel.fit; Rewrote and accelerated StarTable.fit_velocities with StarTable.fit_motion_model --- flystar/motion_model.py | 479 +++-- flystar/parallax.py | 41 +- flystar/startables.py | 119 +- flystar/tests/test_all_detected.fits | 2911 -------------------------- flystar/tests/test_motion_model.py | 411 +--- flystar/tests/test_startable.py | 182 +- 6 files changed, 595 insertions(+), 3548 deletions(-) delete mode 100644 flystar/tests/test_all_detected.fits diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 5a542e0..5ccb6ee 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -1,6 +1,5 @@ import numpy as np from abc import ABC -import pdb from flystar import parallax from astropy.time import Time from scipy.optimize import curve_fit, OptimizeWarning @@ -36,17 +35,19 @@ def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, + params_guess=None, fill_value=np.nan, verbose=True ): # Run a single fit (used both for overall fit + bootstrap iterations) return np.full(self.n_params, fill_value), np.full(self.n_params, np.inf), np.nan, np.nan - def get_weights(self, xe, ye, weighting='var'): + def calc_weights(self, xe, ye, weighting='var'): if weighting=='std': return 1./xe, 1./ye elif weighting=='var': @@ -56,12 +57,15 @@ def get_weights(self, xe, ye, weighting='var'): return 1./xe**2, 1./ye**2 def fit( - self, t, x, y, xe, ye, t0, - bootstrap=0, + self, t, x, y, xe, ye, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, fill_value=np.nan, + params_guess=None, + return_chi2=False, + bootstrap=0, verbose=True, seed=None ): @@ -79,10 +83,8 @@ def fit( Uncertainty of x ye : array-like Uncertainty of y - t0 : array-like - Reference time for fitting, i.e. dt = t - t0 will be used in fitting - bootstrap : int, optional - Bootstrapping uncertainties, by default 0 + fixed_params_dict : dict, optional + Dictionary of fixed parameters, see each motion model's fixed_param_names for details, by default None weighting : str, optional Use standard error weighting ('std': w=1/xe, 1/ye) or variance weighting ('var': w=1/xe**2, 1/ye**2), by default 'var' use_scipy : bool, optional @@ -91,6 +93,12 @@ def fit( Absolute sigma. See scipy.optimize.curve_fit for details, by default True fill_value : float, optional Fill value for parameters when not enough data points to fit model, by default np.nan + params_guess : array-like, optional + Initial guess for the fit parameters used in scipy curve_fit, by default None + return_chi2 : bool, optional + Return chi^2 values along with parameters and uncertainties in params, param_errs, chi2_x, chi2_y, by default False + bootstrap : int, optional + Bootstrapping uncertainties, by default 0 verbose : bool, optional Print warning messages, by default True seed : int, optional @@ -100,39 +108,66 @@ def fit( params, params_err, chi2_x, chi2_y Parameters, uncertainties, and chi squares. The corresponding parameter names are in self.fit_param_names. """ - params, param_errs, chi2_x, chi2_y = self.run_fit( - t, x, y, xe, ye, t0=t0, + fit_result = self.run_fit( + t, x, y, xe, ye, + fixed_params_dict=fixed_params_dict, weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma, fill_value=fill_value, + params_guess=params_guess, + return_chi2=return_chi2, verbose=verbose ) - if seed is not None: - rng = np.random.default_rng(seed) + + if return_chi2: + params, param_errs, chi2_x, chi2_y = fit_result else: - rng = np.random.default_rng() + params, param_errs = fit_result + # Bootstrap errors n_obs = len(t) + if bootstrap > 0 and n_obs > (self.n_params): + # Use m out of n bootstrap to ensure enough unique points + m = np.max([self.n_params, int(len(t) * 0.8)]) + rng = np.random.default_rng(seed) edx = np.arange(n_obs, dtype=int) + # Precompute All Bootstrap Draws at Once + bdx_all = rng.choice(edx, size=(bootstrap, m), replace=True) + + # Count unique indices per bootstrap sample + uniq_counts = np.apply_along_axis(lambda x: len(np.unique(x)), 1, bdx_all) + + # Identify invalid samples + bad = uniq_counts < self.n_params + n_bad = bad.sum() + + while n_bad > 0: + # Resample only bad rows + bdx_all[bad] = rng.choice(edx, size=(n_bad, m), replace=True) + uniq_counts = np.apply_along_axis(lambda x: len(np.unique(x)), 1, bdx_all) + bad = uniq_counts < self.n_params + n_bad = bad.sum() + bb_params = [] bb_params_errs = [] - for bb in range(bootstrap): - bdx = rng.choice(edx, n_obs, replace=False) - params_bdx, param_errs_bdx, chi2x_bdx, chi2y_bdx = self.run_fit( - t[bdx], x[bdx], y[bdx], xe[bdx], ye[bdx], t0=t0, + for bdx in bdx_all: + params_bdx, param_errs_bdx = self.run_fit( + t[bdx], x[bdx], y[bdx], xe[bdx], ye[bdx], + fixed_params_dict=fixed_params_dict, weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma, params_guess=params, fill_value=fill_value, + return_chi2=False, verbose=verbose ) bb_params.append(params_bdx) bb_params_errs.append(param_errs_bdx) - + # Save the errors from the bootstrap param_errs = np.std(bb_params, axis=0) @@ -140,14 +175,18 @@ def fit( inf_errs = [np.all(arr==np.inf) for arr in np.transpose(np.array(bb_params_errs))] param_errs[inf_errs] = 0.0 - return params, param_errs, chi2_x, chi2_y + if return_chi2: + return params, param_errs, chi2_x, chi2_y + else: + return params, param_errs + - def calc_chi2(self, fit_params, fixed_params, t, x, y, xe, ye, reduced=False): + def calc_chi2(self, t, x, y, xe, ye, fit_params, fixed_params_dict=None, reduced=False): """ Get the chi^2 value for the current MM and the input data. """ - x_pred, y_pred = self.model(t, fit_params, fixed_params) + x_pred, y_pred = self.model(t, fit_params, fixed_params_dict) chi2x = np.sum((x - x_pred)**2 / xe**2) chi2y = np.sum((y - y_pred)**2 / ye**2) if reduced: @@ -174,23 +213,86 @@ def __init__(self, **kwargs): def model_fit(self, dt): return np.full_like(dt, np.nan) - def model(self, t, fit_params, fixed_params, fixed_param_errs=None): + def model(self, t, fit_params, fixed_params_dict, fixed_param_errs=None): + """Predicted positions (and uncertainties, if fit_param_errs is provided) at time t of Empty model. + + Parameters + ---------- + t : float or array-like + Time array, shape (N_times,) + fit_params : array-like + Fit parameters, shape (N_params,) or (N_stars, N_params) + fixed_params_dict : dict + Dictionary of fixed parameters, not applicable for Empty model + fixed_param_errs : array-like, optional + Uncertainties for fixed parameters, not applicable for Empty model, by default None + + Returns + ------- + x, y (, xe, ye) + Predicted position (and uncertainties) of Empty model, shape (N_times,) + """ + t = np.atleast_1d(t) + if fixed_param_errs is None: + return np.full_like(t, np.nan), np.full_like(t, np.nan) return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, fill_value=np.nan, + params_guess=None, + return_chi2=False, verbose=True ): + """Fit stellar motion parameters + + Parameters + ---------- + t : float or array-like + Time array, shape (N_times,) + x : array-like + Observed x positions, shape (N_times,) + y : array-like + Observed y positions, shape (N_times,) + xe : array-like + Observed uncertainties in x positions, shape (N_times,) + ye : array-like + Observed uncertainties in y positions, shape (N_times,) + fixed_params_dict : dict, optional + Dictionary of fixed parameters, not applicable for Empty model, by default None + weighting : str, optional + Weighting scheme to use, 'var' or 'std', by default 'var' + use_scipy : bool, optional + Whether to use scipy.optimize for fitting, by default True + absolute_sigma : bool, optional + Whether to treat sigma as absolute, by default True + fill_value : float, optional + Value to fill parameters with when fitting is not possible, by default np.nan + params_guess : array-like, optional + Initial guess for parameters, by default None + return_chi2 : bool, optional + Whether to return chi-squared value, by default False + verbose : bool, optional + Whether to print verbose output, by default True + + Returns + ------- + params, param_errors (, chi2_x, chi2_y) + Fitted parameters, their uncertainties, and optionally chi-squared values + """ if verbose: warnings.warn(f"Empty data cannot be fit. Setting parameters to {fill_value} and uncertainties to np.inf.", OptimizeWarning, stacklevel=2) params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) - return params, param_errors, np.nan, np.nan + if return_chi2: + return params, param_errors, np.nan, np.nan + else: + return params, param_errors class Fixed(MotionModel): @@ -230,7 +332,7 @@ def model_fit(self, dt, x0): x0 = np.asarray(x0) return np.broadcast_to(x0[:, np.newaxis], (x0.shape[0], dt.shape[0])) if x0.ndim > 0 else np.full_like(dt, x0) - def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): + def model(self, t, fit_params, fixed_params_dict=None, fit_param_errs=None): """Predicted positions (and uncertainties, if fit_param_errs is provided) at time t of Fixed model. Parameters @@ -238,8 +340,8 @@ def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): t : float or array-like Time array, shape (N_times,) fit_params : array-like - Fit parameters x0, y0 in shape (N_params,) or (N_stars, N_params) - fixed_params : array-like, optional + x0, y0 in shape (N_params,) or (N_stars, N_params) + fixed_params_dict : dict, optional Not applicable for Fixed, by default None fit_param_errs : array-like, optional Uncertainties for x0, y0 in shape (N_params,) or (N_stars, N_params), by default None @@ -283,12 +385,14 @@ def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): return x, y, x_err, y_err def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, - params_guess=None, fill_value=np.nan, + params_guess=None, + return_chi2=False, verbose=True ): if verbose and (not use_scipy): @@ -309,7 +413,7 @@ def run_fit( # degree_of_freedom >= 0 # Calculate weighted average position - x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) + x_wt, y_wt = self.calc_weights(xe, ye, weighting=weighting) x_wt_norm = x_wt / np.sum(x_wt) y_wt_norm = y_wt / np.sum(y_wt) x0 = np.average(x, weights=x_wt) @@ -320,7 +424,8 @@ def run_fit( params = np.array([x0, y0]) param_errors = np.array([x0e, y0e]) - chi2x, chi2y = self.calc_chi2(params, [], t, x, y, xe, ye) + if (not absolute_sigma) or return_chi2: + chi2x, chi2y = self.calc_chi2(t, x, y, xe, ye, params) if not absolute_sigma: if degree_of_freedom > 0: @@ -338,7 +443,10 @@ def run_fit( # Set parameter uncertainties to np.inf, same behavior as scipy.optimize.curve_fit param_errors = np.full_like(param_errors, np.inf) - return params, param_errors, chi2x, chi2y + if return_chi2: + return params, param_errors, chi2x, chi2y + else: + return params, param_errors class Linear(MotionModel): """ @@ -349,7 +457,6 @@ class Linear(MotionModel): # Number of fit parameters/required observations in each direction n_params = int(np.ceil(len(fit_param_names) / 2)) - name = "Linear" def __init__(self, **kwargs): @@ -377,7 +484,7 @@ def model_fit(self, dt, x0, v): """ return x0 + v * dt - def model(self, t, fit_params, fixed_params, fit_param_errs=None): + def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Linear model. Parameters @@ -385,9 +492,9 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): t : float or array-like Time(s) at which to evaluate the model fit_params : array-like - Fit parameters x0, vx, y0, vy in shape (N_params,) or (N_stars, N_params) - fixed_params : array-like - Fixed parameters t0 in shape (1,) or (N_stars, 1) + x0, vx, y0, vy in shape (N_params,) or (N_stars, N_params) + fixed_params_dict : dict + t0, shape (1,) or (N_stars,) fit_param_errs : array-like, optional Uncertainties of fit parameters in shape (N_params,) or (N_stars, N_params), by default None @@ -396,6 +503,8 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Linear model." + t = np.atleast_1d(t) fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) @@ -403,7 +512,7 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): N_times = len(t) x0, vx, y0, vy = fit_params.T # Each shape (N_stars,) - t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) + t0 = np.atleast_1d(fixed_params_dict['t0']) # Shape (N_stars,) or (1,) dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) @@ -430,14 +539,24 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): return x, y, x_err, y_err def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict, weighting='var', use_scipy=True, absolute_sigma=True, - params_guess=None, fill_value=np.nan, + params_guess=None, + return_chi2=False, verbose=True ): + assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Linear model." + t0 = fixed_params_dict['t0'] + t = np.atleast_1d(t) + x = np.atleast_1d(x) + y = np.atleast_1d(y) + xe = np.atleast_1d(xe) + ye = np.atleast_1d(ye) + n_obs = len(t) degree_of_freedom = n_obs - self.n_params # Not enough data points to fit model @@ -449,11 +568,14 @@ def run_fit( ) params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) - return params, param_errors, np.nan, np.nan + if return_chi2: + return params, param_errors, np.nan, np.nan + else: + return params, param_errors # degree_of_freedom >= 0 dt = t - t0 - x_wt, y_wt = self.get_weights(xe, ye, weighting=weighting) + x_wt, y_wt = self.calc_weights(xe, ye, weighting=weighting) if params_guess is None: params_guess = [x.mean(), 0., y.mean(), 0.] @@ -466,60 +588,65 @@ def run_fit( y0e, vye = np.sqrt(y_cov.diagonal()) params = np.array([x0, vx, y0, vy]) param_errors = np.array([x0e, vxe, y0e, vye]) - chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) - - else: - # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution scheme - x = np.array(x) - y = np.array(y) - dt = np.array(dt) - X_mat_t = np.vander(dt, 2) - # x calculation - W_mat_x = np.diag(x_wt) - XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t - pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix - popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution - perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution - # y calculation - W_mat_y = np.diag(y_wt) - XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t - pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix - popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution - perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution - # prepare values to return - vx, x0 = popt_x - vy, y0 = popt_y - vxe, x0e = perr_x - vye, y0e = perr_y - - # Does not use get_chi2 to accelerate calculation + if return_chi2: + chi2_x, chi2_y = self.calc_chi2(t, x, y, xe, ye, params, fixed_params_dict) + return params, param_errors, chi2_x, chi2_y + else: + return params, param_errors + + # Linear algebraic solution + # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution_scheme + X_mat_t = np.vander(dt, 2) + # x calculation + W_mat_x = np.diag(x_wt) + XTWX_mat_x = X_mat_t.T @ W_mat_x @ X_mat_t + pcov_x = np.linalg.inv(XTWX_mat_x) # Covariance Matrix + popt_x = pcov_x @ X_mat_t.T @ W_mat_x @ x # Linear Solution + perr_x = np.sqrt(np.diag(pcov_x)) # Uncertainty of Linear Solution + # y calculation + W_mat_y = np.diag(y_wt) + XTWX_mat_y = X_mat_t.T @ W_mat_y @ X_mat_t + pcov_y = np.linalg.inv(XTWX_mat_y) # Covariance Matrix + popt_y = pcov_y @ X_mat_t.T @ W_mat_y @ y # Linear Solution + perr_y = np.sqrt(np.diag(pcov_y)) # Uncertainty of Linear Solution + # prepare values to return + vx, x0 = popt_x + vy, y0 = popt_y + vxe, x0e = perr_x + vye, y0e = perr_y + + params = np.array([x0, vx, y0, vy]) + param_errors = np.array([x0e, vxe, y0e, vye]) + + # Does not use get_chi2 to accelerate calculation + if return_chi2 or (not absolute_sigma): residual_x = x - X_mat_t @ popt_x residual_y = y - X_mat_t @ popt_y chi2_x = residual_x.T @ W_mat_x @ residual_x chi2_y = residual_y.T @ W_mat_y @ residual_y - params = np.array([x0, vx, y0, vy]) - param_errors = np.array([x0e, vxe, y0e, vye]) + if not absolute_sigma: + if degree_of_freedom > 0: + reduced_chi2_x = chi2_x / degree_of_freedom + reduced_chi2_y = chi2_y / degree_of_freedom + + param_errors[0:2] *= reduced_chi2_x**0.5 + param_errors[2:4] *= reduced_chi2_y**0.5 - if not absolute_sigma: - if degree_of_freedom > 0: - reduced_chi2_x = chi2_x / degree_of_freedom - reduced_chi2_y = chi2_y / degree_of_freedom - - param_errors[0:2] *= reduced_chi2_x**0.5 - param_errors[2:4] *= reduced_chi2_y**0.5 - - else: - # degree_of_freedom == 0, as < 0 case already handled above - warnings.warn( - f'Degree of freedom < 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value np.inf.', - OptimizeWarning, stacklevel=2 - ) - # Set parameter uncertainties to np.inf, same behavior as scipy.optimize.curve_fit - param_errors = np.full_like(param_errors, np.inf) - - return params, param_errors, chi2_x, chi2_y + else: + # degree_of_freedom == 0, as < 0 case already handled above + warnings.warn( + f'Degree of freedom < 0. Covariance of the parameters could not be estimated. Setting parameter uncertainties to fill value np.inf.', + OptimizeWarning, stacklevel=2 + ) + # Set parameter uncertainties to np.inf, same behavior as scipy.optimize.curve_fit + param_errors = np.full_like(param_errors, np.inf) + + if return_chi2: + return params, param_errors, chi2_x, chi2_y + else: + return params, param_errors class Acceleration(MotionModel): """ @@ -559,7 +686,7 @@ def model_fit(self, t, x0, v0, a): """ return x0 + v0*t + 0.5*a*t**2 - def model(self, t, fit_params, fixed_params, fit_param_errs=None): + def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Acceleration model. Parameters @@ -567,9 +694,9 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): t : float or array-like Time(s) at which to evaluate the model fit_params : array-like - Fit parameters with shape (N_stars, N_params) or (N_params,) - fixed_params : array-like - Fixed parameters with shape (N_stars, N_fixed_params) or (N_fixed_params,) + x0, vx0, ax, y0, vy0, ay in shape (N_params,) or (N_stars, N_params) + fixed_params_dict : dict + t0, shape (1,) or (N_stars,) fit_param_errs : array-like, optional Fit parameter uncertainties with shape (N_stars, N_params) or (N_params,), by default None @@ -578,6 +705,8 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Acceleration model." + t = np.atleast_1d(t) fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) @@ -585,7 +714,7 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): N_times = len(t) x0, vx0, ax, y0, vy0, ay = fit_params.T # Each shape (N_stars,) - t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) + t0 = np.atleast_1d(fixed_params_dict['t0']) # Shape (N_stars,) or (1,) dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) @@ -614,18 +743,28 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict, weighting='var', use_scipy=True, absolute_sigma=True, params_guess=None, fill_value=np.nan, + return_chi2=False, verbose=True ): + assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Acceleration model." + t0 = fixed_params_dict['t0'] + t = np.atleast_1d(t) + x = np.atleast_1d(x) + y = np.atleast_1d(y) + xe = np.atleast_1d(xe) + ye = np.atleast_1d(ye) + if not use_scipy: if verbose: warnings.warn("Acceleration model has no non-scipy fitter option. Running with scipy.") - + n_obs = len(t) degree_of_freedom = n_obs - self.n_params # Not enough data points to fit model @@ -637,11 +776,14 @@ def run_fit( ) params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) - return params, param_errors, np.nan, np.nan + if return_chi2: + return params, param_errors, np.nan, np.nan + else: + return params, param_errors # degree_of_freedom >= 0 dt = t - t0 - x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) + x_wt, y_wt = self.calc_weights(xe,ye, weighting=weighting) if params_guess is None: # Initial guess for velocity: idx_first, idx_last = np.argmin(t), np.argmax(t) @@ -657,9 +799,11 @@ def run_fit( params = np.array([x0, vx0, ax, y0, vy0, ay]) param_errors = np.array([x0e, vx0e, axe, y0e, vy0e, aye]) - chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) - - return params, param_errors, chi2_x, chi2_y + if return_chi2: + chi2_x, chi2_y = self.calc_chi2(t, x, y, xe, ye, params, fixed_params_dict) + return params, param_errors, chi2_x, chi2_y + else: + return params, param_errors class Parallax(MotionModel): """ @@ -671,29 +815,32 @@ class Parallax(MotionModel): Optional obs parameter describes observer location, default is 'earth'. """ fit_param_names = ['x0', 'vx', 'y0', 'vy', 'pi'] - fixed_param_names = ['t0'] - fixed_meta_data = ['RA','Dec','PA','obs'] + fixed_param_names = ['t0', 'ra', 'dec', 'pa', 'obsLocation'] name = "Parallax" # Number of fit parameters/required observations in each direction n_params = int(np.ceil(len(fit_param_names) / 2)) - def __init__(self, ra, dec, pa=0., obs='earth'): + def __init__(self): super().__init__() - self.ra = ra - self.dec = dec - self.pa = pa - self.obs = obs - self.plx_vector_cached = None + self.plx_vector_cached = None # Cache for parallax vector return - def calc_parallax_vector(self, t_mjd): + def calc_parallax_vector(self, t_mjd, ra, dec, pa=0., obsLocation='earth'): """Calculate parallax vector of shape (2, N_times) Parameters ---------- t_mjd : array-like Time array in mjd + ra : float or array-like + Right ascension(s) in degrees + dec : float or array-like + Declination(s) in degrees + pa : float or array-like, optional + Position angle(s) of image y-axis from North in degrees, by default 0. + obsLocation : str, optional + Observer location, by default 'earth' Returns ------- @@ -710,11 +857,11 @@ def calc_parallax_vector(self, t_mjd): elif all(np.isin(t_mjd, t_mjd_cached)): # If all input times are in cached values, return those # Calculate pvec_idxs such that t_mjd_cached[ pvec_idxs ] == t_mjd - pvec_idxs = np.array([np.where(t_mjd_cached==t_mjd_i)[0][0] for t_mjd_i in t_mjd]) + pvec_idxs = np.array([np.where(t_mjd_cached == t_mjd_i)[0][0] for t_mjd_i in t_mjd]) pvec = self.plx_vector_cached[1][:, pvec_idxs] return pvec - pvec = parallax.parallax_in_direction(self.ra, self.dec, t_mjd, obsLocation=self.obs, PA=self.pa).T + pvec = parallax.parallax_in_direction(ra, dec, t_mjd, obsLocation=obsLocation, pa=pa) self.plx_vector_cached = [t_mjd, pvec] return pvec @@ -738,15 +885,20 @@ def model_fit(self, dt, x0, vx, y0, vy, pi): Returns ------- - 2d array - Model positions at time t of Parallax model, shape (2, N_times) + x_res, y_res : array-like + Model positions at time t of Parallax model """ - x_res = x0 + vx*dt + pi * self.pvec[0] - y_res = y0 + vy*dt + pi * self.pvec[1] - return np.vstack([x_res, y_res]) - + # x0, vx, y0, vy, pi are all shape (N_stars, N_times) + x_res = x0 + vx * dt + pi * self.pvec[0] + y_res = y0 + vy * dt + pi * self.pvec[1] + return x_res, y_res + + def _model_fit(self, dt, x0, vx, y0, vy, pi): + """Wrapper for model_fit to return concatenated results for scipy fitting.""" + x_res, y_res = self.model_fit(dt, x0, vx, y0, vy, pi) + return np.hstack([x_res, y_res]) # Shape (N_stars, 2*N_times) - def model(self, t, fit_params, fixed_params, fit_param_errs=None): + def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Parallax model. Parameters @@ -754,9 +906,13 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): t : float or array-like Times at which to evaluate the model fit_params : array-like - Fit parameters for the model - fixed_params : array-like - Fixed parameters for the model + x0, vx, y0, vy, pi in shape (N_params,) or (N_stars, N_params) + fixed_params : dict + - t0, shape (N_stars,) or (1,). + - ra, shape (N_stars,) or (1,). + - dec, shape (N_stars,) or (1,). + - pa, optional, shape (N_stars,) or (1,), by default 0. + - obsLocation, optional,shape (N_stars,) or (1,), by default 'earth' fit_param_errs : array-like, optional Uncertainties in fit parameters, by default None @@ -767,17 +923,22 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): """ t = np.atleast_1d(t) fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) - N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 N_times = len(t) x0, vx, y0, vy, pi = fit_params.T # Each shape (N_stars,) - t0 = np.atleast_1d(fixed_params[0]) # Shape (N_stars,) or (1,) + t0 = np.atleast_1d(fixed_params_dict['t0']) # Shape (N_stars,) or (1,) + ra = np.atleast_1d(fixed_params_dict['ra']) + dec = np.atleast_1d(fixed_params_dict['dec']) + pa = np.atleast_1d(fixed_params_dict.get('pa', 0.0)) + obsLocation = fixed_params_dict.get('obsLocation', 'earth') dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) t_mjd = Time(t, format='decimalyear', scale='utc').mjd # Shape (N_times,) - self.pvec = self.calc_parallax_vector(t_mjd) # Shape (2, N_times) - x, y = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) + self.pvec = self.calc_parallax_vector(t_mjd, ra, dec, pa=pa, obsLocation=obsLocation) # Shape (2, N_times) + xy = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) + x = xy[:, :N_times] # Shape (N_stars, N_times) + y = xy[:, N_times:] # Shape (N_stars, N_times) if N_stars == 1 or N_times == 1: # If only one star, return flattened arrays @@ -800,21 +961,30 @@ def model(self, t, fit_params, fixed_params, fit_param_errs=None): def run_fit( - self, t, x, y, xe, ye, t0, + self, t, x, y, xe, ye, + fixed_params_dict, weighting='var', use_scipy=True, absolute_sigma=True, params_guess=None, fill_value=np.nan, + return_chi2=False, verbose=True ): if not use_scipy: if verbose: warnings.warn("Parallax model has no non-scipy fitter option. Running with scipy.", UserWarning) - + + assert all([k in fixed_params_dict for k in ['t0', 'ra', 'dec']]), "Parallax model requires 't0', 'ra', and 'dec' in fixed_params." t = np.atleast_1d(t) - n_obs = len(t) - degree_of_freedom = n_obs - self.n_params + t0 = np.atleast_1d(fixed_params_dict['t0']) + ra = np.atleast_1d(fixed_params_dict['ra']) + dec = np.atleast_1d(fixed_params_dict['dec']) + pa = np.atleast_1d(fixed_params_dict.get('pa', 0.0)) + obsLocation = fixed_params_dict.get('obsLocation', 'earth') + + n_fit = len(t) + degree_of_freedom = n_fit - self.n_params # Not enough data points to fit model if degree_of_freedom < 0: if verbose: @@ -824,12 +994,15 @@ def run_fit( ) params = np.full(self.n_params, fill_value) param_errors = np.full(self.n_params, np.inf) - return params, param_errors - + if return_chi2: + return params, param_errors, np.nan, np.nan + else: + return params, param_errors + # degree_of_freedom >= 0 t_mjd = Time(t, format='decimalyear', scale='utc').mjd - self.pvec = self.get_parallax_vector(t_mjd) - x_wt, y_wt = self.get_weights(xe,ye, weighting=weighting) + self.pvec = self.calc_parallax_vector(t_mjd, ra, dec, pa=pa, obsLocation=obsLocation) # Shape (2, N_times) + x_wt, y_wt = self.calc_weights(xe, ye, weighting=weighting) # Initial guesses, x0,y0 as x,y averages; # vx,vy as average velocity if first and last points are perfectly measured; @@ -842,20 +1015,22 @@ def run_fit( y.mean(), (y[idx_last] - y[idx_first]) / t_span, 0.1 ] - res = curve_fit( - self.model_fit, t - t0, np.vstack([x, y]), - p0=params_guess, sigma = 1.0/np.hstack([x_wt,y_wt]), + popt, pcov = curve_fit( + self._model_fit, t - t0, np.hstack([x, y]), + p0=params_guess, sigma=np.hstack([x_wt, y_wt]), absolute_sigma=absolute_sigma ) - x0, vx, y0, vy, pi = res[0] - x0_err, vx_err, y0_err, vy_err, pi_err = np.sqrt(np.diag(res[1])) + x0, vx, y0, vy, pi = popt + x0_err, vx_err, y0_err, vy_err, pi_err = np.sqrt(pcov.diagonal()) params = np.array([x0, vx, y0, vy, pi]) param_errors = np.array([x0_err, vx_err, y0_err, vy_err, pi_err]) - chi2_x, chi2_y = self.calc_chi2(params, [t0], t, x, y, xe, ye) - return params, param_errors, chi2_x, chi2_y - + if return_chi2: + chi2_x, chi2_y = self.calc_chi2(t, x, y, xe, ye, params, fixed_params_dict) + return params, param_errors, chi2_x, chi2_y + else: + return params, param_errors def validate_motion_models(motion_models, startable, default_motion_model): """Validate that all the unique motion models in startable and default_motion_model are in the motion_models. If not, add available models to the list. @@ -869,12 +1044,7 @@ def validate_motion_models(motion_models, startable, default_motion_model): default_motion_model : MotionModel Default MotionModel """ - motion_model_map = { - 'Fixed': Fixed, - 'Linear': Linear, - 'Acceleration': Acceleration, - 'Parallax': Parallax - } + motion_model_map = motion_model_map() # Collect names of all motion models that might get used. all_motion_model_names = set() all_motion_model_names.add('Fixed') @@ -975,14 +1145,9 @@ def get_all_motion_model_names(with_errors=True, with_fixed=True): return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) def motion_model_map(): - mm_map = { - 'Empty': Empty, - 'Fixed': Fixed, - 'Linear': Linear, - 'Acceleration': Acceleration, - 'Parallax': Parallax - } - + mm_map = dict( + [(mm.__name__, mm()) for mm in MotionModel.__subclasses__()] + ) # Sort by n_params mm_map = dict(sorted(mm_map.items(), key=lambda item: item[1].n_params)) return mm_map \ No newline at end of file diff --git a/flystar/parallax.py b/flystar/parallax.py index 3f7602b..2bd352a 100755 --- a/flystar/parallax.py +++ b/flystar/parallax.py @@ -23,16 +23,16 @@ # Default cache size is 1 GB cache_memory.reduce_size() -@cache_memory.cache() -def parallax_in_direction(ra, dec, mjd, obsLocation='earth', PA=0.): +# @cache_memory.cache() +def parallax_in_direction(ra, dec, mjd, obsLocation='earth', pa=0.): """ Calculate the parallax vector in a given direction following MulensModel. Parameters ---------- - RA : float + RA : float or array-like Right Ascension in degrees. (J2000) - Dec : float + Dec : float or array-like Declination in degrees. (J2000) mjd : float or array-like Modified Julian Date. @@ -44,33 +44,42 @@ def parallax_in_direction(ra, dec, mjd, obsLocation='earth', PA=0.): Returns ------- pvec : ndarray - Parallax vector components, shape of (N, 2), where N is the number of mjd entries. + Parallax vector components, shape of (2, N) or (2,), where N is the number of stars. """ # Munge inputs into astropy format. # times = Time(mjd + 2400000.5, format='jd', scale='tdb') + ra = np.atleast_1d(ra) + dec = np.atleast_1d(dec) + mjd = np.atleast_1d(mjd) times = Time(mjd, format='mjd', scale='tdb') # convert to TDB coord = SkyCoord(ra, dec, unit=(units.deg, units.deg)) - direction = coord.cartesian.xyz.value + directions = coord.cartesian.xyz.value.T # Shape (N_stars, 3) north = np.array([0., 0., 1.]) - _east_projected = np.cross(north, direction) / np.linalg.norm(np.cross(north, direction)) - _north_projected = np.cross(direction, _east_projected) / np.linalg.norm(np.cross(direction, _east_projected)) + # Cross product of each star with north vector + _east_projected = np.cross(north, directions) + _east_projected /= np.linalg.norm(_east_projected, axis=1)[:, np.newaxis] # Shape (N_stars, 3) + _north_projected = np.cross(directions, _east_projected) + _north_projected /= np.linalg.norm(_north_projected, axis=1)[:, np.newaxis] # Shape (N_stars, 3) obs_pos = get_observer_barycentric(obsLocation, times) sun_pos = get_body_barycentric(body='sun', time=times) sun_obs_pos = sun_pos - obs_pos - pos = sun_obs_pos.xyz.T.to(units.au) + pos = sun_obs_pos.xyz.T.to(units.au).value # Shape (N_stars, 3) + + e = np.einsum('ij,ij->i', pos, _east_projected) # Shape (N_stars,) + n = np.einsum('ij,ij->i', pos, _north_projected) # Shape (N_stars,) - e = np.dot(pos, _east_projected) - n = np.dot(pos, _north_projected) - # Rotate frame e,n->x,y accounting for PA - PA_rad = np.pi/180.0 * PA - x = -e.value*np.cos(PA_rad) + n.value*np.sin(PA_rad) - y = e.value*np.sin(PA_rad) + n.value*np.cos(PA_rad) - pvec = np.array([x, y]).T + pa = np.deg2rad(pa) + x = -e * np.cos(pa) + n * np.sin(pa) + y = e * np.sin(pa) + n * np.cos(pa) + pvec = np.array([x, y]) # Shape (2, N_stars) + + if pvec.shape[1] == 1: + pvec = pvec.flatten() return pvec diff --git a/flystar/startables.py b/flystar/startables.py index 661382f..dd44178 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -125,7 +125,7 @@ def __init__(self, *args, ref_list=0, **kwargs): # We have to have special handling of meta-data (i.e. info that has # dimensions of n_lists). - meta_tab = ('LIST_TIMES', 'LIST_NAMES') + meta_tab = ('list_times', 'list_names') meta_type = ((float, int), str) for mm in range(len(meta_tab)): meta_test = meta_tab[mm] @@ -154,7 +154,7 @@ def __init__(self, *args, ref_list=0, **kwargs): del kwargs[meta_arg] for arg in kwargs: - if arg in ['name', 'x', 'y', 'm']: + if arg in ['name', 'x', 'y', 'm', 'list_times', 'list_names']: continue else: self.add_column(Column(data=kwargs[arg], name=arg)) @@ -218,7 +218,7 @@ def _add_list_data_from_starlist(self, starlist): else: # Add junk data it if wasn't input self._set_invalid_list_values(col_name, -1) - + ########## # Update the table meta-data. Remember that entries are lists not numpy arrays. ########## @@ -246,10 +246,10 @@ def _add_list_data_from_starlist(self, starlist): # Update the n_lists meta keyword. self.meta['n_lists'] += 1 - + return - - + + def _add_list_data_from_keywords(self, **kwargs): # # Check if the required arguments are present # arg_req = ('x', 'y', 'm') @@ -534,14 +534,15 @@ def detections(self): def fit_motion_model( self, - motion_models=[Empty(), Fixed(), Linear()], + motion_models=[Empty, Fixed, Linear], + fixed_params_dict=None, weighting='var', use_scipy=False, absolute_sigma=True, bootstrap=0, - fixed_t0=False, verbose=True, mask_value=None, + mask_lists=None, fill_value=np.nan, show_progress=True ): @@ -551,17 +552,21 @@ def fit_motion_model( ---------- motion_models : list of MotionModel, optional Motion models to use. - Empty() and Fixed() models are always added automatically for stars with n_fit = 0 or 1. + Empty and Fixed models are always added automatically for stars with n_fit = 0 or 1. The behavior is as follows: 1. If 'motion_model_input' column is NOT in table: - Use the most complex model that has enough parameters to fit the data (n_fit >= n_params). - If multiple models are supplied, prioritize the model with the most parameters to fit. - If multiple models have the same number of parameters, raise AssertionError: not sure which to use. - 2. If 'motion_model_input' column is in table: + 2. If 'motion_model_input' column IS in table: - Use the model specified in the 'motion_model_input' column. - - If motion model requires initialization parameters, an instance of the motion model must be provided in motion_models list, i.e., motion_models=[Parallax(RA=0, DEC=0)]. - - If not enough data points to fit the specified model, use the most complex model that has enough parameters to fit the data (n_fit >= n_params) among the provided motion_models and 'motion_model_input'. - The actual used motion model is stored in the 'motion_model_used' column. The default motion_models are [Empty(), Fixed(), Linear()]. + - If not enough data points to fit the specified model, use the most complex model in any 'motion_model_input' column that has enough parameters to fit the data (n_fit >= n_params) among the provided motion_models and 'motion_model_input'. + The actual used motion model is stored in the 'motion_model_used' column. The default motion_models are [Empty, Fixed, Linear]. + fixed_params_dict : dict, optional + Dictionary of fixed parameters for motion models, e.g., {'t0': 0., 'ra': np.array([...]), 'dec': np.array([...])}. + - Scalar values are used for all stars, array values should have length = N_stars. + - t0 is automatically calculated as np.average(t, weights=1/np.hypot(xe, ye)) if not provided. + - The keys should match the fixed parameter names in the motion models. See MotionModel class for details, by default None weighting : str, optional Uncertainty weighting, 'std' for weight=1/xe(ye) or 'var' for weight=1/xe(ye)**2, by default 'var' use_scipy : bool, optional @@ -570,12 +575,12 @@ def fit_motion_model( Use absolute sigma or not, see scipy curve_fit for details, by default True bootstrap : int, optional Number of bootstrap for uncertainty resampling, by default 0 - fixed_t0 : bool or float, optional - If provided, use the fixed t0. Otherwise, use average t weighted by 1/np.hypot(xe, ye), by default False verbose : bool, optional Print verbose messages or not, by default True mask_value : float, optional Values to mask in data, by default None + mask_lists : list of int, optional + Indices of lists to mask/exclude from fitting, by default None fill_value : float, optional Fill value when there is not enough data points to fit, by default np.nan show_progress : bool, optional @@ -596,19 +601,24 @@ def fit_motion_model( if weighting not in ['var', 'std']: raise ValueError(f"fit_velocities: Weighting must either be 'var' or 'std', not {weighting}!") - if ('t' not in self.colnames) and ('LIST_TIMES' not in self.meta): - raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'LIST_TIMES' in meta.") + if ('t' not in self.colnames) and ('list_times' not in self.meta): + raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'list_times' in meta.") # Check if we have the required columns if not all([_ in self.colnames for _ in ['x', 'y']]): raise KeyError(f"fit_velocities: Missing required columns in the table: {', '.join(['x', 'y'])}!") + # Check fixed_params_dict is a dict + if fixed_params_dict is not None: + if not isinstance(fixed_params_dict, dict): + raise ValueError("fit_velocities: fixed_params_dict must be a dictionary!") + # Always add Empty and Fixed in motion models mm_names = [mm.name for mm in motion_models] if 'Fixed' not in mm_names: - motion_models.insert(0, Fixed()) + motion_models.insert(0, Fixed) if 'Empty' not in mm_names: - motion_models.insert(0, Empty()) + motion_models.insert(0, Empty) mm_names = [mm.name for mm in motion_models] # Construct motion models if motion_model_input column exists @@ -643,19 +653,52 @@ def fit_motion_model( N_stars = len(self) x_data = np.ma.masked_invalid(self['x'].data, copy=True) y_data = np.ma.masked_invalid(self['y'].data, copy=True) - xe_data = np.ma.masked_invalid(self['xe'].data, copy=True) if 'xe' in self.colnames else None - ye_data = np.ma.masked_invalid(self['ye'].data, copy=True) if 'ye' in self.colnames else None + xe_data = np.ma.masked_invalid(self['xe'].data, copy=True) if 'xe' in self.colnames else np.ones_like(x_data) + ye_data = np.ma.masked_invalid(self['ye'].data, copy=True) if 'ye' in self.colnames else np.ones_like(y_data) + + if mask_lists is not None: + x_data.mask[:, mask_lists] = True + y_data.mask[:, mask_lists] = True + xe_data.mask[:, mask_lists] = True + ye_data.mask[:, mask_lists] = True # t_data: 2d array with shape (N_stars, N_epochs) # t0: 1d array with shape (N_stars,) if 't' in self.colnames: t_data = copy.deepcopy(self['t'].data) - t0 = np.average(t_data, axis=1, weights=1/np.hypot(xe_data, ye_data)) if not fixed_t0 else np.ones(N_stars)*fixed_t0 else: - t_data = copy.deepcopy(np.array(self.meta['LIST_TIMES'])) + t_data = copy.deepcopy(np.array(self.meta['list_times'])) t_data = np.broadcast_to(t_data, x_data.shape) - t0 = np.average(t_data, axis=1, weights=1/np.hypot(xe_data, ye_data)) if not fixed_t0 else np.ones(N_stars)*fixed_t0 + + # Add default t0 if not provided in fixed_params_dict + if fixed_params_dict is None: + weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None + t0 = np.average(t_data, axis=1, weights=weights) + fixed_params_dict = {'t0': t0} + elif 't0' not in fixed_params_dict: + weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None + fixed_params_dict['t0'] = np.average(t_data, axis=1, weights=weights) + else: + if np.ndim(fixed_params_dict['t0']) == 0: + fixed_params_dict['t0'] = np.full(N_stars, fixed_params_dict['t0']) + t0 = fixed_params_dict['t0'] + + # Prepare fixed_params_dict for each star + # This avoids checking types and slicing inside the fitting loop + fixed_params_stars = [{} for _ in range(N_stars)] + # Identify array parameters (length N_stars) and scalar parameters + array_params = {k: v for k, v in fixed_params_dict.items() if np.ndim(v) > 0 and len(v) == N_stars} + scalar_params = {k: v for k, v in fixed_params_dict.items() if k not in array_params} + + # Construct list of dicts for each star + # Using list comprehension for speed + fixed_params_stars = [ + {**scalar_params, **{k: v[i] for k, v in array_params.items()}} + for i in range(N_stars) + ] + + # Apply mask_value if provided if mask_value: x_data = np.ma.masked_values(x_data, mask_value) y_data = np.ma.masked_values(y_data, mask_value) @@ -664,6 +707,7 @@ def fit_motion_model( if ye_data is not None: ye_data = np.ma.masked_values(ye_data, mask_value) + # Calculate mask array xy_mask = (~x_data.mask) & (~y_data.mask) self['n_fit'] = xy_mask.sum(axis=1) @@ -682,7 +726,6 @@ def fit_motion_model( if 'motion_model_input' in self.colnames: # Determine which motion model to use based on motion_model_input column # If n_fit < required n_params for the input motion model, use the most complicated motion model with n_fit >= n_params - motion_model_names = np.unique(self['motion_model_input']) required_params = [all_mm_map[mm_name].n_params for mm_name in self['motion_model_input']] mm_digitized = np.digitize( x=np.minimum(np.array(self['n_fit']), required_params), @@ -694,7 +737,8 @@ def fit_motion_model( x=np.array(self['n_fit']), bins=mm_n_params ) - 1 # Convert to 0-based index - + + # Assign motion models to stars self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized]) @@ -722,7 +766,8 @@ def fit_motion_model( ) # Add a column to keep track of the number of points used in a fit and number of bootstrap used. - self['n_bootstrap'] = bootstrap + self.meta['n_bootstrap'] = bootstrap + ########################### ######### FITTING ######### @@ -730,9 +775,10 @@ def fit_motion_model( unique_motion_models, unique_inv_indices = np.unique(self['motion_model_used'], return_inverse=True) indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} + # Expensive for loop! Prepare everything beforehand to speed up. for unique_motion_model, unique_index in indices_by_motion_model.items(): # Create motion model instance - motion_model_instance = input_mm_map[unique_motion_model] + motion_model_instance = input_mm_map[unique_motion_model]() # Initialize arrays to store results n_stars_this_model = len(unique_index) n_params = len(motion_model_instance.fit_param_names) @@ -751,12 +797,13 @@ def fit_motion_model( y=y_stars[i_star], xe=xe_stars[i_star], ye=ye_stars[i_star], - t0=t0[i_star], + fixed_params_dict=fixed_params_stars[i_star], weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma, bootstrap=bootstrap, fill_value=fill_value, + return_chi2=True, verbose=verbose ) params_array[idx] = params @@ -808,8 +855,8 @@ def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, b if weighting not in ['var', 'std']: raise ValueError(f"fit_velocities: Weighting must either be 'var' or 'std', not {weighting}!") - if ('t' not in self.colnames) and ('LIST_TIMES' not in self.meta): - raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'LIST_TIMES' in meta.") + if ('t' not in self.colnames) and ('list_times' not in self.meta): + raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'list_times' in meta.") # Check if we have the required columns if not all([_ in self.colnames for _ in ['x', 'y']]): @@ -827,9 +874,9 @@ def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, b if ('motion_model_input' not in self.colnames) or reassign_motion_model: self['motion_model_input'] = default_motion_model self['motion_model_used'] = self['motion_model_input'] - + motion_model_dict = motion_model.validate_motion_model_dict(motion_model_dict, self, default_motion_model) - + # # Fill table with all possible motion model parameter names as new # columns. Make everything empty for now. @@ -864,7 +911,7 @@ def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, b if 't' in self.colnames: self['t0'] = self['t'] else: - self['t0'] = self.meta['LIST_TIMES'][0] + self['t0'] = self.meta['list_times'][0] if 'xe' in self.colnames: self['x0_err'] = self['xe'] self['y0_err'] = self['ye'] @@ -879,7 +926,7 @@ def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, b if 't' in self.colnames: self['t0'] = self['t'][:, 0] else: - self['t0'] = self.meta['LIST_TIMES'][0] + self['t0'] = self.meta['list_times'][0] if 'xe' in self.colnames: self['x0_err'] = self['xe'][:,0] self['y0_err'] = self['ye'][:,0] @@ -996,7 +1043,7 @@ def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scip if 't' in self.colnames: t = np.ma.masked_invalid(self['t'][ss, :].data) else: - t = np.ma.masked_invalid(self.meta['LIST_TIMES']) + t = np.ma.masked_invalid(self.meta['list_times']) if mask_val: t = np.ma.masked_values(t, mask_val) diff --git a/flystar/tests/test_all_detected.fits b/flystar/tests/test_all_detected.fits deleted file mode 100644 index ae56198..0000000 --- a/flystar/tests/test_all_detected.fits +++ /dev/null @@ -1,2911 +0,0 @@ -SIMPLE = T / conforms to FITS standard BITPIX = 8 / array data type NAXIS = 0 / number of array dimensions EXTEND = T END XTENSION= 'BINTABLE' / binary table extension BITPIX = 8 / array data type NAXIS = 2 / number of array dimensions NAXIS1 = 632 / length of dimension 1 NAXIS2 = 2000 / length of dimension 2 PCOUNT = 0 / number of group parameters GCOUNT = 1 / number of groups TFIELDS = 21 / number of table fields TTYPE1 = 'name ' TFORM1 = 'K ' TTYPE2 = 'x ' TFORM2 = '12D ' TDIM2 = '(2,6) ' TTYPE3 = 'y ' TFORM3 = '12D ' TDIM3 = '(2,6) ' TTYPE4 = 'm ' TFORM4 = '12D ' TDIM4 = '(2,6) ' TTYPE5 = 'xe ' TFORM5 = '6D ' TDIM5 = '(6) ' TTYPE6 = 'ye ' TFORM6 = '6D ' TDIM6 = '(6) ' TTYPE7 = 'me ' TFORM7 = '6D ' TDIM7 = '(6) ' TTYPE8 = 'n ' TFORM8 = '6D ' TDIM8 = '(6) ' TTYPE9 = 'det ' TFORM9 = '6D ' TDIM9 = '(6) ' TTYPE10 = 'vx ' TFORM10 = 'D ' TTYPE11 = 'vy ' TFORM11 = 'D ' TTYPE12 = 'vxe ' TFORM12 = 'D ' TTYPE13 = 'vye ' TFORM13 = 'D ' TTYPE14 = 'x0 ' TFORM14 = 'D ' TTYPE15 = 'y0 ' TFORM15 = 'D ' TTYPE16 = 'x0e ' TFORM16 = 'D ' TTYPE17 = 'y0e ' TFORM17 = 'D ' TTYPE18 = 'chi2_vx ' TFORM18 = 'D ' TTYPE19 = 'chi2_vy ' TFORM19 = 'D ' TTYPE20 = 't0 ' TFORM20 = 'D ' TTYPE21 = 'n_vfit ' TFORM21 = 'D ' EPNAMES = '2005_F814W_F1' EPNAMES = '2010_F125W_F3' EPNAMES = '2010_F139M_F2' EPNAMES = '2010_F160W_F1' EPNAMES = '2013_F160W_F1' EPNAMES = '2015_F160W_F1' ZPOINTS = 32.6783 ZPOINTS = 25.2305 ZPOINTS = 23.2835 ZPOINTS = 24.5698 ZPOINTS = 24.5698 ZPOINTS = 24.5698 YEARS = 2005.485 YEARS = 2010.652 YEARS = 2010.652 YEARS = 2010.652 YEARS = 2013.199 YEARS = 2015.148 HIERARCH DATE PRODUCED = '2025-06-30' HIERARCH INSTRUMENT = 'ACSWFC ' HIERARCH INSTRUMENT = 'WFC3IR ' HIERARCH INSTRUMENT = 'WFC3IR ' HIERARCH INSTRUMENT = 'WFC3IR ' HIERARCH INSTRUMENT = 'WFC3IR ' HIERARCH INSTRUMENT = 'WFC3IR ' END @Ÿ ˆ1&éy@Ÿ ›c+Ø(@Ÿ ˆ1&éy@Ÿ “4U‡*@Ÿ ˆ1&éy@Ÿ ¥ÆàOS@Ÿ ˆ1&éy@Ÿ…ÍÅ•Ü@Ÿ ˆ1&éy@Ÿ èÁ Î!@Ÿ ˆ1&éy@Ÿ]H/Ò@¢nzáG®@¢ns2ph@¢nzáG®@¢nˆ:ötä@¢nzáG®@¢mÐüùI±@¢nzáG®@¢mÓÐùòm@¢nzáG®@¢nbö3›@¢nzáG®@¢nsþ¤ÿŠ@8‚ò䎊@8m¥1›Š@4›¥ãSø@3¹Ã!dÏÎ@3š~ùÛ"Ñ@3Q@䩤@2èè§æ›@2h4¥àûZ@2èè§æ›@2•ÄŠÉRd@2èè§æ›@2–&îEK?¤hja¢ÖQ?¤ƒ´Æ*àä?¢iœy‘Ï?ÁÛÆÀï?» -Ld¢?²OU=°6i?¿/nI|Áâ?˜Š·¤‰ÿ?•`«²lñ??ºþ!æàg?Àî’”ï '?»Ï‡Ê1ñ?¶å¿#ý ?–ãjo¼ð?ƒ /±‘OÈ?‘‰©Þ¥e?£ü.Eôv?£ì¶Ñ [\@@"@@"@4@.?ð?ð?ð?ð?ð?ð?“EkŸ€?m¥•oÜ?zÁ•ºS ?œT 8O@ŸËÌÃ@¢n?ð/Ç? ? 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fit_err*n_sigma)) return np.abs(true_val - fit_val) <= n_sigma*fit_err def test_Fixed(): @@ -76,16 +74,31 @@ def test_Fixed(): ) x_sim = np.random.normal(x_true, true_params['x0_err']) y_sim = np.random.normal(y_true, true_params['y0_err']) + xe = np.ones_like(t)*true_params['x0_err'] + ye = np.ones_like(t)*true_params['y0_err'] # Run fit - params, param_errs, _ , _ = mod.fit( + params, param_errs = mod.fit( t, x_sim,y_sim, - xe=np.ones(len(t))*true_params['x0_err'], - ye=np.ones(len(t))*true_params['y0_err'], - t0=np.nan + xe=xe, + ye=ye ) + + x_wt = 1. / xe**2 + y_wt = 1. / ye**2 + x_wt_norm = x_wt / np.sum(x_wt) + y_wt_norm = y_wt / np.sum(y_wt) + x_mean = np.average(x_sim, weights=x_wt) + y_mean = np.average(y_sim, weights=y_wt) + x_std = (np.sum(x_wt_norm**2 * xe**2))**0.5 + y_std = (np.sum(y_wt_norm**2 * ye**2))**0.5 + # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) + np.testing.assert_allclose(params[0], x_mean, atol=1e-5) + np.testing.assert_allclose(params[1], y_mean, atol=1e-5) + np.testing.assert_allclose(param_errs[0], x_std, atol=1e-5) + np.testing.assert_allclose(param_errs[1], y_std, atol=1e-5) def test_Linear(): @@ -95,12 +108,11 @@ def test_Linear(): 't0':2025.0} mod = motion_model.Linear() param_list = mod.fit_param_names - fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t=t0 and array t x_t, y_t = mod.model( t=true_params['t0'], fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) assert x_t==true_params['x0'] assert y_t==true_params['y0'] @@ -108,7 +120,7 @@ def test_Linear(): x_t, y_t = mod.model( t=t_arr, fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) assert (x_t==(true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx'])).all() assert (y_t==(true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy'])).all() @@ -129,25 +141,28 @@ def test_Linear(): t=t_batch, fit_params=np.array([x0_batch, vx_batch, y0_batch, vy_batch]).T, fit_param_errs=np.array([x0_err_batch, vx_err_batch, y0_err_batch, vy_err_batch]).T, - fixed_params=t0_batch + fixed_params_dict={'t0': t0_batch} ) - assert (x_t_batch==(x0_batch+(t_batch-t0_batch)*vx_batch)).all() - assert (y_t_batch==(y0_batch+(t_batch-t0_batch)*vy_batch)).all() - assert (x_err_t_batch==np.hypot(x0_err_batch, (t_batch-t0_batch)*vx_err_batch)).all() - assert (y_err_t_batch==np.hypot(y0_err_batch, (t_batch-t0_batch)*vy_err_batch)).all() + + + np.testing.assert_allclose(x_t_batch, (x0_batch+(t_batch-t0_batch)*vx_batch), atol=1e-5) + np.testing.assert_allclose(y_t_batch, (y0_batch+(t_batch-t0_batch)*vy_batch), atol=1e-5) + np.testing.assert_allclose(x_err_t_batch, np.hypot(x0_err_batch, (t_batch-t0_batch)*vx_err_batch), atol=1e-5) + np.testing.assert_allclose(y_err_t_batch, np.hypot(y0_err_batch, (t_batch-t0_batch)*vy_err_batch), atol=1e-5) + # Multiple times t_batch = np.arange(2015.0,2025.0, 0.5) x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( t=t_batch, fit_params=np.array([x0_batch, vx_batch, y0_batch, vy_batch]).T, fit_param_errs=np.array([x0_err_batch, vx_err_batch, y0_err_batch, vy_err_batch]).T, - fixed_params=t0_batch + fixed_params_dict={'t0': t0_batch} ) - assert (x_t_batch==np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx_batch[i] for i in range(len(x0_batch))])).all() - assert (y_t_batch==np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy_batch[i] for i in range(len(x0_batch))])).all() - assert (x_err_t_batch==np.array([np.hypot(x0_err_batch[i], (t_batch-t0_batch[i])*vx_err_batch[i]) for i in range(len(x0_batch))])).all() - assert (y_err_t_batch==np.array([np.hypot(y0_err_batch[i], (t_batch-t0_batch[i])*vy_err_batch[i]) for i in range(len(x0_batch))])).all() - + np.testing.assert_allclose(x_t_batch, np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx_batch[i] for i in range(len(x0_batch))]), atol=1e-5) + np.testing.assert_allclose(y_t_batch, np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy_batch[i] for i in range(len(x0_batch))]), atol=1e-5) + np.testing.assert_allclose(x_err_t_batch, np.array([np.hypot(x0_err_batch[i], (t_batch-t0_batch[i])*vx_err_batch[i]) for i in range(len(x0_batch))]), atol=1e-5) + np.testing.assert_allclose(y_err_t_batch, np.array([np.hypot(y0_err_batch[i], (t_batch-t0_batch[i])*vy_err_batch[i]) for i in range(len(x0_batch))]), atol=1e-5) + # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter @@ -156,55 +171,73 @@ def test_Linear(): x_true, y_true = mod.model( t=t, fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) x_sim = np.random.normal(x_true, 0.05) y_sim = np.random.normal(y_true, 0.05) # Run fit - params, param_errs, _, _ = mod.fit( - t=t, - x=x_sim, - y=y_sim, - xe=np.repeat(0.05, len(t)), - ye=np.repeat(0.05,len(t)), - t0=true_params['t0'] - ) - print(param_errs) - # Confirm true value is within error bar of fit value - assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) - + xe = np.ones_like(t)*0.05 + ye = np.ones_like(t)*0.05 + + def linear(t, x0, vx): + return x0 + vx * t + + for absolute_sigma in [True, False]: + for weighting in ['std', 'var']: + for use_scipy in [True, False]: + params, param_errs = mod.fit( + t=t, + x=x_sim, + y=y_sim, + xe=xe, + ye=ye, + fixed_params_dict={'t0': true_params['t0']}, + weighting=weighting, + use_scipy=use_scipy, + absolute_sigma=absolute_sigma + ) + + # Scipy + xe_scipy = xe**0.5 if weighting=='std' else xe + ye_scipy = ye**0.5 if weighting=='std' else ye + x_popt, x_pcov = curve_fit( + linear, + t - true_params['t0'], + x_sim, + sigma=xe_scipy, + absolute_sigma=absolute_sigma, + p0=[np.mean(x_sim), 0.0] + ) + y_popt, y_pcov = curve_fit( + linear, + t - true_params['t0'], + y_sim, + sigma=ye_scipy, + absolute_sigma=absolute_sigma, + p0=[np.mean(y_sim), 0.0] + ) + np.testing.assert_allclose(params[:2], x_popt, atol=1e-5) + np.testing.assert_allclose(param_errs[:2], np.sqrt(np.diag(x_pcov)), atol=1e-5) + np.testing.assert_allclose(params[2:], y_popt, atol=1e-5) + np.testing.assert_allclose(param_errs[2:], np.sqrt(np.diag(y_pcov)), atol=1e-5) + # Test fitter with bootstrap - t = np.arange(2015.0,2025.0, 0.5) + t = np.arange(2015.0, 2025.0, 0.5) # Get values from model and add scatter - x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list],t) - x_true_err, y_true_err = np.repeat(0.05,len(t)), np.repeat(0.05,len(t)) + x_true, y_true = mod.model( + t=t, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params_dict={'t0': true_params['t0']} + ) + x_true_err, y_true_err = np.ones_like(t)*0.05, np.ones_like(t)*0.05 x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0'],bootstrap=10) + params, param_errs = mod.fit(t, x_sim, y_sim, x_true_err, y_true_err, fixed_params_dict={'t0': true_params['t0']}, bootstrap=10) print(param_errs) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) -# # Test fitter for 2 pts -# t = np.array([2015.0,2025.0]) -# # Get values from model and add scatter -# x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], -# [true_params[p] for p in fixed_param_list],t) -# x_true_err, y_true_err = np.repeat(0.05,len(t)), np.repeat(0.05,len(t)) -# x_sim = np.random.normal(x_true, x_true_err) -# y_sim = np.random.normal(y_true, y_true_err) -# # Run fit -# mod_fit = motion_model.Linear(t0=true_params['t0']) -# params, param_errs = mod_fit.fit_motion_model(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0']) -# print("DJSKBGJ",param_list) -# print([true_params[p] for p in param_list]) -# print(params) -# print(param_errs) -# # Confirm true value is within error bar of fit value -# assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params),2)]) - def test_Acceleration(): # Test handling of a single star @@ -214,12 +247,11 @@ def test_Acceleration(): 't0':2025.0} mod = motion_model.Acceleration() param_list = mod.fit_param_names - fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t=t0 and array t x_t, y_t = mod.model( t=true_params['t0'], fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) np.testing.assert_allclose(x_t, true_params['x0']) np.testing.assert_allclose(y_t, true_params['y0']) @@ -227,7 +259,7 @@ def test_Acceleration(): x_t, y_t = mod.model( t=t_arr, fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) np.testing.assert_allclose(x_t, true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ax']) np.testing.assert_allclose(y_t, true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ay']) @@ -252,7 +284,7 @@ def test_Acceleration(): t=t_batch, fit_params=np.array([x0_batch, vx0_batch, ax_batch, y0_batch, vy0_batch, ay_batch]).T, fit_param_errs=np.array([x0_err_batch, vx0_err_batch, ax_err_batch, y0_err_batch, vy0_err_batch, ay_err_batch]).T, - fixed_params=t0_batch + fixed_params_dict={'t0': t0_batch} ) np.testing.assert_allclose(x_t_batch, x0_batch + (t_batch-t0_batch)*vx0_batch + 0.5*(t_batch-t0_batch)**2*ax_batch) np.testing.assert_allclose(y_t_batch, y0_batch + (t_batch-t0_batch)*vy0_batch + 0.5*(t_batch-t0_batch)**2*ay_batch) @@ -267,7 +299,7 @@ def test_Acceleration(): t=t_batch, fit_params=np.array([x0_batch, vx0_batch, ax_batch, y0_batch, vy0_batch, ay_batch]).T, fit_param_errs=np.array([x0_err_batch, vx0_err_batch, ax_err_batch, y0_err_batch, vy0_err_batch, ay_err_batch]).T, - fixed_params=t0_batch + fixed_params_dict={'t0': t0_batch} ) np.testing.assert_allclose(x_t_batch, np.array([x0_batch[i] + (t_batch-t0_batch[i])*vx0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ax_batch[i] for i in range(len(x0_batch))])) np.testing.assert_allclose(y_t_batch, np.array([y0_batch[i] + (t_batch-t0_batch[i])*vy0_batch[i] + 0.5*(t_batch-t0_batch[i])**2*ay_batch[i] for i in range(len(x0_batch))])) @@ -280,7 +312,7 @@ def test_Acceleration(): x_true, y_true = mod.model( t=t, fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params=np.array([true_params[p] for p in fixed_param_list]).T + fixed_params_dict={'t0': true_params['t0']} ) x_true_err = np.sqrt(true_params['x0_err']**2 + ((t - true_params['t0']) * true_params['vx0_err'])**2 + (0.5*(t - true_params['t0'])**2 * true_params['ax_err'])**2) @@ -290,280 +322,65 @@ def test_Acceleration(): y_sim = np.random.normal(y_true, y_true_err) # Run fit mod_fit = motion_model.Acceleration() - params, param_errs, _, _ = mod_fit.fit( + params, param_errs = mod_fit.fit( t=t, x=x_sim, y=y_sim, xe=x_true_err, ye=y_true_err, - t0=true_params['t0'] + fixed_params_dict={'t0': true_params['t0']} ) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) - + #@pytest.mark.skip(reason="not written") def test_Parallax(): # Test handling of a single star true_params = {'x0': 1.0, 'y0':-0.5, 'x0_err':0.1, 'y0_err':0.1, 'vx':-0.2, 'vy':0.5, 'vx_err':0.05, 'vy_err':0.05, - 'pi':0.5, 'RA':17.76, 'Dec':-28.933, 'PA':0, - 't0':2020.0} - mod = motion_model.Parallax(**{'RA':17.76, 'Dec':-28.933, 'PA':0}) + 'pi':0.5, 'ra':17.76, 'dec':-28.933, 'pa':0, + 't0':2020.0, 'obsLocation': 'earth'} + mod = motion_model.Parallax() param_list = mod.fit_param_names fixed_param_list = mod.fixed_param_names - print(param_list) - + # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - [true_params[p] for p in fixed_param_list],t) - x_true_err, y_true_err = np.repeat(0.1,len(t)), np.repeat(0.1,len(t)) + x_true, y_true = mod.model( + t=t, + fit_params=np.array([true_params[p] for p in param_list]).T, + fixed_params_dict={p: true_params[p] for p in fixed_param_list} + ) + x_true_err, y_true_err = np.ones_like(t)*true_params['x0_err'], np.ones_like(t)*true_params['y0_err'] x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, true_params['t0']) + params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, fixed_params_dict={p: true_params[p] for p in fixed_param_list}) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) - def test_Parallax_PA(): # Set PA=0 model x0, y0 = 2.0, -1.0 vx, vy = 0.2, 0.5 ra, dec = 17.76, -28.933 pi = 0.5 - mod_pa0 = motion_model.Parallax(ra=ra, dec=dec, pa=0) + mod_pa0 = motion_model.Parallax() # Set PA=90 model with equivalent parameters in that frame - mod_pa90 = motion_model.Parallax(ra=ra, dec=dec, pa=90) + mod_pa90 = motion_model.Parallax() t_set = np.arange(2018, 2024, 0.01) + t0 = 2020.0 dat_pa0 = mod_pa0.model( t = t_set, fit_params = np.array([x0, vx, y0, vy, pi]).T, - fixed_params = [2020.0] + fixed_params_dict = {'t0': t0, 'ra': ra, 'dec': dec, 'pa': 0} ) dat_pa90 = mod_pa90.model( t = t_set, fit_params = np.array([y0, vy, -x0, -vx, pi]).T, - fixed_params = [2020.0] + fixed_params_dict = {'t0': t0, 'ra': ra, 'dec': dec, 'pa': 90} ) np.testing.assert_allclose(dat_pa0[0], -dat_pa90[1], atol=1e-10) - np.testing.assert_allclose(dat_pa0[1], dat_pa90[0], atol=1e-10) - - -def test_Linear_fit_vs_scipy(): - # Compare Linear fit results to scipy curve_fit results - t = np.array([0, 1., 2.2, 3.5, 5.]) - - x = np.array([ - [0., 0.5, 2.1, 3.2, 6.0], # Increasing 5 Epochs - [10.0, 8.9, 9.2, 7.4, 7.0], # Decreasing 5 Epochs - [2.5, np.nan, 5.2, np.nan, 5.0], # 3 Epochs - [np.nan, 6.2, np.nan, np.nan, 9.2], # 2 Epochs - # [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch - # [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs - ]) - - y = np.array([ - [10.2, 8.5, 9.1, 12.2, 13.0], # Increasing 5 Epochs - [8.0, 9.9, 8.2, 7.4, 7.0], # Decreasing 5 Epochs - [5.2, np.nan, 4.7, np.nan, 6.0], # 3 Epochs - [np.nan, 1.2, np.nan, np.nan, 3.2], # 2 Epochs - # [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch - # [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs - ]) - - xe = np.array([ - [0.2, 0.5, 0.3, 0.4, 0.6], - [0.5, 0.2, 0.7, 0.3, 0.2], - [0.5, np.nan, 0.6, np.nan, 0.3], - [np.nan, 0.6, np.nan, np.nan, 0.3], - # [np.nan, 0.4, np.nan, np.nan, np.nan], - # [np.nan, np.nan, np.nan, np.nan, np.nan] - ]) - - ye = np.array([ - [0.3, 0.2, 0.5, 0.2, 0.4], - [0.2, 0.5, 0.6, 0.4, 0.2], - [0.7, np.nan, 0.5, np.nan, 0.2], - [np.nan, 0.4, np.nan, np.nan, 0.5], - # [np.nan, 0.5, np.nan, np.nan, np.nan], - # [np.nan, np.nan, np.nan, np.nan, np.nan] - ]) - - x = np.ma.masked_invalid(x) - y = np.ma.masked_invalid(y) - xe = np.ma.masked_invalid(xe) - ye = np.ma.masked_invalid(ye) - mask = np.ma.getmaskarray(x) | np.ma.getmaskarray(y) | np.ma.getmaskarray(xe) | np.ma.getmaskarray(ye) - - # tab = StarTable({ - # 'x': x, - # 'y': y, - # 'xe': xe, - # 'ye': ye - # }) - # tab.meta['LIST_TIMES'] = t - # tab.fit_velocities(use_scipy=True, absolute_sigma=True) - - # Plot data - N = x.shape[0] - fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6)) - for i in range(N): - line_mask = ~np.isnan(x[i]) & ~mask[i] - ax1.errorbar(t[line_mask], x[i][line_mask], yerr=xe[i][line_mask], fmt='o-', label=f'Line {i}') - ax2.errorbar(t[line_mask], y[i][line_mask], yerr=ye[i][line_mask], fmt='o-', label=f'Line {i}') - ax1.set_xlabel('Time') - ax1.set_ylabel('Position') - ax1.legend() - ax1.set_title('X vs Time') - ax2.set_xlabel('Time') - ax2.set_ylabel('Position') - ax2.legend() - ax2.set_title('Y vs Time') - plt.show() - - N = len(x) - t0 = np.average(np.broadcast_to(t, x.shape), weights=1./np.hypot(xe, ye), axis=1) - dt = np.zeros_like(x) - - # velfit - # vx_velfit = np.zeros(N) - # vxe_velfit = np.zeros(N) - # vy_velfit = np.zeros(N) - # vye_velfit = np.zeros(N) - # x0_velfit = np.zeros(N) - # x0e_velfit = np.zeros(N) - # y0_velfit = np.zeros(N) - # y0e_velfit = np.zeros(N) - - # scipy - vx_scipy = np.zeros(N) - vxe_scipy = np.zeros(N) - vy_scipy = np.zeros(N) - vye_scipy = np.zeros(N) - x0_scipy = np.zeros(N) - x0e_scipy = np.zeros(N) - y0_scipy = np.zeros(N) - y0e_scipy = np.zeros(N) - - # motion_model - mm = motion_model.Linear() - - vx_mm_scipy = np.zeros(N) - vxe_mm_scipy = np.zeros(N) - vy_mm_scipy = np.zeros(N) - vye_mm_scipy = np.zeros(N) - x0_mm_scipy = np.zeros(N) - x0e_mm_scipy = np.zeros(N) - y0_mm_scipy = np.zeros(N) - y0e_mm_scipy = np.zeros(N) - - vx_mm = np.zeros(N) - vxe_mm = np.zeros(N) - vy_mm = np.zeros(N) - vye_mm = np.zeros(N) - x0_mm = np.zeros(N) - x0e_mm = np.zeros(N) - y0_mm = np.zeros(N) - y0e_mm = np.zeros(N) - - def linear(t, c0, c1): - return c0 + c1*t - - # Absolute sigma - for absolute_sigma in [True, False]: - for i in range(N): - dt[i] = t - t0[i] - - # # velfit.linear_fit - # vx_velfit_results = linear_fit(dt[i][~mask[i]], x[i][~mask[i]], sigma=xe[i][~mask[i]], absolute_sigma=absolute_sigma) - # vy_velfit_results = linear_fit(dt[i][~mask[i]], y[i][~mask[i]], sigma=ye[i][~mask[i]], absolute_sigma=absolute_sigma) - - # vx_velfit[i] = vx_velfit_results['slope'] - # vxe_velfit[i] = vx_velfit_results['e_slope'] - # vy_velfit[i] = vy_velfit_results['slope'] - # vye_velfit[i] = vy_velfit_results['e_slope'] - # x0_velfit[i] = vx_velfit_results['intercept'] - # x0e_velfit[i] = vx_velfit_results['e_intercept'] - # y0_velfit[i] = vy_velfit_results['intercept'] - # y0e_velfit[i] = vy_velfit_results['e_intercept'] - - # scipy.curve_fit - p0x = np.array([0., x[i][~mask[i]].mean()]) - p0y = np.array([0., y[i][~mask[i]].mean()]) - popt_x, pcov_x = curve_fit(linear, dt[i][~mask[i]], x[i][~mask[i]], p0=p0x, sigma=xe[i][~mask[i]], absolute_sigma=absolute_sigma) - vx_scipy[i], vxe_scipy[i] = popt_x[1], np.sqrt(pcov_x[1, 1]) - x0_scipy[i], x0e_scipy[i] = popt_x[0], np.sqrt(pcov_x[0, 0]) - popt_y, pcov_y = curve_fit(linear, dt[i][~mask[i]], y[i][~mask[i]], p0=p0y, sigma=ye[i][~mask[i]], absolute_sigma=absolute_sigma) - vy_scipy[i], vye_scipy[i] = popt_y[1], np.sqrt(pcov_y[1, 1]) - y0_scipy[i], y0e_scipy[i] = popt_y[0], np.sqrt(pcov_y[0, 0]) - - # motion_model without scipy - params, param_errs = mm.fit( - t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], - xe[i][~mask[i]], ye[i][~mask[i]], t0[i], - weighting='var', - use_scipy=False, - absolute_sigma=absolute_sigma - ) - vx_mm[i] = params[mm.fit_param_names.index('vx')] - vy_mm[i] = params[mm.fit_param_names.index('vy')] - vxe_mm[i] = param_errs[mm.fit_param_names.index('vx')] - vye_mm[i] = param_errs[mm.fit_param_names.index('vy')] - x0_mm[i] = params[mm.fit_param_names.index('x0')] - y0_mm[i] = params[mm.fit_param_names.index('y0')] - x0e_mm[i] = param_errs[mm.fit_param_names.index('x0')] - y0e_mm[i] = param_errs[mm.fit_param_names.index('y0')] - - # motion_model with scipy - params, param_errs = mm.fit( - t[~mask[i]], x[i][~mask[i]], y[i][~mask[i]], - xe[i][~mask[i]], ye[i][~mask[i]], t0[i], - weighting='var', - use_scipy=True, - absolute_sigma=absolute_sigma - ) - vx_mm_scipy[i] = params[mm.fit_param_names.index('vx')] - vy_mm_scipy[i] = params[mm.fit_param_names.index('vy')] - vxe_mm_scipy[i] = param_errs[mm.fit_param_names.index('vx')] - vye_mm_scipy[i] = param_errs[mm.fit_param_names.index('vy')] - x0_mm_scipy[i] = params[mm.fit_param_names.index('x0')] - y0_mm_scipy[i] = params[mm.fit_param_names.index('y0')] - x0e_mm_scipy[i] = param_errs[mm.fit_param_names.index('x0')] - y0e_mm_scipy[i] = param_errs[mm.fit_param_names.index('y0')] - - rtol = 1e-5 - # np.testing.assert_allclose(vx_velfit, vx_scipy, rtol=rtol) - # np.testing.assert_allclose(vxe_velfit, vxe_scipy, rtol=rtol) - # np.testing.assert_allclose(vy_velfit, vy_scipy, rtol=rtol) - # np.testing.assert_allclose(vye_velfit, vye_scipy, rtol=rtol) - # np.testing.assert_allclose(x0_velfit, x0_scipy, rtol=rtol) - # np.testing.assert_allclose(x0e_velfit, x0e_scipy, rtol=rtol) - # np.testing.assert_allclose(y0_velfit, y0_scipy, rtol=rtol) - # np.testing.assert_allclose(y0e_velfit, y0e_scipy, rtol=rtol) - # np.testing.assert_allclose(vx_velfit, vx_mm, rtol=rtol) - # np.testing.assert_allclose(vxe_velfit, vxe_mm, rtol=rtol) - # np.testing.assert_allclose(vy_velfit, vy_mm, rtol=rtol) - # np.testing.assert_allclose(vye_velfit, vye_mm, rtol=rtol) - # np.testing.assert_allclose(x0_velfit, x0_mm, rtol=rtol) - # np.testing.assert_allclose(x0e_velfit, x0e_mm, rtol=rtol) - # np.testing.assert_allclose(y0_velfit, y0_mm, rtol=rtol) - # np.testing.assert_allclose(y0e_velfit, y0e_mm, rtol=rtol) - np.testing.assert_allclose(vx_scipy, vx_mm, rtol=rtol) - np.testing.assert_allclose(vxe_scipy, vxe_mm, rtol=rtol) - np.testing.assert_allclose(vy_scipy, vy_mm, rtol=rtol) - np.testing.assert_allclose(vye_scipy, vye_mm, rtol=rtol) - np.testing.assert_allclose(x0_scipy, x0_mm, rtol=rtol) - np.testing.assert_allclose(x0e_scipy, x0e_mm, rtol=rtol) - np.testing.assert_allclose(y0_scipy, y0_mm, rtol=rtol) - np.testing.assert_allclose(y0e_scipy, y0e_mm, rtol=rtol) - np.testing.assert_allclose(vx_scipy, vx_mm_scipy, rtol=rtol) - np.testing.assert_allclose(vxe_scipy, vxe_mm_scipy, rtol=rtol) - np.testing.assert_allclose(vy_scipy, vy_mm_scipy, rtol=rtol) - np.testing.assert_allclose(vye_scipy, vye_mm_scipy, rtol=rtol) - np.testing.assert_allclose(x0_scipy, x0_mm_scipy, rtol=rtol) - np.testing.assert_allclose(x0e_scipy, x0e_mm_scipy, rtol=rtol) - np.testing.assert_allclose(y0_scipy, y0_mm_scipy, rtol=rtol) - np.testing.assert_allclose(y0e_scipy, y0e_mm_scipy, rtol=rtol) + np.testing.assert_allclose(dat_pa0[1], dat_pa90[0], atol=1e-10) \ No newline at end of file diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 1b8e5cb..804d4e7 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -41,9 +41,14 @@ def test_StarTable_init1(): starlist_names = np.array(['file1', 'file2', 'file3', 'file4', 'file5', 'file6', 'file7', 'file8']) # Generate the startable - startable = StarTable(name=name_in, x=x_in, y=y_in, m=m_in, xe=xe_in, ye=ye_in, me=me_in, - ref_list=1, - list_times=starlist_times, list_names=starlist_names) + startable = StarTable( + name=name_in, + x=x_in, y=y_in, m=m_in, + xe=xe_in, ye=ye_in, me=me_in, + ref_list=1, + list_times=starlist_times, + list_names=starlist_names + ) # Now put in some assertions to make sure all our startable columns # have the right dimensions. @@ -57,7 +62,7 @@ def test_StarTable_init1(): assert len(startable['name']) == N_stars assert startable.meta['list_times'][0] == starlist_times[0] assert type(startable) == StarTable - + return def test_StarTable_init2(): @@ -102,7 +107,7 @@ def test_combine_lists(): t.combine_lists('x', mask_val=-100000) assert t['x0'][0] == x_avg_0 assert t['x0'][-1] == pytest.approx(2108.855, 0.001) - + # Test 4: weighted average of x. x_wgt_0 = 1.0 / t['xe'][0, :]**2 x_avg_0 = np.average(t['x'][0, :], weights=x_wgt_0) @@ -204,8 +209,12 @@ def test_add_starlist(): assert t.meta['n_lists'] == 9 # Test 2: Add as starlist rather than with keywords. - starlist = StarList(name=t_orig['name'], x=x_new, y=y_new, m=m_new, - xe=xe_new, ye=ye_new, me=me_new, list_time=2001.0, list_name='A.lis') + starlist = StarList( + name=t_orig['name'], + x=x_new, y=y_new, m=m_new, + xe=xe_new, ye=ye_new, me=me_new, + list_time=2001.0, list_name='A.lis' + ) t = make_star_table() t.add_starlist(starlist=starlist) @@ -257,7 +266,7 @@ def test_get_starlist(): assert t['x'][0,2] == t_list['x'][0] assert type(t_list) == StarList assert len(t_list['x'].shape) == 1 - + return @@ -305,7 +314,7 @@ def test_fit_velocities(): tab = table.vstack((tab1, tab2, tab3)) tab.meta = tab1.meta - tab.fit_motion_model(verbose=True) + tab.fit_motion_model(verbose=True, mask_value=-100000.) # Test creation of new variables assert len(tab['vx']) == len(tab) @@ -323,18 +332,11 @@ def test_fit_velocities(): assert (tab['n_fit'][idx] == 2).all() # Test that the velocity errors were calculated. - assert (tab['vx_err'][0:100] > 0).all() - assert (tab['x0_err'][0:100] > 0).all() - assert (tab['vy_err'][0:100] > 0).all() - assert (tab['y0_err'][0:100] > 0).all() - assert np.isfinite(tab['x0']).all() - assert np.isfinite(tab['vx']).all() - assert np.isfinite(tab['y0']).all() - assert np.isfinite(tab['vy']).all() - assert np.isfinite(tab['x0_err']).all() - assert np.isfinite(tab['vx_err']).all() - assert np.isfinite(tab['y0_err']).all() - assert np.isfinite(tab['vy_err']).all() + assert (~(tab['vx_err'][0:100] < 0)).all() + assert (~(tab['x0_err'][0:100] < 0)).all() + assert (~(tab['vy_err'][0:100] < 0)).all() + assert (~(tab['y0_err'][0:100] < 0)).all() + ########## # Test running a second time. We should get the same results. @@ -343,28 +345,27 @@ def test_fit_velocities(): x0_orig = tab['x0'] vxe_orig = tab['vx_err'] x0e_orig = tab['x0_err'] - tab.fit_velocities(verbose=False) - - assert (vx_orig == tab['vx']).all() - assert (x0_orig == tab['x0']).all() - assert (vxe_orig == tab['vx_err']).all() - assert (x0e_orig == tab['x0_err']).all() + tab.fit_motion_model(verbose=False, mask_value=-100000.) + + np.testing.assert_allclose(tab['vx'], vx_orig) + np.testing.assert_allclose(tab['x0'], x0_orig) + np.testing.assert_allclose(tab['vx_err'], vxe_orig) + np.testing.assert_allclose(tab['x0_err'], x0e_orig) ########## # Test fixed_t0 functionality ########## fixed_t0 = tab['t0'] + np.random.normal(size=len(tab)) - tab.fit_velocities(fixed_t0=fixed_t0) - - assert(np.sum(abs(tab['t0'] - fixed_t0)) == 0) + tab.fit_motion_model(verbose=False, mask_value=-100000., fixed_params_dict={'t0': fixed_t0}) + np.testing.assert_allclose(tab['t0'], fixed_t0) ########## # Test bootstrap ########## tab_b = table.vstack((tab1, tab2, tab3)) tab_b.meta = tab1.meta - tab_b.fit_velocities(verbose=True, bootstrap=50) - + tab_b.fit_motion_model(verbose=True, bootstrap=50) + assert tab_b.meta['n_bootstrap'] == 50 assert tab_b['x0_err'][0] > tab['x0_err'][0] assert tab_b['vx_err'][0] > tab['vx_err'][0] @@ -375,83 +376,36 @@ def test_fit_velocities(): # Test what happens with no velocity errors ########## tab.remove_columns(['xe', 'ye', 'x0', 'y0', 'x0_err', 'y0_err', 'vx', 'vy', 'vx_err', 'vy_err', 'n_fit']) - tab.fit_velocities(verbose=False) + tab.fit_motion_model(verbose=False) assert len(tab['vx']) == len(tab) assert len(tab['vy']) == len(tab) assert len(tab['vx_err']) == len(tab) assert len(tab['vy_err']) == len(tab) assert len(tab['n_fit']) == len(tab) - assert (tab['vx_err'][0:100] > 0).all() - assert (tab['x0_err'][0:100] > 0).all() - assert (tab['vy_err'][0:100] > 0).all() - assert (tab['y0_err'][0:100] > 0).all() + assert (~(tab['vx_err'][0:100] < 0)).all() + assert (~(tab['x0_err'][0:100] < 0)).all() + assert (~(tab['vy_err'][0:100] < 0)).all() + assert (~(tab['y0_err'][0:100] < 0)).all() ######### # Test mask_list ######### # Test 5a: Masked print("Testing Masked List") - tt.fit_velocities(bootstrap=0, verbose=False, mask_lists=[1]) - assert np.arange(2.25, 48, 5) == pytest.approx(tt['x0'].data) - assert np.arange(2.25, 48, 5) == pytest.approx(tt['y0'].data) - assert np.full(10, 0.05) == pytest.approx(tt['x0_err'].data) - assert np.full(10, 0.05) == pytest.approx(tt['y0_err'].data) - assert np.ones(10) == pytest.approx(tt['vx'].data) - assert np.ones(10) == pytest.approx(tt['vy'].data) - assert np.full(10, 0.03380617) == pytest.approx(tt['vx_err'].data) - assert np.full(10, 0.03380617) == pytest.approx(tt['vy_err'].data) - assert 2017.25 * np.ones(10) == pytest.approx(tt['t0'].data) - - # Test 5b: Things that should break the code. - with pytest.raises(RuntimeError): - tt.fit_velocities(bootstrap=0, verbose=False, mask_lists=np.arange(2)) - with pytest.raises(RuntimeError): - tt.fit_velocities(bootstrap=0, verbose=False, mask_lists=True) + tt.fit_motion_model(verbose=False, mask_lists=[1]) + np.testing.assert_allclose(np.arange(2.25, 48, 5), tt['x0'].data) + np.testing.assert_allclose(np.arange(2.25, 48, 5), tt['y0'].data) + np.testing.assert_allclose(np.full(10, 0.05), tt['x0_err'].data) + np.testing.assert_allclose(np.full(10, 0.05), tt['y0_err'].data) + np.testing.assert_allclose(np.ones(10), tt['vx'].data) + np.testing.assert_allclose(np.ones(10), tt['vy'].data) + np.testing.assert_allclose(np.full(10, 0.03380617), tt['vx_err'].data) + np.testing.assert_allclose(np.full(10, 0.03380617), tt['vy_err'].data) + np.testing.assert_allclose(2017.25 * np.ones(10), tt['t0'].data) return -def test_fit_velocities_1epoch(): - ########## - # Test: only 1 epoch - ########## - tab = make_star_table_1epoch() - - # We don't need the entire table... lets just - # pull a small subset for faster testing. - tab1 = tab[0:100] - tab2 = tab[10000:10100] - tab3 = tab[-100:] - tab_1 = table.vstack((tab1, tab2, tab3)) - tab_1.meta = tab1.meta - - tab_1.fit_velocities(verbose=False) - - assert 'n_fit' in tab_1.colnames - assert 't0' in tab_1.colnames - assert 'x0' in tab_1.colnames - assert 'y0' in tab_1.colnames - assert 'vx' in tab_1.colnames - assert 'vy' in tab_1.colnames - assert 'x0_err' in tab_1.colnames - assert 'y0_err' in tab_1.colnames - assert 'vx_err' in tab_1.colnames - assert 'vy_err' in tab_1.colnames - - assert (tab_1['x0'] == tab_1['x'][:,0]).all() - assert (tab_1['y0'] == tab_1['y'][:,0]).all() - assert (tab_1['x0_err'] == tab_1['xe'][:,0]).all() - assert (tab_1['y0_err'] == tab_1['ye'][:,0]).all() - - assert(np.isnan(tab_1['vx'])).all() - assert(np.isnan(tab_1['vy'])).all() - assert(np.isnan(tab_1['vx_err'])).all() - assert(np.isnan(tab_1['vy_err'])).all() - - assert(tab_1['t0'] == 2001.0).all() - assert(tab_1['n_fit'] == 1).all() - - return def test_fit_velocities_2epoch(): @@ -468,7 +422,7 @@ def test_fit_velocities_2epoch(): tab_2 = table.vstack((tab1, tab2, tab3)) tab_2.meta=tab1.meta - tab_2.fit_velocities(verbose=False) + tab_2.fit_motion_model(verbose=False, mask_value=-100000.) assert 'n_fit' in tab_2.colnames assert 't0' in tab_2.colnames @@ -496,40 +450,6 @@ def test_fit_velocities_2epoch(): return -def test_fit_velocities_all_detected(): - """ - Test the fit_velocities function when all stars are detected in all epochs. - """ - tab = StarTable.read(test_dir + '/test_all_detected.fits') - tab_orig = tab.copy() - # tab = tab[:1] - - epochs = ['2005_F814W', '2010_F160W', '2013_F160W', '2015_F160W'] - epoch_cols = [['_'.join(_.split('_')[:2]) for _ in tab.meta['EPNAMES']].index(epoch) for epoch in epochs] - - mm = motion_model.Linear() - tab.fit_velocities_all_detected( - weighting='var', - use_scipy=False, absolute_sigma=False, - motion_model_to_fit=mm, - epoch_cols=epoch_cols, - art_star=True - ) - - # Check that the output table has the expected columns - for col in ['n_fit', 't0', 'x0', 'y0', 'vx', 'vy', 'x0_err', 'y0_err', 'vx_err', 'vy_err']: - assert col in tab.colnames - - # Check that the fitted values match the original values - np.testing.assert_almost_equal(tab['x0'], tab_orig['x0']) - np.testing.assert_almost_equal(tab['y0'], tab_orig['y0']) - np.testing.assert_almost_equal(tab['t0'], tab_orig['t0']) - np.testing.assert_almost_equal(tab['vx'], tab_orig['vx']) - np.testing.assert_almost_equal(tab['vy'], tab_orig['vy']) - np.testing.assert_almost_equal(tab['vxe'], tab_orig['vxe']) - np.testing.assert_almost_equal(tab['vye'], tab_orig['vye']) - - return def make_star_table(): # User input @@ -561,8 +481,8 @@ def make_star_table(): n=n_in, ref_list=1 ) - startable.meta['LIST_TIMES'] = starlist_times - startable.meta['LIST_NAMES'] = starlist_names + startable.meta['list_times'] = starlist_times + startable.meta['list_names'] = starlist_names return startable From f932e230684738777337c778e1d8ce0643911a7e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Wed, 10 Dec 2025 00:33:26 -0800 Subject: [PATCH 19/29] Add Parallax test plot --- flystar/motion_model.py | 25 ++++---------- flystar/tests/test_motion_model.py | 52 +++++++++++++++++------------- 2 files changed, 37 insertions(+), 40 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 5ccb6ee..42a5e54 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -135,21 +135,10 @@ def fit( rng = np.random.default_rng(seed) edx = np.arange(n_obs, dtype=int) # Precompute All Bootstrap Draws at Once - bdx_all = rng.choice(edx, size=(bootstrap, m), replace=True) - - # Count unique indices per bootstrap sample - uniq_counts = np.apply_along_axis(lambda x: len(np.unique(x)), 1, bdx_all) - - # Identify invalid samples - bad = uniq_counts < self.n_params - n_bad = bad.sum() - - while n_bad > 0: - # Resample only bad rows - bdx_all[bad] = rng.choice(edx, size=(n_bad, m), replace=True) - uniq_counts = np.apply_along_axis(lambda x: len(np.unique(x)), 1, bdx_all) - bad = uniq_counts < self.n_params - n_bad = bad.sum() + # Ensure there are enough unique points in each bootstrap sample + bdx_unique = rng.choice(edx, size=(bootstrap, self.n_params), replace=False) + bdx_extra = rng.choice(edx, size=(bootstrap, m - self.n_params), replace=True) + bdx_all = np.hstack((bdx_unique, bdx_extra)) bb_params = [] bb_params_errs = [] @@ -936,9 +925,9 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) t_mjd = Time(t, format='decimalyear', scale='utc').mjd # Shape (N_times,) self.pvec = self.calc_parallax_vector(t_mjd, ra, dec, pa=pa, obsLocation=obsLocation) # Shape (2, N_times) - xy = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) - x = xy[:, :N_times] # Shape (N_stars, N_times) - y = xy[:, N_times:] # Shape (N_stars, N_times) + x, y = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) + # x = xy[:, :N_times] # Shape (N_stars, N_times) + # y = xy[:, N_times:] # Shape (N_stars, N_times) if N_stars == 1 or N_times == 1: # If only one star, return flattened arrays diff --git a/flystar/tests/test_motion_model.py b/flystar/tests/test_motion_model.py index 0215dbe..b3bb4e8 100755 --- a/flystar/tests/test_motion_model.py +++ b/flystar/tests/test_motion_model.py @@ -11,19 +11,13 @@ def test_Fixed(): true_params = {'x0': 1.0, 'y0':0.5, 'x0_err':0.1, 'y0_err':0.1} mod = motion_model.Fixed() param_list = mod.fit_param_names - fixed_param_list = mod.fixed_param_names # Confirm return of proper values for single t and array t - # x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - # [true_params[p] for p in fixed_param_list], 0.0) x_t, y_t = mod.model( 0.0, fit_params=np.array([true_params['x0'], true_params['y0']]).T ) assert x_t==true_params['x0'] assert y_t==true_params['y0'] - # x_t, y_t = mod.get_pos_at_time([true_params[p] for p in param_list], - # [true_params[p] for p in fixed_param_list], - # [0.0,2025.0,10000]) x_t, y_t = mod.model( [0.0,2025.0,10000], fit_params=np.array([true_params['x0'], true_params['y0']]).T @@ -31,15 +25,13 @@ def test_Fixed(): assert (x_t==true_params['x0']).all() assert (y_t==true_params['y0']).all() - # Check behavior of get_batch_pos_at_time + # Check behavior of model x0_batch = np.random.uniform(-2.0,2.0, 50) y0_batch = np.random.uniform(-2.0,2.0, 50) x0_err_batch = np.repeat(0.1, 50) y0_err_batch = np.repeat(0.1, 50) # Single epoch t_batch=2020.0 - # x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - # x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( t_batch, fit_params=np.array([x0_batch, y0_batch]).T, @@ -51,8 +43,6 @@ def test_Fixed(): assert (y_err_t_batch==y0_err_batch).all() # Multiple times t_batch = np.arange(2015.0,2025.0, 0.5) - # x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.get_batch_pos_at_time(t_batch, - # x0=x0_batch, y0=y0_batch, x0_err=x0_err_batch, y0_err=y0_err_batch) x_t_batch, y_t_batch, x_err_t_batch, y_err_t_batch = mod.model( t_batch, fit_params=np.array([x0_batch, y0_batch]).T, @@ -66,8 +56,6 @@ def test_Fixed(): # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - # x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - # [true_params[p] for p in fixed_param_list], t) x_true, y_true = mod.model( t, fit_params=np.array([true_params['x0'], true_params['y0']]) @@ -125,7 +113,7 @@ def test_Linear(): assert (x_t==(true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx'])).all() assert (y_t==(true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy'])).all() - # Check behavior of get_batch_pos_at_time + # Check behavior of model x0_batch = np.random.uniform(-2.0,2.0, 50) y0_batch = np.random.uniform(-2.0,2.0, 50) vx_batch = np.random.uniform(-2.0,2.0, 50) @@ -166,8 +154,6 @@ def test_Linear(): # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter - # x_true, y_true = mod.get_pos_at_time([true_params[p] for p in param_list], - # [true_params[p] for p in fixed_param_list],t) x_true, y_true = mod.model( t=t, fit_params=np.array([true_params[p] for p in param_list]).T, @@ -234,7 +220,6 @@ def linear(t, x0, vx): y_sim = np.random.normal(y_true, y_true_err) # Run fit params, param_errs = mod.fit(t, x_sim, y_sim, x_true_err, y_true_err, fixed_params_dict={'t0': true_params['t0']}, bootstrap=10) - print(param_errs) # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) @@ -264,7 +249,7 @@ def test_Acceleration(): np.testing.assert_allclose(x_t, true_params['x0'] + (t_arr-true_params['t0'])*true_params['vx0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ax']) np.testing.assert_allclose(y_t, true_params['y0'] + (t_arr-true_params['t0'])*true_params['vy0'] + 0.5*(t_arr-true_params['t0'])**2*true_params['ay']) - # Check behavior of get_batch_pos_at_time + # Check behavior of model x0_batch = np.random.uniform(-2.0,2.0, 50) y0_batch = np.random.uniform(-2.0,2.0, 50) vx0_batch = np.random.uniform(-2.0,2.0, 50) @@ -342,21 +327,44 @@ def test_Parallax(): 't0':2020.0, 'obsLocation': 'earth'} mod = motion_model.Parallax() param_list = mod.fit_param_names - fixed_param_list = mod.fixed_param_names - + fixed_params_dict = { + 't0': true_params['t0'], + 'ra': true_params['ra'], + 'dec': true_params['dec'], + 'pa': true_params['pa'], + 'obsLocation': true_params['obsLocation'] + } + # Test fitter t = np.arange(2015.0,2025.0, 0.5) # Get values from model and add scatter x_true, y_true = mod.model( t=t, fit_params=np.array([true_params[p] for p in param_list]).T, - fixed_params_dict={p: true_params[p] for p in fixed_param_list} + fixed_params_dict=fixed_params_dict ) x_true_err, y_true_err = np.ones_like(t)*true_params['x0_err'], np.ones_like(t)*true_params['y0_err'] x_sim = np.random.normal(x_true, x_true_err) y_sim = np.random.normal(y_true, y_true_err) # Run fit - params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, fixed_params_dict={p: true_params[p] for p in fixed_param_list}) + params, param_errs = mod.fit(t, x_sim,y_sim, x_true_err, y_true_err, fixed_params_dict=fixed_params_dict) + + x_model, y_model = mod.model( + t=t, + fit_params=params, + fixed_params_dict=fixed_params_dict + ) + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5)) + ax1.plot(t, x_true, 'k-', label='True x') + ax1.errorbar(t, x_sim, yerr=x_true_err, fmt='ro', label='Sim x') + ax1.plot(t, x_model, 'r-', label='Model x') + ax1.set_xlabel('t') + ax1.set_ylabel('x') + ax1.legend() + ax2.plot(t, y_true, 'k-', label='True x') + ax2.errorbar(t, y_sim, yerr=x_true_err, fmt='ro', label='Sim x') + ax2.plot(t, y_model, 'r-', label='Model x') + ax2.set_xlabel('t') # Confirm true value is within error bar of fit value assert np.all([within_error(true_params[param_list[i]], params[i], param_errs[i]) for i in range(len(params))]) From be254926a2116bfa4aa8ba1336929309ce38eed8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Mon, 15 Dec 2025 06:46:35 -0800 Subject: [PATCH 20/29] Partial Update of align and test_align --- flystar/align.py | 264 ++++++++++++++++++++---------------- flystar/tests/test_align.py | 79 +++++------ 2 files changed, 185 insertions(+), 158 deletions(-) diff --git a/flystar/align.py b/flystar/align.py index 8215246..ca9bc93 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -1,10 +1,10 @@ import numpy as np -from flystar import match -from flystar import transforms -from flystar import plots -from flystar.starlists import StarList -from flystar.startables import StarTable -from flystar import motion_model +from . import match +from . import transforms +from . import plots +from .starlists import StarList +from .startables import StarTable +from . import motion_model from astropy.table import Table, Column, vstack import datetime import copy @@ -21,12 +21,12 @@ def __init__(self, list_of_starlists, ref_index=0, iters=2, outlier_tol=[None, None], trans_args=[{'order': 2}, {'order': 2}], init_order=1, - mag_trans=True, mag_lim=None, trans_weights=None, vel_weights='var', + mag_trans=True, mag_lim=None, trans_weighting=None, vel_weighting='var', trans_input=None, trans_class=transforms.PolyTransform, calc_trans_inverse=False, init_guess_mode='miracle', iter_callback=None, - default_motion_model='Fixed', - motion_model_dict = {}, + motion_models=['Empty', 'Fixed'], + fixed_params_dict = None, use_scipy=True, absolute_sigma=False, save_path=None, @@ -89,13 +89,13 @@ def __init__(self, list_of_starlists, ref_index=0, iters=2, separately for each list and each iteration, you need to pass in a 2D array that has shape (N_lists, 2). - trans_weights : str + trans_weighting : str Either None (def), 'both,var', 'list,var', or 'ref,var' depending on whether you want to weight by the positional uncertainties (variances) in the individual starlists, or also with the uncertainties in the reference frame itself. Note weighting only works when there are positional uncertainties availabe. Other options include 'both,std', 'list,std', 'list,var'. - vel_weights : str + vel_weighting : str Either 'var' (def) or 'std', depending on whether you want to weight the motion model fits by the variance or standard deviation of the position data @@ -130,11 +130,11 @@ def = None. If not None, then this should contain an array or list of transform A function to call (that accepts a StarTable object and an iteration number) at the end of every iteration. This can be used for plotting or printing state. - default_motion_model : string - Name of motion model to use for new or unassigned stars + motion_models : list of MotionModel or str, optional + Motion models or their names to use for new or unassigned stars - motion_model_dict : None or dict - Dict of motion model name keys (strings) and corresponding MotionModel object values + fixed_params_dict : None or dict + Dictionary of motion model fixed parameters use_scipy : bool, optional If True, use scipy.optimize.curve_fit for velocity fitting. If False, use linear @@ -192,20 +192,34 @@ def = None. If not None, then this should contain an array or list of transform self.init_order = init_order self.mag_trans = mag_trans self.mag_lim = mag_lim - self.trans_weights = trans_weights - self.vel_weights = vel_weights + self.trans_weighting = trans_weighting + self.vel_weighting = vel_weighting self.trans_input = trans_input self.trans_class = trans_class self.calc_trans_inverse = calc_trans_inverse - self.motion_model_dict = motion_model_dict self.use_scipy = use_scipy self.absolute_sigma = absolute_sigma - self.default_motion_model = default_motion_model + self.fixed_params_dict = fixed_params_dict self.init_guess_mode = init_guess_mode self.iter_callback = iter_callback self.save_path = save_path self.verbose = verbose + all_mm_map = motion_model.motion_model_map() + if all(isinstance(mm, str) for mm in motion_models): + mm_names = motion_models + motion_models = [all_mm_map[mm] for mm in motion_models] + else: + mm_names = [mm.name for mm in motion_models] + if 'Empty' not in mm_names: + motion_models.append(all_mm_map['Empty']) + if 'Fixed' not in mm_names: + motion_models.append(all_mm_map['Fixed']) + + # Sort by increasing n_params + motion_models = sorted(motion_models, key=lambda mm: mm.n_params) + self.motion_models = motion_models + # For backwards compatibility. if self.verbose is True: self.verbose = 9 @@ -235,8 +249,8 @@ def = None. If not None, then this should contain an array or list of transform self.setup_trans_info() # Make sure the motion models are ready - self.motion_model_dict = motion_model.validate_motion_model_dict(self.motion_model_dict, - StarTable(), self.default_motion_model) + # self.motion_model_dict = motion_model.validate_motion_model_dict(self.motion_model_dict, + # StarTable(), self.default_motion_model) return @@ -397,6 +411,7 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar print(" **********") star_list = self.star_lists[ii] + pdb.set_trance() ref_list = self.get_ref_list_from_table(star_list['t'][0]) trans = self.trans_list[ii] @@ -413,11 +428,15 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar # Only use "use_in_trans" reference stars, even for initial guessing. keepers = np.where(ref_list['use_in_trans'] == True)[0] - trans = trans_initial_guess(ref_list[keepers], star_list_orig_trim, self.trans_args[0], self.motion_model_dict, - mode=self.init_guess_mode, - order=self.init_order, - verbose=self.verbose, - mag_trans=self.mag_trans) + trans = trans_initial_guess( + ref_list[keepers], + star_list_orig_trim, + self.trans_args[0], + mode=self.init_guess_mode, + order=self.init_order, + verbose=self.verbose, + mag_trans=self.mag_trans + ) if self.mag_trans: star_list_T.transform_xym(trans) # trimmed, transformed @@ -700,14 +719,14 @@ def setup_ref_table_from_starlist(self, star_list, motion_model_used=None): for col_name in ref_table.colnames: if len(ref_table[col_name].data.shape) == 2: # Find the 2D columns ref_table._set_invalid_list_values(col_name, -1) - + if 'motion_model_input' not in ref_table.colnames: - ref_table.add_column(Column(np.repeat(self.default_motion_model, len(ref_table)), name='motion_model_input')) - if 'motion_model_used' not in ref_table.colnames: - if motion_model_used is None: - ref_table.add_column(Column(np.repeat(self.default_motion_model, len(ref_table)), name='motion_model_used')) - else: - ref_table.add_column(Column(np.repeat(motion_model_used, len(ref_table)), name='motion_model_used')) + ref_table.add_column(Column(np.repeat(self.motion_models[-1].name, len(ref_table)), name='motion_model_input')) + # if 'motion_model_used' not in ref_table.colnames: + # if motion_model_used is None: + # ref_table.add_column(Column(np.repeat(self.default_motion_model, len(ref_table)), name='motion_model_used')) + # else: + # ref_table.add_column(Column(np.repeat(motion_model_used, len(ref_table)), name='motion_model_used')) return ref_table @@ -807,35 +826,34 @@ def update_ref_table_from_list(self, star_list, star_list_T, ii, idx_ref, idx_li if ((self.ref_table['x'].shape[1] != len(self.star_lists)) and (ii != self.ref_index) and (ii >= self.ref_table['x'].shape[1])): - + self.ref_table.add_starlist() - + copy_over_values(self.ref_table, star_list, star_list_T, ii, idx_ref, idx_lis) self.ref_table['used_in_trans'][idx_ref_in_trans, ii] = True ### Add the unmatched stars and grow the size of the reference table. - self.ref_table, idx_lis_new, idx_ref_new = add_rows_for_new_stars(self.ref_table, star_list, idx_lis, - default_motion_model=self.default_motion_model) + self.ref_table, idx_lis_new, idx_ref_new = add_rows_for_new_stars(self.ref_table, star_list, idx_lis) if len(idx_ref_new) > 0: if self.verbose > 0: print(' Adding {0:d} new stars to the reference table.'.format(len(idx_ref_new))) - + copy_over_values(self.ref_table, star_list, star_list_T, ii, idx_ref_new, idx_lis_new) # Copy the single-epoch values to the aggregate (only for new stars). self.ref_table['x0'][idx_ref_new] = star_list_T['x'][idx_lis_new] self.ref_table['y0'][idx_ref_new] = star_list_T['y'][idx_lis_new] self.ref_table['m0'][idx_ref_new] = star_list_T['m'][idx_lis_new] - + self.ref_table['name'] = update_old_and_new_names(self.ref_table, ii, idx_ref_new) if self.use_ref_new == True: self.ref_table['use_in_trans'][idx_ref_new] = True else: self.ref_table['use_in_trans'][idx_ref_new] = False - + return - + def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): """ Average positions or fit velocities. @@ -852,7 +870,9 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): vals_orig = {} vals_orig['m0'] = self.ref_table['m0'][keep_orig] vals_orig['m0_err'] = self.ref_table['m0_err'][keep_orig] - motion_model_class_names = self.ref_table['motion_model_input'].tolist() + motion_model_class_names = [] + if 'motion_model_input' in self.ref_table.keys(): + motion_model_class_names += self.ref_table['motion_model_input'].tolist() if 'motion_model_used' in self.ref_table.keys(): motion_model_class_names += self.ref_table['motion_model_used'][keep_orig].tolist() vals_orig['motion_model_used'] = self.ref_table['motion_model_used'][keep_orig] @@ -863,24 +883,23 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): fit_star_idxs = [idx for idx in range(len(self.ref_table)) if idx not in keep_orig] else: fit_star_idxs = None - #pdb.set_trace() + # Figure out whether motion fits are necessary - all_fixed = np.all(self.ref_table['motion_model_input']=='Fixed') - if all_fixed: + if ('motion_model_input' in self.ref_table.keys()) and np.all(self.ref_table['motion_model_input']=='Fixed'): weighted_xy = ('xe' in self.ref_table.colnames) and ('ye' in self.ref_table.colnames) weighted_m = ('me' in self.ref_table.colnames) self.ref_table.combine_lists_xym(weighted_xy=weighted_xy, weighted_m=weighted_m) else: # Combine positions with a velocity fit. - self.ref_table.fit_velocities(bootstrap=n_boot, - verbose=self.verbose, - show_progress=(self.verbose>0), - default_motion_model=self.default_motion_model, - select_stars=fit_star_idxs, - motion_model_dict=self.motion_model_dict, - weighting=self.vel_weights, - use_scipy=self.use_scipy, - absolute_sigma=self.absolute_sigma) + self.ref_table.fit_motion_model( + motion_models=self.motion_models, + fixed_params_dict=self.fixed_params_dict, + weighting=self.vel_weighting, + use_scipy=self.use_scipy, + absolute_sigma=self.absolute_sigma, + bootstrap=n_boot, + verbose=self.verbose + ) # Combine (transformed) magnitudes if 'me' in self.ref_table.colnames: @@ -910,18 +929,18 @@ def get_weights_for_lists(self, ref_list, star_list): var_xlis = 0.0 var_ylis = 0.0 - if self.trans_weights != None: - if self.trans_weights == 'both,var': + if self.trans_weighting != None: + if self.trans_weighting == 'both,var': weight = 1.0 / (var_xref + var_xlis + var_yref + var_ylis) - if self.trans_weights == 'both,std': + if self.trans_weighting == 'both,std': weight = 1.0 / np.sqrt(var_xref + var_xlis + var_yref + var_ylis) - if self.trans_weights == 'ref,var': + if self.trans_weighting == 'ref,var': weight = 1.0 / (var_xref + var_yref) - if self.trans_weights == 'ref,std': + if self.trans_weighting == 'ref,std': weight = 1.0 / np.sqrt(var_xref + var_yref) - if self.trans_weights == 'list,var': + if self.trans_weighting == 'list,var': weight = 1.0 / (var_xlis + var_ylis) - if self.trans_weights == 'list,std': + if self.trans_weighting == 'list,std': weight = 1.0 / np.sqrt(var_xlis, var_ylis) else: weight = None @@ -963,7 +982,7 @@ def match_lists(self, dr_tol, dm_tol): else: star_list_T.transform_xy(self.trans_list[ii]) - xref, yref = get_pos_at_time(star_list_T['t'][0], self.ref_table, self.motion_model_dict) + xref, yref = infer_positions(star_list_T['t'][0], self.ref_table) mref = self.ref_table['m0'] idx_lis, idx_ref, dr, dm = match.match(star_list_T['x'], star_list_T['y'], star_list_T['m'], @@ -997,7 +1016,8 @@ def get_ref_list_from_table(self, epoch): name = self.ref_table['name'] if ('motion_model_used' in self.ref_table.colnames): - x,y,xe,ye = self.ref_table.get_star_positions_at_time(epoch, self.motion_model_dict, allow_alt_models=True) + print(f'{epoch=}, {epoch.shape=}') + x, y, xe, ye = self.ref_table.infer_positions(epoch) else: # No velocities... just used average positions. x = self.ref_table['x0'] @@ -1144,20 +1164,24 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot m2_boot_sum = np.zeros((len(ref_table['x']), n_epochs)) # Set up motion model parameters - motion_model_list = ['Fixed', self.default_motion_model] if 'motion_model_used' in ref_table.keys(): - motion_model_list += ref_table['motion_model_used'].tolist() + motion_model_list = np.unique(ref_table['motion_model_used']).tolist() elif 'motion_model_input' in ref_table.keys(): - motion_model_list += ref_table['motion_model_input'].tolist() - motion_col_list = motion_model.get_list_motion_model_param_names(np.unique(motion_model_list).tolist(), with_errors=False, with_fixed=False) + motion_model_list = np.unique(ref_table['motion_model_input']).tolist() + + all_mm_map = motion_model.motion_model_map() + motion_model_list = [all_mm_map[mm_name] for mm_name in motion_model_list] + + motion_col_list = motion_model.get_list_motion_model_param_names(motion_model_list, with_errors=False, with_fixed=False) if calc_vel_in_bootstrap: motion_boot_sum = {} motion2_boot_sum = {} for col in motion_col_list: motion_boot_sum[col] = np.zeros((len(ref_table['x']))) motion2_boot_sum[col] = np.zeros((len(ref_table['x']))) - motion_boot_min_epochs = np.max([self.motion_model_dict[mod].n_pts_req - for mod in np.unique(motion_model_list)]) + + all_mm_map = motion_model.motion_model_map() + motion_boot_min_epochs = np.max([all_mm_map[mm].n_params for mm in motion_model_list]) ### IF MEMORY PROBLEMS HERE: ### DEFINE MEAN, STD VARIABLES AND BUILD THEM RATHER THAN SAVING FULL ARRAY @@ -1215,7 +1239,7 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot # Calculate weights based on weights keyword. If weights desired, will need to # make starlist objects for this - if self.trans_weights != None: + if self.trans_weighting != None: # In order for weights calculation to work, we need to apply a transformation # to the star_list_T so it is in the same units as ref_boot. So, we'll apply # the final transformation for the epoch to get close enough for the @@ -1296,10 +1320,16 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot # Now, do proper motion calculation, making sure to fix t0 to the # orig value (so we can get a reasonable error on x0, y0) - star_table.fit_velocities( - fixed_t0=t0_arr, - default_motion_model=self.default_motion_model, - motion_model_dict=self.motion_model_dict, + if self.fixed_params_dict is None: + fixed_params_dict = {'t0': t0_arr} + elif 't0' not in self.fixed_params_dict.keys(): + fixed_params_dict = self.fixed_params_dict.copy() + fixed_params_dict['t0'] = t0_arr + + star_table.fit_motion_model( + motion_models=self.motion_models, + fixed_params_dict=fixed_params_dict, + weighting=self.vel_weighting, use_scipy=self.use_scipy, absolute_sigma=self.absolute_sigma ) @@ -1351,7 +1381,7 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot self.ref_table.add_column(col) # Calculate chi^2 with bootstrap positional errors - x_pred, y_pred, _, _ = self.ref_table.get_star_positions_at_time(t_arr, self.motion_model_dict, allow_alt_models=True) + x_pred, y_pred, _, _ = self.ref_table.infer_positions(t_arr) xe_comb = np.hypot(self.ref_table['xe'], self.ref_table['xe_boot']) ye_comb = np.hypot(self.ref_table['ye'], self.ref_table['ye_boot']) data_dict['chi2_x_boot'] = np.nansum((self.ref_table['x']-x_pred)**2/(xe_comb)**2,axis=1) @@ -1373,7 +1403,6 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot col[idx_good] = data_dict[ff] self.ref_table.add_column(col) - #pdb.set_trace() print('===============================') print('Done with bootstrap') @@ -1389,7 +1418,7 @@ def __init__(self, ref_list, list_of_starlists, iters=2, trans_args=[{'order': 2}, {'order': 2}], init_order=1, mag_trans=True, mag_lim=None, ref_mag_lim=None, - trans_weights=None, vel_weights='var', + trans_weighting=None, vel_weighting='var', trans_input=None, trans_class=transforms.PolyTransform, calc_trans_inverse=False, @@ -1397,8 +1426,8 @@ def __init__(self, ref_list, list_of_starlists, iters=2, update_ref_orig=False, init_guess_mode='miracle', iter_callback=None, - default_motion_model='Fixed', - motion_model_dict={}, + motion_models=['Empty', 'Fixed'], + fixed_params_dict=None, use_scipy=True, absolute_sigma=False, save_path=None, @@ -1463,13 +1492,13 @@ def __init__(self, ref_list, list_of_starlists, iters=2, If different from None, it indicates the minimum and maximum magnitude on the reference catalog for finding the transformations. - trans_weights : str + trans_weighting : str Either None (def), 'both,var', 'list,var', or 'ref,var' depending on whether you want to weight by the positional uncertainties (variances) in the individual starlists, or also with the uncertainties in the reference frame itself. Note weighting only works when there are positional uncertainties availabe. Other options include 'both,std', 'list,std', 'list,var'. - vel_weights : str + vel_weighting : str Either 'var' (def) or 'std', depending on whether you want to weight the motion model fits by the variance or standard deviation of the position data @@ -1529,9 +1558,12 @@ def = None. If not None, then this should contain an array or list of transform default_motion_model : string Name of motion model to use for new or unassigned stars - - motion_model_dict : None or dict - Dict of motion model name keys (strings) and corresponding MotionModel object values + + motion_models : list of str or MotionModel objects + List of motion model names (strings) or MotionModel objects to use + + fixed_params_dict : None or dict + Dictionary of fixed parameters for motion models use_scipy : bool, optional If True, use scipy.optimize.curve_fit for velocity fitting. If False, use linear algebra fitting, by default True. @@ -1578,13 +1610,13 @@ def = None. If not None, then this should contain an array or list of transform outlier_tol=outlier_tol, trans_args=trans_args, init_order=init_order, mag_trans=mag_trans, mag_lim=mag_lim, - trans_weights=trans_weights, vel_weights=vel_weights, + trans_weighting=trans_weighting, vel_weighting=vel_weighting, trans_input=trans_input, trans_class=trans_class, calc_trans_inverse=calc_trans_inverse, - default_motion_model = default_motion_model, init_guess_mode=init_guess_mode, iter_callback=iter_callback, - motion_model_dict=motion_model_dict, + motion_models=motion_models, + fixed_params_dict=fixed_params_dict, verbose=verbose, use_scipy=use_scipy, absolute_sigma=absolute_sigma, save_path=save_path) @@ -1606,10 +1638,10 @@ def = None. If not None, then this should contain an array or list of transform self.ref_list['me'] = self.ref_list['m0_err'] if ('t' not in self.ref_list.colnames) and ('t0' in self.ref_list.colnames): self.ref_list['t'] = self.ref_list['t0'] - + # Make sure the motion models are ready - self.motion_model_dict = motion_model.validate_motion_model_dict(self.motion_model_dict, - self.ref_list, self.default_motion_model) + # self.motion_model_dict = motion_model.validate_motion_model_dict(self.motion_model_dict, + # self.ref_list, self.default_motion_model) return @@ -1646,13 +1678,13 @@ def fit(self): logger(_log, ' mag_trans = ' + str(self.mag_trans), self.verbose) logger(_log, ' mag_lim = ' + str(self.mag_lim), self.verbose) logger(_log, ' ref_mag_lim = ' + str(self.ref_mag_lim), self.verbose) - logger(_log, ' trans_weights = ' + str(self.trans_weights), self.verbose) - logger(_log, ' vel_weights = ' + str(self.vel_weights), self.verbose) + logger(_log, ' trans_weighting = ' + str(self.trans_weighting), self.verbose) + logger(_log, ' vel_weighting = ' + str(self.vel_weighting), self.verbose) logger(_log, ' trans_input = ' + str(self.trans_input), self.verbose) logger(_log, ' trans_class = ' + str(self.trans_class), self.verbose) logger(_log, ' calc_trans_inverse = ' + str(self.calc_trans_inverse), self.verbose) logger(_log, ' use_ref_new = ' + str(self.use_ref_new), self.verbose) - logger(_log, ' default_motion_model = ' + str(self.default_motion_model), self.verbose) + logger(_log, ' motion_models = ' + str([mm.name for mm in self.motion_models]), self.verbose) logger(_log, ' update_ref_orig = ' + str(self.update_ref_orig), self.verbose) logger(_log, ' init_guess_mode = ' + str(self.init_guess_mode), self.verbose) logger(_log, ' iter_callback = ' + str(self.iter_callback), self.verbose) @@ -1687,13 +1719,13 @@ def fit(self): print('Starting iter {0:d} with ref_table shape:'.format(nn), self.ref_table['x'].shape) print("**********") print("**********") - + # ALL the action is in here. Match and transform the stack of starlists. # This updates trans objects and the ref_table. self.match_and_transform(self.ref_mag_lim, self.dr_tol[nn], self.dm_tol[nn], self.outlier_tol[nn], self.trans_args[nn]) - + # Clean up the reference table # Find where stars are detected. self.ref_table.detections() @@ -1898,7 +1930,7 @@ def reset_ref_values(ref_table): return -def add_rows_for_new_stars(ref_table, star_list, idx_lis, default_motion_model='Fixed'): +def add_rows_for_new_stars(ref_table, star_list, idx_lis): """ For each star that is in star_list and NOT in idx_list, make a new row in the reference table. The values will be empty (None, NAN, etc.). @@ -1943,12 +1975,12 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis, default_motion_model=' elif ref_table[col_name].dtype == np.dtype('bool'): new_col_empty = False elif col_name=='motion_model_input': - new_col_empty = default_motion_model + new_col_empty = 'Empty' elif col_name=='motion_model_used': - new_col_empty = 'Fixed' + new_col_empty = 'Empty' else: new_col_empty = np.nan - + if len(ref_table[col_name].shape) == 1: new_col_shape = len(idx_lis_new) else: @@ -1966,7 +1998,7 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis, default_motion_model=' ref_table = vstack([ref_table, ref_table_new]) idx_ref_new = np.arange(last_star_idx, len(ref_table)) - + return ref_table, idx_lis_new, idx_ref_new """ @@ -2863,7 +2895,7 @@ def check_trans_input(list_of_starlists, trans_input, mag_trans): return -def trans_initial_guess(ref_list, star_list, trans_args, motion_model_dict, mode='miracle', +def trans_initial_guess(ref_list, star_list, trans_args, mode='miracle', ignore_contains='star', verbose=True, n_req_match=3, mag_trans=True, order=1): """ @@ -2901,7 +2933,7 @@ def trans_initial_guess(ref_list, star_list, trans_args, motion_model_dict, mode # If there are velocities in the reference list, use them. # We assume velocities are in the same units as the positions. - xref, yref = get_pos_at_time(star_list['t'][0], ref_list, motion_model_dict) + xref, yref = infer_positions(star_list['t'][0], ref_list) if 'm' in ref_list.colnames: mref = ref_list['m'] else: @@ -3140,9 +3172,9 @@ def get_weighting_scheme(weights, ref_list, star_list): return weight # TODO: This is sometimes run on a startable, not a starlist, at least as currently used -def get_pos_at_time(t, starlist, motion_model_dict): +def infer_positions(t, startable): """ - Take a starlist, check to see if it has motion/velocity columns. + Take a startable, check to see if it has motion/velocity columns. If it does, then propogate the positions forward in time to the desired epoch. If no motion/velocities exist, then just use ['x0', 'y0'] or ['x', 'y'] @@ -3155,21 +3187,23 @@ def get_pos_at_time(t, starlist, motion_model_dict): as the 't0' column in starlist. """ # Check for motion model - if 'motion_model_used' in starlist.colnames: - x,y,xe,ye = starlist.get_star_positions_at_time(t, motion_model_dict, allow_alt_models=True) + if 'motion_model_used' in startable.colnames: + x, y, xe, ye = startable.infer_positions(t) + # If no motion model, check for velocities - elif ('vx' in starlist.colnames) and ('vy' in starlist.colnames): - x = starlist['x0'] + starlist['vx']*(t-starlist['t0']) - y = starlist['y0'] + starlist['vy']*(t-starlist['t0']) + elif ('vx' in startable.colnames) and ('vy' in startable.colnames): + x = startable['x0'] + startable['vx'] * (t - startable['t0']) + y = startable['y0'] + startable['vy'] * (t - startable['t0']) + # If no velocities, try fitted positon - elif ('x0' in starlist.colnames) and ('y0' in starlist.colnames): - x = starlist['x0'] - y = starlist['y0'] + elif ('x0' in startable.colnames) and ('y0' in startable.colnames): + x = startable['x0'] + y = startable['y0'] # Otherwise, use measured position else: - x = starlist['x'] - y = starlist['y'] - + x = startable['x'] + y = startable['y'] + return (x, y) def logger(logfile, message, verbose = 9): diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index 195a67b..cc4de2a 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -6,10 +6,8 @@ from flystar import motion_model from astropy.table import Table import numpy as np -import pylab as plt +import matplotlib.pyplot as plt import pdb -import datetime -import pytest def test_MosaicSelfRef(): """ @@ -28,7 +26,7 @@ def test_MosaicSelfRef(): trans_args={'order': 2}) msc.fit() - + # Check some of the output quantities on the final table. assert 'x0' in msc.ref_table.colnames assert 'x0_err' in msc.ref_table.colnames @@ -42,7 +40,6 @@ def test_MosaicSelfRef(): assert msc.ref_table['use_in_trans'].shape == msc.ref_table['x0'].shape assert msc.ref_table['used_in_trans'].shape == msc.ref_table['x'].shape - # Check that we have some matched stars... should be at least 35 stars # that are detected in all 4 starlists. @@ -50,11 +47,11 @@ def test_MosaicSelfRef(): assert len(idx) > 35 # Check that the transformation error isn't too big - assert (msc.ref_table['x0_err'] < 3.0).all() # less than 1 pix - assert (msc.ref_table['y0_err'] < 3.0).all() - #assert (msc.ref_table['m0_err'] < 1.0).all() # less than 0.5 mag - assert (msc.ref_table['m0_err'] < 1.5).all() # less than 0.5 mag - + valid_err = np.isfinite(msc.ref_table['x0_err']) & np.isfinite(msc.ref_table['y0_err']) & np.isfinite(msc.ref_table['m0_err']) + assert (msc.ref_table['x0_err'][valid_err] < 3.0).all() # less than 1 pix + assert (msc.ref_table['y0_err'][valid_err] < 3.0).all() + #assert (msc.ref_table['m0_err'][valid_err] < 1.0).all() # less than 0.5 mag + assert (msc.ref_table['m0_err'][valid_err] < 1.5).all() # less than 0.5 mag # Check that the transformation lists aren't too wacky for ii in range(4): np.testing.assert_allclose(msc.trans_list[ii].px.c1_0, 1.0, rtol=1e-2) @@ -81,7 +78,7 @@ def test_MosaicSelfRef(): plt.plot(msc.ref_table['x0'], msc.ref_table['y0'], '.', color='black', alpha=0.2) - + return @@ -102,11 +99,11 @@ def test_MosaicSelfRef_vel_tconst(): dr_tol=[3, 3], dm_tol=[1, 1], trans_class=transforms.PolyTransform, trans_args={'order': 2}, - default_motion_model='Linear', + motion_models=['Empty', 'Fixed', 'Linear'], verbose=False) msc.fit() - + # Check some of the output quantities on the final table. assert 'x0' in msc.ref_table.colnames assert 'x0_err' in msc.ref_table.colnames @@ -126,21 +123,16 @@ def test_MosaicSelfRef_vel_tconst(): assert len(idx) > 35 # Check that the transformation error isn't too big - assert (msc.ref_table['x0_err'] < 3.0).all() # less than 1 pix - assert (msc.ref_table['y0_err'] < 3.0).all() - assert (msc.ref_table['m0_err'] < 1.0).all() # less than 0.5 mag - + valid_err = np.isfinite(msc.ref_table['x0_err']) & np.isfinite(msc.ref_table['y0_err']) & np.isfinite(msc.ref_table['m0_err']) + assert (msc.ref_table['x0_err'][valid_err] < 3.0).all() # less than 1 pix + assert (msc.ref_table['y0_err'][valid_err] < 3.0).all() + assert (msc.ref_table['m0_err'][valid_err] < 1.0).all() # less than 0.5 mag + # Check that the transformation lists aren't too wacky for ii in range(4): np.testing.assert_allclose(msc.trans_list[ii].px.c1_0, 1.0, rtol=1e-2) np.testing.assert_allclose(msc.trans_list[ii].py.c0_1, 1.0, rtol=1e-2) - # Check that the velocities aren't crazy... - # they should be non-existent (since there is no time difference) - assert np.isnan(msc.ref_table['vx']).all() - assert np.isnan(msc.ref_table['vy']).all() - assert np.isnan(msc.ref_table['vx_err']).all() - assert np.isnan(msc.ref_table['vy_err']).all() return @@ -172,7 +164,7 @@ def test_MosaicSelfRef_vel(): msc = align.MosaicSelfRef(lists, ref_index=0, iters=3, dr_tol=[5, 3, 3], dm_tol=[1, 1, 0.5], outlier_tol=None, trans_class=transforms.PolyTransform, - trans_args={'order': 2}, default_motion_model='Linear', + trans_args={'order': 2}, motion_models=['Empty', 'Fixed', 'Linear'], verbose=False) msc.fit() @@ -196,10 +188,11 @@ def test_MosaicSelfRef_vel(): assert len(idx) > 35 # Check that the transformation error isn't too big - assert (msc.ref_table['x0_err'] < 3.0).all() # less than 1 pix - assert (msc.ref_table['y0_err'] < 3.0).all() - assert (msc.ref_table['m0_err'] < 1.0).all() # less than 0.5 mag - + valid_err = np.isfinite(msc.ref_table['x0_err']) & np.isfinite(msc.ref_table['y0_err']) & np.isfinite(msc.ref_table['m0_err']) + assert (msc.ref_table['x0_err'][valid_err] < 3.0).all() # less than 1 pix + assert (msc.ref_table['y0_err'][valid_err] < 3.0).all() + assert (msc.ref_table['m0_err'][valid_err] < 1.0).all() # less than 0.5 mag + # Check that the transformation lists aren't too wacky for ii in range(4): np.testing.assert_allclose(msc.trans_list[ii].px.c1_0, 1.0, rtol=1e-2) @@ -214,7 +207,7 @@ def test_MosaicSelfRef_vel(): def test_MosaicToRef(): make_fake_starlists_poly1(seed=42) - + ref_file = 'random_ref.fits' list_files = ['random_0.fits', 'random_1.fits', @@ -235,7 +228,7 @@ def test_MosaicToRef(): msc = align.MosaicToRef(ref_list, lists, iters=2, dr_tol=[0.2, 0.1], dm_tol=[1, 0.5], trans_class=transforms.PolyTransform, - trans_args={'order': 2}, default_motion_model='Fixed', + trans_args={'order': 2}, motion_models=['Empty', 'Fixed'], update_ref_orig=False, verbose=False) msc.fit() @@ -300,7 +293,7 @@ def test_MosaicToRef_p0_vel(): dr_tol=[0.2, 0.1], dm_tol=[1, 0.5], outlier_tol=[None, None], trans_class=transforms.PolyTransform, - trans_args={'order': 1}, default_motion_model='Linear', + trans_args={'order': 1}, motion_models=['Empty', 'Fixed', 'Linear'], update_ref_orig=False, verbose=False) msc.fit() @@ -326,18 +319,18 @@ def test_MosaicToRef_p0_vel(): # The velocities should be almost the same (but not as close as before) # as the input velocities since update_ref == True. assert (msc.ref_table['name']==ref_list['name']).all() - np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], rtol=1e-1) - np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], rtol=1e-1) + np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], atol=1e-2) + np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], atol=1e-2) # Also double check that they aren't exactly the same for the reference stars. #assert np.any(np.not_equal(msc.ref_table['vx'], ref_list['vx'])) assert np.not_equal(msc.ref_table['vx'], ref_list['vx']).any() - + return msc def test_MosaicToRef_vel(): make_fake_starlists_poly1_vel(seed=42) - + ref_file = 'random_vel_ref.fits' list_files = ['random_vel_0.fits', 'random_vel_1.fits', @@ -359,14 +352,14 @@ def test_MosaicToRef_vel(): # Switch our list to a "increasing to the West" list. ref_list['x0'] *= -1.0 ref_list['vx'] *= -1.0 - + lists = [starlists.StarList.read(lf) for lf in list_files] msc = align.MosaicToRef(ref_list, lists, iters=2, dr_tol=[0.2, 0.1], dm_tol=[1, 0.5], outlier_tol=[None, None], trans_class=transforms.PolyTransform, - trans_args={'order': 1}, default_motion_model='Linear', + trans_args={'order': 1}, motion_models=['Empty', 'Fixed', 'Linear'], update_ref_orig=False, verbose=False) msc.fit() @@ -392,8 +385,8 @@ def test_MosaicToRef_vel(): # The velocities should be almost the same (but not as close as before) # as the input velocities since update_ref == True. assert (msc.ref_table['name']==ref_list['name']).all() - np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], rtol=1e-1) - np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], rtol=1e-1) + np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], atol=1e-2) + np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], atol=1e-2) # Also double check that they aren't exactly the same for the reference stars. #assert np.any(np.not_equal(msc.ref_table['vx'], ref_list['vx'])) @@ -403,7 +396,7 @@ def test_MosaicToRef_vel(): def test_MosaicToRef_acc(): make_fake_starlists_poly1_acc(seed=42) - + ref_file = 'random_acc_ref.fits' list_files = ['random_acc_0.fits', 'random_acc_1.fits', @@ -427,19 +420,19 @@ def test_MosaicToRef_acc(): ref_list['ay'] *= 1e-3 ref_list['ax_err'] *= 1e-3 ref_list['ay_err'] *= 1e-3 - + # Switch our list to a "increasing to the West" list. ref_list['x0'] *= -1.0 ref_list['vx0'] *= -1.0 ref_list['ax'] *= -1.0 - + lists = [starlists.StarList.read(lf) for lf in list_files] msc = align.MosaicToRef(ref_list, lists, iters=2, dr_tol=[0.4, 0.2], dm_tol=[1, 0.5], trans_class=transforms.PolyTransform, trans_args={'order': 2}, - default_motion_model='Acceleration', + motion_models=['Acceleration'], update_ref_orig=False, verbose=False) msc.fit() From a19b10678e4c38b90c16265ebe657a6e0abf3c18 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E2=80=9CLingfeng?= Date: Tue, 16 Dec 2025 04:16:42 -0800 Subject: [PATCH 21/29] Passed startable tests; Accelerated imports with relative import --- flystar/analysis.py | 13 +- flystar/match.py | 5 +- flystar/motion_model.py | 34 +- flystar/parallax.py | 24 +- flystar/plots.py | 8 +- flystar/startables.py | 573 +++++++------------------------- flystar/tests/test_startable.py | 173 +++++----- 7 files changed, 241 insertions(+), 589 deletions(-) diff --git a/flystar/analysis.py b/flystar/analysis.py index 81ab3f4..9ac826f 100644 --- a/flystar/analysis.py +++ b/flystar/analysis.py @@ -1,17 +1,15 @@ import numpy as np import pylab as plt -from flystar import starlists -from flystar import startables -from flystar import align -from flystar import match -from flystar import transforms +from . import starlists +from . import startables +from . import align +from . import match +from . import transforms from astropy import table from astropy.table import Table, Column from astropy.coordinates import SkyCoord from astropy import units as u from astropy.wcs import WCS -from astroquery.gaia import Gaia -from astroquery.mast import Observations, Catalogs import pdb, copy import math from scipy.stats import f @@ -42,6 +40,7 @@ def query_gaia(ra, dec, search_radius=30.0, table_name='gaiadr3'): table_name : string Options are 'gaiadr2' or 'gaiaedr3' """ + from astroquery.gaia import Gaia target_coords = SkyCoord(ra, dec, unit=(u.hourangle, u.deg), frame='icrs') ra = target_coords.ra.degree dec = target_coords.dec.degree diff --git a/flystar/match.py b/flystar/match.py index d7c391e..4cd5e36 100644 --- a/flystar/match.py +++ b/flystar/match.py @@ -1,5 +1,7 @@ import numpy as np -from flystar import starlists, transforms, startables, align +from . import starlists +from . import transforms +from . import startables from collections import Counter from scipy.spatial import cKDTree as KDT from astropy.table import Column, Table @@ -526,6 +528,7 @@ def generic_match(sl1, sl2, init_mode='triangle', Startable of the two matched catalogs """ + from . import align # Check the input StarLists and transform them into astropy Tables if not isinstance(sl1, starlists.StarList): diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 42a5e54..6741c65 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -538,8 +538,7 @@ def run_fit( return_chi2=False, verbose=True ): - assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Linear model." - t0 = fixed_params_dict['t0'] + t0 = fixed_params_dict.get('t0', np.average(t, weights=1./np.hypot(xe, ye))) t = np.atleast_1d(t) x = np.atleast_1d(x) y = np.atleast_1d(y) @@ -742,8 +741,7 @@ def run_fit( return_chi2=False, verbose=True ): - assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Acceleration model." - t0 = fixed_params_dict['t0'] + t0 = fixed_params_dict.get('t0', np.average(t, weights=1./np.hypot(xe, ye))) t = np.atleast_1d(t) x = np.atleast_1d(x) y = np.atleast_1d(y) @@ -839,7 +837,7 @@ def calc_parallax_vector(self, t_mjd, ra, dec, pa=0., obsLocation='earth'): if self.plx_vector_cached is not None: t_mjd = np.atleast_1d(t_mjd) t_mjd_cached = self.plx_vector_cached[0] - if np.allclose(t_mjd, t_mjd_cached): + if np.array_equal(t_mjd, t_mjd_cached): # If cached values match input times, return cached values return self.plx_vector_cached[1] @@ -901,7 +899,7 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): - ra, shape (N_stars,) or (1,). - dec, shape (N_stars,) or (1,). - pa, optional, shape (N_stars,) or (1,), by default 0. - - obsLocation, optional,shape (N_stars,) or (1,), by default 'earth' + - obsLocation, optional, string, by default 'earth' fit_param_errs : array-like, optional Uncertainties in fit parameters, by default None @@ -910,6 +908,9 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + + assert all([_ in fixed_params_dict for _ in ['t0', 'ra', 'dec']]), "Fixed parameters t0, ra, and dec are required for Parallax model." + t = np.atleast_1d(t) fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) N_stars = fit_params.shape[0] if fit_params.ndim > 1 else 1 @@ -922,12 +923,13 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): pa = np.atleast_1d(fixed_params_dict.get('pa', 0.0)) obsLocation = fixed_params_dict.get('obsLocation', 'earth') + # TODO: vectorize parallax.parallax_in_direction to handle multiple obsLocation? + assert type(obsLocation) == str, "obsLocation must be a single string for all stars at this time." + dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) t_mjd = Time(t, format='decimalyear', scale='utc').mjd # Shape (N_times,) self.pvec = self.calc_parallax_vector(t_mjd, ra, dec, pa=pa, obsLocation=obsLocation) # Shape (2, N_times) x, y = self.model_fit(dt, x0[:, np.newaxis], vx[:, np.newaxis], y0[:, np.newaxis], vy[:, np.newaxis], pi[:, np.newaxis]) # Shape (N_stars, N_times) - # x = xy[:, :N_times] # Shape (N_stars, N_times) - # y = xy[:, N_times:] # Shape (N_stars, N_times) if N_stars == 1 or N_times == 1: # If only one star, return flattened arrays @@ -1068,14 +1070,18 @@ def get_one_motion_model_param_names(motion_model, with_errors=True, with_fixed= Add uncertainty names with '_err' suffix or not, by default True with_fixed : bool, optional Add fixed param names with '_fixed' suffix or not, by default True - + Returns ------- list List of all parameter names for the motion model """ - list_of_parameters = [] + if isinstance(motion_model, str): + all_mm_map = motion_model_map() + motion_model = all_mm_map[motion_model] + list_of_parameters = [] + def list_add(name): if name not in list_of_parameters: list_of_parameters.append(name) @@ -1112,6 +1118,10 @@ def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_ """ list_of_parameters = [] + if len(motion_model_list) > 0 and isinstance(motion_model_list[0], str): + all_mm_map = motion_model_map() + motion_model_list = [all_mm_map[mm_name] for mm_name in motion_model_list] + def list_add(name): if name not in list_of_parameters: list_of_parameters.append(name) @@ -1130,12 +1140,12 @@ def list_add(name): return list(list_of_parameters) -def get_all_motion_model_names(with_errors=True, with_fixed=True): +def get_all_motion_model_param_names(with_errors=True, with_fixed=True): return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) def motion_model_map(): mm_map = dict( - [(mm.__name__, mm()) for mm in MotionModel.__subclasses__()] + [(mm.__name__, mm) for mm in MotionModel.__subclasses__()] ) # Sort by n_params mm_map = dict(sorted(mm_map.items(), key=lambda item: item[1].n_params)) diff --git a/flystar/parallax.py b/flystar/parallax.py index 2bd352a..1a6dcf1 100755 --- a/flystar/parallax.py +++ b/flystar/parallax.py @@ -44,7 +44,7 @@ def parallax_in_direction(ra, dec, mjd, obsLocation='earth', pa=0.): Returns ------- pvec : ndarray - Parallax vector components, shape of (2, N) or (2,), where N is the number of stars. + Parallax vector components, shape of (2, N_stars, N_times), or (2, N_stars) if N_times=1, or (2, N_times) if N_stars=1. """ # Munge inputs into astropy format. # times = Time(mjd + 2400000.5, format='jd', scale='tdb') @@ -62,24 +62,24 @@ def parallax_in_direction(ra, dec, mjd, obsLocation='earth', pa=0.): _north_projected = np.cross(directions, _east_projected) _north_projected /= np.linalg.norm(_north_projected, axis=1)[:, np.newaxis] # Shape (N_stars, 3) - obs_pos = get_observer_barycentric(obsLocation, times) - sun_pos = get_body_barycentric(body='sun', time=times) + obs_pos = get_observer_barycentric(obsLocation, times) # Shape (N_times,) + sun_pos = get_body_barycentric(body='sun', time=times) # Shape (N_times,) sun_obs_pos = sun_pos - obs_pos - pos = sun_obs_pos.xyz.T.to(units.au).value # Shape (N_stars, 3) + pos = sun_obs_pos.xyz.T.to(units.au).value # Shape (N_times, 3) - e = np.einsum('ij,ij->i', pos, _east_projected) # Shape (N_stars,) - n = np.einsum('ij,ij->i', pos, _north_projected) # Shape (N_stars,) + e = np.einsum('ti,si->st', pos, _east_projected) # Shape (N_stars, N_times) + n = np.einsum('ti,si->st', pos, _north_projected) # Shape (N_stars, N_times) # Rotate frame e,n->x,y accounting for PA - pa = np.deg2rad(pa) - x = -e * np.cos(pa) + n * np.sin(pa) - y = e * np.sin(pa) + n * np.cos(pa) - pvec = np.array([x, y]) # Shape (2, N_stars) + pa = np.deg2rad(pa) # shape (N_stars,) + x = -e * np.cos(pa[:, np.newaxis]) + n * np.sin(pa[:, np.newaxis]) # Shape (N_stars, N_times) + y = e * np.sin(pa[:, np.newaxis]) + n * np.cos(pa[:, np.newaxis]) # Shape (N_stars, N_times) + pvec = np.array([x, y]) # Shape (2, N_stars, N_times) - if pvec.shape[1] == 1: - pvec = pvec.flatten() + if pvec.shape[1] == 1 or pvec.shape[2] == 1: + pvec = pvec.reshape(2, -1) # Shape (2, N_stars) or (2, N_times) return pvec diff --git a/flystar/plots.py b/flystar/plots.py index 8df9d51..8a2127c 100755 --- a/flystar/plots.py +++ b/flystar/plots.py @@ -1,4 +1,4 @@ -from flystar import analysis, motion_model, startables +from . import motion_model, startables import numpy as np import matplotlib.mlab as mlab import matplotlib @@ -193,6 +193,7 @@ def pos_diff_err_hist(ref_mat, starlist_mat, transform, nbins=25, bin_width=None an outlier. """ + from . import analysis diff_x = ref_mat['x'] - starlist_mat['x'] diff_y = ref_mat['y'] - starlist_mat['y'] @@ -1069,16 +1070,15 @@ def plot_mag_error(tab): return -def plot_mean_residuals_by_epoch(tab, motion_model_dict={}): +def plot_mean_residuals_by_epoch(tab): """ Plot mean position and magnitude residuals vs. epoch. Note we are plotting the mean( |dx} ) to see the size of the mean residual. """ # Predicted model positions at each epoch - motion_model_dict = motion_model.validate_motion_model_dict(motion_model_dict, tab, None) i_all_detected = np.where(~np.any(np.isnan(tab['t']),axis=1))[0][0] - xt_mod, yt_mod, xt_mod_err, yt_mod_err = tab.get_star_positions_at_time(tab['t'][i_all_detected], motion_model_dict, allow_alt_models=True) + xt_mod, yt_mod, xt_mod_err, yt_mod_err = tab.predict_positions(tab['t'][i_all_detected]) # Residuals dx = tab['x'] - xt_mod diff --git a/flystar/startables.py b/flystar/startables.py index dd44178..bdcb880 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -227,7 +227,7 @@ def _add_list_data_from_starlist(self, starlist): lis_meta_keys = list(starlist.meta.keys()) # append 's' to the end to pluralize the input starlist. lis_meta_keys_plural = [lis_meta_key + 's' for lis_meta_key in lis_meta_keys] - + for kk in range(len(tab_meta_keys)): tab_key = tab_meta_keys[kk] @@ -237,9 +237,9 @@ def _add_list_data_from_starlist(self, starlist): # If we find the key in the starlists' meta argument, then add the new values. # Otherwise, add "None". - idx = np.where(lis_meta_keys_plural == tab_key)[0] - if len(idx) > 0: - lis_key = lis_meta_keys[idx[0]] + idx = lis_meta_keys_plural.index(tab_key) if tab_key in lis_meta_keys_plural else None + if idx is not None: + lis_key = lis_meta_keys[idx] self.meta[tab_key] = np.append(self.meta[tab_key], [starlist.meta[lis_key]]) else: self._append_invalid_meta_values(tab_key) @@ -550,7 +550,7 @@ def fit_motion_model( Parameters ---------- - motion_models : list of MotionModel, optional + motion_models : list of MotionModel or str, optional Motion models to use. Empty and Fixed models are always added automatically for stars with n_fit = 0 or 1. The behavior is as follows: @@ -612,9 +612,16 @@ def fit_motion_model( if fixed_params_dict is not None: if not isinstance(fixed_params_dict, dict): raise ValueError("fit_velocities: fixed_params_dict must be a dictionary!") - + + # Convert motion_models to MotionModel objects if they are strings: + all_mm_map = motion_model.motion_model_map() + if all(isinstance(mm, str) for mm in motion_models): + mm_names = motion_models + motion_models = [all_mm_map[mm] for mm in motion_models] + else: + mm_names = [mm.name for mm in motion_models] + # Always add Empty and Fixed in motion models - mm_names = [mm.name for mm in motion_models] if 'Fixed' not in mm_names: motion_models.insert(0, Fixed) if 'Empty' not in mm_names: @@ -622,17 +629,13 @@ def fit_motion_model( mm_names = [mm.name for mm in motion_models] # Construct motion models if motion_model_input column exists - all_mm_map = motion_model.motion_model_map() if 'motion_model_input' in self.colnames: input_mm_names = np.unique(self['motion_model_input']) assert all([name in all_mm_map.keys() for name in input_mm_names]), \ f"fit_velocities: Unknown motion model name(s) in 'motion_model_input' column. Available motion models are: {', '.join(all_mm_map.keys())}." for mm_name in input_mm_names: if mm_name not in mm_names: - try: - motion_models.append(all_mm_map[mm_name]()) - except Exception as e: - raise ValueError(f"fit_velocities: An instance of motion model {mm_name} with initialization parameters is missing in motion_models: {e}") + motion_models.append(all_mm_map[mm_name]) # Sort motion models by n_params motion_models = sorted(motion_models, key=lambda mm: mm.n_params) @@ -673,15 +676,16 @@ def fit_motion_model( # Add default t0 if not provided in fixed_params_dict if fixed_params_dict is None: weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None - t0 = np.average(t_data, axis=1, weights=weights) - fixed_params_dict = {'t0': t0} + fixed_params_dict = {'t0': np.average(t_data, axis=1, weights=weights)} + elif 't0' not in fixed_params_dict: weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None fixed_params_dict['t0'] = np.average(t_data, axis=1, weights=weights) else: if np.ndim(fixed_params_dict['t0']) == 0: fixed_params_dict['t0'] = np.full(N_stars, fixed_params_dict['t0']) - t0 = fixed_params_dict['t0'] + + t0 = fixed_params_dict['t0'] # Prepare fixed_params_dict for each star @@ -739,7 +743,7 @@ def fit_motion_model( ) - 1 # Convert to 0-based index # Assign motion models to stars - self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized]) + self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized], dtype='U20') ############################ @@ -747,8 +751,9 @@ def fit_motion_model( ############################ # Fill table with all possible motion model parameter names as new columns. motion_model_used = [all_mm_map[name] for name in np.unique(self['motion_model_used'])] - new_col_list = motion_model.get_list_motion_model_param_names(motion_model_used, with_errors=True) + new_col_list = motion_model.get_list_motion_model_param_names(motion_model_used, with_errors=True, with_fixed=False) new_col_list += ['chi2_x', 'chi2_y', 'n_params'] + if 't0' not in new_col_list: new_col_list.append('t0') @@ -765,6 +770,32 @@ def fit_motion_model( rename_duplicate=True ) + # Add fixed parameter columns if they do not exist + fixed_param_names = [] + for mm in motion_model_used: + for param in mm.fixed_param_names: + if param not in fixed_param_names: + fixed_param_names.append(param) + if 't0' in fixed_param_names: + fixed_param_names.remove('t0') + + # Add fixed parameter columns + for param in fixed_param_names: + coldata = np.array([fixed_params_stars[i][param] for i in range(N_stars)]) + if param in self.colnames: + # If the column already exists, check if the data are the same + if np.allclose(self[param], coldata, equal_nan=True): + # Same data, skip + continue + else: + # Different data, add with _mm suffix to avoid name conflict + colname = param + '_mm' + else: + colname = param + + self.add_column(Column(data=coldata, name=colname)) + + # Add a column to keep track of the number of points used in a fit and number of bootstrap used. self.meta['n_bootstrap'] = bootstrap @@ -822,332 +853,87 @@ def fit_motion_model( self['t0'][unique_index] = t0[unique_index] return - - def fit_velocities(self, weighting='var', use_scipy=True, absolute_sigma=True, bootstrap=0, - fixed_t0=False, verbose=False, mask_val=None, mask_lists=False, show_progress=True, - default_motion_model='Linear', reassign_motion_model=False, select_stars=None, motion_model_dict={}): - """Fit velocities for all stars in the table and add to the columns 'vx', 'vxe', 'vy', 'vye', 'x0', 'x0e', 'y0', 'y0e'. + def infer_positions(self, times, fill_value=np.nan): + """Infer star positions at given times using fitted motion models. Parameters ---------- - weighting : str, optional - Weight by variance 'var' or standard deviation 'std', by default 'var' - bootstrap : int, optional - Calculate uncertainty using bootstraping or not, by default 0 - fixed_t0 : bool or array-like, optional - Fix the t0 in dt = time - t0 if user provides an array with the same length of the table, or automatically calculate t0 = np.average(time, weights=1/np.hypot(xe, ye)) if False, by default False - verbose : bool, optional - Output verbose information or not, by default False - mask_val : float, optional - Value that needs to be masked in the data, e.g. -100000, by default None - mask_lists : list, optional - Columns that needs to be masked, by default False - show_progress : bool, optional - Show progress bar or not, by default True + times : array_like + Times at which to predict positions. + fill_value : float, optional + Value to use for missing data, by default np.nan - Raises - ------ - ValueError - If weighting is neither 'var' or 'std' - KeyError - If there's not time information in the table + Returns + ------- + x, y, xe, ye : ndarray + Arrays of predicted x, y positions and their uncertainties xe, ye, with shape (N_stars, N_times) or (N_stars,) if N_times=1, or (N_times,) if N_stars=1, or scalar. """ - if weighting not in ['var', 'std']: - raise ValueError(f"fit_velocities: Weighting must either be 'var' or 'std', not {weighting}!") - - if ('t' not in self.colnames) and ('list_times' not in self.meta): - raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'list_times' in meta.") - - # Check if we have the required columns - if not all([_ in self.colnames for _ in ['x', 'y']]): - raise KeyError(f"fit_velocities: Missing required columns in the table: {', '.join(['x', 'y'])}!") - - N_stars = len(self) + assert 'motion_model_used' in self.colnames, \ + "infer_positions: 'motion_model_used' column not found in the table. Please run fit_motion_model() first." - if verbose: - start_time = time.time() - msg = 'Starting startable.fit_velocities for {0:d} stars with n={1:d} bootstrap' - print(msg.format(N_stars, bootstrap)) - - # Set all to default_motion_model if none assigned already. - # Reset motion_model_used to the inputs for now -> will change as fits run - if ('motion_model_input' not in self.colnames) or reassign_motion_model: - self['motion_model_input'] = default_motion_model - self['motion_model_used'] = self['motion_model_input'] - - motion_model_dict = motion_model.validate_motion_model_dict(motion_model_dict, self, default_motion_model) - - # - # Fill table with all possible motion model parameter names as new - # columns. Make everything empty for now. - # - all_motion_models = np.unique(self['motion_model_input'].tolist() + ['Fixed']+[default_motion_model]).tolist() - new_col_list = motion_model.get_list_motion_model_param_names(all_motion_models, with_errors=True) - # Append goodness of fit metrics and t0. - new_col_list += ['chi2_x', 'chi2_y', 'n_params'] - if 't0' not in new_col_list: - new_col_list.append('t0') + N_stars = len(self) + times = np.atleast_1d(times) + N_times = len(times) + + if (N_stars > 1) and (N_times > 1): + x_pred = np.full((N_stars, N_times), fill_value, dtype=float) + y_pred = np.full((N_stars, N_times), fill_value, dtype=float) + xe_pred = np.full((N_stars, N_times), np.inf, dtype=float) + ye_pred = np.full((N_stars, N_times), np.inf, dtype=float) + elif N_stars==1: + x_pred = np.full(N_times, fill_value, dtype=float) + y_pred = np.full(N_times, fill_value, dtype=float) + xe_pred = np.full(N_times, np.inf, dtype=float) + ye_pred = np.full(N_times, np.inf, dtype=float) + else: + x_pred = np.full(N_stars, fill_value, dtype=float) + y_pred = np.full(N_stars, fill_value, dtype=float) + xe_pred = np.full(N_stars, np.inf, dtype=float) + ye_pred = np.full(N_stars, np.inf, dtype=float) - # Define output arrays for the best-fit parameters. - for col in new_col_list: - # Clean/remove up old arrays. - if col in self.colnames: self.remove_column(col) - # Add column #TODO: is this good for filling??? - self.add_column(Column(data = np.full(N_stars, np.nan, dtype=float), name = col)) - # Add a column to keep track of the number of points used in a fit. - self['n_fit'] = 0 - - # Preserve the number of bootstraps that will be run (if any). - self.meta['n_fit_bootstrap'] = bootstrap - - # (FIXME: Do we need to catch the case where there's a single *unmasked* epoch?) - # Catch the case when there is only a single epoch. Just return 0 velocity - # and the same input position for the x0/y0. - if len(self['x'].shape) == 1: - self['motion_model_used'] = 'Fixed' - self['x0'] = self['x'] - self['y0'] = self['y'] - if 't' in self.colnames: - self['t0'] = self['t'] - else: - self['t0'] = self.meta['list_times'][0] - if 'xe' in self.colnames: - self['x0_err'] = self['xe'] - self['y0_err'] = self['ye'] - self['n_fit'] = 1 - self['n_params'] = 1 - return - - if (self['x'].shape[1] == 1): - self['motion_model_used'] = 'Fixed' - self['x0'] = self['x'][:,0] - self['y0'] = self['y'][:,0] - if 't' in self.colnames: - self['t0'] = self['t'][:, 0] - else: - self['t0'] = self.meta['list_times'][0] - if 'xe' in self.colnames: - self['x0_err'] = self['xe'][:,0] - self['y0_err'] = self['ye'][:,0] - self['n_fit'] = 1 - self['n_params'] = 1 - return - - # Only fit selected stars, if list given - fit_star_idxs = range(N_stars) - if select_stars is not None: - fit_star_idxs = select_stars - # STARS LOOP through the stars and work on them 1 at a time. - # This is slow; but robust. - if show_progress: - for ss in tqdm(fit_star_idxs): - self.fit_velocity_for_star(ss, motion_model_dict, weighting=weighting, bootstrap=bootstrap, - use_scipy=use_scipy, absolute_sigma=absolute_sigma, - fixed_t0=fixed_t0, default_motion_model=default_motion_model, - mask_val=mask_val, mask_lists=mask_lists) - else: - for ss in fit_star_idxs: - self.fit_velocity_for_star(ss, motion_model_dict, weighting=weighting, bootstrap=bootstrap, - use_scipy=use_scipy, absolute_sigma=absolute_sigma, - fixed_t0=fixed_t0, default_motion_model=default_motion_model, - mask_val=mask_val, mask_lists=mask_lists) - if verbose: - stop_time = time.time() - print('startable.fit_velocities runtime = {0:.0f} s for {1:d} stars'.format(stop_time - start_time, N_stars)) + unique_motion_models, unique_inv_indices = np.unique(self['motion_model_used'], return_inverse=True) + indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} - return - - def fit_velocity_for_star(self, ss, motion_model_dict, weighting='var', use_scipy=True, absolute_sigma=True, - bootstrap=False, fixed_t0=False, mask_val=None, mask_lists=False, - default_motion_model='Linear'): - # TODO: "weighting" is not used - # - # Make a mask of invalid (NaN) values and a user-specified invalid value. - # + # Prepare fit_params, fixed_params, fit_param_errs for each star - x = np.ma.masked_invalid(self['x'][ss, :].data) - y = np.ma.masked_invalid(self['y'][ss, :].data) - if mask_val: - x = np.ma.masked_values(x, mask_val) - y = np.ma.masked_values(y, mask_val) - # If no mask, convert x.mask to list - if not np.ma.is_masked(x): - x.mask = np.zeros_like(x.data, dtype=bool) - if not np.ma.is_masked(y): - y.mask = np.zeros_like(y.data, dtype=bool) - - if mask_lists is not False: - # Remove a list - if isinstance(mask_lists, list): - if all(isinstance(item, int) for item in mask_lists): - x.mask[mask_lists] = True - y.mask[mask_lists] = True - - # Throw a warning if mask_lists is not a list - if not isinstance(mask_lists, list): - raise RuntimeError('mask_lists needs to be a list.') - # - # Assign the appropriate positional errors - # - if 'xe' in self.colnames: - # Make a mask of invalid (NaN) values and a user-specified invalid value. - xe = np.ma.masked_invalid(self['xe'][ss, :].data) - ye = np.ma.masked_invalid(self['ye'][ss, :].data) - - # Catch the case where we have positions but no errors for - # some of the entries... we need to "fill in" reasonable - # weights for these... just use the average weights over - # all the other epochs. - pos_no_err = np.where((np.isfinite(x) & np.isfinite(y)) & - (np.isfinite(xe) == False) & (np.isfinite(ye) == False))[0] - pos_with_err = np.where((np.isfinite(x) & np.isfinite(y)) & - (np.isfinite(xe) & np.isfinite(ye)))[0] - - if len(pos_with_err) > 0: - xe[pos_no_err] = xe[pos_with_err].mean() - ye[pos_no_err] = ye[pos_with_err].mean() - else: - xe[pos_no_err] = 1.0 - ye[pos_no_err] = 1.0 - else: - N_epochs = len(x) - xe = np.ones(N_epochs, dtype=float) - ye = np.ones(N_epochs, dtype=float) - xe = np.ma.masked_invalid(xe) - ye = np.ma.masked_invalid(xe) - - if mask_val: - xe = np.ma.masked_values(xe, mask_val) - ye = np.ma.masked_values(ye, mask_val) - # If no mask, convert xe.mask to list - if not np.ma.is_masked(xe): - xe.mask = np.zeros_like(xe.data, dtype=bool) - if not np.ma.is_masked(ye): - ye.mask = np.zeros_like(ye.data, dtype=bool) + for unique_motion_model, unique_index in indices_by_motion_model.items(): + # Create motion model instance + motion_model_instance = motion_model.motion_model_map()[unique_motion_model]() + # Prepare parameters for prediction + fit_params = np.array([ + self[param_name][unique_index] for param_name in motion_model_instance.fit_param_names + ]).T # shape (N_stars_this_model, N_params) + + fit_param_errs = np.array([ + self[param_name + '_err'][unique_index] for param_name in motion_model_instance.fit_param_names + ]).T # shape (N_stars_this_model, N_params) + + fixed_params = {} + for param_name in motion_model_instance.fixed_param_names: + col_name = param_name + if param_name + '_mm' in self.colnames: + col_name = param_name + '_mm' + fixed_params[param_name] = self[col_name][unique_index] - if mask_lists is not False: - # Remove a list - if isinstance(mask_lists, list): - if all(isinstance(item, int) for item in mask_lists): - xe.mask[mask_lists] = True - ye.mask[mask_lists] = True - - # Throw a warning if mask_lists is not a list - if not isinstance(mask_lists, list): - raise RuntimeError('mask_lists needs to be a list.') + # TODO: vectorize obsLocation handling in motion models + if (param_name == 'obsLocation'): + assert np.unique(fixed_params[param_name]).size == 1, \ + "infer_positions: obsLocation fixed parameter has different values for different stars. Vectorized handling not implemented yet." + fixed_params[param_name] = fixed_params[param_name][0] - # - # Make a mask of invalid (NaN) values and a user-specified invalid value. - # - if 't' in self.colnames: - t = np.ma.masked_invalid(self['t'][ss, :].data) - else: - t = np.ma.masked_invalid(self.meta['list_times']) + # Predict positions + x, y, xe, ye = motion_model_instance.model( + times, fit_params, fixed_params, fit_param_errs + ) + x_pred[unique_index] = x + y_pred[unique_index] = y + xe_pred[unique_index] = xe + ye_pred[unique_index] = ye - if mask_val: - t = np.ma.masked_values(t, mask_val) - if not np.ma.is_masked(t): - t.mask = np.zeros_like(t.data, dtype=bool) - - if mask_lists is not False: - # Remove a list - if isinstance(mask_lists, list): - if all(isinstance(item, int) for item in mask_lists): - t.mask[mask_lists] = True + return x_pred, y_pred, xe_pred, ye_pred - # Throw a warning if mask_lists is not a list - if not isinstance(mask_lists, list): - raise RuntimeError('mask_lists needs to be a list.') - # For inconsistent masks, mask the star if any of the values are masked. - new_mask = np.logical_or.reduce((t.mask, x.mask, y.mask, xe.mask, ye.mask)) - - # - # Figure out where we have detections (as indicated by error columns) - # - good = np.where((xe != 0) & (ye != 0) & - np.isfinite(xe) & np.isfinite(ye) & - np.isfinite(x) & np.isfinite(y) & ~new_mask)[0] - - N_good = len(good) - - # Catch the case where there is NO good data. - if N_good == 0: - #self['motion_model_used'][ss] = 'None' - self['n_fit'][ss] = N_good - self['n_params'][ss] = 0 - return - - # Everything below has N_good >= 1 - x = x[good] - y = y[good] - t = t[good] - xe = xe[good] - ye = ye[good] - - # - # Unless t0 is fixed, calculate the t0 for the stars. - # - if fixed_t0 is False: - t_weight = 1.0 / np.hypot(xe, ye) - t0 = np.average(t, weights=t_weight) - elif fixed_t0 is True: - t0 = self.t0 - else: - t0 = fixed_t0[ss] - self['t0'][ss] = t0 - self['n_fit'][ss] = N_good - - # - # Decide which motion_model to fit. - # - motion_model_use = self['motion_model_input'][ss] - # Go to default model if not enough points for assigned but enough for default - # TODO: think about whether we want other fallbacks besides the singular default and Fixed - if (N_good < motion_model_dict[motion_model_use].n_pts_req) and \ - (N_good >= motion_model_dict[default_motion_model].n_pts_req): - motion_model_use = default_motion_model - # If not enough points for either, go to a fixed model - elif (N_good < motion_model_dict[motion_model_use].n_pts_req) and \ - (N_good < motion_model_dict[default_motion_model].n_pts_req): - motion_model_use = 'Fixed' - # If the points do not cover multiple times, go to a fixed model - if (t == t[0]).all(): - motion_model_use = 'Fixed' - - self['motion_model_used'][ss] = motion_model_use - -# # Get the motion model object. -# modClass = motion_model_dict[motion_model_use] -# -# # Load up any prior information on parameters for this model. -# param_dict = {} -# for par in modClass.fit_param_names+modClass.fixed_param_names: -# if ~np.isnan(self[par][ss]): -# param_dict[par] = self[par][ss] - - # Model object - mod = motion_model_dict[motion_model_use] - fixed_params = [self[par][ss] for par in mod.fixed_param_names] - - # Fit for the best parameters - params, param_errs, chi2_x, chi2_y = mod.fit_motion_model(t, x, y, xe, ye, t0, bootstrap=bootstrap, - weighting=weighting, use_scipy=use_scipy, absolute_sigma=absolute_sigma) - # chi2_x,chi2_y = mod.get_chi2(params,fixed_params, t,x,y,xe,ye) - self['chi2_x'][ss]=chi2_x - self['chi2_y'][ss]=chi2_y - self['n_params'][ss] = mod.n_params - - # Save parameters and errors to table. - for pp in range(len(mod.fit_param_names)): - par = mod.fit_param_names[pp] - par_err = par + '_err' - self[par][ss] = params[pp] - self[par_err][ss] = param_errs[pp] - - return - # New function, to use in align def get_star_positions_at_time(self, t, motion_model_dict, allow_alt_models=True): """ Get current x,y positions of each star according to its motion_model @@ -1200,137 +986,6 @@ def get_star_positions_at_time(self, t, motion_model_dict, allow_alt_models=True return x, y, xe, ye - def fit_velocities_all_detected(self, motion_model_to_fit, weighting='var', use_scipy=True, absolute_sigma=True, times=None, - select_stars=None, epoch_cols='all', mask_val=None, art_star=False, return_result=False): - """Fit velocities for stars detected in all epochs specified by epoch_cols. - Criterion: xe/ye error > 0 and finite, x/y not masked. - - Parameters - ---------- - motion_model_to_fit : MotionModel - Motion model object to use for fitting all stars - weighting : str, optional - Variance weighting('var') or standard deviation weighting ('std'), by default 'var' - select_idx : array-like, optional - Indices of stars to select for fitting, by default None (fit all detected stars) - epoch_cols : str or list of intergers, optional - List of epoch column indices used for fitting velocity, by default 'all' - mask_val : float, optional - Values in x, y to be masked - art_star : bool, optional - Artificial star or observation star catalog. If artificial star, use 'det' column to select stars detected in all epochs, by default False - return_result : bool, optional - Return the velocity results or not, by default False - - Returns - ------- - vel_result : astropy Table - Astropy Table with velocity results - """ - - N_stars = len(self) - if select_stars is None: - select_stars = np.arange(N_stars) - else: - select_stars = np.asarray(select_stars) - - if epoch_cols == 'all': - epoch_cols = np.arange(np.shape(self['x'])[1]) - - # Artificial Star - if art_star: - detected_in_all_epochs = np.all(self['det'][select_stars, :][:, epoch_cols], axis=1) - - # Observation Star - else: - valid_xe = np.all(self['xe'][select_stars, :][:, epoch_cols]!=0, axis=1) & np.all(np.isfinite(self['xe'][select_stars, :][:, epoch_cols]), axis=1) - valid_ye = np.all(self['ye'][select_stars, :][:, epoch_cols]!=0, axis=1) & np.all(np.isfinite(self['ye'][select_stars, :][:, epoch_cols]), axis=1) - - if mask_val: - x = np.ma.masked_values(self['x'][select_stars, :][:, epoch_cols], mask_val, shrink=False) - y = np.ma.masked_values(self['y'][select_stars, :][:, epoch_cols], mask_val, shrink=False) - valid_x = ~np.any(x.mask, axis=1) - valid_y = ~np.any(y.mask, axis=1) - detected_in_all_epochs = np.logical_and.reduce(( - valid_x, valid_y, valid_xe, valid_ye)) - else: - detected_in_all_epochs = np.logical_and(valid_xe, valid_ye) - - N = len(self['x'][select_stars, :]) - fit_params = motion_model_to_fit.fit_param_names - param_data = {p: np.zeros(N) for p in fit_params} - param_data.update({p+'_err': np.zeros(N) for p in fit_params}) - param_data.update({p: np.zeros(N) for p in motion_model_to_fit.fixed_param_names}) - param_data['chi2_x'] = np.zeros(N) - param_data['chi2_y'] = np.zeros(N) - - if times is None: - if 'YEARS' in self.meta: - times = np.array(self.meta['YEARS'])[epoch_cols] - elif 't' in self.colnames: - times = self['t'][0, epoch_cols] - else: - raise ValueError("No valid time column found.") - - if not art_star: - x_arr = self['x'][select_stars, :][:, epoch_cols] - y_arr = self['y'][select_stars, :][:, epoch_cols] - else: - x_arr = self['x'][select_stars, :][:, epoch_cols, 1] - y_arr = self['y'][select_stars, :][:, epoch_cols, 1] - - xe_arr = self['xe'][select_stars, :][:, epoch_cols] - ye_arr = self['ye'][select_stars, :][:, epoch_cols] - - # Only fit for >1 epochs, otherwise all velocities will be 0 - if len(epoch_cols) > 1: - # For each star - for i in tqdm(range(N)): - x = x_arr[i] - y = y_arr[i] - xe = xe_arr[i] - ye = ye_arr[i] - t0 = np.average(times, weights=1. / np.hypot(xe, ye)) - - # Run fit and record results - params, param_errs = motion_model_to_fit.fit_motion_model( - times, x, y, xe, ye, t0, weighting=weighting, - use_scipy=use_scipy, absolute_sigma=absolute_sigma - ) - if 't0' in motion_model_to_fit.fixed_param_names: - param_data['t0'][i] = t0 - for j, param in enumerate(fit_params): - param_data[param][i] = params[j] - param_data[f'{param}_err'][i] = param_errs[j] - chi2x, chi2y = motion_model_to_fit.get_chi2(params, [t0], times, x, y, xe, ye) - param_data['chi2_x'][i] = chi2x - param_data['chi2_y'][i] = chi2y - - vel_result = Table.from_pandas(pd.DataFrame(param_data)) - - # Add n_vfit - n_fit = len(epoch_cols) - vel_result['n_fit'] = n_fit - - # Clean/remove up old arrays. - columns = [*vel_result.keys(), 'n_fit'] - for column in columns: - if column in self.colnames: self.remove_column(column) - - # Update self - for column in columns: - column_array = MaskedColumn(np.ma.zeros(N_stars), dtype=float, name=column) - column_array[select_stars] = vel_result[column] - column_array[select_stars][~detected_in_all_epochs] = np.nan - column_array.mask[select_stars] = ~detected_in_all_epochs - # Mask unselected indices - column_array.mask[~np.isin(np.arange(N_stars), select_stars)] = True - self[column] = column_array - - if return_result: - return vel_result - else: - return def shift_reference_frame(self, delta_vx=0.0, delta_vy=0.0, delta_pi=0.0, motion_model_dict={}): diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 804d4e7..f9cd97c 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -82,7 +82,6 @@ def test_StarTable_init2(): assert len(tab) == len(list1) - return def test_combine_lists(): @@ -175,39 +174,37 @@ def test_add_starlist(): t.add_starlist(x=x_new, y=y_new, m=m_new, xe=xe_new, ye=ye_new, me=me_new, meta={'list_times': t_new}) - assert len(t) == len(t_orig) + np.testing.assert_equal(len(t), len(t_orig)) expected_shape = np.array(t_orig['x'].shape) expected_shape[1] += 1 - - assert len(t['x'].shape) == len(expected_shape) - assert t['x'].shape[0] == expected_shape[0] + + np.testing.assert_equal(len(t['x'].shape), len(expected_shape)) + np.testing.assert_equal(t['x'].shape[0], expected_shape[0]) assert t['x'].shape[1] == expected_shape[1] - assert len(t['y'].shape) == len(expected_shape) - assert t['y'].shape[0] == expected_shape[0] + np.testing.assert_equal(len(t['y'].shape), len(expected_shape)) + np.testing.assert_equal(t['y'].shape[0], expected_shape[0]) assert t['y'].shape[1] == expected_shape[1] - assert len(t['m'].shape) == len(expected_shape) - assert t['m'].shape[0] == expected_shape[0] + np.testing.assert_equal(len(t['m'].shape), len(expected_shape)) + np.testing.assert_equal(t['m'].shape[0], expected_shape[0]) assert t['m'].shape[1] == expected_shape[1] - assert len(t['xe'].shape) == len(expected_shape) - assert t['xe'].shape[0] == expected_shape[0] - assert t['xe'].shape[1] == expected_shape[1] - - assert len(t['ye'].shape) == len(expected_shape) - assert t['ye'].shape[0] == expected_shape[0] - assert t['ye'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['xe'].shape), len(expected_shape)) + np.testing.assert_equal(t['xe'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['xe'].shape[1], expected_shape[1]) - assert len(t['me'].shape) == len(expected_shape) - assert t['me'].shape[0] == expected_shape[0] - assert t['me'].shape[1] == expected_shape[1] - - assert len(t['name']) == len(t_orig['name']) - assert len(t.meta['list_times']) == expected_shape[1] - assert t.meta['n_lists'] == 9 + np.testing.assert_equal(len(t['ye'].shape), len(expected_shape)) + np.testing.assert_equal(t['ye'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['ye'].shape[1], expected_shape[1]) + np.testing.assert_equal(len(t['me'].shape), len(expected_shape)) + np.testing.assert_equal(t['me'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['me'].shape[1], expected_shape[1]) + np.testing.assert_equal(len(t['name']), len(t_orig['name'])) + np.testing.assert_equal(len(t.meta['list_times']), expected_shape[1]) + np.testing.assert_equal(t.meta['n_lists'], 9) # Test 2: Add as starlist rather than with keywords. starlist = StarList( name=t_orig['name'], @@ -219,38 +216,37 @@ def test_add_starlist(): t = make_star_table() t.add_starlist(starlist=starlist) - assert len(t) == len(t_orig) + np.testing.assert_equal(len(t), len(t_orig)) expected_shape = np.array(t_orig['x'].shape) expected_shape[1] += 1 - - assert len(t['x'].shape) == len(expected_shape) - assert t['x'].shape[0] == expected_shape[0] - assert t['x'].shape[1] == expected_shape[1] - assert len(t['y'].shape) == len(expected_shape) - assert t['y'].shape[0] == expected_shape[0] - assert t['y'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['x'].shape), len(expected_shape)) + np.testing.assert_equal(t['x'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['x'].shape[1], expected_shape[1]) - assert len(t['m'].shape) == len(expected_shape) - assert t['m'].shape[0] == expected_shape[0] - assert t['m'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['y'].shape), len(expected_shape)) + np.testing.assert_equal(t['y'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['y'].shape[1], expected_shape[1]) - assert len(t['xe'].shape) == len(expected_shape) - assert t['xe'].shape[0] == expected_shape[0] - assert t['xe'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['m'].shape), len(expected_shape)) + np.testing.assert_equal(t['m'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['m'].shape[1], expected_shape[1]) - assert len(t['ye'].shape) == len(expected_shape) - assert t['ye'].shape[0] == expected_shape[0] - assert t['ye'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['xe'].shape), len(expected_shape)) + np.testing.assert_equal(t['xe'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['xe'].shape[1], expected_shape[1]) + np.testing.assert_equal(len(t['ye'].shape), len(expected_shape)) + np.testing.assert_equal(t['ye'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['ye'].shape[1], expected_shape[1]) - assert len(t['me'].shape) == len(expected_shape) - assert t['me'].shape[0] == expected_shape[0] - assert t['me'].shape[1] == expected_shape[1] + np.testing.assert_equal(len(t['me'].shape), len(expected_shape)) + np.testing.assert_equal(t['me'].shape[0], expected_shape[0]) + np.testing.assert_equal(t['me'].shape[1], expected_shape[1]) - assert len(t['name']) == len(t_orig['name']) - assert len(t.meta['list_times']) == expected_shape[1] - assert t.meta['n_lists'] == 9 + np.testing.assert_equal(len(t['name']), len(t_orig['name'])) + np.testing.assert_equal(len(t.meta['list_times']), expected_shape[1]) + np.testing.assert_equal(t.meta['n_lists'], 9) return @@ -298,11 +294,11 @@ def test_combine_1col(): t.combine_lists('x', weights_col='xe') - assert t['x0'][0] == t['x'][0] + np.testing.assert_equal(t['x0'][0], t['x'][0]) return -def test_fit_velocities(): +def test_fit_motion_models(): tab = make_star_table() tt = make_tiny_star_table() @@ -317,26 +313,25 @@ def test_fit_velocities(): tab.fit_motion_model(verbose=True, mask_value=-100000.) # Test creation of new variables - assert len(tab['vx']) == len(tab) - assert len(tab['vy']) == len(tab) - assert len(tab['vx_err']) == len(tab) - assert len(tab['vy_err']) == len(tab) - assert len(tab['n_fit']) == len(tab) - assert tab.meta['n_bootstrap'] == 0 + np.testing.assert_equal(len(tab['vx']), len(tab)) + np.testing.assert_equal(len(tab['vy']), len(tab)) + np.testing.assert_equal(len(tab['vx_err']), len(tab)) + np.testing.assert_equal(len(tab['vy_err']), len(tab)) + np.testing.assert_equal(len(tab['n_fit']), len(tab)) + np.testing.assert_equal(tab.meta['n_bootstrap'], 0) # Test no-fit for stars with N<2 epochs. n_epochs = (tab['x'] >= 0).sum(axis=1) idx = np.where(n_epochs < 2)[0] - assert (tab['vx'][idx] == 0).all() - assert (tab['vx_err'][idx] == 0).all() - assert (tab['n_fit'][idx] == 2).all() + np.testing.assert_equal((tab['vx'][idx] == 0).all(), True) + np.testing.assert_equal((tab['vx_err'][idx] == 0).all(), True) + np.testing.assert_equal((tab['n_fit'][idx] == 2).all(), True) # Test that the velocity errors were calculated. - assert (~(tab['vx_err'][0:100] < 0)).all() - assert (~(tab['x0_err'][0:100] < 0)).all() - assert (~(tab['vy_err'][0:100] < 0)).all() - assert (~(tab['y0_err'][0:100] < 0)).all() - + np.testing.assert_equal((~(tab['vx_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['x0_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['vy_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['y0_err'][0:100] < 0)).all(), True) ########## # Test running a second time. We should get the same results. @@ -366,11 +361,11 @@ def test_fit_velocities(): tab_b.meta = tab1.meta tab_b.fit_motion_model(verbose=True, bootstrap=50) - assert tab_b.meta['n_bootstrap'] == 50 - assert tab_b['x0_err'][0] > tab['x0_err'][0] - assert tab_b['vx_err'][0] > tab['vx_err'][0] - assert tab_b['y0_err'][0] > tab['y0_err'][0] - assert tab_b['vy_err'][0] > tab['vy_err'][0] + np.testing.assert_equal(tab_b.meta['n_bootstrap'], 50) + np.testing.assert_array_less(tab['x0_err'][0], tab_b['x0_err'][0]) + np.testing.assert_array_less(tab['vx_err'][0], tab_b['vx_err'][0]) + np.testing.assert_array_less(tab['y0_err'][0], tab_b['y0_err'][0]) + np.testing.assert_array_less(tab['vy_err'][0], tab_b['vy_err'][0]) ########## # Test what happens with no velocity errors @@ -378,15 +373,15 @@ def test_fit_velocities(): tab.remove_columns(['xe', 'ye', 'x0', 'y0', 'x0_err', 'y0_err', 'vx', 'vy', 'vx_err', 'vy_err', 'n_fit']) tab.fit_motion_model(verbose=False) - assert len(tab['vx']) == len(tab) - assert len(tab['vy']) == len(tab) - assert len(tab['vx_err']) == len(tab) - assert len(tab['vy_err']) == len(tab) - assert len(tab['n_fit']) == len(tab) - assert (~(tab['vx_err'][0:100] < 0)).all() - assert (~(tab['x0_err'][0:100] < 0)).all() - assert (~(tab['vy_err'][0:100] < 0)).all() - assert (~(tab['y0_err'][0:100] < 0)).all() + np.testing.assert_equal(len(tab['vx']), len(tab)) + np.testing.assert_equal(len(tab['vy']), len(tab)) + np.testing.assert_equal(len(tab['vx_err']), len(tab)) + np.testing.assert_equal(len(tab['vy_err']), len(tab)) + np.testing.assert_equal(len(tab['n_fit']), len(tab)) + np.testing.assert_equal((~(tab['vx_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['x0_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['vy_err'][0:100] < 0)).all(), True) + np.testing.assert_equal((~(tab['y0_err'][0:100] < 0)).all(), True) ######### # Test mask_list @@ -408,7 +403,6 @@ def test_fit_velocities(): def test_fit_velocities_2epoch(): - ########## # Test: only 2 epoch2 ########## @@ -424,30 +418,21 @@ def test_fit_velocities_2epoch(): tab_2.fit_motion_model(verbose=False, mask_value=-100000.) - assert 'n_fit' in tab_2.colnames - assert 't0' in tab_2.colnames - assert 'x0' in tab_2.colnames - assert 'y0' in tab_2.colnames - assert 'vx' in tab_2.colnames - assert 'vy' in tab_2.colnames - assert 'x0_err' in tab_2.colnames - assert 'y0_err' in tab_2.colnames - assert 'vx_err' in tab_2.colnames - assert 'vy_err' in tab_2.colnames + assert all([_ in tab_2.colnames for _ in ['n_fit', 't0', 'x0', 'y0', 'vx', 'vy', 'x0_err', 'y0_err', 'vx_err', 'vy_err']]) # 2 detections print(tab1.meta) np.testing.assert_almost_equal(tab_2['x0'][0], tab_2['x'][0,0], 1) - assert tab_2['n_fit'][0] == 2 + np.testing.assert_equal(tab_2['n_fit'][0], 2) # 1 detection - assert tab_2['x0'][100] == tab_2['x'][100, 0] - assert tab_2['n_fit'][100] == 1 - + np.testing.assert_equal(tab_2['x0'][100], tab_2['x'][100, 0]) + np.testing.assert_equal(tab_2['n_fit'][100], 1) + # 0 detections - assert np.isnan(tab_2['x0'][-1]) - assert tab_2['n_fit'][-1] == 0 - + np.testing.assert_equal(np.isnan(tab_2['x0'][-1]), True) + np.testing.assert_equal(tab_2['n_fit'][-1], 0) + return From 48321cbc93e1c38afd18be389b01344f51c6b638 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Tue, 16 Dec 2025 20:19:14 +0800 Subject: [PATCH 22/29] Resolve undefined variables and cleaned imports --- flystar/align.py | 45 +++++++++++++++------------------ flystar/analysis.py | 6 +---- flystar/examples.py | 10 ++------ flystar/match.py | 8 ++---- flystar/motion_model.py | 7 +++-- flystar/tests/test_startable.py | 1 - flystar/transforms.py | 19 +++++++------- 7 files changed, 41 insertions(+), 55 deletions(-) diff --git a/flystar/align.py b/flystar/align.py index ca9bc93..53db62f 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -1,10 +1,7 @@ import numpy as np -from . import match -from . import transforms -from . import plots +from . import match, transforms, plots, motion_model from .starlists import StarList from .startables import StarTable -from . import motion_model from astropy.table import Table, Column, vstack import datetime import copy @@ -411,7 +408,6 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar print(" **********") star_list = self.star_lists[ii] - pdb.set_trance() ref_list = self.get_ref_list_from_table(star_list['t'][0]) trans = self.trans_list[ii] @@ -880,9 +876,9 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): for mm in motion_model_col_names: if mm in self.ref_table.keys(): vals_orig[mm] = self.ref_table[mm][keep_orig] - fit_star_idxs = [idx for idx in range(len(self.ref_table)) if idx not in keep_orig] - else: - fit_star_idxs = None + # fit_star_idxs = [idx for idx in range(len(self.ref_table)) if idx not in keep_orig] + # else: + # fit_star_idxs = None # Figure out whether motion fits are necessary if ('motion_model_input' in self.ref_table.keys()) and np.all(self.ref_table['motion_model_input']=='Fixed'): @@ -2331,10 +2327,10 @@ def find_transform_new(table1_mat, table2_mat, if transInit != None: table1T_mat = table1_mat.copy() - table1T_mat = transform_by_object(table1T_mat, transInit) + table1T_mat = transform_from_object(table1T_mat, transInit) - x1e = table1T_mag['xe'] - y1e = table1T_mag['ye'] + x1e = table1T_mat['xe'] + y1e = table1T_mat['ye'] # Calculate weights as to user specification if weights == 'both': @@ -2419,8 +2415,7 @@ def write_transform(transform, starlist, reference, N_trans, deltaMag=0, restric Xcoeff = transform.px.parameters Ycoeff = transform.py.parameters else: - print(( '{0} not yet supported!'.format(transType))) - return + raise Exception(f'{trans_name} not yet supported!') # Write output _out = open(outFile, 'w') @@ -2437,7 +2432,7 @@ def write_transform(transform, starlist, reference, N_trans, deltaMag=0, restric _out.write('## N_trans: {0}\n'.format(N_trans)) _out.write('## Delta Mag: {0}\n'.format(deltaMag)) _out.write('{0:16s} {1:16s}\n'.format('# Xcoeff', 'Ycoeff')) - + # Write the coefficients such that the orders are together as defined in # documentation. This is a pain because PolyTransform output is weird. # (see astropy Polynomial2D documentation) @@ -2648,7 +2643,7 @@ def position_transform_from_object(x, y, xe, ye, transform): order = transform.order else: txt = 'Transform not yet supported by position_transform_from_object' - raise StandardError(txt) + raise Exception(txt) # How the transformation is applied depends on the type of transform. # This can be determined by the length of Xcoeff, Ycoeff @@ -2747,7 +2742,7 @@ def velocity_transform_from_object(x0, y0, x0e, y0e, vx, vy, vxe, vye, transform order = transform.order else: txt = 'Transform not yet supported by velocity_transform_from_object' - raise StandardError(txt) + raise Exception(txt) # How the transformation is applied depends on the type of transform. # This can be determined by the length of Xcoeff, Ycoeff @@ -2939,13 +2934,15 @@ def trans_initial_guess(ref_list, star_list, trans_args, mode='miracle', else: mref = ref_list['m0'] - N, x1m, y1m, m1m, x2m, y2m, m2m = match.miracle_match_briteN(star_list['x'], - star_list['y'], - star_list['m'], - xref, - yref, - mref, - briteN) + N, x1m, y1m, m1m, x2m, y2m, m2m = match.miracle_match_briteN( + star_list['x'], + star_list['y'], + star_list['m'], + xref, + yref, + mref, + briteN + ) err_msg = 'Failed to find more than '+str(n_req_match) err_msg += ' (only ' + str(len(x1m)) + ') matches, giving up.' @@ -3066,7 +3063,7 @@ def outlier_rejection_indices(star_list, ref_list, outlier_tol, verbose=True): """ # Optionally propogate the reference positions forward in time. xref, yref = get_pos_in_time(star_list['t'][0], ref_list) - + # Residuals x_resid_on_old_trans = star_list['x'] - xref y_resid_on_old_trans = star_list['y'] - yref diff --git a/flystar/analysis.py b/flystar/analysis.py index 81ab3f4..ab16f77 100644 --- a/flystar/analysis.py +++ b/flystar/analysis.py @@ -1,10 +1,6 @@ import numpy as np import pylab as plt -from flystar import starlists -from flystar import startables -from flystar import align -from flystar import match -from flystar import transforms +from . import starlists, match from astropy import table from astropy.table import Table, Column from astropy.coordinates import SkyCoord diff --git a/flystar/examples.py b/flystar/examples.py index 8059562..65723ec 100644 --- a/flystar/examples.py +++ b/flystar/examples.py @@ -1,11 +1,5 @@ -from flystar import transforms -from flystar import match -from flystar import align -from flystar import starlists -from flystar import plots import numpy as np -import copy -import pdb +from . import transforms, match, align, starlists, plots def align_example(labelFile, reference, transModel=transforms.four_paramNW, order=1, N_loop=2, @@ -83,7 +77,7 @@ def align_example(labelFile, reference, transModel=transforms.four_paramNW, orde trans, N_trans = align.find_transform(label[idx_label], label_trans[idx_label], - starlist_mat[idx_starlist], + starlist[idx_starlist], transModel=transModel, order=order, weights=weights) diff --git a/flystar/match.py b/flystar/match.py index d7c391e..9bda523 100644 --- a/flystar/match.py +++ b/flystar/match.py @@ -1,14 +1,10 @@ import numpy as np -from flystar import starlists, transforms, startables, align +from . import starlists, transforms, startables, align from collections import Counter from scipy.spatial import cKDTree as KDT -from astropy.table import Column, Table +from astropy.table import Column import itertools import copy -import scipy.signal -from scipy.spatial import distance -import math -import pdb def miracle_match_briteN(xin1, yin1, min1, xin2, yin2, min2, Nbrite, diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 42a5e54..e85d7a7 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -1098,7 +1098,7 @@ def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_ Parameters ---------- - motion_model_list : list + motion_model_list : list of MotionModels or str List of MotionModels with_errors : bool, optional Add uncertainty names with '_err' suffix or not, by default True @@ -1116,7 +1116,10 @@ def list_add(name): if name not in list_of_parameters: list_of_parameters.append(name) + mm_map = motion_model_map() for mm in motion_model_list: + if isinstance(mm, str): + mm = mm_map[mm] for param in mm.fit_param_names: # Fitter params list_add(param) @@ -1130,7 +1133,7 @@ def list_add(name): return list(list_of_parameters) -def get_all_motion_model_names(with_errors=True, with_fixed=True): +def get_all_motion_model_param_names(with_errors=True, with_fixed=True): return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) def motion_model_map(): diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 804d4e7..b0ee1b9 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -3,7 +3,6 @@ from flystar import motion_model from flystar.startables import StarTable from flystar.starlists import StarList -from flystar import motion_model import numpy as np import pytest import os diff --git a/flystar/transforms.py b/flystar/transforms.py index 6cc865a..8cb9525 100755 --- a/flystar/transforms.py +++ b/flystar/transforms.py @@ -5,8 +5,9 @@ from astropy.table import Table import collections import re -import pdb -from flystar import motion_model +import copy +import datetime +from . import motion_model class Transform2D(object): ''' @@ -220,7 +221,7 @@ def evaluate(self, x, y): yn = self.py[0] + self.py[1]*x + self.py[2]*y return xn, yn - def evaluate_error(self, x, y): + def evaluate_error(self, x, y, xe, ye): """ Transform positional uncertainties. @@ -245,7 +246,7 @@ def evaluate_error(self, x, y): """ xe_new = np.hypot(self.px[1] * xe, self.px[2] * ye) - xe_new = np.hpyot(self.px[1] * xe, self.px[2] * ye) + ye_new = np.hpyot(self.px[1] * xe, self.px[2] * ye) return xe_new, ye_new @@ -666,7 +667,7 @@ def from_file(cls, trans_file): return trans_obj - def to_file(self, trans_file): + def to_file(self, transform, outFile): """ Given a transformation object, write out the coefficients in a text file (readable by java align). Outfile name is specified by user. @@ -677,9 +678,9 @@ def to_file(self, trans_file): Parameters: ---------- - trans_file : str - The name of the output file to save the coefficients and meta data to. - This file can be read back in with + transform : PolyTransform + The transformation object containing the coefficients and meta data to save. + This object can be recreated with trans_obj = PolyTransfrom.from_file(trans_file). @@ -695,7 +696,7 @@ def to_file(self, trans_file): # Write output _out = open(outFile, 'w') - + # Write the header. DO NOT CHANGE, HARDCODED IN JAVA ALIGN _out.write('## Date: {0}\n'.format(datetime.date.today()) ) _out.write('## File: {0}, Reference: {1}\n'.format(starlist, reference) ) From f0e8884deb5ccbc68a897648f6f204ce1a57c453 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Tue, 16 Dec 2025 20:57:17 +0800 Subject: [PATCH 23/29] Fix bootstrap sampling strategy and 100% passed startable test --- flystar/motion_model.py | 10 ++++++++-- flystar/tests/test_startable.py | 4 ++-- 2 files changed, 10 insertions(+), 4 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 60c213b..11f6b16 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -136,8 +136,14 @@ def fit( edx = np.arange(n_obs, dtype=int) # Precompute All Bootstrap Draws at Once # Ensure there are enough unique points in each bootstrap sample - bdx_unique = rng.choice(edx, size=(bootstrap, self.n_params), replace=False) - bdx_extra = rng.choice(edx, size=(bootstrap, m - self.n_params), replace=True) + bdx_unique = np.stack([ + rng.choice(edx, size=self.n_params, replace=False) + for _ in range(bootstrap) + ]) + bdx_extra = np.stack([ + rng.choice(edx, size=self.n_params, replace=True) + for _ in range(bootstrap) + ]) bdx_all = np.hstack((bdx_unique, bdx_extra)) bb_params = [] diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 70ec18a..5580daf 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -340,7 +340,7 @@ def test_fit_motion_models(): vxe_orig = tab['vx_err'] x0e_orig = tab['x0_err'] tab.fit_motion_model(verbose=False, mask_value=-100000.) - + np.testing.assert_allclose(tab['vx'], vx_orig) np.testing.assert_allclose(tab['x0'], x0_orig) np.testing.assert_allclose(tab['vx_err'], vxe_orig) @@ -423,7 +423,7 @@ def test_fit_velocities_2epoch(): print(tab1.meta) np.testing.assert_almost_equal(tab_2['x0'][0], tab_2['x'][0,0], 1) np.testing.assert_equal(tab_2['n_fit'][0], 2) - + # 1 detection np.testing.assert_equal(tab_2['x0'][100], tab_2['x'][100, 0]) np.testing.assert_equal(tab_2['n_fit'][100], 1) From a1ff8f345ac5c661ca6aa9f4b6e3beb0e53e7a82 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Sat, 20 Dec 2025 15:24:37 +0800 Subject: [PATCH 24/29] Midway save of align --- flystar/align.py | 179 ++++++++++++++++++++++++------------ flystar/match.py | 2 +- flystar/motion_model.py | 59 ++---------- flystar/startables.py | 8 +- flystar/tests/test_align.py | 104 ++++++++++----------- flystar/transforms.py | 2 +- 6 files changed, 185 insertions(+), 169 deletions(-) diff --git a/flystar/align.py b/flystar/align.py index 53db62f..3a3160d 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -23,7 +23,7 @@ def __init__(self, list_of_starlists, ref_index=0, iters=2, calc_trans_inverse=False, init_guess_mode='miracle', iter_callback=None, motion_models=['Empty', 'Fixed'], - fixed_params_dict = None, + fixed_params_dict=None, use_scipy=True, absolute_sigma=False, save_path=None, @@ -301,7 +301,7 @@ def fit(self): # x_orig, y_orig, m_orig, (opt. errors) -- the transformed errors for the lists: 2D # w, w_orig (optiona) -- the input and output weights of stars in transform: 2D ########## - self.ref_table = self.setup_ref_table_from_starlist(self.star_lists[self.ref_index],motion_model_used='Fixed') + self.ref_table = self.setup_ref_table_from_starlist(self.star_lists[self.ref_index]) # Save the reference index to the meta data on the reference list. self.ref_table.meta['ref_list'] = self.ref_index @@ -423,11 +423,10 @@ def match_and_transform(self, ref_mag_lim, dr_tol, dm_tol, outlier_tol, trans_ar if trans is None: # Only use "use_in_trans" reference stars, even for initial guessing. keepers = np.where(ref_list['use_in_trans'] == True)[0] - trans = trans_initial_guess( - ref_list[keepers], - star_list_orig_trim, - self.trans_args[0], + ref_list[keepers], + star_list_orig_trim, + self.trans_args[0], mode=self.init_guess_mode, order=self.init_order, verbose=self.verbose, @@ -603,12 +602,12 @@ def setup_trans_info(self): # Add inverse trans list, if desired if self.calc_trans_inverse: - trans_list_inverse = [None for ii in range(N_lists)] + trans_list_inverse = [None] * N_lists self.trans_list_inverse = trans_list_inverse return - def setup_ref_table_from_starlist(self, star_list, motion_model_used=None): + def setup_ref_table_from_starlist(self, star_list): """ Start with the reference list.... this will change and grow over time, so make a copy that we will keep updating. @@ -616,7 +615,7 @@ def setup_ref_table_from_starlist(self, star_list, motion_model_used=None): array in the original reference star list. """ col_arrays = {} - motion_model_col_names = motion_model.get_all_motion_model_param_names(with_errors=True, with_fixed=True) + ['m0','m0_err','use_in_trans', 'motion_model_input', 'motion_model_used'] + motion_model_col_names = motion_model.motion_model_param_names(self.motion_models, with_errors=True, with_fixed=True) + ['m0','m0_err','use_in_trans', 'motion_model_input', 'motion_model_used'] for col_name in star_list.colnames: if col_name == 'name': # The "name" column will be 1D; but we will also add a "name_in_list" column. @@ -829,7 +828,12 @@ def update_ref_table_from_list(self, star_list, star_list_T, ii, idx_ref, idx_li self.ref_table['used_in_trans'][idx_ref_in_trans, ii] = True ### Add the unmatched stars and grow the size of the reference table. - self.ref_table, idx_lis_new, idx_ref_new = add_rows_for_new_stars(self.ref_table, star_list, idx_lis) + self.ref_table, idx_lis_new, idx_ref_new = add_rows_for_new_stars( + self.ref_table, + star_list, + idx_lis, + motion_model=self.motion_models[-1].name + ) if len(idx_ref_new) > 0: if self.verbose > 0: print(' Adding {0:d} new stars to the reference table.'.format(len(idx_ref_new))) @@ -862,7 +866,7 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): """ # Keep track of the original reference values. # In certain cases, we will NOT update these. - if keep_orig is not None: + if (keep_orig is not None) and (len(keep_orig) > 0): vals_orig = {} vals_orig['m0'] = self.ref_table['m0'][keep_orig] vals_orig['m0_err'] = self.ref_table['m0_err'][keep_orig] @@ -872,22 +876,41 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): if 'motion_model_used' in self.ref_table.keys(): motion_model_class_names += self.ref_table['motion_model_used'][keep_orig].tolist() vals_orig['motion_model_used'] = self.ref_table['motion_model_used'][keep_orig] - motion_model_col_names = motion_model.get_list_motion_model_param_names(motion_model_class_names, with_errors=True, with_fixed=True) + motion_model_col_names = motion_model.motion_model_param_names(motion_model_class_names, with_errors=True, with_fixed=True) for mm in motion_model_col_names: if mm in self.ref_table.keys(): vals_orig[mm] = self.ref_table[mm][keep_orig] - # fit_star_idxs = [idx for idx in range(len(self.ref_table)) if idx not in keep_orig] - # else: - # fit_star_idxs = None + fit_star_idxs = np.array([idx for idx in range(len(self.ref_table)) if idx not in keep_orig], dtype=int) + else: + fit_star_idxs = None # Figure out whether motion fits are necessary if ('motion_model_input' in self.ref_table.keys()) and np.all(self.ref_table['motion_model_input']=='Fixed'): weighted_xy = ('xe' in self.ref_table.colnames) and ('ye' in self.ref_table.colnames) weighted_m = ('me' in self.ref_table.colnames) self.ref_table.combine_lists_xym(weighted_xy=weighted_xy, weighted_m=weighted_m) + elif fit_star_idxs is None: + self.ref_table.fit_motion_model( + motion_models=self.motion_models, + fixed_params_dict=self.fixed_params_dict, + weighting=self.vel_weighting, + use_scipy=self.use_scipy, + absolute_sigma=self.absolute_sigma, + bootstrap=n_boot, + verbose=self.verbose + ) + # Combine (transformed) magnitudes + if 'me' in self.ref_table.colnames: + weights_col = None + else: + weights_col = 'me' + self.ref_table.combine_lists('m', weights_col=weights_col, ismag=True) + else: # Combine positions with a velocity fit. - self.ref_table.fit_motion_model( + update_ref_table = self.ref_table[fit_star_idxs] + keep_ref_table = self.ref_table[keep_orig] + update_ref_table.fit_motion_model( motion_models=self.motion_models, fixed_params_dict=self.fixed_params_dict, weighting=self.vel_weighting, @@ -897,14 +920,33 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): verbose=self.verbose ) + # Determine motion models for keep_ref_table + pdb.set_trace() + if 'motion_model_used' not in keep_ref_table.colnames: + all_mm_map = motion_model.motion_model_map() + mm_n_params = np.sort([mm.n_params for mm in self.motion_models]) + required_params = np.array([all_mm_map[mm_name].n_params for mm_name in keep_ref_table['motion_model_input']]) + mm_digitized = np.digitize( + x=np.minimum(np.array(keep_ref_table['n_detect']), required_params), + bins=mm_n_params + ) - 1 + keep_ref_table['motion_model_used'] = np.array([self.motion_models[d].name for d in mm_digitized]) + + # Merge back into the full ref_table + new_ref_table = vstack([keep_ref_table, update_ref_table]) + self.ref_table = new_ref_table.copy() + self.ref_table[keep_orig] = new_ref_table[0:len(keep_orig)] + self.ref_table[fit_star_idxs] = new_ref_table[len(keep_orig):] + # Combine (transformed) magnitudes if 'me' in self.ref_table.colnames: weights_col = None else: weights_col = 'me' self.ref_table.combine_lists('m', weights_col=weights_col, ismag=True) + # Replace the originals if we are supposed to keep them fixed. - if keep_orig is not None: + if (keep_orig is not None) and (len(keep_orig) > 0): for val in vals_orig.keys(): self.ref_table[val][keep_orig] = vals_orig[val] @@ -977,14 +1019,14 @@ def match_lists(self, dr_tol, dm_tol): star_list_T.transform_xym(self.trans_list[ii]) else: star_list_T.transform_xy(self.trans_list[ii]) - + xref, yref = infer_positions(star_list_T['t'][0], self.ref_table) mref = self.ref_table['m0'] idx_lis, idx_ref, dr, dm = match.match(star_list_T['x'], star_list_T['y'], star_list_T['m'], xref, yref, mref, dr_tol=dr_tol, dm_tol=dm_tol, verbose=self.verbose) - + if self.verbose > 0: fmt = 'Matched {0:5d} out of {1:5d} stars in list {2:2d} [dr = {3:7.4f} +/- {4:6.4f}, dm = {5:5.2f} +/- {6:4.2f}' print(fmt.format(len(idx_lis), len(star_list_T), ii, dr.mean(), dr.std(), dm.mean(), dm.std())) @@ -1012,7 +1054,6 @@ def get_ref_list_from_table(self, epoch): name = self.ref_table['name'] if ('motion_model_used' in self.ref_table.colnames): - print(f'{epoch=}, {epoch.shape=}') x, y, xe, ye = self.ref_table.infer_positions(epoch) else: # No velocities... just used average positions. @@ -1158,17 +1199,19 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot y2_boot_sum = np.zeros((len(ref_table['x']), n_epochs)) m_boot_sum = np.zeros((len(ref_table['x']), n_epochs)) m2_boot_sum = np.zeros((len(ref_table['x']), n_epochs)) - + # Set up motion model parameters if 'motion_model_used' in ref_table.keys(): motion_model_list = np.unique(ref_table['motion_model_used']).tolist() elif 'motion_model_input' in ref_table.keys(): motion_model_list = np.unique(ref_table['motion_model_input']).tolist() - all_mm_map = motion_model.motion_model_map() - motion_model_list = [all_mm_map[mm_name] for mm_name in motion_model_list] + if 'Empty' not in motion_model_list: + motion_model_list.append('Empty') + if 'Fixed' not in motion_model_list: + motion_model_list.append('Fixed') - motion_col_list = motion_model.get_list_motion_model_param_names(motion_model_list, with_errors=False, with_fixed=False) + motion_col_list = motion_model.motion_model_param_names(motion_model_list, with_errors=False, with_fixed=False) if calc_vel_in_bootstrap: motion_boot_sum = {} motion2_boot_sum = {} @@ -1177,7 +1220,8 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot motion2_boot_sum[col] = np.zeros((len(ref_table['x']))) all_mm_map = motion_model.motion_model_map() - motion_boot_min_epochs = np.max([all_mm_map[mm].n_params for mm in motion_model_list]) + motion_model_list = [all_mm_map[mm_name] for mm_name in motion_model_list] + motion_boot_min_epochs = np.max([mm.n_params for mm in motion_model_list]) ### IF MEMORY PROBLEMS HERE: ### DEFINE MEAN, STD VARIABLES AND BUILD THEM RATHER THAN SAVING FULL ARRAY @@ -1257,7 +1301,6 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot m=starlist_boot['m'], mref=ref_boot['m'], weights=weight, mag_trans=self.mag_trans) #print(jj) - #pdb.set_trace() # Apply transformation to *all* orig positions in this epoch. Need to make a new # FLYSTAR starlist object with the original positions for this. We don't @@ -1337,7 +1380,7 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot # Quick check to make sure bootstrap calc was valid: output t0 should be # same as input t0_arr, since we used fixed_t0 option - assert np.sum(abs(star_table['t0'] - t0_arr) == 0) + np.testing.assert_array_equal(star_table['t0'], t0_arr) #t3 = time.time() #print('=================================================') @@ -1376,7 +1419,19 @@ def calc_bootstrap_errors(self, n_boot=100, boot_epochs_min=-1, calc_vel_in_boot col[idx_good] = data_dict[ff] self.ref_table.add_column(col) - # Calculate chi^2 with bootstrap positional errors + # # Calculate chi^2 with bootstrap positional errors + # # Determine which motion model to use: + # motion_model_list = sorted(motion_model_list, key=lambda mm: mm.n_params) + # mm_n_params = np.sort([mm.n_params for mm in motion_model_list]) + + # required_params = [all_mm_map[mm_name].n_params for mm_name in self.ref_table['motion_model_input']] + # mm_digitized = np.digitize( + # x=np.minimum(np.array(self.ref_table['n_detect']), required_params), + # bins=mm_n_params + # ) - 1 + # self.ref_table['motion_model_used'] = np.array([motion_model_list[d].name for d in mm_digitized], dtype='U20') + + x_pred, y_pred, _, _ = self.ref_table.infer_positions(t_arr) xe_comb = np.hypot(self.ref_table['xe'], self.ref_table['xe_boot']) ye_comb = np.hypot(self.ref_table['ye'], self.ref_table['ye_boot']) @@ -1551,9 +1606,6 @@ def = None. If not None, then this should contain an array or list of transform iter_callback : None or function A function to call (that accepts a StarTable object and an iteration number) at the end of every iteration. This can be used for plotting or printing state. - - default_motion_model : string - Name of motion model to use for new or unassigned stars motion_models : list of str or MotionModel objects List of motion model names (strings) or MotionModel objects to use @@ -1702,7 +1754,6 @@ def fit(self): # ########## for nn in range(self.iters): - # If we are on subsequent iterations, remove matching results from the # prior iteration. This leaves aggregated (1D) columns alone. if nn > 0: @@ -1749,11 +1800,10 @@ def fit(self): print("**********") self.match_lists(self.dr_tol[-1], self.dm_tol[-1]) - keep_ref_orig = (self.update_ref_orig==False) - if keep_ref_orig: - keep_orig = np.where(self.ref_table['ref_orig'])[0] - else: + if self.update_ref_orig: keep_orig=None + else: + keep_orig = np.where(self.ref_table['ref_orig'])[0] self.update_ref_table_aggregates(keep_orig=keep_orig) ########## @@ -1804,7 +1854,7 @@ def get_all_epochs(t): return all_epochs -def setup_ref_table_from_starlist(star_list): +def setup_ref_table_from_starlist(star_list, motion_models): """ Start with the reference list.... this will change and grow over time, so make a copy that we will keep updating. @@ -1812,7 +1862,7 @@ def setup_ref_table_from_starlist(star_list): array in the original reference star list. """ col_arrays = {} - motion_model_col_names = motion_model.get_all_motion_model_param_names(with_errors=True) + motion_model_col_names = motion_model.motion_model_param_names(motion_models, with_errors=True) for col_name in star_list.colnames: if col_name == 'name': # The "name" column will be 1D; but we will also add a "name_in_list" column. @@ -1820,7 +1870,7 @@ def setup_ref_table_from_starlist(star_list): new_col_name = "name_in_list" else: new_col_name = col_name - + # Make every column's 2D arrays except "name" and those # columns used for the motion model. if col_name in motion_model_col_names: @@ -1856,7 +1906,7 @@ def setup_ref_table_from_starlist(star_list): if not new_cols_arr[ii] in ref_cols: # Some munging to convert data shape from (N,1) to (N,), # since these are all 1D cols - vals = np.transpose(np.array(ref_table[orig_cols_arr[ii]]))[0] + vals =np.array(ref_table[orig_cols_arr[ii]]).flatten() # Now add to ref_table new_col = Column(vals, name=new_cols_arr[ii]) @@ -1926,7 +1976,7 @@ def reset_ref_values(ref_table): return -def add_rows_for_new_stars(ref_table, star_list, idx_lis): +def add_rows_for_new_stars(ref_table, star_list, idx_lis, motion_model='Fixed'): """ For each star that is in star_list and NOT in idx_list, make a new row in the reference table. The values will be empty (None, NAN, etc.). @@ -1935,13 +1985,13 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis): ---------- ref_table : StarTable The reference table that the rows will be added to. - star_list : StarList The starlist that will be used to estimate how many new stars there are. - idx_lis : array or list The indices of the non-new stars (those that matched already). The complement of this array will be used as the new stars. + motion_model : str + The motion model to assign to the new stars. Returns ---------- @@ -1957,8 +2007,9 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis): idx_lis_orig = np.arange(len(star_list)) idx_lis_new = np.array(list(set(idx_lis_orig) - set(idx_lis))) + N_newstars = len(idx_lis_new) - if len(idx_lis_new) > 0: + if N_newstars > 0: col_arrays = {} for col_name in ref_table.colnames: @@ -1971,16 +2022,16 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis): elif ref_table[col_name].dtype == np.dtype('bool'): new_col_empty = False elif col_name=='motion_model_input': - new_col_empty = 'Empty' + new_col_empty = motion_model elif col_name=='motion_model_used': - new_col_empty = 'Empty' + new_col_empty = 'Fixed' else: new_col_empty = np.nan - + if len(ref_table[col_name].shape) == 1: - new_col_shape = len(idx_lis_new) + new_col_shape = N_newstars else: - new_col_shape = [len(idx_lis_new), ref_table[col_name].shape[1]] + new_col_shape = [N_newstars, ref_table[col_name].shape[1]] new_col_data = Column(data=np.tile(new_col_empty, new_col_shape), name=col_name, dtype=ref_table[col_name].dtype) @@ -2609,7 +2660,7 @@ def transform_from_object(starlist, transform): # For more complicated motion_models, # we can't easily transform them, set the values to nans and refit later. if mot: - motion_model_params = motion_model.get_all_motion_model_param_names() + motion_model_params = motion_model.motion_model_param_names() for param in motion_model_params: if param in keys: starlist_f[param] = np.nan @@ -2933,7 +2984,7 @@ def trans_initial_guess(ref_list, star_list, trans_args, mode='miracle', mref = ref_list['m'] else: mref = ref_list['m0'] - + N, x1m, y1m, m1m, x2m, y2m, m2m = match.miracle_match_briteN( star_list['x'], star_list['y'], @@ -2943,10 +2994,9 @@ def trans_initial_guess(ref_list, star_list, trans_args, mode='miracle', mref, briteN ) - - err_msg = 'Failed to find more than '+str(n_req_match) - err_msg += ' (only ' + str(len(x1m)) + ') matches, giving up.' - assert len(x1m) >= n_req_match, err_msg + + assert len(x1m) >= n_req_match, \ + f'Failed to find more than {n_req_match} (only {len(x1m)}) matches, giving up.' if verbose > 1: print('initial_guess: {0:d} stars matched between starlist and reference list'.format(N)) @@ -2965,12 +3015,12 @@ def trans_initial_guess(ref_list, star_list, trans_args, mode='miracle', trans.mag_offset = np.mean(m2m - m1m) else: trans.mag_offset = 0 - + if verbose > 1: print('init guess: ', trans.px.parameters, trans.py.parameters) warnings.filterwarnings('default', category=AstropyUserWarning) - + return trans @@ -3062,7 +3112,7 @@ def outlier_rejection_indices(star_list, ref_list, outlier_tol, verbose=True): The indicies of the stars to keep. """ # Optionally propogate the reference positions forward in time. - xref, yref = get_pos_in_time(star_list['t'][0], ref_list) + xref, yref = infer_positions(star_list['t'][0], ref_list) # Residuals x_resid_on_old_trans = star_list['x'] - xref @@ -3176,12 +3226,19 @@ def infer_positions(t, startable): to the desired epoch. If no motion/velocities exist, then just use ['x0', 'y0'] or ['x', 'y'] - Inputs + Parameters ---------- t_array : float The time to propogate to. Usually in decimal years; but it should be in the same units as the 't0' column in starlist. + startable : StarTable + Startable that needs to be inferred. + + Returns + ------- + x, y : tuple + Inferred position at time t """ # Check for motion model if 'motion_model_used' in startable.colnames: @@ -3201,10 +3258,10 @@ def infer_positions(t, startable): x = startable['x'] y = startable['y'] - return (x, y) + return x, y def logger(logfile, message, verbose = 9): if verbose > 4: print(message) logfile.write(message + '\n') - return + return \ No newline at end of file diff --git a/flystar/match.py b/flystar/match.py index 56710a9..f564cd3 100644 --- a/flystar/match.py +++ b/flystar/match.py @@ -1,5 +1,5 @@ import numpy as np -from . import starlists, transforms, startables, align +from . import starlists, transforms, startables from collections import Counter from scipy.spatial import cKDTree as KDT from astropy.table import Column diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 11f6b16..1ba2dcf 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -1065,53 +1065,13 @@ def validate_motion_models(motion_models, startable, default_motion_model): return motion_models -def get_one_motion_model_param_names(motion_model, with_errors=True, with_fixed=True): - """Get all the motion model parameters +def motion_model_param_names(motion_models, with_errors=True, with_fixed=True): + """Get the motion model parameter names from a list of MotionModels. Parameters ---------- - motion_model : MotionModel - MotionModel instance - with_errors : bool, optional - Add uncertainty names with '_err' suffix or not, by default True - with_fixed : bool, optional - Add fixed param names with '_fixed' suffix or not, by default True - - Returns - ------- - list - List of all parameter names for the motion model - """ - if isinstance(motion_model, str): - all_mm_map = motion_model_map() - motion_model = all_mm_map[motion_model] - - list_of_parameters = [] - - def list_add(name): - if name not in list_of_parameters: - list_of_parameters.append(name) - - for param in motion_model.fit_param_names: - # Fitter params - list_add(param) - # Error params - if with_errors: - list_add(param + '_err') - # Fixed params - if with_fixed: - for param in motion_model.fixed_param_names: - list_add(param) - return list_of_parameters - - -def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_fixed=True): - """Get all the motion model parameters - - Parameters - ---------- - motion_model_list : list of MotionModels or str - List of MotionModels + motion_models : MotionModel, str, or list of MotionModels/strings. + Motion model to query parameter names from. If str, should be the name of a MotionModel class. with_errors : bool, optional Add uncertainty names with '_err' suffix or not, by default True with_fixed : bool, optional @@ -1127,9 +1087,10 @@ def get_list_motion_model_param_names(motion_model_list, with_errors=True, with_ def list_add(name): if name not in list_of_parameters: list_of_parameters.append(name) - + + motion_models = np.atleast_1d(motion_models) mm_map = motion_model_map() - for mm in motion_model_list: + for mm in motion_models: if isinstance(mm, str): mm = mm_map[mm] for param in mm.fit_param_names: @@ -1142,11 +1103,11 @@ def list_add(name): if with_fixed: for param in mm.fixed_param_names: list_add(param) - return list(list_of_parameters) + return list_of_parameters -def get_all_motion_model_param_names(with_errors=True, with_fixed=True): - return get_list_motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) +def all_motion_model_param_names(with_errors=True, with_fixed=True): + return motion_model_param_names(MotionModel.__subclasses__(), with_errors=with_errors, with_fixed=with_fixed) def motion_model_map(): mm_map = dict( diff --git a/flystar/startables.py b/flystar/startables.py index bdcb880..861775e 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -730,7 +730,7 @@ def fit_motion_model( if 'motion_model_input' in self.colnames: # Determine which motion model to use based on motion_model_input column # If n_fit < required n_params for the input motion model, use the most complicated motion model with n_fit >= n_params - required_params = [all_mm_map[mm_name].n_params for mm_name in self['motion_model_input']] + required_params = np.array([all_mm_map[mm_name].n_params for mm_name in self['motion_model_input']]) mm_digitized = np.digitize( x=np.minimum(np.array(self['n_fit']), required_params), bins=mm_n_params @@ -751,7 +751,7 @@ def fit_motion_model( ############################ # Fill table with all possible motion model parameter names as new columns. motion_model_used = [all_mm_map[name] for name in np.unique(self['motion_model_used'])] - new_col_list = motion_model.get_list_motion_model_param_names(motion_model_used, with_errors=True, with_fixed=False) + new_col_list = motion_model.motion_model_param_names(motion_model_used, with_errors=True, with_fixed=False) new_col_list += ['chi2_x', 'chi2_y', 'n_params'] if 't0' not in new_col_list: @@ -810,9 +810,10 @@ def fit_motion_model( for unique_motion_model, unique_index in indices_by_motion_model.items(): # Create motion model instance motion_model_instance = input_mm_map[unique_motion_model]() + param_names = motion_model_instance.fit_param_names # Initialize arrays to store results n_stars_this_model = len(unique_index) - n_params = len(motion_model_instance.fit_param_names) + n_params = len(param_names) params_array = np.full((n_stars_this_model, n_params), fill_value, dtype=float) param_errs_array = np.full((n_stars_this_model, n_params), np.inf, dtype=float) @@ -843,7 +844,6 @@ def fit_motion_model( chi2_y_array[idx] = chi2_y # Store results back to the table - param_names = motion_model_instance.fit_param_names for j, param_name in enumerate(param_names): self[param_name][unique_index] = params_array[:, j] self[param_name + '_err'][unique_index] = param_errs_array[:, j] diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index cc4de2a..ea76ee8 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -259,12 +259,12 @@ def test_MosaicToRef(): # Also double check that they aren't exactly the same for the reference stars. assert np.not_equal(msc.ref_table['x0'], ref_list['x0']).all() assert np.not_equal(msc.ref_table['y0'], ref_list['y0']).all() - + return msc def test_MosaicToRef_p0_vel(): make_fake_starlists_poly0_vel(seed=42) - + ref_file = 'random_vel_ref.fits' list_files = ['random_vel_p0_0.fits', 'random_vel_p0_1.fits', @@ -286,7 +286,8 @@ def test_MosaicToRef_p0_vel(): # Switch our list to a "increasing to the West" list. ref_list['x0'] *= -1.0 ref_list['vx'] *= -1.0 - + ref_list['motion_model_used'] = 'Linear' + lists = [starlists.StarList.read(lf) for lf in list_files] msc = align.MosaicToRef(ref_list, lists, iters=2, @@ -391,7 +392,7 @@ def test_MosaicToRef_vel(): # Also double check that they aren't exactly the same for the reference stars. #assert np.any(np.not_equal(msc.ref_table['vx'], ref_list['vx'])) assert np.not_equal(msc.ref_table['vx'], ref_list['vx']).any() - + return msc def test_MosaicToRef_acc(): @@ -469,12 +470,13 @@ def test_MosaicToRef_acc(): if ~np.isnan(msc.ref_table['ax'][ix_fit]): i_orig.append(i) i_fit.append(ix_fit) - np.testing.assert_allclose(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig], rtol=1e-1) - np.testing.assert_allclose(msc.ref_table['ay'][i_fit], ref_list['ay'][i_orig], rtol=1e-1) + # Accelerations all too small, rtol doesn't work well here. + np.testing.assert_allclose(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig], atol=1e-3) + np.testing.assert_allclose(msc.ref_table['ay'][i_fit], ref_list['ay'][i_orig], atol=1e-3) # Also double check that they aren't exactly the same for the reference stars. - assert np.any(np.not_equal(msc.ref_table['ax'], ref_list['ax'])) - + assert np.any(np.not_equal(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig])) + return msc @@ -483,12 +485,12 @@ def make_fake_starlists_shifts(): x = np.random.rand(N_stars) * 1000 y = np.random.rand(N_stars) * 1000 m = (np.random.rand(N_stars) * 8) + 9 - + sdx = np.argsort(m) x = x[sdx] y = y[sdx] m = m[sdx] - + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] # Save original positions as reference (1st) list. @@ -1016,7 +1018,7 @@ def make_fake_starlists_poly1_par(seed=-1): return (xy_trans, mag_trans) - + def test_MosaicToRef_hst_me(): """ Test Casey's issue with 'me' not getting propogated @@ -1025,30 +1027,30 @@ def test_MosaicToRef_hst_me(): Use data from MB10-364 microlensing target for the test. """ # Target RA and Dec (MOA data download) - ra = '17:57:05.401' - dec = '-34:27:05.01' - + # ra = '17:57:05.401' + # dec = '-34:27:05.01' + # Load up a Gaia catalog (queried around the RA/Dec above) my_gaia = Table.read('mb10364_data/my_gaia.fits') my_gaia['me'] = 0.01 - + # Gather the list of starlists. For first pass, don't modify the starlists. # Loop through the observations and read them in, in prep for alignment with Gaia epochs = [2011.83, 2012.73, 2013.81] starlist_names = ['mb10364_data/2011_10_31_F606W_MATCHUP_XYMEEE_final.calib', 'mb10364_data/2012_09_25_F606W_MATCHUP_XYMEEE_final.calib', 'mb10364_data/2013_10_24_F606W_MATCHUP_XYMEEE_final.calib'] - + list_of_starlists = [] - + # Just using the F606W filters first. for ee in range(len(starlist_names)): lis = starlists.StarList.from_lis_file(starlist_names[ee]) - + # # Add additive error term. MAYBE YOU DON'T NEED THIS # lis['xe'] = np.hypot(lis['xe'], 0.01) # Adding 0.01 pix (0.1 mas) in quadrature. # lis['ye'] = np.hypot(lis['ye'], 0.01) - + lis['t'] = epochs[ee] # Lets dump the faint stars. @@ -1056,23 +1058,21 @@ def test_MosaicToRef_hst_me(): lis = lis[idx] list_of_starlists.append(lis) - + msc = align.MosaicToRef(my_gaia, list_of_starlists, iters=1, dr_tol=[0.1], dm_tol=[5], outlier_tol=[None], mag_lim=[13, 21], trans_class=transforms.PolyTransform, trans_args=[{'order': 1}], - default_motion_model='Fixed', + motion_models=['Empty', 'Fixed'], use_ref_new=False, update_ref_orig=False, mag_trans=False, - trans_weights='both,std', + trans_weighting='both,std', init_guess_mode='miracle', verbose=False) msc.fit() - tab = msc.ref_table - - assert 'me' in tab.colnames + assert 'me' in msc.ref_table.colnames return def test_bootstrap(): @@ -1099,7 +1099,7 @@ def test_bootstrap(): outlier_tol = None mag_lim = None ref_mag_lim = None - trans_weights = 'both,var' + trans_weighting = 'both,var' mag_trans = False n_boot = 15 @@ -1113,8 +1113,8 @@ def test_bootstrap(): mag_trans=mag_trans, mag_lim=mag_lim, ref_mag_lim=ref_mag_lim, - trans_weights=trans_weights, - default_motion_model='Linear', + trans_weighting=trans_weighting, + motion_models=['Linear'], use_ref_new=False, update_ref_orig=False, init_guess_mode='name', @@ -1134,7 +1134,6 @@ def test_bootstrap(): assert np.sum(np.isnan(match1.ref_table['ye_boot'])) == 0 assert np.sum(np.isnan(match1.ref_table['vx_err_boot'])) == 0 assert np.sum(np.isnan(match1.ref_table['vy_err_boot'])) == 0 - #pdb.set_trace() # Test 2: make sure boot_epochs_min is working # Eliminate some rows to list2, so some stars are only in 1 epoch. @@ -1148,8 +1147,8 @@ def test_bootstrap(): mag_trans=mag_trans, mag_lim=mag_lim, ref_mag_lim=ref_mag_lim, - trans_weights=trans_weights, - default_motion_model='Linear', + trans_weighting=trans_weighting, + motion_models=['Linear'], use_ref_new=False, update_ref_orig=False, init_guess_mode='name', @@ -1171,10 +1170,10 @@ def test_bootstrap(): assert len(good[0]) > 0 # For "good" stars: all bootstrap vals should be present - assert np.sum(np.isnan(out['xe_boot'][good])) == 0 - assert np.sum(np.isnan(out['ye_boot'][good])) == 0 - assert np.sum(np.isnan(out['vx_err_boot'][good])) == 0 - assert np.sum(np.isnan(out['vy_err_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['xe_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['ye_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['vx_err_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['vy_err_boot'][good])) == 0 # For "bad" stars, all bootstrap vals should be nans assert np.sum(np.isfinite(out['xe_boot'][bad])) == 0 @@ -1193,7 +1192,7 @@ def test_calc_vel_in_bootstrap(): """ import copy - + # Define match parameters ref = Table.read('ref_vel.lis', format='ascii') @@ -1212,7 +1211,7 @@ def test_calc_vel_in_bootstrap(): outlier_tol = None mag_lim = None ref_mag_lim = None - trans_weights = 'both,var' + trans_weighting = 'both,var' mag_trans = False n_boot = 15 @@ -1226,8 +1225,8 @@ def test_calc_vel_in_bootstrap(): mag_trans=mag_trans, mag_lim=mag_lim, ref_mag_lim=ref_mag_lim, - trans_weights=trans_weights, - default_motion_model='Linear', + trans_weighting=trans_weighting, + motion_models=['Linear'], use_ref_new=False, update_ref_orig=False, init_guess_mode='name', @@ -1280,7 +1279,7 @@ def test_transform_xym(): outlier_tol = None mag_lim = None ref_mag_lim = None - trans_weights = 'both,var' + trans_weighting = 'both,var' n_boot = 15 mag_trans = False @@ -1293,8 +1292,8 @@ def test_transform_xym(): mag_trans=mag_trans, mag_lim=mag_lim, ref_mag_lim=ref_mag_lim, - trans_weights=trans_weights, - default_motion_model='Fixed', + trans_weighting=trans_weighting, + motion_models=['Fixed'], use_ref_new=False, update_ref_orig=False, init_guess_mode='name', @@ -1328,7 +1327,7 @@ def test_transform_xym(): mag_trans=mag_trans, mag_lim=mag_lim, ref_mag_lim=ref_mag_lim, - trans_weights=trans_weights, + trans_weighting=trans_weighting, default_motion_model='Fixed', use_ref_new=False, update_ref_orig=False, @@ -1372,7 +1371,7 @@ def test_MosaicToRef_mag_bug(): outlier_tol=None, trans_class=transforms.PolyTransform, trans_args=[{'order': 1}], - default_motion_model='Fixed', + motion_models=['Fixed'], use_ref_new=False, update_ref_orig=False, verbose=True) @@ -1400,15 +1399,16 @@ def test_masked_cols(): """ # Get gaia reference stars using analysis.py # around a test location. - target = 'ob150029' + # target = 'ob150029' ra = '17:59:46.60' dec = '-28:38:41.8' # Coordinates are arcsecs offset +x to the East. - targets_dict = {'ob150029': [0.0, 0.0], - 'S005': [1.1416, 3.7405], - 'S002': [-4.421, 0.027] - } + targets_dict = { + 'ob150029': [0.0, 0.0], + 'S005': [1.1416, 3.7405], + 'S002': [-4.421, 0.027] + } # Get gaia catalog stars. Note that this produces a masked column table search_rad = 10.0 # arcsec @@ -1418,7 +1418,7 @@ def test_masked_cols(): assert isinstance(my_gaia, Table) # Let's make sure the entire align runs, just to be safe - + # Get starlists to align to gaia epochs = ['15jun07','16jul14', '17may21'] @@ -1427,7 +1427,6 @@ def test_masked_cols(): for ee in range(len(epochs)): lis_file = 'mag' + epochs[ee] + '_ob150029_kp_rms_named.lis' lis = starlists.StarList.from_lis_file(lis_file) - list_of_starlists.append(lis) # Run the align @@ -1435,12 +1434,11 @@ def test_masked_cols(): dr_tol=[0.2, 0.1], dm_tol=[1, 1], trans_class=transforms.PolyTransform, trans_args=[{'order': 1}, {'order': 1}], - default_motion_model='Linear', + motion_models=['Linear'], use_ref_new=False, update_ref_orig=False, mag_trans=True, init_guess_mode='name', verbose=True) msc.fit() - return diff --git a/flystar/transforms.py b/flystar/transforms.py index 8cb9525..968ccfa 100755 --- a/flystar/transforms.py +++ b/flystar/transforms.py @@ -127,7 +127,7 @@ def evaluate_starlist(self, star_list): complex_motion_model=False # Cannot transform more complex motion models - set values to nan if complex_motion_model: - motion_params = motion_model.get_list_motion_model_param_names(new_list['motion_model_input'], with_errors=True, with_fixed=False) + motion_params = motion_model.motion_model_param_names(new_list['motion_model_input'], with_errors=True, with_fixed=False) for param in motion_params: if param in new_list.colnames: new_list[param] = np.nan From 04fd8eae9b72e1e9d75c006517db0ca3573e6caf Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Sat, 20 Dec 2025 18:46:35 +0800 Subject: [PATCH 25/29] Add select_stars functionality in fit_motion_model --- flystar/align.py | 48 ++++++------------------------------- flystar/startables.py | 17 +++++++++++-- flystar/tests/test_align.py | 1 - 3 files changed, 22 insertions(+), 44 deletions(-) diff --git a/flystar/align.py b/flystar/align.py index 3a3160d..b4c03c4 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -834,6 +834,7 @@ def update_ref_table_from_list(self, star_list, star_list_T, ii, idx_ref, idx_li idx_lis, motion_model=self.motion_models[-1].name ) + pdb.set_trace() if len(idx_ref_new) > 0: if self.verbose > 0: print(' Adding {0:d} new stars to the reference table.'.format(len(idx_ref_new))) @@ -889,55 +890,19 @@ def update_ref_table_aggregates(self, keep_orig=None, n_boot=0): weighted_xy = ('xe' in self.ref_table.colnames) and ('ye' in self.ref_table.colnames) weighted_m = ('me' in self.ref_table.colnames) self.ref_table.combine_lists_xym(weighted_xy=weighted_xy, weighted_m=weighted_m) - elif fit_star_idxs is None: - self.ref_table.fit_motion_model( - motion_models=self.motion_models, - fixed_params_dict=self.fixed_params_dict, - weighting=self.vel_weighting, - use_scipy=self.use_scipy, - absolute_sigma=self.absolute_sigma, - bootstrap=n_boot, - verbose=self.verbose - ) - # Combine (transformed) magnitudes - if 'me' in self.ref_table.colnames: - weights_col = None - else: - weights_col = 'me' - self.ref_table.combine_lists('m', weights_col=weights_col, ismag=True) else: - # Combine positions with a velocity fit. - update_ref_table = self.ref_table[fit_star_idxs] - keep_ref_table = self.ref_table[keep_orig] - update_ref_table.fit_motion_model( + self.ref_table.fit_motion_model( motion_models=self.motion_models, fixed_params_dict=self.fixed_params_dict, weighting=self.vel_weighting, use_scipy=self.use_scipy, absolute_sigma=self.absolute_sigma, + select_stars=fit_star_idxs, bootstrap=n_boot, verbose=self.verbose ) - # Determine motion models for keep_ref_table - pdb.set_trace() - if 'motion_model_used' not in keep_ref_table.colnames: - all_mm_map = motion_model.motion_model_map() - mm_n_params = np.sort([mm.n_params for mm in self.motion_models]) - required_params = np.array([all_mm_map[mm_name].n_params for mm_name in keep_ref_table['motion_model_input']]) - mm_digitized = np.digitize( - x=np.minimum(np.array(keep_ref_table['n_detect']), required_params), - bins=mm_n_params - ) - 1 - keep_ref_table['motion_model_used'] = np.array([self.motion_models[d].name for d in mm_digitized]) - - # Merge back into the full ref_table - new_ref_table = vstack([keep_ref_table, update_ref_table]) - self.ref_table = new_ref_table.copy() - self.ref_table[keep_orig] = new_ref_table[0:len(keep_orig)] - self.ref_table[fit_star_idxs] = new_ref_table[len(keep_orig):] - # Combine (transformed) magnitudes if 'me' in self.ref_table.colnames: weights_col = None @@ -1949,6 +1914,7 @@ def copy_over_values(ref_table, star_list, star_list_T, idx_epoch, idx_ref, idx_ The indices into the star_list or star_list_T where values are copied from. """ for col_name in ref_table.colnames: + if col_name=='x': pdb.set_trace() if col_name in star_list_T.colnames: if col_name == 'name': ref_table['name_in_list'][idx_ref, idx_epoch] = star_list_T[col_name][list(idx_lis)] @@ -1976,7 +1942,7 @@ def reset_ref_values(ref_table): return -def add_rows_for_new_stars(ref_table, star_list, idx_lis, motion_model='Fixed'): +def add_rows_for_new_stars(ref_table, star_list, idx_list, motion_model='Fixed'): """ For each star that is in star_list and NOT in idx_list, make a new row in the reference table. The values will be empty (None, NAN, etc.). @@ -1987,7 +1953,7 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis, motion_model='Fixed'): The reference table that the rows will be added to. star_list : StarList The starlist that will be used to estimate how many new stars there are. - idx_lis : array or list + idx_list : array or list The indices of the non-new stars (those that matched already). The complement of this array will be used as the new stars. motion_model : str @@ -2006,7 +1972,7 @@ def add_rows_for_new_stars(ref_table, star_list, idx_lis, motion_model='Fixed'): last_star_idx = len(ref_table) idx_lis_orig = np.arange(len(star_list)) - idx_lis_new = np.array(list(set(idx_lis_orig) - set(idx_lis))) + idx_lis_new = np.array(list(set(idx_lis_orig) - set(idx_list))) N_newstars = len(idx_lis_new) if N_newstars > 0: diff --git a/flystar/startables.py b/flystar/startables.py index 861775e..25e15dd 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -539,6 +539,7 @@ def fit_motion_model( weighting='var', use_scipy=False, absolute_sigma=True, + select_stars=None, bootstrap=0, verbose=True, mask_value=None, @@ -573,6 +574,8 @@ def fit_motion_model( Use scipy.optimize.curve_fit or algebraic solution (for Linear model only), by default False absolute_sigma : bool, optional Use absolute sigma or not, see scipy curve_fit for details, by default True + select_stars : list of int, optional + Indices of stars to fit, by default None (fit all stars) bootstrap : int, optional Number of bootstrap for uncertainty resampling, by default 0 verbose : bool, optional @@ -757,8 +760,11 @@ def fit_motion_model( if 't0' not in new_col_list: new_col_list.append('t0') - # Replace old columns if they exist + # Add new columns if they do not exist for col in new_col_list: + if col in self.colnames: + # Keep old data if the column already exists + continue if col.endswith('_err'): self.add_column( Column(data=np.full(N_stars, np.inf, dtype=float), name=col), @@ -804,7 +810,14 @@ def fit_motion_model( ######### FITTING ######### ########################### unique_motion_models, unique_inv_indices = np.unique(self['motion_model_used'], return_inverse=True) - indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} + if select_stars is not None: + select_stars = np.asarray(select_stars) + if select_stars.dtype == bool: + select_stars = np.flatnonzero(select_stars) + indices_by_motion_model = {key: np.intersect1d(select_stars, np.flatnonzero(unique_inv_indices == k)) for k, key in enumerate(unique_motion_models)} + else: + indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} + # Expensive for loop! Prepare everything beforehand to speed up. for unique_motion_model, unique_index in indices_by_motion_model.items(): diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index ea76ee8..3e55e2c 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -286,7 +286,6 @@ def test_MosaicToRef_p0_vel(): # Switch our list to a "increasing to the West" list. ref_list['x0'] *= -1.0 ref_list['vx'] *= -1.0 - ref_list['motion_model_used'] = 'Linear' lists = [starlists.StarList.read(lf) for lf in list_files] From 87d7cc444f6cff384e7ce52cb987e9b4b187b430 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Sun, 21 Dec 2025 11:57:30 +0800 Subject: [PATCH 26/29] Passed all tests! --- flystar/align.py | 24 +- flystar/analysis.py | 2 +- flystar/startables.py | 14 +- flystar/tests/test_align.ipynb | 366 ------- flystar/tests/test_align.py | 1588 ++++++++++++++++--------------- flystar/tests/test_startable.py | 2 +- 6 files changed, 829 insertions(+), 1167 deletions(-) delete mode 100644 flystar/tests/test_align.ipynb diff --git a/flystar/align.py b/flystar/align.py index b4c03c4..2820ae5 100755 --- a/flystar/align.py +++ b/flystar/align.py @@ -616,6 +616,8 @@ def setup_ref_table_from_starlist(self, star_list): """ col_arrays = {} motion_model_col_names = motion_model.motion_model_param_names(self.motion_models, with_errors=True, with_fixed=True) + ['m0','m0_err','use_in_trans', 'motion_model_input', 'motion_model_used'] + if 't0' not in motion_model_col_names: + motion_model_col_names.insert(0, 't0') for col_name in star_list.colnames: if col_name == 'name': # The "name" column will be 1D; but we will also add a "name_in_list" column. @@ -657,7 +659,7 @@ def setup_ref_table_from_starlist(self, star_list): if not new_cols_arr[ii] in ref_cols: # Some munging to convert data shape from (N,1) to (N,), # since these are all 1D cols - vals = np.transpose(np.array(ref_table[orig_cols_arr[ii]]))[0] + vals = np.array(ref_table[orig_cols_arr[ii]]).flatten() # Now add to ref_table new_col = Column(vals, name=new_cols_arr[ii]) @@ -717,11 +719,14 @@ def setup_ref_table_from_starlist(self, star_list): if 'motion_model_input' not in ref_table.colnames: ref_table.add_column(Column(np.repeat(self.motion_models[-1].name, len(ref_table)), name='motion_model_input')) - # if 'motion_model_used' not in ref_table.colnames: - # if motion_model_used is None: - # ref_table.add_column(Column(np.repeat(self.default_motion_model, len(ref_table)), name='motion_model_used')) - # else: - # ref_table.add_column(Column(np.repeat(motion_model_used, len(ref_table)), name='motion_model_used')) + if 'motion_model_used' not in ref_table.colnames: + # Order self.motion_models by decreasing n_params + sorted_mms = sorted(self.motion_models, key=lambda mm: mm.n_params, reverse=True) + # Save the most complex motion model that can infer the positions with the existing columns. + for mm in sorted_mms: + if all([_ in ref_table.colnames for _ in mm.fit_param_names]) and all([_ in ref_table.colnames for _ in mm.fixed_param_names]): + ref_table.add_column(Column(np.repeat(mm.name, len(ref_table)), name='motion_model_used')) + break return ref_table @@ -834,7 +839,7 @@ def update_ref_table_from_list(self, star_list, star_list_T, ii, idx_ref, idx_li idx_lis, motion_model=self.motion_models[-1].name ) - pdb.set_trace() + if len(idx_ref_new) > 0: if self.verbose > 0: print(' Adding {0:d} new stars to the reference table.'.format(len(idx_ref_new))) @@ -1880,10 +1885,10 @@ def setup_ref_table_from_starlist(star_list, motion_models): if 'use_in_trans' not in ref_table.colnames: new_col = Column(np.ones(len(ref_table), dtype=bool), name='use_in_trans') ref_table.add_column(new_col) - + # Now reset the original values to invalids... they will be filled in # at later times. Preserve content only in the columns: name, x0, y0, m0 (and 0e). - # Note that these are all the 1D columsn. + # Note that these are all the 1D columns. for col_name in ref_table.colnames: if len(ref_table[col_name].data.shape) == 2: # Find the 2D columns ref_table._set_invalid_list_values(col_name, -1) @@ -1914,7 +1919,6 @@ def copy_over_values(ref_table, star_list, star_list_T, idx_epoch, idx_ref, idx_ The indices into the star_list or star_list_T where values are copied from. """ for col_name in ref_table.colnames: - if col_name=='x': pdb.set_trace() if col_name in star_list_T.colnames: if col_name == 'name': ref_table['name_in_list'][idx_ref, idx_epoch] = star_list_T[col_name][list(idx_lis)] diff --git a/flystar/analysis.py b/flystar/analysis.py index f502375..ceca739 100644 --- a/flystar/analysis.py +++ b/flystar/analysis.py @@ -44,7 +44,7 @@ def query_gaia(ra, dec, search_radius=30.0, table_name='gaiadr3'): search_radius *= u.arcsec Gaia.ROW_LIMIT = 50000 - gaia_job = Gaia.cone_search_async(target_coords, search_radius, table_name = table_name + '.gaia_source') + gaia_job = Gaia.cone_search_async(target_coords, radius=search_radius, table_name=table_name + '.gaia_source') gaia = gaia_job.get_results() #Change new 'SOURCE_ID' column header back to lowercase 'source_id' so all subsequent functions still work: diff --git a/flystar/startables.py b/flystar/startables.py index 25e15dd..3de41cc 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -602,19 +602,19 @@ def fit_motion_model( ####### Check Params ###### ########################### if weighting not in ['var', 'std']: - raise ValueError(f"fit_velocities: Weighting must either be 'var' or 'std', not {weighting}!") + raise ValueError(f"fit_motion_model: Weighting must either be 'var' or 'std', not {weighting}!") if ('t' not in self.colnames) and ('list_times' not in self.meta): - raise KeyError("fit_velocities: Failed to access time values. No 't' column in table, no 'list_times' in meta.") + raise KeyError("fit_motion_model: Failed to access time values. No 't' column in table, no 'list_times' in meta.") # Check if we have the required columns if not all([_ in self.colnames for _ in ['x', 'y']]): - raise KeyError(f"fit_velocities: Missing required columns in the table: {', '.join(['x', 'y'])}!") + raise KeyError(f"fit_motion_model: Missing required columns in the table: {', '.join(['x', 'y'])}!") # Check fixed_params_dict is a dict if fixed_params_dict is not None: if not isinstance(fixed_params_dict, dict): - raise ValueError("fit_velocities: fixed_params_dict must be a dictionary!") + raise ValueError("fit_motion_model: fixed_params_dict must be a dictionary!") # Convert motion_models to MotionModel objects if they are strings: all_mm_map = motion_model.motion_model_map() @@ -635,7 +635,7 @@ def fit_motion_model( if 'motion_model_input' in self.colnames: input_mm_names = np.unique(self['motion_model_input']) assert all([name in all_mm_map.keys() for name in input_mm_names]), \ - f"fit_velocities: Unknown motion model name(s) in 'motion_model_input' column. Available motion models are: {', '.join(all_mm_map.keys())}." + f"fit_motion_model: Unknown motion model name(s) in 'motion_model_input' column. Available motion models are: {', '.join(all_mm_map.keys())}." for mm_name in input_mm_names: if mm_name not in mm_names: motion_models.append(all_mm_map[mm_name]) @@ -649,7 +649,7 @@ def fit_motion_model( if 'motion_model_input' not in self.colnames: # If motion_model_input column is not provided, assert that motion model n_params are unique and sorted # Otherwise the fitter does not know which motion model to use based on n_obs - assert len(mm_n_params) == len(set(mm_n_params)), "fit_velocities: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs. Please provide unique motion_models or a 'motion_model_input' column." + assert len(mm_n_params) == len(set(mm_n_params)), "fit_motion_model: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs. Please provide unique motion_models or a 'motion_model_input' column." ########################### @@ -814,6 +814,8 @@ def fit_motion_model( select_stars = np.asarray(select_stars) if select_stars.dtype == bool: select_stars = np.flatnonzero(select_stars) + else: + select_stars = np.asarray(select_stars, dtype=int) indices_by_motion_model = {key: np.intersect1d(select_stars, np.flatnonzero(unique_inv_indices == k)) for k, key in enumerate(unique_motion_models)} else: indices_by_motion_model = {key: np.flatnonzero(unique_inv_indices == k) for k, key in enumerate(unique_motion_models)} diff --git a/flystar/tests/test_align.ipynb b/flystar/tests/test_align.ipynb deleted file mode 100644 index 02442b9..0000000 --- a/flystar/tests/test_align.ipynb +++ /dev/null @@ -1,366 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Notebook for Running Align Tests" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "from flystar.tests import test_align\n", - "from flystar import starlists\n", - "from astropy.table import Table" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test: make_fake_starlists_poly1_vel\n", - "\n", - "Just make sure the tables look sensible and are in the right units." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " name m0 m0e ... vye t0 \n", - "-------- ----------------- -------------------- ... ------------------- ------\n", - "star_155 9.106905292995506 0.054167528156861204 ... 0.1564397531527286 2019.5\n", - "star_113 9.153031462110043 0.0421090989942197 ... 0.08128628950126615 2019.5\n", - "star_077 9.16547870263162 0.02021147759307802 ... 0.05907352582911862 2019.5\n", - "star_069 9.169817788300977 0.027788213230369625 ... 0.04965351499764548 2019.5\n", - "star_037 9.173200786855755 0.007665400875860144 ... 0.22723357600795704 2019.5\n", - " name m me ... ye t \n", - "-------- ----------------- -------------------- ... -------------------- ------\n", - "star_155 9.198437965086988 0.054167528156861204 ... 0.02649499466969545 2018.5\n", - "star_113 9.257333243243941 0.0421090989942197 ... 0.02606700846524875 2018.5\n", - "star_077 9.252158908537464 0.02021147759307802 ... 0.04250920654497108 2018.5\n", - "star_069 9.267901667333167 0.027788213230369625 ... 0.042689240225924296 2018.5\n", - "star_037 9.276780126418494 0.007665400875860144 ... 0.03592203011554212 2018.5\n", - " name m me ... ye t \n", - "-------- ----------------- -------------------- ... -------------------- ------\n", - "star_155 9.478887659623185 0.054167528156861204 ... 0.02649499466969545 2019.5\n", - "star_113 9.569878576042546 0.0421090989942197 ... 0.02606700846524875 2019.5\n", - "star_077 9.575998150724095 0.02021147759307802 ... 0.04250920654497108 2019.5\n", - "star_069 9.593581807234129 0.027788213230369625 ... 0.042689240225924296 2019.5\n", - "star_037 9.553127108740597 0.007665400875860144 ... 0.03592203011554212 2019.5\n", - "['name', 'm0', 'm0e', 'x0', 'x0e', 'y0', 'y0e', 'vx', 'vxe', 'vy', 'vye', 't0']\n", - "['name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't']\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/jlu/code/python/flystar/flystar/starlists.py:386: UserWarning: The StarList class requires a arguments('name', 'x', 'y', 'm')\n", - " warnings.warn(err_msg, UserWarning)\n" - ] - } - ], - "source": [ - "test_align.make_fake_starlists_poly1_vel()\n", - "\n", - "ref = Table.read('random_vel_ref.fits')\n", - "lis0 = Table.read('random_vel_0.fits')\n", - "lis1 = Table.read('random_vel_1.fits')\n", - "\n", - "print(ref[0:5])\n", - "print(lis0[0:5])\n", - "print(lis1[0:5])\n", - "\n", - "print(ref.colnames)\n", - "print(lis0.colnames)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## test_align_vel\n", - "\n", - "Make sure it runs, make some plots along the way, etc." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/jlu/code/python/flystar/flystar/starlists.py:386: UserWarning: The StarList class requires a arguments('name', 'x', 'y', 'm')\n", - " warnings.warn(err_msg, UserWarning)\n", - "/Users/jlu/code/python/flystar/flystar/starlists.py:386: UserWarning: The StarList class requires a arguments('name', 'x', 'y', 'm')\n", - " warnings.warn(err_msg, UserWarning)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " \n", - "**********\n", - "**********\n", - "Starting iter 0 with ref_table shape: (200, 1)\n", - "**********\n", - "**********\n", - " \n", - " **********\n", - " Matching catalog 1 / 4 in iteration 0 with 200 stars\n", - " **********\n", - "initial_guess: 50 stars matched between starlist and reference list\n", - "initial_guess: [-6.05144456e+00 1.01098279e+00 -2.50608887e-04] [-1.07161761e+01 4.89226304e-05 1.01096529e+00]\n", - " Found 0 duplicates out of 196 matches\n", - "In Loop 0 found 196 matches\n", - " Found 0 duplicates out of 196 matches\n", - " \n", - " **********\n", - " Matching catalog 2 / 4 in iteration 0 with 200 stars\n", - " **********\n", - "initial_guess: 49 stars matched between starlist and reference list\n", - "initial_guess: [-1.02158015e+02 1.02080743e+00 -1.45081519e-04] [-5.07779471e+01 -2.60729494e-05 9.99423500e-01]\n", - " Found 0 duplicates out of 200 matches\n", - "In Loop 0 found 200 matches\n", - " Found 0 duplicates out of 200 matches\n", - " \n", - " **********\n", - " Matching catalog 3 / 4 in iteration 0 with 200 stars\n", - " **********\n", - "initial_guess: 50 stars matched between starlist and reference list\n", - "initial_guess: [-2.14220566e-10 1.00000000e+00 -2.24089697e-16] [2.50622339e-10 0.00000000e+00 1.00000000e+00]\n", - " Found 0 duplicates out of 200 matches\n", - "In Loop 0 found 200 matches\n", - " Found 0 duplicates out of 200 matches\n", - " \n", - " **********\n", - " Matching catalog 4 / 4 in iteration 0 with 200 stars\n", - " **********\n", - "initial_guess: 50 stars matched between starlist and reference list\n", - "initial_guess: [-2.57803428e+02 1.03052409e+00 -5.28390832e-05] [ 2.49886631e+02 -6.00884405e-05 9.98642952e-01]\n", - " Found 0 duplicates out of 200 matches\n", - "In Loop 0 found 200 matches\n", - " Found 0 duplicates out of 200 matches\n", - " \n", - "**********\n", - "**********\n", - "Starting iter 1 with ref_table shape: (204, 4)\n", - "**********\n", - "**********\n", - " \n", - " **********\n", - " Matching catalog 1 / 4 in iteration 1 with 200 stars\n", - " **********\n", - " Found 0 duplicates out of 199 matches\n", - "In Loop 1 found 199 matches\n", - " Found 0 duplicates out of 199 matches\n", - " \n", - " **********\n", - " Matching catalog 2 / 4 in iteration 1 with 200 stars\n", - " **********\n", - " Found 0 duplicates out of 198 matches\n", - "In Loop 1 found 198 matches\n", - " Found 0 duplicates out of 199 matches\n", - " \n", - " **********\n", - " Matching catalog 3 / 4 in iteration 1 with 200 stars\n", - " **********\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/jlu/code/python/flystar/flystar/starlists.py:386: UserWarning: The StarList class requires a arguments('name', 'x', 'y', 'm')\n", - " warnings.warn(err_msg, UserWarning)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Found 0 duplicates out of 200 matches\n", - "In Loop 1 found 200 matches\n", - " Found 0 duplicates out of 200 matches\n", - " \n", - " **********\n", - " Matching catalog 4 / 4 in iteration 1 with 200 stars\n", - " **********\n", - " Found 0 duplicates out of 200 matches\n", - "In Loop 1 found 200 matches\n", - " Found 0 duplicates out of 200 matches\n", - "**********\n", - "Final Matching\n", - "**********\n", - " Found 0 duplicates out of 199 matches\n", - "Matched 199 out of 200 stars in list 0\n", - " Found 0 duplicates out of 199 matches\n", - "Matched 199 out of 200 stars in list 1\n", - " Found 0 duplicates out of 200 matches\n", - "Matched 200 out of 200 stars in list 2\n", - " Found 0 duplicates out of 199 matches\n", - "Matched 199 out of 200 stars in list 3\n", - "\n", - " Preparing the reference table...\n" - ] - } - ], - "source": [ - "test_align.test_mosaic_lists_vel()" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "> /Users/jlu/code/python/flystar/flystar/align.py(3244)apply_mag_lim()\n", - "-> star_list_T.restrict_by_value(**conditions)\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) conditions\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'m0_min': None, 'm0_max': None}\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) type(star_list_T)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) type(ref_list)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "*** NameError: name 'ref_list' is not defined\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) ref_list\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "*** NameError: name 'ref_list' is not defined\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) u\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "> /Users/jlu/code/python/flystar/flystar/align.py(991)mosaic_lists()\n", - "-> ref_list_T = apply_mag_lim(ref_list, mag_lim[ref_index])\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) type(ref_list)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "name": "stdin", - "output_type": "stream", - "text": [ - "(Pdb) q\n" - ] - } - ], - "source": [ - "import pdb\n", - "pdb.pm()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index 3e55e2c..080ded3 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -470,442 +470,510 @@ def test_MosaicToRef_acc(): i_orig.append(i) i_fit.append(ix_fit) # Accelerations all too small, rtol doesn't work well here. - np.testing.assert_allclose(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig], atol=1e-3) - np.testing.assert_allclose(msc.ref_table['ay'][i_fit], ref_list['ay'][i_orig], atol=1e-3) + atol = 3e-4 + np.testing.assert_allclose(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig], atol=atol) + np.testing.assert_allclose(msc.ref_table['ay'][i_fit], ref_list['ay'][i_orig], atol=atol) + + ax_min = np.min(ref_list['ax'][i_orig]) + ax_max = np.max(ref_list['ax'][i_orig]) + ay_min = np.min(ref_list['ay'][i_orig]) + ay_max = np.max(ref_list['ay'][i_orig]) + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5)) + ax1.plot(ref_list['ax'][i_orig], msc.ref_table['ax'][i_fit], '.') + ax1.plot([ax_min, ax_max], [ax_min, ax_max], color='C3') + ax1.plot([ax_min, ax_max], [ax_min - atol, ax_max - atol], ls='--', color='C3') + ax1.plot([ax_min, ax_max], [ax_min + atol, ax_max + atol], ls='--', color='C3') + ax1.set_xlabel('Input ax') + ax1.set_ylabel('Ref Table ax') + ax1.set_title('Acceleration in X') + + ax2.plot(ref_list['ay'][i_orig], msc.ref_table['ay'][i_fit], '.') + ax2.plot([ay_min, ay_max], [ay_min, ay_max], color='C3') + ax2.plot([ay_min, ay_max], [ay_min - atol, ay_max - atol], ls='--', color='C3') + ax2.plot([ay_min, ay_max], [ay_min + atol, ay_max + atol], ls='--', color='C3') + ax2.set_xlabel('Input ay') + ax2.set_ylabel('Ref Table ay') + ax2.set_title('Acceleration in Y') + plt.tight_layout() + plt.show() # Also double check that they aren't exactly the same for the reference stars. assert np.any(np.not_equal(msc.ref_table['ax'][i_fit], ref_list['ax'][i_orig])) return msc +def test_MosaicToRef_hst_me(): + """ + Test Casey's issue with 'me' not getting propogated + from the input starlists to the output table. -def make_fake_starlists_shifts(): - N_stars = 200 - x = np.random.rand(N_stars) * 1000 - y = np.random.rand(N_stars) * 1000 - m = (np.random.rand(N_stars) * 8) + 9 + Use data from MB10-364 microlensing target for the test. + """ + # Target RA and Dec (MOA data download) + # ra = '17:57:05.401' + # dec = '-34:27:05.01' - sdx = np.argsort(m) - x = x[sdx] - y = y[sdx] - m = m[sdx] + # Load up a Gaia catalog (queried around the RA/Dec above) + my_gaia = Table.read('mb10364_data/my_gaia.fits') + my_gaia['me'] = 0.01 - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] + # Gather the list of starlists. For first pass, don't modify the starlists. + # Loop through the observations and read them in, in prep for alignment with Gaia + epochs = [2011.83, 2012.73, 2013.81] + starlist_names = ['mb10364_data/2011_10_31_F606W_MATCHUP_XYMEEE_final.calib', + 'mb10364_data/2012_09_25_F606W_MATCHUP_XYMEEE_final.calib', + 'mb10364_data/2013_10_24_F606W_MATCHUP_XYMEEE_final.calib'] - # Save original positions as reference (1st) list. - fmt = '{0:10s} {1:5.2f} 2015.0 {2:9.4f} {3:9.4f} 0 0 0 0\n' - _out = open('random_0.lis', 'w') - for ii in range(N_stars): - _out.write(fmt.format(name[ii], m[ii], x[ii], y[ii])) - _out.close() + list_of_starlists = [] + # Just using the F606W filters first. + for ee in range(len(starlist_names)): + lis = starlists.StarList.from_lis_file(starlist_names[ee]) - ########## - # Shifts - ########## - # Make 4 new starlists with different shifts. - shifts = [[ 6.5, 10.1], - [100.3, 50.5], - [-30.0,-100.7], - [250.0,-250.0]] + # # Add additive error term. MAYBE YOU DON'T NEED THIS + # lis['xe'] = np.hypot(lis['xe'], 0.01) # Adding 0.01 pix (0.1 mas) in quadrature. + # lis['ye'] = np.hypot(lis['ye'], 0.01) - for ss in range(len(shifts)): - xnew = x - shifts[ss][0] - ynew = y - shifts[ss][1] + lis['t'] = epochs[ee] - # Perturb with small errors (0.1 pix) - xnew += np.random.randn(N_stars) * 0.1 - ynew += np.random.randn(N_stars) * 0.1 + # Lets dump the faint stars. + idx = np.where(lis['m'] < 20.0)[0] + lis = lis[idx] - mnew = m + np.random.randn(N_stars) * 0.05 + list_of_starlists.append(lis) - _out = open('random_shift_{0:d}.lis'.format(ss+1), 'w') - for ii in range(N_stars): - _out.write(fmt.format(name[ii], mnew[ii], xnew[ii], ynew[ii])) - _out.close() + msc = align.MosaicToRef(my_gaia, list_of_starlists, iters=1, + dr_tol=[0.1], dm_tol=[5], + outlier_tol=[None], mag_lim=[13, 21], + trans_class=transforms.PolyTransform, + trans_args=[{'order': 1}], + motion_models=['Empty', 'Fixed'], + use_ref_new=False, + update_ref_orig=False, + mag_trans=False, + trans_weighting='both,std', + init_guess_mode='miracle', verbose=False) + msc.fit() - return shifts + assert 'me' in msc.ref_table.colnames + return -def make_fake_starlists_poly1(seed=-1): - # If seed >=0, then set random seed to that value - if seed >= 0: - np.random.seed(seed=seed) - - N_stars = 200 +def test_bootstrap(): + """ + Test to make sure calc_bootstrap_error() call is working + properly (e.g., only called when user calls calc_bootstrap_error, + n_boot param for calc_bootstrap_error only, boot_epochs_min working, + etc.) + """ + # Read in starlists for MosaicToRef + ref = Table.read('ref_vel.lis', format='ascii') + list1 = Table.read('E.lis', format='ascii') + list2 = Table.read('F.lis', format='ascii') - x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) - y0 = np.random.rand(N_stars) * 10.0 # arcsec - x0e = np.random.randn(N_stars) * 5.0e-4 # arcsec - y0e = np.random.randn(N_stars) * 5.0e-4 # arcsec - m0 = (np.random.rand(N_stars) * 8) + 9 # mag - m0e = np.random.randn(N_stars) * 0.05 # mag - t0 = np.ones(N_stars) * 2019.5 + list1 = starlists.StarList.from_table(list1) + list2 = starlists.StarList.from_table(list2) + + # Set parameters for alignment + transModel = transforms.PolyTransform + trans_args = {'order':2} + N_loop = 1 + dr_tol = 0.08 + dm_tol = 99 + outlier_tol = None + mag_lim = None + ref_mag_lim = None + trans_weighting = 'both,var' + mag_trans = False - # Make all the errors positive - x0e = np.abs(x0e) - y0e = np.abs(y0e) - m0e = np.abs(m0e) - - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] + n_boot = 15 + boot_epochs_min=-1 - # Make an StarList - lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, t0], - names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', 't0')) - - sdx = np.argsort(m0) - lis = lis[sdx] + # Run FLYSTAR, no bootstraps yet! + match1 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, + dm_tol=dm_tol, outlier_tol=outlier_tol, + trans_class=transModel, + trans_args=trans_args, + mag_trans=mag_trans, + mag_lim=mag_lim, + ref_mag_lim=ref_mag_lim, + trans_weighting=trans_weighting, + motion_models=['Linear'], + use_ref_new=False, + update_ref_orig=False, + init_guess_mode='name', + verbose=False) + match1.fit() - # Save original positions as reference (1st) list - # in a StarList format (with velocities). - lis.write('random_ref.fits', overwrite=True) + # Make sure no bootstrap columns exist + assert 'xe_boot' not in match1.ref_table.keys() + assert 'ye_boot' not in match1.ref_table.keys() + assert 'vxe_boot' not in match1.ref_table.keys() + assert 'vye_boot' not in match1.ref_table.keys() - ########## - # Shifts - ########## - # Make 4 new starlists with different shifts. - times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] - xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], - [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], - [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.0]], - [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]], - [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], - [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], - [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], - [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] - mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] - - # Convert into pixels (undistorted) with the following info. - scale = 0.01 # arcsec / pix - shift = [1.0, 1.0] # pix + # Run bootstrap: no boot_epochs_min + match1.calc_bootstrap_errors(n_boot=n_boot, boot_epochs_min=boot_epochs_min) + # Make sure columns exist, and none of them are nan values + assert np.sum(np.isnan(match1.ref_table['xe_boot'])) == 0 + assert np.sum(np.isnan(match1.ref_table['ye_boot'])) == 0 + assert np.sum(np.isnan(match1.ref_table['vx_err_boot'])) == 0 + assert np.sum(np.isnan(match1.ref_table['vy_err_boot'])) == 0 - for ss in range(len(times)): - dt = times[ss] - lis['t0'] - - x = lis['x0'] - y = lis['y0'] - t = np.ones(N_stars) * times[ss] + # Test 2: make sure boot_epochs_min is working + # Eliminate some rows to list2, so some stars are only in 1 epoch. + # Rerun align. Some stars should only be detected in 1 epoch + list3 = list2[0:60] - # Convert into pixels - xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) - yp = (y / scale) + shift[1] - xpe = lis['x0_err'] / scale - ype = lis['y0_err'] / scale + match2 = align.MosaicToRef(ref, [list1, list3], iters=N_loop, dr_tol=dr_tol, + dm_tol=dm_tol, outlier_tol=outlier_tol, + trans_class=transModel, + trans_args=trans_args, + mag_trans=mag_trans, + mag_lim=mag_lim, + ref_mag_lim=ref_mag_lim, + trans_weighting=trans_weighting, + motion_models=['Linear'], + use_ref_new=False, + update_ref_orig=False, + init_guess_mode='name', + verbose=False) + match2.fit() - # Distort the positions - trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) - xd, yd = trans.evaluate(xp, yp) - md = trans.evaluate_mag(lis['m0']) + # Now run_calc_bootstrap_error, with boot_epochs_min engaged + boot_epochs_min2 = 2 + match2.calc_bootstrap_errors(n_boot=n_boot, boot_epochs_min=boot_epochs_min2) - # Perturb with small errors (0.1 pix) - xd += np.random.randn(N_stars) * 0.1 - yd += np.random.randn(N_stars) * 0.1 - md += np.random.randn(N_stars) * 0.02 - xde = xpe - yde = ype - mde = lis['m0_err'] + # Make sure boot_epochs_min cut worked as intended + out = match2.ref_table + bad = np.where( (out['n_detect'] == 1) & (out['use_in_trans'] == False) ) + good = np.where(out['n_detect'] == 2) - # Save the new list as a starlist. - new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], - names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) + # Some stars must exist in both "good" and "bad" criteria, + # otherwise this test isn't as useful as intended. + assert len(bad[0]) > 0 + assert len(good[0]) > 0 - new_lis.write('random_{0:d}.fits'.format(ss), overwrite=True) + # For "good" stars: all bootstrap vals should be present + assert np.sum(~np.isfinite(out['xe_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['ye_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['vx_err_boot'][good])) == 0 + assert np.sum(~np.isfinite(out['vy_err_boot'][good])) == 0 - return (xy_trans,mag_trans) + # For "bad" stars, all bootstrap vals should be nans + assert np.sum(np.isfinite(out['xe_boot'][bad])) == 0 + assert np.sum(np.isfinite(out['ye_boot'][bad])) == 0 + assert np.sum(np.isfinite(out['vx_err_boot'][bad])) == 0 + assert np.sum(np.isfinite(out['vy_err_boot'][bad])) == 0 -def make_fake_starlists_poly0_vel(seed=-1): - # If seed >=0, then set random seed to that value - if seed >= 0: - np.random.seed(seed=seed) - - N_stars = 200 + return - x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) - y0 = np.random.rand(N_stars) * 10.0 # arcsec - x0e = np.ones(N_stars) * 1.0e-4 # arcsec - y0e = np.ones(N_stars) * 1.0e-4 # arcsec - vx = np.random.randn(N_stars) * 5.0 # mas / yr - vy = np.random.randn(N_stars) * 5.0 # mas / yr - vxe = np.ones(N_stars) * 0.05 # mas / yr - vye = np.ones(N_stars) * 0.05 # mas / yr - m0 = (np.random.rand(N_stars) * 8) + 9 # mag - m0e = np.random.randn(N_stars) * 0.05 # mag - t0 = np.ones(N_stars) * 2019.5 - - # Make all the errors positive - x0e = np.abs(x0e) - y0e = np.abs(y0e) - m0e = np.abs(m0e) - vxe = np.abs(vxe) - vye = np.abs(vye) +def test_calc_vel_in_bootstrap(): + """ + Check calc_vel_in_bootstrap performance in calc_bootstrap_errors() - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] + Only calculate velocity bootstrap (e.g., bootstrap over epochs and + calculating proper motions) if calc_vel_in_bootstrap=True. - # Make an StarList - lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, vx, vxe, vy, vye, t0], - names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', - 'vx', 'vx_err', 'vy', 'vy_err', 't0')) + """ + import copy + + # Define match parameters + ref = Table.read('ref_vel.lis', format='ascii') + + list1 = Table.read('E.lis', format='ascii') + list2 = Table.read('F.lis', format='ascii') + + list1 = starlists.StarList.from_table(list1) + list2 = starlists.StarList.from_table(list2) + + # Set parameters for alignment + transModel = transforms.PolyTransform + trans_args = {'order':2} + N_loop = 1 + dr_tol = 0.08 + dm_tol = 99 + outlier_tol = None + mag_lim = None + ref_mag_lim = None + trans_weighting = 'both,var' + mag_trans = False + + n_boot = 15 + boot_epochs_min=-1 + + # Run match + match = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, + dm_tol=dm_tol, outlier_tol=outlier_tol, + trans_class=transModel, + trans_args=trans_args, + mag_trans=mag_trans, + mag_lim=mag_lim, + ref_mag_lim=ref_mag_lim, + trans_weighting=trans_weighting, + motion_models=['Linear'], + use_ref_new=False, + update_ref_orig=False, + init_guess_mode='name', + verbose=False) + match.fit() + + # Make 2 copies of match object: one to test + # each case of calc_vel_in_bootstrap + match_vel = copy.deepcopy(match) + + # Run calc_bootstrap_error function with calc_vel_in_bootstrap=True. + # Make sure bootstrap velocity errors are calculated and valid + n_boot = 50 + match_vel.calc_bootstrap_errors(n_boot=n_boot, calc_vel_in_bootstrap=True) + + assert 'xe_boot' in match_vel.ref_table.keys() + assert np.sum(np.isnan(match_vel.ref_table['xe_boot'])) == 0 + assert 'vx_err_boot' in match_vel.ref_table.keys() + assert np.sum(np.isnan(match_vel.ref_table['vx_err_boot'])) == 0 + + # Run without calc_vel_in_bootstrap, make sure velocities are NOT calculated + match.calc_bootstrap_errors(n_boot=n_boot, calc_vel_in_bootstrap=False) + + assert 'xe_boot' in match.ref_table.keys() + assert np.sum(np.isnan(match.ref_table['xe_boot'])) == 0 + assert 'vx_err_boot' not in match.ref_table.keys() - sdx = np.argsort(m0) - lis = lis[sdx] + return - # Save original positions as reference (1st) list - # in a StarList format (with velocities). - lis.write('random_vel_ref.fits', overwrite=True) +def test_transform_xym(): + """ + Test to make sure transforms are being done to mags only + if mag_trans = True. This can cause subtle bugs + otherwise + """ + #---Align 1: self.mag_Trans = False---# + ref = Table.read('ref_vel.lis', format='ascii') + list1 = Table.read('E.lis', format='ascii') + list2 = Table.read('F.lis', format='ascii') + + list1 = starlists.StarList.from_table(list1) + list2 = starlists.StarList.from_table(list2) + + # Set parameters for alignment + transModel = transforms.PolyTransform + trans_args = {'order':2} + N_loop = 1 + dr_tol = 0.08 + dm_tol = 99 + outlier_tol = None + mag_lim = None + ref_mag_lim = None + trans_weighting = 'both,var' + n_boot = 15 + + mag_trans = False + + # Run FLYSTAR, with bootstraps + match1 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, + dm_tol=dm_tol, outlier_tol=outlier_tol, + trans_class=transModel, + trans_args=trans_args, + mag_trans=mag_trans, + mag_lim=mag_lim, + ref_mag_lim=ref_mag_lim, + trans_weighting=trans_weighting, + motion_models=['Fixed'], + use_ref_new=False, + update_ref_orig=False, + init_guess_mode='name', + verbose=False) + + match1.fit() + match1.calc_bootstrap_errors(n_boot=n_boot) + + # Make sure all transformations have mag_offset = 0 + trans_list = match1.trans_list + + for ii in trans_list: + assert ii.mag_offset == 0 + + # Check that no mag transformation has been applied to m col in ref_table + tab1 = match1.ref_table + assert np.all(tab1['m'] == tab1['m_orig']) - ########## - # Propogate to new times and distort. - ########## - # Make 4 new starlists with different epochs and transformations. - times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] - xy_trans = [[[ 6.5], [ 10.1]], - [[100.3], [ 50.5]], - [[ 0.0], [ 0.0]], - [[250.0], [-250.0]], - [[ 50.0], [ -31.0]], - [[ 78.0], [ 45.0]], - [[-13.0], [ 150]], - [[ 94.0], [-182.0]]] - mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] + # Check me_boost == 0 or really small (should be the case + # since we don't transform mags) + assert np.isclose(np.max(tab1['me_boot']), 0, rtol=10**-5) + print('Done mag_trans = False case') - # Convert into pixels (undistorted) with the following info. - scale = 0.01 # arcsec / pix - shift = [1.0, 1.0] # pix + #---Align 2: self.mag_Trans = True---# + # Repeat, this time with mag_trans = False + mag_trans = True + match2 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, + dm_tol=dm_tol, outlier_tol=outlier_tol, + trans_class=transModel, + trans_args=trans_args, + mag_trans=mag_trans, + mag_lim=mag_lim, + ref_mag_lim=ref_mag_lim, + trans_weighting=trans_weighting, + motion_models=['Fixed'], + use_ref_new=False, + update_ref_orig=False, + init_guess_mode='name', + verbose=False) + + match2.fit() + match2.calc_bootstrap_errors(n_boot=n_boot) + + + # Make sure all transformations have correct mag offset + trans_list2 = match2.trans_list + + for ii in trans_list2: + assert ii.mag_offset > 20 + + # Make sure final table mags have transform applied (i.e, + tab2 = match2.ref_table + assert np.all(tab2['m'] != tab2['m_orig']) - for ss in range(len(times)): - dt = times[ss] - lis['t0'] - - x = lis['x0'] + (lis['vx']/1e3) * dt - y = lis['y0'] + (lis['vy']/1e3) * dt - t = np.ones(N_stars) * times[ss] + # Check me_boost > 0 + assert np.min(tab2['me_boot']) > 10**-3 - # Convert into pixels - xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) - yp = (y / scale) + shift[1] - xpe = lis['x0_err'] / scale - ype = lis['y0_err'] / scale + print('Done mag_trans = True case') + + return - # Distort the positions - trans = transforms.PolyTransform(0, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) - xd, yd = trans.evaluate(xp, yp) - md = trans.evaluate_mag(lis['m0']) +def test_MosaicToRef_mag_bug(): + """ + Bug found by Tuan Do on 2020-04-12. + """ + make_fake_starlists_poly1_vel() - # Perturb with small errors (0.1 pix) - xd += np.random.randn(N_stars) * xpe - yd += np.random.randn(N_stars) * ype - md += np.random.randn(N_stars) * 0.02 - xde = xpe - yde = ype - mde = lis['m0_err'] + ref_list = starlists.StarList.read('random_vel_0.fits') + lists = [ref_list] - # Save the new list as a starlist. - new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], - names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) + msc = align.MosaicToRef(ref_list, lists, + mag_trans=True, + iters=1, + dr_tol=[0.2], dm_tol=[1], + outlier_tol=None, + trans_class=transforms.PolyTransform, + trans_args=[{'order': 1}], + motion_models=['Fixed'], + use_ref_new=False, + update_ref_orig=False, + verbose=True) - new_lis.write('random_vel_p0_{0:d}.fits'.format(ss), overwrite=True) + msc.fit() - return (xy_trans, mag_trans) + out_tab = msc.ref_table + # The issue is that in the initial guess with + # mag_trans = True + # somehow the transformed magnitudes are nan. + # This causes zero matches to occur. + assert len(out_tab) == len(ref_list) -def make_fake_starlists_poly1_vel(seed=-1): - # If seed >=0, then set random seed to that value - if seed >= 0: - np.random.seed(seed=seed) - - N_stars = 200 + return - x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) - y0 = np.random.rand(N_stars) * 10.0 # arcsec - x0e = np.ones(N_stars) * 1.0e-4 # arcsec - y0e = np.ones(N_stars) * 1.0e-4 # arcsec - vx = np.random.randn(N_stars) * 5.0 # mas / yr - vy = np.random.randn(N_stars) * 5.0 # mas / yr - vxe = np.ones(N_stars) * 0.05 # mas / yr - vye = np.ones(N_stars) * 0.05 # mas / yr - m0 = (np.random.rand(N_stars) * 8) + 9 # mag - m0e = np.random.randn(N_stars) * 0.05 # mag - t0 = np.ones(N_stars) * 2019.5 +def test_masked_cols(): + """ + Test to make sure analysis.prepare_gaia_for_flystar + produces an astropy.table.Table, NOT a masked column + table. MosaicToRef cannot handle masked column tables. - # Make all the errors positive - x0e = np.abs(x0e) - y0e = np.abs(y0e) - m0e = np.abs(m0e) - vxe = np.abs(vxe) - vye = np.abs(vye) - - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] + Also make sure this example works, since we use it for the examples + jupyter notebook. + """ + # Get gaia reference stars using analysis.py + # around a test location. + # target = 'ob150029' + ra = '17:59:46.60' + dec = '-28:38:41.8' - # Make an StarList - lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, vx, vxe, vy, vye, t0], - names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', - 'vx', 'vx_err', 'vy', 'vy_err', 't0')) - - sdx = np.argsort(m0) - lis = lis[sdx] + # Coordinates are arcsecs offset +x to the East. + targets_dict = { + 'ob150029': [0.0, 0.0], + 'S005': [1.1416, 3.7405], + 'S002': [-4.421, 0.027] + } - # Save original positions as reference (1st) list - # in a StarList format (with velocities). - lis.write('random_vel_ref.fits', overwrite=True) - - ########## - # Propogate to new times and distort. - ########## - # Make 4 new starlists with different epochs and transformations. - times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] - xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], - [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], - [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.000]], - [[250.0, 1.01, 2e-5], [-250.0, 1e-5, 0.98]], - [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], - [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], - [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], - [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] - mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] + # Get gaia catalog stars. Note that this produces a masked column table + search_rad = 10.0 # arcsec + gaia = analysis.query_gaia(ra, dec, search_radius=search_rad) + my_gaia = analysis.prepare_gaia_for_flystar(gaia, ra, dec, targets_dict=targets_dict) - # Convert into pixels (undistorted) with the following info. - scale = 0.01 # arcsec / pix - shift = [1.0, 1.0] # pix - - for ss in range(len(times)): - dt = times[ss] - lis['t0'] - - x = lis['x0'] + (lis['vx']/1e3) * dt - y = lis['y0'] + (lis['vy']/1e3) * dt - t = np.ones(N_stars) * times[ss] + assert isinstance(my_gaia, Table) - # Convert into pixels - xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) - yp = (y / scale) + shift[1] - xpe = lis['x0_err'] / scale - ype = lis['y0_err'] / scale + # Let's make sure the entire align runs, just to be safe - # Distort the positions - trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) - xd, yd = trans.evaluate(xp, yp) - md = trans.evaluate_mag(lis['m0']) + # Get starlists to align to gaia + epochs = ['15jun07','16jul14', '17may21'] - # Perturb with small errors (0.1 mas) - xd += np.random.randn(N_stars) * xpe - yd += np.random.randn(N_stars) * ype - md += np.random.randn(N_stars) * 0.02 - xde = xpe - yde = ype - mde = lis['m0_err'] + list_of_starlists = [] - # Save the new list as a starlist. - new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], - names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) + for ee in range(len(epochs)): + lis_file = 'mag' + epochs[ee] + '_ob150029_kp_rms_named.lis' + lis = starlists.StarList.from_lis_file(lis_file) + list_of_starlists.append(lis) - new_lis.write('random_vel_{0:d}.fits'.format(ss), overwrite=True) + # Run the align + msc = align.MosaicToRef(my_gaia, list_of_starlists, iters=2, + dr_tol=[0.2, 0.1], dm_tol=[1, 1], + trans_class=transforms.PolyTransform, + trans_args=[{'order': 1}, {'order': 1}], + motion_models=['Linear'], + use_ref_new=False, + update_ref_orig=False, + mag_trans=True, + init_guess_mode='name', verbose=True) - return (xy_trans, mag_trans) + msc.fit() + return -def make_fake_starlists_poly1_acc(seed=-1): - # If seed >=0, then set random seed to that value - if seed >= 0: - np.random.seed(seed=seed) - +def make_fake_starlists_shifts(): N_stars = 200 + x = np.random.rand(N_stars) * 1000 + y = np.random.rand(N_stars) * 1000 + m = (np.random.rand(N_stars) * 8) + 9 - x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) - y0 = np.random.rand(N_stars) * 10.0 # arcsec - x0e = np.ones(N_stars) * 1.0e-4 # arcsec - y0e = np.ones(N_stars) * 1.0e-4 # arcsec - vx = np.random.randn(N_stars) * 5.0 # mas / yr - vy = np.random.randn(N_stars) * 5.0 # mas / yr - vxe = np.ones(N_stars) * 0.1 # mas / yr - vye = np.ones(N_stars) * 0.1 # mas / yr - ax = np.random.randn(N_stars) * 0.5 # mas / yr^2 - ay = np.random.randn(N_stars) * 0.5 # mas / yr^2 - axe = np.ones(N_stars) * 0.01 # mas / yr^2 - aye = np.ones(N_stars) * 0.01 # mas / yr^2 - m0 = (np.random.rand(N_stars) * 8) + 9 # mag - m0e = np.random.randn(N_stars) * 0.05 # mag - t0 = np.ones(N_stars) * 2019.5 + sdx = np.argsort(m) + x = x[sdx] + y = y[sdx] + m = m[sdx] - # Make all the errors positive - x0e = np.abs(x0e) - y0e = np.abs(y0e) - m0e = np.abs(m0e) - vxe = np.abs(vxe) - vye = np.abs(vye) - axe = np.abs(axe) - aye = np.abs(aye) - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - # Make an StarList - lis = starlists.StarList([name, m0, m0e, - x0, x0e, y0, y0e, - vx, vxe, vy, vye, - ax, axe, ay, aye, - t0], - names = ('name', 'm0', 'm0_err', - 'x0', 'x0_err', 'y0', 'y0_err', - 'vx0', 'vx0_err', 'vy0', 'vy0_err', - 'ax', 'ax_err', 'ay', 'ay_err', - 't0')) - - sdx = np.argsort(m0) - lis = lis[sdx] + # Save original positions as reference (1st) list. + fmt = '{0:10s} {1:5.2f} 2015.0 {2:9.4f} {3:9.4f} 0 0 0 0\n' + _out = open('random_0.lis', 'w') + for ii in range(N_stars): + _out.write(fmt.format(name[ii], m[ii], x[ii], y[ii])) + _out.close() + - # Save original positions as reference (1st) list - # in a StarList format (with velocities). - lis.write('random_acc_ref.fits', overwrite=True) - ########## - # Propogate to new times and distort. + # Shifts ########## - # Make 4 new starlists with different epochs and transformations. - times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] - xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], - [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], - [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.000]], - [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]], - [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], - [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], - [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], - [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] - mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] - - # Convert into pixels (undistorted) with the following info. - scale = 0.01 # arcsec / pix - shift = [1.0, 1.0] # pix - - for ss in range(len(times)): - dt = times[ss] - lis['t0'] - - x = lis['x0'] + (lis['vx0']/1e3) * dt + 0.5*(lis['ax']/1e3) * dt**2 - y = lis['y0'] + (lis['vy0']/1e3) * dt + 0.5*(lis['ay']/1e3) * dt**2 - t = np.ones(N_stars) * times[ss] - - # Convert into pixels - xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) - yp = (y / scale) + shift[1] - xpe = lis['x0_err'] / scale - ype = lis['y0_err'] / scale + # Make 4 new starlists with different shifts. + shifts = [[ 6.5, 10.1], + [100.3, 50.5], + [-30.0,-100.7], + [250.0,-250.0]] - # Distort the positions - trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) - xd, yd = trans.evaluate(xp, yp) - md = trans.evaluate_mag(lis['m0']) + for ss in range(len(shifts)): + xnew = x - shifts[ss][0] + ynew = y - shifts[ss][1] # Perturb with small errors (0.1 pix) - xd += np.random.randn(N_stars) * xpe - yd += np.random.randn(N_stars) * ype - md += np.random.randn(N_stars) * 0.02 - xde = xpe - yde = ype - mde = lis['m0_err'] + xnew += np.random.randn(N_stars) * 0.1 + ynew += np.random.randn(N_stars) * 0.1 - # Save the new list as a starlist. - new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], - names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) + mnew = m + np.random.randn(N_stars) * 0.05 - new_lis.write('random_acc_{0:d}.fits'.format(ss), overwrite=True) + _out = open('random_shift_{0:d}.lis'.format(ss+1), 'w') + for ii in range(N_stars): + _out.write(fmt.format(name[ii], mnew[ii], xnew[ii], ynew[ii])) + _out.close() - return (xy_trans, mag_trans) - -def make_fake_starlists_poly1_par(seed=-1): + return shifts + +def make_fake_starlists_poly1(seed=-1): # If seed >=0, then set random seed to that value if seed >= 0: np.random.seed(seed=seed) @@ -916,12 +984,6 @@ def make_fake_starlists_poly1_par(seed=-1): y0 = np.random.rand(N_stars) * 10.0 # arcsec x0e = np.random.randn(N_stars) * 5.0e-4 # arcsec y0e = np.random.randn(N_stars) * 5.0e-4 # arcsec - vx = np.random.randn(N_stars) * 5.0 # mas / yr - vy = np.random.randn(N_stars) * 5.0 # mas / yr - vxe = np.random.randn(N_stars) * 0.1 # mas / yr - vye = np.random.randn(N_stars) * 0.1 # mas / yr - pi = np.random.randn(N_stars) * 0.5 # mas - pie = np.random.randn(N_stars) * 0.01 # mas m0 = (np.random.rand(N_stars) * 8) + 9 # mag m0e = np.random.randn(N_stars) * 0.05 # mag t0 = np.ones(N_stars) * 2019.5 @@ -929,65 +991,45 @@ def make_fake_starlists_poly1_par(seed=-1): # Make all the errors positive x0e = np.abs(x0e) y0e = np.abs(y0e) - m0e = np.abs(m0e) - vxe = np.abs(vxe) - vye = np.abs(vye) - pie = np.abs(pie) - - name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - - # Make an StarList - lis = starlists.StarList([name, m0, m0e, - x0, x0e, y0, y0e, - vx, vxe, vy, vye, - pi, pie, - t0], - names = ('name', 'm0', 'm0_err', - 'x0', 'x0_err', 'y0', 'y0_err', - 'vx', 'vx_err', 'vy', 'vy_err', - 'pi', 'pi_err', - 't0')) + m0e = np.abs(m0e) + + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] + + # Make an StarList + lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, t0], + names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', 't0')) sdx = np.argsort(m0) lis = lis[sdx] # Save original positions as reference (1st) list # in a StarList format (with velocities). - lis.write('random_par_ref.fits', overwrite=True) - + lis.write('random_ref.fits', overwrite=True) + ########## - # Propogate to new times and distort. + # Shifts ########## - # Make 4 new starlists with different epochs and transformations. - '''times = [2018.5, 2019.5, 2020.5, 2021.5] - xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], - [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], - [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.0]], - [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]]] - mag_trans = [0.1, 0.4, 0.0, -0.3]''' - + # Make 4 new starlists with different shifts. times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.0]], [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]], - [[ 50.0, 1.00, 0.0], [ -31.0, 0.0, 1.000]], - [[ 78.0, 1.00, 0.0 ], [ 45.0, 0.0, 1.00]], - [[-13.0, 1.00, 0.0], [ 150, 0.0, 1.00]], - [[ 94.0, 1.00, 0.0], [-182.0, 0.0, 1.00]]] - mag_trans = [0.1, 0.4, 0.0, -0.3, 0.0, 0.0, 0.0, 0.0] - + [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], + [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], + [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], + [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] + mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] + # Convert into pixels (undistorted) with the following info. scale = 0.01 # arcsec / pix shift = [1.0, 1.0] # pix - + for ss in range(len(times)): dt = times[ss] - lis['t0'] - par_mod = motion_model.Parallax(pa=0,ra=18.0, dec=-30.0) - par_mod_dat = par_mod.get_batch_pos_at_time(dt+lis['t0'], x0=lis['x0'],vx=lis['vx']/1e3, pi=lis['pi'], - y0=lis['y0'], vy=lis['vy']/1e3, t0=lis['t0']) - x,y = par_mod_dat[0], par_mod_dat[1] + x = lis['x0'] + y = lis['y0'] t = np.ones(N_stars) * times[ss] # Convert into pixels @@ -1013,431 +1055,411 @@ def make_fake_starlists_poly1_par(seed=-1): new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) - new_lis.write('random_par_{0:d}.fits'.format(ss), overwrite=True) - - return (xy_trans, mag_trans) - - -def test_MosaicToRef_hst_me(): - """ - Test Casey's issue with 'me' not getting propogated - from the input starlists to the output table. - - Use data from MB10-364 microlensing target for the test. - """ - # Target RA and Dec (MOA data download) - # ra = '17:57:05.401' - # dec = '-34:27:05.01' - - # Load up a Gaia catalog (queried around the RA/Dec above) - my_gaia = Table.read('mb10364_data/my_gaia.fits') - my_gaia['me'] = 0.01 - - # Gather the list of starlists. For first pass, don't modify the starlists. - # Loop through the observations and read them in, in prep for alignment with Gaia - epochs = [2011.83, 2012.73, 2013.81] - starlist_names = ['mb10364_data/2011_10_31_F606W_MATCHUP_XYMEEE_final.calib', - 'mb10364_data/2012_09_25_F606W_MATCHUP_XYMEEE_final.calib', - 'mb10364_data/2013_10_24_F606W_MATCHUP_XYMEEE_final.calib'] - - list_of_starlists = [] - - # Just using the F606W filters first. - for ee in range(len(starlist_names)): - lis = starlists.StarList.from_lis_file(starlist_names[ee]) - - # # Add additive error term. MAYBE YOU DON'T NEED THIS - # lis['xe'] = np.hypot(lis['xe'], 0.01) # Adding 0.01 pix (0.1 mas) in quadrature. - # lis['ye'] = np.hypot(lis['ye'], 0.01) - - lis['t'] = epochs[ee] - - # Lets dump the faint stars. - idx = np.where(lis['m'] < 20.0)[0] - lis = lis[idx] - - list_of_starlists.append(lis) - - msc = align.MosaicToRef(my_gaia, list_of_starlists, iters=1, - dr_tol=[0.1], dm_tol=[5], - outlier_tol=[None], mag_lim=[13, 21], - trans_class=transforms.PolyTransform, - trans_args=[{'order': 1}], - motion_models=['Empty', 'Fixed'], - use_ref_new=False, - update_ref_orig=False, - mag_trans=False, - trans_weighting='both,std', - init_guess_mode='miracle', verbose=False) - msc.fit() - - assert 'me' in msc.ref_table.colnames - return + new_lis.write('random_{0:d}.fits'.format(ss), overwrite=True) -def test_bootstrap(): - """ - Test to make sure calc_bootstrap_error() call is working - properly (e.g., only called when user calls calc_bootstrap_error, - n_boot param for calc_bootstrap_error only, boot_epochs_min working, - etc.) - """ - # Read in starlists for MosaicToRef - ref = Table.read('ref_vel.lis', format='ascii') - list1 = Table.read('E.lis', format='ascii') - list2 = Table.read('F.lis', format='ascii') + return (xy_trans,mag_trans) - list1 = starlists.StarList.from_table(list1) - list2 = starlists.StarList.from_table(list2) +def make_fake_starlists_poly0_vel(seed=-1): + # If seed >=0, then set random seed to that value + if seed >= 0: + np.random.seed(seed=seed) - # Set parameters for alignment - transModel = transforms.PolyTransform - trans_args = {'order':2} - N_loop = 1 - dr_tol = 0.08 - dm_tol = 99 - outlier_tol = None - mag_lim = None - ref_mag_lim = None - trans_weighting = 'both,var' - mag_trans = False - - n_boot = 15 - boot_epochs_min=-1 - - # Run FLYSTAR, no bootstraps yet! - match1 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, - dm_tol=dm_tol, outlier_tol=outlier_tol, - trans_class=transModel, - trans_args=trans_args, - mag_trans=mag_trans, - mag_lim=mag_lim, - ref_mag_lim=ref_mag_lim, - trans_weighting=trans_weighting, - motion_models=['Linear'], - use_ref_new=False, - update_ref_orig=False, - init_guess_mode='name', - verbose=False) - match1.fit() - - # Make sure no bootstrap columns exist - assert 'xe_boot' not in match1.ref_table.keys() - assert 'ye_boot' not in match1.ref_table.keys() - assert 'vxe_boot' not in match1.ref_table.keys() - assert 'vye_boot' not in match1.ref_table.keys() - - # Run bootstrap: no boot_epochs_min - match1.calc_bootstrap_errors(n_boot=n_boot, boot_epochs_min=boot_epochs_min) - # Make sure columns exist, and none of them are nan values - assert np.sum(np.isnan(match1.ref_table['xe_boot'])) == 0 - assert np.sum(np.isnan(match1.ref_table['ye_boot'])) == 0 - assert np.sum(np.isnan(match1.ref_table['vx_err_boot'])) == 0 - assert np.sum(np.isnan(match1.ref_table['vy_err_boot'])) == 0 - - # Test 2: make sure boot_epochs_min is working - # Eliminate some rows to list2, so some stars are only in 1 epoch. - # Rerun align. Some stars should only be detected in 1 epoch - list3 = list2[0:60] - - match2 = align.MosaicToRef(ref, [list1, list3], iters=N_loop, dr_tol=dr_tol, - dm_tol=dm_tol, outlier_tol=outlier_tol, - trans_class=transModel, - trans_args=trans_args, - mag_trans=mag_trans, - mag_lim=mag_lim, - ref_mag_lim=ref_mag_lim, - trans_weighting=trans_weighting, - motion_models=['Linear'], - use_ref_new=False, - update_ref_orig=False, - init_guess_mode='name', - verbose=False) - match2.fit() - - # Now run_calc_bootstrap_error, with boot_epochs_min engaged - boot_epochs_min2 = 2 - match2.calc_bootstrap_errors(n_boot=n_boot, boot_epochs_min=boot_epochs_min2) - - # Make sure boot_epochs_min cut worked as intended - out = match2.ref_table - bad = np.where( (out['n_detect'] == 1) & (out['use_in_trans'] == False) ) - good = np.where(out['n_detect'] == 2) - - # Some stars must exist in both "good" and "bad" criteria, - # otherwise this test isn't as useful as intended. - assert len(bad[0]) > 0 - assert len(good[0]) > 0 + N_stars = 200 - # For "good" stars: all bootstrap vals should be present - assert np.sum(~np.isfinite(out['xe_boot'][good])) == 0 - assert np.sum(~np.isfinite(out['ye_boot'][good])) == 0 - assert np.sum(~np.isfinite(out['vx_err_boot'][good])) == 0 - assert np.sum(~np.isfinite(out['vy_err_boot'][good])) == 0 + x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) + y0 = np.random.rand(N_stars) * 10.0 # arcsec + x0e = np.ones(N_stars) * 1.0e-4 # arcsec + y0e = np.ones(N_stars) * 1.0e-4 # arcsec + vx = np.random.randn(N_stars) * 5.0 # mas / yr + vy = np.random.randn(N_stars) * 5.0 # mas / yr + vxe = np.ones(N_stars) * 0.05 # mas / yr + vye = np.ones(N_stars) * 0.05 # mas / yr + m0 = (np.random.rand(N_stars) * 8) + 9 # mag + m0e = np.random.randn(N_stars) * 0.05 # mag + t0 = np.ones(N_stars) * 2019.5 - # For "bad" stars, all bootstrap vals should be nans - assert np.sum(np.isfinite(out['xe_boot'][bad])) == 0 - assert np.sum(np.isfinite(out['ye_boot'][bad])) == 0 - assert np.sum(np.isfinite(out['vx_err_boot'][bad])) == 0 - assert np.sum(np.isfinite(out['vy_err_boot'][bad])) == 0 + # Make all the errors positive + x0e = np.abs(x0e) + y0e = np.abs(y0e) + m0e = np.abs(m0e) + vxe = np.abs(vxe) + vye = np.abs(vye) + + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - return + # Make an StarList + lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, vx, vxe, vy, vye, t0], + names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', + 'vx', 'vx_err', 'vy', 'vy_err', 't0')) + + sdx = np.argsort(m0) + lis = lis[sdx] -def test_calc_vel_in_bootstrap(): - """ - Check calc_vel_in_bootstrap performance in calc_bootstrap_errors() + # Save original positions as reference (1st) list + # in a StarList format (with velocities). + lis.write('random_vel_ref.fits', overwrite=True) - Only calculate velocity bootstrap (e.g., bootstrap over epochs and - calculating proper motions) if calc_vel_in_bootstrap=True. + ########## + # Propogate to new times and distort. + ########## + # Make 4 new starlists with different epochs and transformations. + times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] + xy_trans = [[[ 6.5], [ 10.1]], + [[100.3], [ 50.5]], + [[ 0.0], [ 0.0]], + [[250.0], [-250.0]], + [[ 50.0], [ -31.0]], + [[ 78.0], [ 45.0]], + [[-13.0], [ 150]], + [[ 94.0], [-182.0]]] + mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] - """ - import copy + # Convert into pixels (undistorted) with the following info. + scale = 0.01 # arcsec / pix + shift = [1.0, 1.0] # pix + + for ss in range(len(times)): + dt = times[ss] - lis['t0'] + + x = lis['x0'] + (lis['vx']/1e3) * dt + y = lis['y0'] + (lis['vy']/1e3) * dt + t = np.ones(N_stars) * times[ss] - # Define match parameters - ref = Table.read('ref_vel.lis', format='ascii') + # Convert into pixels + xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) + yp = (y / scale) + shift[1] + xpe = lis['x0_err'] / scale + ype = lis['y0_err'] / scale - list1 = Table.read('E.lis', format='ascii') - list2 = Table.read('F.lis', format='ascii') + # Distort the positions + trans = transforms.PolyTransform(0, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) + xd, yd = trans.evaluate(xp, yp) + md = trans.evaluate_mag(lis['m0']) - list1 = starlists.StarList.from_table(list1) - list2 = starlists.StarList.from_table(list2) - - # Set parameters for alignment - transModel = transforms.PolyTransform - trans_args = {'order':2} - N_loop = 1 - dr_tol = 0.08 - dm_tol = 99 - outlier_tol = None - mag_lim = None - ref_mag_lim = None - trans_weighting = 'both,var' - mag_trans = False + # Perturb with small errors (0.1 pix) + xd += np.random.randn(N_stars) * xpe + yd += np.random.randn(N_stars) * ype + md += np.random.randn(N_stars) * 0.02 + xde = xpe + yde = ype + mde = lis['m0_err'] - n_boot = 15 - boot_epochs_min=-1 + # Save the new list as a starlist. + new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], + names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) - # Run match - match = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, - dm_tol=dm_tol, outlier_tol=outlier_tol, - trans_class=transModel, - trans_args=trans_args, - mag_trans=mag_trans, - mag_lim=mag_lim, - ref_mag_lim=ref_mag_lim, - trans_weighting=trans_weighting, - motion_models=['Linear'], - use_ref_new=False, - update_ref_orig=False, - init_guess_mode='name', - verbose=False) - match.fit() + new_lis.write('random_vel_p0_{0:d}.fits'.format(ss), overwrite=True) - # Make 2 copies of match object: one to test - # each case of calc_vel_in_bootstrap - match_vel = copy.deepcopy(match) + return (xy_trans, mag_trans) - # Run calc_bootstrap_error function with calc_vel_in_bootstrap=True. - # Make sure bootstrap velocity errors are calculated and valid - n_boot = 50 - match_vel.calc_bootstrap_errors(n_boot=n_boot, calc_vel_in_bootstrap=True) - assert 'xe_boot' in match_vel.ref_table.keys() - assert np.sum(np.isnan(match_vel.ref_table['xe_boot'])) == 0 - assert 'vx_err_boot' in match_vel.ref_table.keys() - assert np.sum(np.isnan(match_vel.ref_table['vx_err_boot'])) == 0 +def make_fake_starlists_poly1_vel(seed=-1): + # If seed >=0, then set random seed to that value + if seed >= 0: + np.random.seed(seed=seed) + + N_stars = 200 - # Run without calc_vel_in_bootstrap, make sure velocities are NOT calculated - match.calc_bootstrap_errors(n_boot=n_boot, calc_vel_in_bootstrap=False) + x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) + y0 = np.random.rand(N_stars) * 10.0 # arcsec + x0e = np.ones(N_stars) * 1.0e-4 # arcsec + y0e = np.ones(N_stars) * 1.0e-4 # arcsec + vx = np.random.randn(N_stars) * 5.0 # mas / yr + vy = np.random.randn(N_stars) * 5.0 # mas / yr + vxe = np.ones(N_stars) * 0.05 # mas / yr + vye = np.ones(N_stars) * 0.05 # mas / yr + m0 = (np.random.rand(N_stars) * 8) + 9 # mag + m0e = np.random.randn(N_stars) * 0.05 # mag + t0 = np.ones(N_stars) * 2019.5 - assert 'xe_boot' in match.ref_table.keys() - assert np.sum(np.isnan(match.ref_table['xe_boot'])) == 0 - assert 'vx_err_boot' not in match.ref_table.keys() + # Make all the errors positive + x0e = np.abs(x0e) + y0e = np.abs(y0e) + m0e = np.abs(m0e) + vxe = np.abs(vxe) + vye = np.abs(vye) - return - -def test_transform_xym(): - """ - Test to make sure transforms are being done to mags only - if mag_trans = True. This can cause subtle bugs - otherwise - """ - #---Align 1: self.mag_Trans = False---# - ref = Table.read('ref_vel.lis', format='ascii') - list1 = Table.read('E.lis', format='ascii') - list2 = Table.read('F.lis', format='ascii') + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - list1 = starlists.StarList.from_table(list1) - list2 = starlists.StarList.from_table(list2) + # Make an StarList + lis = starlists.StarList([name, m0, m0e, x0, x0e, y0, y0e, vx, vxe, vy, vye, t0], + names = ('name', 'm0', 'm0_err', 'x0', 'x0_err', 'y0', 'y0_err', + 'vx', 'vx_err', 'vy', 'vy_err', 't0')) - # Set parameters for alignment - transModel = transforms.PolyTransform - trans_args = {'order':2} - N_loop = 1 - dr_tol = 0.08 - dm_tol = 99 - outlier_tol = None - mag_lim = None - ref_mag_lim = None - trans_weighting = 'both,var' - n_boot = 15 + sdx = np.argsort(m0) + lis = lis[sdx] - mag_trans = False + # Save original positions as reference (1st) list + # in a StarList format (with velocities). + lis.write('random_vel_ref.fits', overwrite=True) + + ########## + # Propogate to new times and distort. + ########## + # Make 4 new starlists with different epochs and transformations. + times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] + xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], + [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], + [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.000]], + [[250.0, 1.01, 2e-5], [-250.0, 1e-5, 0.98]], + [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], + [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], + [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], + [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] + mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] - # Run FLYSTAR, with bootstraps - match1 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, - dm_tol=dm_tol, outlier_tol=outlier_tol, - trans_class=transModel, - trans_args=trans_args, - mag_trans=mag_trans, - mag_lim=mag_lim, - ref_mag_lim=ref_mag_lim, - trans_weighting=trans_weighting, - motion_models=['Fixed'], - use_ref_new=False, - update_ref_orig=False, - init_guess_mode='name', - verbose=False) + # Convert into pixels (undistorted) with the following info. + scale = 0.01 # arcsec / pix + shift = [1.0, 1.0] # pix + + for ss in range(len(times)): + dt = times[ss] - lis['t0'] + + x = lis['x0'] + (lis['vx']/1e3) * dt + y = lis['y0'] + (lis['vy']/1e3) * dt + t = np.ones(N_stars) * times[ss] - match1.fit() - match1.calc_bootstrap_errors(n_boot=n_boot) + # Convert into pixels + xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) + yp = (y / scale) + shift[1] + xpe = lis['x0_err'] / scale + ype = lis['y0_err'] / scale - # Make sure all transformations have mag_offset = 0 - trans_list = match1.trans_list + # Distort the positions + trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) + xd, yd = trans.evaluate(xp, yp) + md = trans.evaluate_mag(lis['m0']) - for ii in trans_list: - assert ii.mag_offset == 0 + # Perturb with small errors (0.1 mas) + xd += np.random.randn(N_stars) * xpe + yd += np.random.randn(N_stars) * ype + md += np.random.randn(N_stars) * 0.02 + xde = xpe + yde = ype + mde = lis['m0_err'] - # Check that no mag transformation has been applied to m col in ref_table - tab1 = match1.ref_table - assert np.all(tab1['m'] == tab1['m_orig']) - - # Check me_boost == 0 or really small (should be the case - # since we don't transform mags) - assert np.isclose(np.max(tab1['me_boot']), 0, rtol=10**-5) - print('Done mag_trans = False case') + # Save the new list as a starlist. + new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], + names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) - #---Align 2: self.mag_Trans = True---# - # Repeat, this time with mag_trans = False - mag_trans = True - match2 = align.MosaicToRef(ref, [list1, list2], iters=N_loop, dr_tol=dr_tol, - dm_tol=dm_tol, outlier_tol=outlier_tol, - trans_class=transModel, - trans_args=trans_args, - mag_trans=mag_trans, - mag_lim=mag_lim, - ref_mag_lim=ref_mag_lim, - trans_weighting=trans_weighting, - default_motion_model='Fixed', - use_ref_new=False, - update_ref_orig=False, - init_guess_mode='name', - verbose=False) + new_lis.write('random_vel_{0:d}.fits'.format(ss), overwrite=True) - match2.fit() - match2.calc_bootstrap_errors(n_boot=n_boot) + return (xy_trans, mag_trans) +def make_fake_starlists_poly1_acc(seed=-1): + # If seed >=0, then set random seed to that value + if seed >= 0: + np.random.seed(seed=seed) + + N_stars = 200 - # Make sure all transformations have correct mag offset - trans_list2 = match2.trans_list + x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) + y0 = np.random.rand(N_stars) * 10.0 # arcsec + x0e = np.ones(N_stars) * 1.0e-4 # arcsec + y0e = np.ones(N_stars) * 1.0e-4 # arcsec + vx = np.random.randn(N_stars) * 5.0 # mas / yr + vy = np.random.randn(N_stars) * 5.0 # mas / yr + vxe = np.ones(N_stars) * 0.1 # mas / yr + vye = np.ones(N_stars) * 0.1 # mas / yr + ax = np.random.randn(N_stars) * 0.5 # mas / yr^2 + ay = np.random.randn(N_stars) * 0.5 # mas / yr^2 + axe = np.ones(N_stars) * 0.01 # mas / yr^2 + aye = np.ones(N_stars) * 0.01 # mas / yr^2 + m0 = (np.random.rand(N_stars) * 8) + 9 # mag + m0e = np.random.randn(N_stars) * 0.05 # mag + t0 = np.ones(N_stars) * 2019.5 - for ii in trans_list2: - assert ii.mag_offset > 20 + # Make all the errors positive + x0e = np.abs(x0e) + y0e = np.abs(y0e) + m0e = np.abs(m0e) + vxe = np.abs(vxe) + vye = np.abs(vye) + axe = np.abs(axe) + aye = np.abs(aye) + + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - # Make sure final table mags have transform applied (i.e, - tab2 = match2.ref_table - assert np.all(tab2['m'] != tab2['m_orig']) + # Make an StarList + lis = starlists.StarList([name, m0, m0e, + x0, x0e, y0, y0e, + vx, vxe, vy, vye, + ax, axe, ay, aye, + t0], + names = ('name', 'm0', 'm0_err', + 'x0', 'x0_err', 'y0', 'y0_err', + 'vx0', 'vx0_err', 'vy0', 'vy0_err', + 'ax', 'ax_err', 'ay', 'ay_err', + 't0')) - # Check me_boost > 0 - assert np.min(tab2['me_boot']) > 10**-3 + sdx = np.argsort(m0) + lis = lis[sdx] - print('Done mag_trans = True case') - - return + # Save original positions as reference (1st) list + # in a StarList format (with velocities). + lis.write('random_acc_ref.fits', overwrite=True) + + ########## + # Propogate to new times and distort. + ########## + # Make 4 new starlists with different epochs and transformations. + times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] + xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], + [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], + [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.000]], + [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]], + [[ 50.0, 1.01, 1e-5], [ -31.0, 1e-5, 1.000]], + [[ 78.0, 0.98, 0.0 ], [ 45.0, 9e-6, 1.001]], + [[-13.0, 0.99, 1e-5], [ 150, 2e-5, 1.002]], + [[ 94.0, 1.00, 9e-6], [-182.0, 0.0, 0.99]]] + mag_trans = [0.1, 0.4, 0.0, -0.3, 0.2, 0.0, -0.1, -0.3] -def test_MosaicToRef_mag_bug(): - """ - Bug found by Tuan Do on 2020-04-12. - """ - make_fake_starlists_poly1_vel() + # Convert into pixels (undistorted) with the following info. + scale = 0.01 # arcsec / pix + shift = [1.0, 1.0] # pix + + for ss in range(len(times)): + dt = times[ss] - lis['t0'] + + x = lis['x0'] + (lis['vx0']/1e3) * dt + 0.5*(lis['ax']/1e3) * dt**2 + y = lis['y0'] + (lis['vy0']/1e3) * dt + 0.5*(lis['ay']/1e3) * dt**2 + t = np.ones(N_stars) * times[ss] - ref_list = starlists.StarList.read('random_vel_0.fits') - lists = [ref_list] + # Convert into pixels + xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) + yp = (y / scale) + shift[1] + xpe = lis['x0_err'] / scale + ype = lis['y0_err'] / scale - msc = align.MosaicToRef(ref_list, lists, - mag_trans=True, - iters=1, - dr_tol=[0.2], dm_tol=[1], - outlier_tol=None, - trans_class=transforms.PolyTransform, - trans_args=[{'order': 1}], - motion_models=['Fixed'], - use_ref_new=False, - update_ref_orig=False, - verbose=True) + # Distort the positions + trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) + xd, yd = trans.evaluate(xp, yp) + md = trans.evaluate_mag(lis['m0']) - msc.fit() + # Perturb with small errors (0.1 pix) + xd += np.random.randn(N_stars) * xpe + yd += np.random.randn(N_stars) * ype + md += np.random.randn(N_stars) * 0.02 + xde = xpe + yde = ype + mde = lis['m0_err'] - out_tab = msc.ref_table + # Save the new list as a starlist. + new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], + names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) - # The issue is that in the initial guess with - # mag_trans = True - # somehow the transformed magnitudes are nan. - # This causes zero matches to occur. - assert len(out_tab) == len(ref_list) + new_lis.write('random_acc_{0:d}.fits'.format(ss), overwrite=True) - return + return (xy_trans, mag_trans) + +def make_fake_starlists_poly1_par(seed=-1): + # If seed >=0, then set random seed to that value + if seed >= 0: + np.random.seed(seed=seed) + + N_stars = 200 -def test_masked_cols(): - """ - Test to make sure analysis.prepare_gaia_for_flystar - produces an astropy.table.Table, NOT a masked column - table. MosaicToRef cannot handle masked column tables. + x0 = np.random.rand(N_stars) * 10.0 # arcsec (increasing to East) + y0 = np.random.rand(N_stars) * 10.0 # arcsec + x0e = np.random.randn(N_stars) * 5.0e-4 # arcsec + y0e = np.random.randn(N_stars) * 5.0e-4 # arcsec + vx = np.random.randn(N_stars) * 5.0 # mas / yr + vy = np.random.randn(N_stars) * 5.0 # mas / yr + vxe = np.random.randn(N_stars) * 0.1 # mas / yr + vye = np.random.randn(N_stars) * 0.1 # mas / yr + pi = np.random.randn(N_stars) * 0.5 # mas + pie = np.random.randn(N_stars) * 0.01 # mas + m0 = (np.random.rand(N_stars) * 8) + 9 # mag + m0e = np.random.randn(N_stars) * 0.05 # mag + t0 = np.ones(N_stars) * 2019.5 - Also make sure this example works, since we use it for the examples - jupyter notebook. - """ - # Get gaia reference stars using analysis.py - # around a test location. - # target = 'ob150029' - ra = '17:59:46.60' - dec = '-28:38:41.8' + # Make all the errors positive + x0e = np.abs(x0e) + y0e = np.abs(y0e) + m0e = np.abs(m0e) + vxe = np.abs(vxe) + vye = np.abs(vye) + pie = np.abs(pie) + + name = ['star_{0:03d}'.format(ii) for ii in range(N_stars)] - # Coordinates are arcsecs offset +x to the East. - targets_dict = { - 'ob150029': [0.0, 0.0], - 'S005': [1.1416, 3.7405], - 'S002': [-4.421, 0.027] - } + # Make an StarList + lis = starlists.StarList([name, m0, m0e, + x0, x0e, y0, y0e, + vx, vxe, vy, vye, + pi, pie, + t0], + names = ('name', 'm0', 'm0_err', + 'x0', 'x0_err', 'y0', 'y0_err', + 'vx', 'vx_err', 'vy', 'vy_err', + 'pi', 'pi_err', + 't0')) + + sdx = np.argsort(m0) + lis = lis[sdx] - # Get gaia catalog stars. Note that this produces a masked column table - search_rad = 10.0 # arcsec - gaia = analysis.query_gaia(ra, dec, search_radius=search_rad) - my_gaia = analysis.prepare_gaia_for_flystar(gaia, ra, dec, targets_dict=targets_dict) + # Save original positions as reference (1st) list + # in a StarList format (with velocities). + lis.write('random_par_ref.fits', overwrite=True) + + ########## + # Propogate to new times and distort. + ########## + # Make 4 new starlists with different epochs and transformations. + '''times = [2018.5, 2019.5, 2020.5, 2021.5] + xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], + [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], + [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.0]], + [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]]] + mag_trans = [0.1, 0.4, 0.0, -0.3]''' + + times = [2018.5, 2019.0, 2019.5, 2020.0, 2020.5, 2021.0, 2021.5, 2022.0] + xy_trans = [[[ 6.5, 0.99, 1e-5], [ 10.1, 1e-5, 0.99]], + [[100.3, 0.98, 1e-5], [ 50.5, 9e-6, 1.001]], + [[ 0.0, 1.00, 0.0], [ 0.0, 0.0, 1.0]], + [[250.0, 0.97, 2e-5], [-250.0, 1e-5, 1.001]], + [[ 50.0, 1.00, 0.0], [ -31.0, 0.0, 1.000]], + [[ 78.0, 1.00, 0.0 ], [ 45.0, 0.0, 1.00]], + [[-13.0, 1.00, 0.0], [ 150, 0.0, 1.00]], + [[ 94.0, 1.00, 0.0], [-182.0, 0.0, 1.00]]] + mag_trans = [0.1, 0.4, 0.0, -0.3, 0.0, 0.0, 0.0, 0.0] - assert isinstance(my_gaia, Table) + # Convert into pixels (undistorted) with the following info. + scale = 0.01 # arcsec / pix + shift = [1.0, 1.0] # pix + + for ss in range(len(times)): + dt = times[ss] - lis['t0'] + + par_mod = motion_model.Parallax(pa=0,ra=18.0, dec=-30.0) + par_mod_dat = par_mod.get_batch_pos_at_time(dt+lis['t0'], x0=lis['x0'],vx=lis['vx']/1e3, pi=lis['pi'], + y0=lis['y0'], vy=lis['vy']/1e3, t0=lis['t0']) + x,y = par_mod_dat[0], par_mod_dat[1] + t = np.ones(N_stars) * times[ss] - # Let's make sure the entire align runs, just to be safe + # Convert into pixels + xp = (x / -scale) + shift[0] # -1 from switching to increasing to West (right) + yp = (y / scale) + shift[1] + xpe = lis['x0_err'] / scale + ype = lis['y0_err'] / scale - # Get starlists to align to gaia - epochs = ['15jun07','16jul14', '17may21'] + # Distort the positions + trans = transforms.PolyTransform(1, xy_trans[ss][0], xy_trans[ss][1], mag_offset=mag_trans[ss]) + xd, yd = trans.evaluate(xp, yp) + md = trans.evaluate_mag(lis['m0']) - list_of_starlists = [] + # Perturb with small errors (0.1 pix) + xd += np.random.randn(N_stars) * 0.1 + yd += np.random.randn(N_stars) * 0.1 + md += np.random.randn(N_stars) * 0.02 + xde = xpe + yde = ype + mde = lis['m0_err'] - for ee in range(len(epochs)): - lis_file = 'mag' + epochs[ee] + '_ob150029_kp_rms_named.lis' - lis = starlists.StarList.from_lis_file(lis_file) - list_of_starlists.append(lis) + # Save the new list as a starlist. + new_lis = starlists.StarList([lis['name'], md, mde, xd, xde, yd, yde, t], + names=('name', 'm', 'me', 'x', 'xe', 'y', 'ye', 't')) - # Run the align - msc = align.MosaicToRef(my_gaia, list_of_starlists, iters=2, - dr_tol=[0.2, 0.1], dm_tol=[1, 1], - trans_class=transforms.PolyTransform, - trans_args=[{'order': 1}, {'order': 1}], - motion_models=['Linear'], - use_ref_new=False, - update_ref_orig=False, - mag_trans=True, - init_guess_mode='name', verbose=True) + new_lis.write('random_par_{0:d}.fits'.format(ss), overwrite=True) - msc.fit() - return + return (xy_trans, mag_trans) \ No newline at end of file diff --git a/flystar/tests/test_startable.py b/flystar/tests/test_startable.py index 5580daf..4475970 100644 --- a/flystar/tests/test_startable.py +++ b/flystar/tests/test_startable.py @@ -401,7 +401,7 @@ def test_fit_motion_models(): return -def test_fit_velocities_2epoch(): +def test_fit_motion_model_2epoch(): ########## # Test: only 2 epoch2 ########## From a685011dd0ba2205bc8cf3e3c185532f95a628e5 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Sun, 21 Dec 2025 13:32:53 +0800 Subject: [PATCH 27/29] Merge with upstream mm_rework branch --- flystar/analysis.py | 7 +- flystar/motion_model.py | 9 +- flystar/parallax.py | 186 +----------------------------------- flystar/tests/test_align.py | 8 +- 4 files changed, 16 insertions(+), 194 deletions(-) diff --git a/flystar/analysis.py b/flystar/analysis.py index ceca739..55094e5 100644 --- a/flystar/analysis.py +++ b/flystar/analysis.py @@ -433,7 +433,8 @@ def startable_subset(tab, idx, mag_trans=True, mag_trans_orig=False): combined astrometry + uncombined photometry table. """ # Multiples: ['x', 'y', 'm', 'name_in_list', 'xe', 'ye', 'me', 't', - # 'x_orig', 'y_orig', 'm_orig', 'xe_orig', 'ye_orig', 'me_orig', 'used_in_trans'] + # 'x_orig', 'y_orig', 'm_orig', 'xe_orig', 'ye_orig', 'me_orig', 'used_in_trans', + # 'xe_boot','ye_boot','me_boot'] # Single: ['name', 'm0', 'm0_err', 'use_in_trans', 'ref_orig', 'n_detect', # 'x0', 'vx', 'y0', 'vy', 'x0_err', 'vx_err', 'y0_err', 'vy_err', 't0'] # Don't include n_vfit @@ -441,8 +442,8 @@ def startable_subset(tab, idx, mag_trans=True, mag_trans_orig=False): new_tab = copy.deepcopy(tab) #new_tab.remove_column('n_fit') new_tab.remove_column('n_detect') - for col in ['x','y','m','xe','ye','me','t','x_orig','y_orig','m_orig', - 'xe_orig','ye_orig','me_orig','used_in_trans']: + for col in ['x','y','m','name_in_list','xe','ye','me','t','x_orig','y_orig','m_orig', + 'xe_orig','ye_orig','me_orig','used_in_trans','xe_boot','ye_boot','me_boot']: new_tab[col] = tab[col][:,idx] new_tab.combine_lists('m', weights_col='me', sigma=3, ismag=True) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 1ba2dcf..9a79c89 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -24,6 +24,12 @@ class MotionModel(ABC): name = "MotionModel" def __init__(self, *args, **kwargs): + """ + Make a motion model object. This object defines the fit and fixed parameters, + and contains functions to fit the model to data and infer positions at given times. + Each instance corresponds to a given motion model, not an individual star, + and thus the fit values are only input/returned in functions, not stored in the object. + """ return def model_fit(self, dt): @@ -802,8 +808,7 @@ class Parallax(MotionModel): """ Motion model for linear proper motion + parallax - Requires RA, Dec, and PA parameters (degrees) for parallax calculation. - RA, Dec in J2000 + Requires RA and Dec J2000 (degrees) for parallax calculation. Optional PA is counterclockwise offset of the image y-axis from North. Optional obs parameter describes observer location, default is 'earth'. """ diff --git a/flystar/parallax.py b/flystar/parallax.py index 1a6dcf1..a4f0f8c 100755 --- a/flystar/parallax.py +++ b/flystar/parallax.py @@ -84,39 +84,6 @@ def parallax_in_direction(ra, dec, mjd, obsLocation='earth', pa=0.): return pvec -def dparallax_dt_in_direction(ra, dec, mjd, obsLocation='earth'): - """ - R.A. in degrees. (J2000) - Dec. in degrees. (J2000) - MJD - - Equations following MulensModel. - Time derivative --> units are yr^-1 - - """ - # print('parallax_in_direction: len(t) = ', len(mjd)) - # Munge inputs into astropy format. - times = Time(mjd, format='mjd', scale='tdb') - coord = SkyCoord(ra, dec, unit=(units.deg, units.deg)) - - direction = coord.cartesian.xyz.value - north = np.array([0., 0., 1.]) - _east_projected = np.cross(north, direction) / np.linalg.norm(np.cross(north, direction)) - _north_projected = np.cross(direction, _east_projected) / np.linalg.norm(np.cross(direction, _east_projected)) - - obs_posvel = get_observer_barycentric(obsLocation, times, velocity=True)[1] - sun_posvel = get_body_barycentric_posvel('Sun', times)[1] - sun_obs_vel = sun_posvel - obs_posvel - vel = sun_obs_vel.xyz.T.to(units.au / units.year) - - e = np.dot(vel, _east_projected) - n = np.dot(vel, _north_projected) - - dpvec_dt = np.array([e.value, n.value]).T - - return dpvec_dt - - def get_observer_barycentric(body, times, min_ephem_step=1, velocity=False): """ Get the barycentric position of a satellite or other Solar System body @@ -197,155 +164,4 @@ def get_observer_barycentric(body, times, min_ephem_step=1, velocity=False): if velocity: return (obs_pos, obs_vel) else: - return obs_pos - - -def sun_position(mjd, radians=False): - """ - - NAME: - SUNPOS - - PURPOSE: - To compute the RA and Dec of the Sun at a given date. - - INPUTS: - mjd - The modified Julian date of the day (and time), scalar or vector - - OUTPUTS: - ra: - | The right ascension of the sun at that date in DEGREES - | double precision, same number of elements as jd - dec: - The declination of the sun at that date in DEGREES - elong: - Ecliptic longitude of the sun at that date in DEGREES. - obliquity: - the obliquity of the ecliptic, in DEGREES - - OPTIONAL INPUT KEYWORD: - RADIAN [def=False] - If this keyword is set to True, then all output variables - are given in Radians rather than Degrees - - NOTES: - Patrick Wallace (Rutherford Appleton Laboratory, UK) has tested the - accuracy of a C adaptation of the sunpos.pro code and found the - following results. From 1900-2100 SUNPOS gave 7.3 arcsec maximum - error, 2.6 arcsec RMS. Over the shorter interval 1950-2050 the figures - were 6.4 arcsec max, 2.2 arcsec RMS. - - The returned RA and Dec are in the given date's equinox. - - Procedure was extensively revised in May 1996, and the new calling - sequence is incompatible with the old one. - METHOD: - Uses a truncated version of Newcomb's Sun. Adapted from the IDL - routine SUN_POS by CD Pike, which was adapted from a FORTRAN routine - by B. Emerson (RGO). - EXAMPLE: - (1) Find the apparent RA and Dec of the Sun on May 1, 1982 - - | IDL> jdcnv, 1982, 5, 1,0 ,jd ;Find Julian date jd = 2445090.5 - | IDL> sunpos, jd, ra, dec - | IDL> print,adstring(ra,dec,2) - | 02 31 32.61 +14 54 34.9 - - The Astronomical Almanac gives 02 31 32.58 +14 54 34.9 so the error - in SUNPOS for this case is < 0.5". - - (2) Find the apparent RA and Dec of the Sun for every day in 1997 - - | IDL> jdcnv, 1997,1,1,0, jd ;Julian date on Jan 1, 1997 - | IDL> sunpos, jd+ dindgen(365), ra, dec ;RA and Dec for each day - - MODIFICATION HISTORY: - - * Written by Michael R. Greason, STX, 28 October 1988. - * Accept vector arguments, W. Landsman - April,1989 - * Eliminated negative right ascensions - MRG, Hughes STX, 6 May 1992. - * Rewritten using the 1993 Almanac. Keywords added. MRG, HSTX, 10 February 1994. - * Major rewrite, improved accuracy, always return values in degrees - W. Landsman May, 1996 - * Added /RADIAN keyword; W. Landsman; August, 1997 - * Converted to IDL V5.0; W. Landsman; September 1997 - * Converted to python; J. R. Lu; August 2016 - """ - # form time in Julian centuries from 1900.0 - t_obj = Time(mjd, format='mjd') - t = (t_obj.jd - 2415020.0) / 36525.0 - - # form sun's mean longitude - l = (279.696678 + ((36000.768925 * t) % 360.0)) * 3600.0 - - # allow for ellipticity of the orbit (equation of centre) - # using the Earth's mean anomaly ME - me = 358.475844 + ((35999.049750 * t) % 360.0) - ellcor = (6910.1 - 17.2 * t) * np.sin(np.radians(me)) + 72.3 * np.sin( - np.radians(2.0 * me)) - l = l + ellcor - - # allow for the Venus perturbations using the mean anomaly of Venus MV - mv = 212.603219 + ((58517.803875 * t) % 360.0) - vencorr = 4.8 * np.cos(np.radians(299.1017 + mv - me)) + \ - 5.5 * np.cos(np.radians(148.3133 + 2.0 * mv - 2.0 * me)) + \ - 2.5 * np.cos(np.radians(315.9433 + 2.0 * mv - 3.0 * me)) + \ - 1.6 * np.cos(np.radians(345.2533 + 3.0 * mv - 4.0 * me)) + \ - 1.0 * np.cos(np.radians(318.1500 + 3.0 * mv - 5.0 * me)) - l += vencorr - - # Allow for the Mars perturbations using the mean anomaly of Mars MM - mm = 319.529425 + ((19139.858500 * t) % 360.0) - marscorr = 2.0 * np.cos(np.radians(343.8883 - 2.0 * mm + 2.0 * me)) + \ - 1.8 * np.cos(np.radians(200.4017 - 2.0 * mm + me)) - l += marscorr - - # Allow for the Jupiter perturbations using the mean anomaly of Jupiter MJ - mj = 225.328328 + ((3034.6920239 * t) % 360.0) - jupcorr = 7.2 * np.cos(np.radians(179.5317 - mj + me)) + \ - 2.6 * np.cos(np.radians(263.2167 - mj)) + \ - 2.7 * np.cos(np.radians(87.1450 - 2.0 * mj + 2.0 * me)) + \ - 1.6 * np.cos(np.radians(109.4933 - 2.0 * mj + me)) - l += jupcorr - - # Allow for the Moons perturbations using the mean elongation of - # the Moon from the Sun D - d = 350.7376814 + ((445267.11422 * t) % 360.0) - mooncorr = 6.5 * np.sin(np.radians(d)) - l += mooncorr - - # Allow for long period terms - longterm = + 6.4 * np.sin(np.radians(231.19 + 20.20 * t)) - l += longterm - l = (l + 2592000.0) % 1296000.0 - longmed = l / 3600.0 - - # Allow for Aberration - l -= 20.5 - - # Allow for Nutation using the longitude of the Moons mean node OMEGA - omega = 259.183275 - ((1934.142008 * t) % 360.0) - l -= 17.2 * np.sin(np.radians(omega)) - - # Form the True Obliquity - oblt = 23.452294 - 0.0130125 * t + ( - 9.2 * np.cos(np.radians(omega))) / 3600.0 - - # Form Right Ascension and Declination - l = l / 3600.0 - l_rad = np.radians(l) - oblt_rad = np.radians(oblt) - ra = np.arctan2(np.sin(l_rad) * np.cos(oblt_rad), np.cos(l_rad)) - - if (len(ra) > 1): - neg = np.where(ra < 0.0)[0] - ra[neg] = ra[neg] + 2.0 * math.pi - - dec = np.arcsin(np.sin(l_rad) * np.sin(oblt_rad)) - - if radians: - oblt = oblt_rad - longmed = np.radians(longmed) - else: - ra = np.degrees(ra) - dec = np.degrees(dec) - - return ra, dec, longmed, oblt + return obs_pos \ No newline at end of file diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index 080ded3..ad082cb 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -319,8 +319,8 @@ def test_MosaicToRef_p0_vel(): # The velocities should be almost the same (but not as close as before) # as the input velocities since update_ref == True. assert (msc.ref_table['name']==ref_list['name']).all() - np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], atol=1e-2) - np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], atol=1e-2) + np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], rtol=1e-1, atol=3e-4) + np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], rtol=1e-1, atol=3e-4) # Also double check that they aren't exactly the same for the reference stars. #assert np.any(np.not_equal(msc.ref_table['vx'], ref_list['vx'])) @@ -385,8 +385,8 @@ def test_MosaicToRef_vel(): # The velocities should be almost the same (but not as close as before) # as the input velocities since update_ref == True. assert (msc.ref_table['name']==ref_list['name']).all() - np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], atol=1e-2) - np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], atol=1e-2) + np.testing.assert_allclose(msc.ref_table['vx'], ref_list['vx'], rtol=1e-1, atol=3e-4) + np.testing.assert_allclose(msc.ref_table['vy'], ref_list['vy'], rtol=1e-1, atol=3e-4) # Also double check that they aren't exactly the same for the reference stars. #assert np.any(np.not_equal(msc.ref_table['vx'], ref_list['vx'])) From f75a55febe8bca3a61bb792571d821069a716cd2 Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Mon, 22 Dec 2025 23:48:07 +0800 Subject: [PATCH 28/29] Added Motion Model Example Notebook; Revert Acceleration Velocity Names --- .../examples/motion_model_example.ipynb | 1363 +++++++++++++++++ flystar/motion_model.py | 94 +- flystar/startables.py | 39 +- flystar/tests/test_align.py | 10 +- 4 files changed, 1458 insertions(+), 48 deletions(-) create mode 100644 docs/flystar/examples/motion_model_example.ipynb diff --git a/docs/flystar/examples/motion_model_example.ipynb b/docs/flystar/examples/motion_model_example.ipynb new file mode 100644 index 0000000..413b616 --- /dev/null +++ b/docs/flystar/examples/motion_model_example.ipynb @@ -0,0 +1,1363 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "333cd262", + "metadata": {}, + "source": [ + "# Motion Model Examples" + ] + }, + { + "cell_type": "markdown", + "id": "9251851e", + "metadata": {}, + "source": [ + "# Table of Contents" + ] + }, + { + "cell_type": "markdown", + "id": "1e4364ed", + "metadata": {}, + "source": [ + "# Table of Contents\n", + "- [1. Motion Model](#1-motion-model)\n", + " - [1.1. Example: Linear Model Fit](#11-example-linear-model-fit)\n", + " - [1.2. Example: Acceleration Model Fit](#12-example-acceleration-model-fit)\n", + " - [1.3. Example: Parallax Model Fit](#13-example-parallax-model-fit)\n", + "- [2. Fit Motion Model in StarTable](#2-fit-motion-model-in-startable)\n", + " - [2.1. Example: Default Fitting](#21-example-default-fitting)\n", + " - [2.2 Example: Specify Motion Models](#22-example-specify-motion-models)\n", + " - [2.3. Example: Specify the `motion_model_input` Column](#23-example-specify-the-motion_model_input-column)\n", + " - [2.4. Example: Infer Positions](#24-example-infer-positions)\n", + " - [2.5. Speed Test](#25-speed-test)\n" + ] + }, + { + "cell_type": "markdown", + "id": "4bd92a9d", + "metadata": {}, + "source": [ + "# 1. Motion Model" + ] + }, + { + "cell_type": "markdown", + "id": "0d084c38", + "metadata": {}, + "source": [ + "Summary of currently implemented motion models" + ] + }, + { + "cell_type": "markdown", + "id": "faddd6d8", + "metadata": {}, + "source": [ + "| Motion Model | n_params | params | fixed_params | model | Description |\n", + "|--------------|----------|--------------------------------------------|-------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n", + "| Empty | 0 | NA | NA | $x(t) = $ NaN / fill_value
$x_e(t) = $ Inf | |\n", + "| Fixed | 1 | $x_0$
$y_0$ | NA | $x(t) = $ np.average($x$, weights=$x_{wt}$) | $x_{wt} = 1/xe^2$ if weighting='var'
$x_{wt} = 1/\\|xe\\|$ if weighting = 'std' |\n", + "| Linear | 2 | $x_0, v_x$
$y_0, v_y$ | optional: $t_0 =$ np.average($t, 1/\\sqrt{x_e^2 + y_e^2}$) | $x(t) = x_0 + v_x * (t - t_0)$ | |\n", + "| Acceleration | 3 | $x_0, v_{x0}, a_x$
$y_0, v_{y0}, a_y$ | optional: $t_0 =$ np.average($t, 1/\\sqrt{x_e^2 + y_e^2}$) | $x(t) = x_0 + v_{x0} * (t - t_0) + 1/2 * a_x * (t - t_0)^2$ | |\n", + "| Parallax | 3 | $x_0, v_x, pi$
$y_0, v_y$ | required: ra, dec
optional: $t_0 =$ np.average($t, 1/\\sqrt{x_e^2 + y_e^2}$); $pa=0$; obsLocation='earth' | $x(t) = x_0 + v_x * (t - t_0) + pvec * (t - t_0)$ | pvec is the parallax vector calculated based on ra, dec, pa, and obsLocation.
Only supports the same obsLocation for all stars in StarTable.fit_motion_model right now. |" + ] + }, + { + "cell_type": "markdown", + "id": "6fdc98af", + "metadata": {}, + "source": [ + "Examples on using `flystar.MotionModel`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "51c963a1", + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "id": "473b0674", + "metadata": {}, + "source": [ + "Imports" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ce4edb88", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from flystar import motion_model\n", + "from flystar.startables import StarTable\n", + "from flystar.motion_model import Empty, Fixed, Linear, Acceleration, Parallax" + ] + }, + { + "cell_type": "markdown", + "id": "8c0e8559", + "metadata": {}, + "source": [ + "Prepare data" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "86b6319d", + "metadata": {}, + "outputs": [], + "source": [ + "t = np.array([0, 1., 2.2, 3.5, 5.]) + 2025.0\n", + "x = np.array([0., 0.5, 2.1, 3.2, 8.0])\n", + "y = np.array([10.2, 8.5, 9.1, 10.5, 13.0])\n", + "xe = np.array([0.2, 0.5, 0.3, 0.4, 0.6])\n", + "ye = np.array([0.3, 0.2, 0.5, 0.2, 0.4])\n", + "t_test = np.linspace(2025.0, 2030.0, 100) # Test times for model evaluation" + ] + }, + { + "cell_type": "markdown", + "id": "b1a87102", + "metadata": {}, + "source": [ + "## 1.1. Example: Linear Model Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "0926c0a8", + "metadata": {}, + "outputs": [], + "source": [ + "mm = Linear()\n", + "params, param_errs = mm.fit(t, x, y, xe, ye)" + ] + }, + { + "cell_type": "markdown", + "id": "1fad1962", + "metadata": {}, + "source": [ + "Evaluate model at time t:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "840693ae", + "metadata": {}, + "outputs": [], + "source": [ + "x_model, y_model = mm.model(t, params)" + ] + }, + { + "cell_type": "markdown", + "id": "42fbd575", + "metadata": {}, + "source": [ + "Or if uncertainties of parameters is provided at the same time, the model will return the model uncertainties as well:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8fcbdc5d", + "metadata": {}, + "outputs": [], + "source": [ + "x_model, y_model, xe_model, ye_model = mm.model(t, params, param_errs)" + ] + }, + { + "cell_type": "markdown", + "id": "6f9954ef", + "metadata": {}, + "source": [ + "Note that we did not provide the `fixed_params_dict` parameter in the `model` function, so the MotionModel will use the saved self.fixed_params_dict. One can also specify the fixed_params_dict as:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "6752e477", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'t0': np.float64(2027.0454838983064)}" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mm.fixed_params_dict" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "eba675c8", + "metadata": {}, + "outputs": [], + "source": [ + "x_model, y_model, xe_model, ye_model = mm.model(t_test, params, param_errs, mm.fixed_params_dict)" + ] + }, + { + "cell_type": "markdown", + "id": "a2acbe90", + "metadata": {}, + "source": [ + "Define a helper function to visualize result" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "7dba325f", + "metadata": {}, + "outputs": [], + "source": [ + "def visualize_fit(t, x, y, xe, ye, x_model, y_model, xe_model, ye_model, mm_name, t_test=None):\n", + " if t_test is None:\n", + " t_test = t\n", + " x = np.atleast_2d(x)\n", + " y = np.atleast_2d(y)\n", + " xe = np.atleast_2d(xe)\n", + " ye = np.atleast_2d(ye)\n", + " x_model = np.atleast_2d(x_model)\n", + " y_model = np.atleast_2d(y_model)\n", + " xe_model = np.atleast_2d(xe_model)\n", + " ye_model = np.atleast_2d(ye_model)\n", + " \n", + " N_cases = x.shape[0]\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))\n", + " for i in range(N_cases):\n", + " l0 = ax1.errorbar(t, x[i], yerr=xe[i], fmt='o', color=f'C{i%10}', label='Data')\n", + " l1, = ax1.plot(t_test, x_model[i], label=f'{mm_name} Fit')\n", + " l2 = ax1.fill_between(t_test, x_model[i] - xe_model[i], x_model[i] + xe_model[i], color=f'C{i%10}', alpha=0.3, label='Model Uncertainty')\n", + "\n", + " r0 = ax2.errorbar(t, y[i], yerr=ye[i], fmt='o', color=f'C{i%10}', label='Data')\n", + " r1, = ax2.plot(t_test, y_model[i], label=f'{mm_name} Fit')\n", + " r2 = ax2.fill_between(t_test, y_model[i] - ye_model[i], y_model[i] + ye_model[i], color=f'C{i%10}', alpha=0.3, label='Model Uncertainty')\n", + " ax1.set_xlabel('Time')\n", + " ax1.set_ylabel('X Position')\n", + " ax1.set_title(f'{mm_name} Motion Model Fit')\n", + " ax1.legend(\n", + " [l0, (l1, l2)], \n", + " ['Data', 'Model Fit'],\n", + " )\n", + " \n", + " ax2.set_xlabel('Time')\n", + " ax2.set_ylabel('Y Position')\n", + " ax2.set_title(f'{mm_name} Motion Model Fit')\n", + " ax2.legend(\n", + " [r0, (r1, r2)], \n", + " ['Data', 'Model Fit'],\n", + " )\n", + " plt.tight_layout()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "ad03fc67", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize_fit(t, x, y, xe, ye, x_model, y_model, xe_model, ye_model, mm.name, t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "98d3e2c4", + "metadata": {}, + "source": [ + "## 1.2. Example: Acceleration Model Fit" + ] + }, + { + "cell_type": "markdown", + "id": "ede486e5", + "metadata": {}, + "source": [ + "Upon further inspection, acceleration model seems to be a better representation of the data" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "0a0d9d1f", + "metadata": {}, + "outputs": [], + "source": [ + "mm = Acceleration()\n", + "params, param_errs = mm.fit(t, x, y, xe, ye)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "b3d63417", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_model, y_model, xe_model, ye_model = mm.model(t_test, params, param_errs)\n", + "visualize_fit(t, x, y, xe, ye, x_model, y_model, xe_model, ye_model, mm.name, t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "9d1f63b4", + "metadata": {}, + "source": [ + "Moreover, `MotionModel.model` is fully vectorized, and can infer positions of multiple stars at multiple times, and the resulting inferred positions has shape (N_stars, N_times). See the example below:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d1e406c5", + "metadata": {}, + "outputs": [], + "source": [ + "t = np.array([0, 1., 2.2, 3.5, 5.]) + 2025.0\n", + "\n", + "xs = np.array([\n", + " [0., 0.5, 2.1, 3.2, 8.0],\n", + " [10.0, 8.9, 9.2, 7.4, 7.0],\n", + " [2.5, 6.2, 5.2, 3.2, 5.0]\n", + "])\n", + "\n", + "ys = np.array([\n", + " [10.2, 8.5, 9.1, 10.5, 13.0],\n", + " [8.0, 9.9, 8.2, 7.4, 7.0],\n", + " [5.2, 6.2, 4.7, 3.2, 6.0]\n", + "])\n", + "\n", + "xes = np.array([\n", + " [0.2, 0.5, 0.3, 0.4, 0.6],\n", + " [0.5, 0.2, 0.7, 0.3, 0.2],\n", + " [0.5, 0.7, 0.6, 0.4, 0.3]\n", + "])\n", + "\n", + "yes = np.array([\n", + " [0.3, 0.2, 0.5, 0.2, 0.4],\n", + " [0.2, 0.5, 0.6, 0.4, 0.2],\n", + " [0.4, 0.2, 0.3, 0.4, 0.5]\n", + "])" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "4adebbe8", + "metadata": {}, + "outputs": [], + "source": [ + "params = []\n", + "param_errs = []\n", + "for xi, yi, xei, yei in zip(xs, ys, xes, yes):\n", + " p, pe = mm.fit(t, xi, yi, xei, yei)\n", + " params.append(p)\n", + " param_errs.append(pe)" + ] + }, + { + "cell_type": "markdown", + "id": "4e0424df", + "metadata": {}, + "source": [ + "Once we have the params and param errors, we can infer the model positions at any given time." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "95745baa", + "metadata": {}, + "outputs": [], + "source": [ + "x_model, y_model, xe_model, ye_model = mm.model(t_test, params, param_errs)" + ] + }, + { + "cell_type": "markdown", + "id": "06fdca50", + "metadata": {}, + "source": [ + "The inferred positions should have shape (N_stars, N_times):" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "54206834", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(3, 100)" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x_model.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "e6a4e42e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vf6WiooK8vLwhv7QZDAbuvvtu/u3f/o1LLrmEz372s8RiMb7//e/j9XpzGteRstlsQ2Z5DpTr+3LjjTfy61//mosvvpjvfe97lJWV8eijjw5qjwNqvdvPfvYzrrnmGnp6erjyyispLS2ls7OTd999l87OzkOewR8tS5YsAeAnP/kJ11xzDWazmXnz5h0y4ySEmJrkeC3Hazley/FajIOJq9cmjlUf+MAHdIvFond0dAy7z8c+9jHdZDLpbW1tuq7r+r59+/Trr79eLy8v181ms15ZWal/5CMf0dvb2/vu09vbq3/pS1/Sa2pqdLPZrJeWluoXX3yxvm3btr59EomE/oMf/EBfunSpbrPZdJfLpc+fP1//7Gc/q+/cubNvvwOrno7kvrW1tfrFF1885Ov661//2nf/qqoq/atf/ar+7LPPDqpuqeu63tPTo1955ZV6fn6+rmmaPvC/IgdU19R1Xd+4caN+6aWX6h6PR7dYLPrSpUsHVarU9f7KoX/84x8HXT9UZcuhDKx6eigHVj3VdV3v7u7WP/e5z+kVFRW6yWTSa2tr9a9//et6NBodtN+GDRv00047TXc4HDrQ9zgHVj3Neuqpp/STTz5Zt9lsutPp1M855xz99ddfH7RPtuppZ2fnkK/ncNU7B1Y9Hc5QVU91Pbf3Rdd1fcuWLfp5552n22w2vbCwUP/Upz6l/+UvfxnyNb/yyiv6xRdfrBcWFupms1mvqqrSL7744kHv60irng73ng732fj617+uV1ZW6gaDYcgxCiGODXK8luO1HK8Hk+O1GAuaruv62If1QgghhBBCCCHE9CJtwYQQQgghhBBCiDEgAbcQQgghhBBCCDEGJOAWQgghhBBCCCHGgATcQgghhBBCCCHEGJCAWwghhBBCCCGEGAMScAshhBBCCCGEEGPANNEDGGvpdJqWlhby8vLQNG2ihyOEEEIMS9d1AoEAlZWVGAzT75y4HLOFEEJMBSM5Xh/zAXdLSwvV1dUTPQwhhBAiZ/v27WPGjBkTPYxxJ8dsIYQQU0kux+tjPuDOy8sD1D+G2+2e4NEIIYQQw/P7/VRXV/cdu6YbOWYLIYSYCkZyvD7mA+7slDS32y0HbyGEEFPCdJ1OLcdsIYQQU0kux+vpt0BMCCGEEEIIIYQYBxJwCyGEEEIIIYQQY0ACbiGEEEIIIYQQYgwc82u4hRDiWJVKpUgkEhM9DDECZrMZo9E40cOY0uRzP/XI514IMZ1JwC2EEFOMruu0tbXh9XoneijiCOTn51NeXj5tC6MdKfncT23yuRdCTFcScAshxBSTDTpKS0txOBzyBXaK0HWdcDhMR0cHABUVFRM8oqlFPvdTk3zuhRDTnQTcQggxhaRSqb6go6ioaKKHI0bIbrcD0NHRQWlpqUyzzZF87qc2+dwLIaYzKZomhBBTSHbtqsPhmOCRiCOVfe9kHXLu5HM/9cnnXggxXUnALYQQU5BMp5265L07cvJvN3XJeyeEmK4k4BZCiGkqnAiz5OElLHl4CeFEeKKHI8S4kM+9EEKI8SQBtxBCCCGEEEIIMQYk4BZCiGkqlU71/f52+9uDLo+Fa6+9Fk3T0DQNs9lMWVkZ5513Hr/+9a9Jp9M5P85DDz1Efn7+2A1UHNPkcy+EEGI8ScAthBDT0AuNL/CBpz/Qd/mGf97A+U+czwuNL4zp815wwQW0trayd+9enn32WVatWsWXvvQlLrnkEpLJ5Jg+txDyuRdCCDHeJOAWQohp5oXGF7jp5ZvoCHcMur4j3MFNL980psGH1WqlvLycqqoqli9fzje+8Q3+8pe/8Oyzz/LQQw8BcM8997BkyRKcTifV1dXccMMNBINBAF5++WWuu+46fD5fX9bw1ltvBeCRRx7hxBNPJC8vj/Lycq666qq+3r9CyOdeCCHERJCAWwghppFUOsWda+5ERz/otux1d625a8yn2Q509tlns3TpUp588kkADAYDP/3pT9m0aRMPP/wwL774Il/72tcAWLlyJT/+8Y9xu920trbS2trKV77yFQDi8Tjf/e53effdd3nqqadoaGjg2muvHbfXISYv+dwLIYSYKKaJHoAQQojxs75jPe3h9mFv19FpC7exvmM9J5WfNG7jmj9/Pu+99x4AN954Y9/19fX1fPe73+Xzn/889957LxaLBY/Hg6ZplJeXD3qM66+/vu/3mTNn8tOf/pQVK1YQDAZxuVzj8jrE5CSfeyGEEBNFMtwjEQ/BrR61xUMTPRohhBixznDnqO43WnRd7+vT+9JLL3HeeedRVVVFXl4eV199Nd3d3YRCh/67+84773D55ZdTW1tLXl4eZ511FgBNTU1jPXwxycnnXgghprdwPEndLc9Qd8szhOPjWztDAm4hhJhGShwlo7rfaNm6dSv19fU0NjZy0UUXsXjxYp544gnefvttfvGLXwCQSCSGvX8oFOL9738/LpeLRx55hLVr1/LnP/8ZUFNuxfQmn3shhBATRaaUCyHENLK8dDlljjI6wh1DrmfV0ChzlLG8dPm4jenFF19k48aNfPnLX2bdunUkk0l++MMfYjCoc8J/+MMfBu1vsVhIpQavtd22bRtdXV3ceeedVFdXA7Bu3brxeQFi0pPPvRBCiIkiGW4hhJhGjAYjt6y4ZcjbNNTU1ptX3IzRYByT54/FYrS1tdHc3Mz69eu5/fbbufzyy7nkkku4+uqrmTVrFslkkp/97Gfs2bOH3/72t9x///2DHqOuro5gMMg///lPurq6CIfD1NTUYLFY+u739NNP893vfndMXoOYeuRzL4QQYqJIwC2EENPMubXncs9Z91DqKB10fZmjjHvOuodza88ds+d+7rnnqKiooK6ujgsuuICXXnqJn/70p/zlL3/BaDSybNky7rnnHu666y4WL17Mo48+yh133DHoMVauXMnnPvc5PvrRj1JSUsLdd99NSUkJDz30EH/84x9ZuHAhd955Jz/4wQ/G7HWIqUc+90IIISaCpuv6wXOrjiF+vx+Px4PP58Ptdh/dg8VDcHul+v0bLWBxHv0AhRBiBKLRKA0NDdTX12Oz2Y7qsQKxACt/txKAe8+5l5WVK8cswyf6Heo9HNVj1hQ03OuXz/3UN5rvoRBCjFQ4nmTht/4OwJbvnI/DcnQrq0dyvJYMtxBCTFMDg4wTyk6QoENMC/K5F0IIMZ6kaJoQQkxTDrODjddsnOhhCDGu5HMvhBBiPEmGWwghhBBCCCGEGAMScAshhBBCCCGEOGal0v1ly9Y09Ay6PNYk4BZCCCGEEEIIcUx6blMr597zSt/lax9cy+l3vchzm1rH5fkl4BZCCCGEEEIIccx5blMrn39kPe3+2KDr23xRPv/I+nEJuic04H711Ve59NJLqaysRNM0nnrqqUG367rOrbfeSmVlJXa7nbPOOovNmzdPzGAB0qn+3xvfGHxZCCGEEEIIIcSkkErr3PbXLQw1eTx73W1/3TLm08snNOAOhUIsXbqUn//850Pefvfdd3PPPffw85//nLVr11JeXs55551HIBAY55ECW56GX6zov/zolfDjxep6IYQQQgghhBCTxpqGHlp90WFv14FWX5Q1DT1jOo4JbQt24YUXcuGFFw55m67r/PjHP+ab3/wmH/rQhwB4+OGHKSsr47HHHuOzn/3s+A10y9Pwh6vhwPMj/lZ1/Ud+AwsvG7/xCCGEEEIIIYQYVkdg+GD7SPY7UpO2D3dDQwNtbW28//3v77vOarVy5pln8sYbb4xfwJ1OwXM3c1CwDZnrNHjuFph/MRiM4zMmIYQYQjQZJZFOjNvzmQ1mbCbbuD1fLl5++WVWrVpFb28v+fn5Od2nrq6OG2+8kRtvvHHEz3fttdfi9XoPWhIlxo987uVzL4QQQynNy+1vda77HalJG3C3tbUBUFZWNuj6srIyGhsbh71fLBYjFutfFO/3+49uII1vgL/lEDvo4G9W+9WfcXTPJYQQRyiajPJS00v440f5N28E3BY3q2pW5Rx8XHvttTz88MN89rOf5f777x902w033MB9993HNddcw0MPPTQGoz1yt956K7fddttB1z///PP85Cc/Qdf7T8ieddZZLFu2jB//+MfjOMLpSz73Y0c+90KIqW5FfSEVHhttvuiQqVMNKPfYWFFfOKbjmLQBd5amaYMu67p+0HUD3XHHHUMeII5YsH109xNCiDGQSCfwx/1YTVasRuuYP18sFcMf95NIJ7CR+5nh6upqfve73/GjH/0Iu90OQDQa5fHHH6empmashnvUFi1axAsvvDDousLCQiwWywSNSIB87seafO6FEFOZ0aDx7UsX8vlH1qMxeL5yNpr89qULMRqGjy1Hw6RtC1ZeXg70Z7qzOjo6Dsp6D/T1r38dn8/Xt+3bt+/oBuIa/rkG0yCdPrrnEkKIo2Q1WrGb7GO+HWlws3z5cmpqanjyySf7rnvyySeprq7m+OOPH7RvLBbji1/8IqWlpdhsNk4//XTWrl07aJ//+7//Y+7cudjtdlatWsXevXsPes433niD973vfdjtdqqrq/niF79IKBQa0bhNJhPl5eWDNovFwrXXXssHPvABQGUyX3nlFX7yk5+gaRqapg05HjH65HO/96DnlM+9EELABYsruO8Tyyl1D/77Xe6xcd8nlnPB4ooxH8OkDbjr6+spLy/n+eef77suHo/zyiuvsHLlymHvZ7Vacbvdg7ajUrsS3JX0nwcZgs0DgTbY8Rz0NEAqeXTPKYQQI6DrOpFEhHg6TiwZG7ctno4Pmlaaq+uuu44HH3yw7/Kvf/1rrr/++oP2+9rXvsYTTzzBww8/zPr165k9ezbnn38+PT2qmui+ffv40Ic+xEUXXcSGDRv49Kc/zS233DLoMTZu3Mj555/Phz70Id577z1+//vf89prr/Hv//7vIx734fzkJz/h1FNP5TOf+Qytra20trZSXV096s8jFPncy+deCCFyccHiCn7//53ad/mh607itZvPHpdgGyZ4SnkwGGTXrl19lxsaGtiwYQOFhYXU1NRw4403cvvttzNnzhzmzJnD7bffjsPh4Kqrrhq/QRqMcMFdmSrlB05GyDjxUyoo9zapgNtTBWWLIL8WTDLtSkyAeAhur1S/f6MFLM6JHY8YU5FkhHP+dM6EPPf5tefjto7sxOYnP/lJvv71r7N37140TeP111/nd7/7HS+//HLfPqFQiPvuu4+HHnqor5vFr371K55//nkeeOABvvrVr3Lfffcxc+ZMfvSjH6FpGvPmzWPjxo3cddddfY/z/e9/n6uuuqqvMNScOXP46U9/yplnnsl9992HzZbbtOCNGzficrn6Li9cuJA1a9YM2sfj8WCxWHA4HH2ztMTYkc+9fO6FECIXwViStxv7W3+tqC8c82nkA01owL1u3TpWrVrVd/mmm24C6Cse8rWvfY1IJMINN9xAb28vJ598Mv/4xz/Iy8sb34EuvEy1/nr2axBo7b/eUQTLr4HqTH/uglpIxiHUDjv2QV45lC6Cwnow28d3zEIIMUkVFxdz8cUX8/DDD6PrOhdffDHFxcWD9tm9ezeJRILTTjut7zqz2cyKFSvYunUrAFu3buWUU04ZVNfj1FNPHfQ4b7/9Nrt27eLRRx/tu07XddLpNA0NDSxYsCCnMc+bN4+nn36677LVOvbrhcWxRT73Qggx/uLJNGsbemj1jm3rr0OZ0ID7rLPOOuS0LE3TuPXWW7n11lvHb1DDWXgZzDwL7sxMkzrzZihfCoYDZuWbLOCpVtPKQx2w6wVwFkPpAiicBbajnOIuhBAHsJvs/PPKf/L3xr+TZ87Dbhr7E3yRZIRAInDE7ZGuv/76vumtv/jFLw66PXtsOFThzFym9abTaT772c/yxS9+8aDbRlKsymKxMHv27Jz3F2NPPvfDk8+9EEJAOq3zTlMvO9oDVBVMXPJz0lcpn1QG9tkuXXBwsD2Q0aSmmadTEO6GPa9C63tQMh+KZoOzaOzHK4SYFjRNw262YzFYVLVm09hnodKkiaVih+wacSgXXHAB8XgcgPPPP/+g22fPno3FYuG1117rW0aUSCRYt25d3zTZhQsXHtQH+M033xx0efny5WzevHncggaLxUIqlRqX55ru5HPfTz73QghxsC2tPt7b76XcbcM0jlPIDzRpi6YdMwxGcJVC8WwwmGDfm7DlL7D7ZdXf+wgKrwghxFRnNBrZunUrW7duxWg0HnS70+nk85//PF/96ld57rnn2LJlC5/5zGcIh8N86lOfAuBzn/scu3fv5qabbmL79u089thjB/Uyvvnmm1m9ejVf+MIX2LBhAzt37uTpp5/mP/7jP8bkddXV1fHWW2+xd+9eurq6SEv3CjGAfO6FEGJ87OkM8najl3yHBad1YnPMkuEeL5oBHIVqi/qhfRN0bYf8GpX19lSrrLgQQhyFWCo2ZZ7ncF0k7rzzTtLpNJ/85CcJBAKceOKJ/P3vf6egoABQU2OfeOIJvvzlL3PvvfeyYsUKbr/99kGVn4877jheeeUVvvnNb3LGGWeg6zqzZs3iox/96FGPfyhf+cpXuOaaa1i4cCGRSISGhgbq6urG5LlEP/ncy+deCCGy2nxR1jT0YDRoFDgmvoC1ph9Jb4spxO/34/F48Pl8R98ibGDl5w8/BEe4hqtPIgyBDtDT4K6A0oWq8JoUWBNHS6qUH7Oi0SgNDQ3U19cPqjQcTUZ5qekl/HH/uI3FbXGzqmbVEa9nna6Gew9hlI9ZU9Bwr18+91PfoT73QggxWrzhOC9t66Q3HKem0NF3fSyR4guPvwPAlu+cj8NydInOkRyvJaU6kcwOKKyDVByCnbDzebW2u3QBFNSDPX+iRyiEmCJsJhuralaRSCfG7TnNBrMEHWJCyedeCCFEVjie5M093XQGo9QVTZ5kkwTck4HRonp3DyywZtsAxXNUgTVXGRxhgRYhxPRhM9mwIYGAmF7kcy+EECKeTLOmoYe93WHqihwYDoidrGYjd3xwCXaL8aiz2yMlAfdkki2w5iyBqA9a3oGOLWp9d8m8zDpv80SPUgghhBBCCCEmhWz7r+1tAaoL7JgO1UlqAkjAPRlpmppObs+HeBh6G6F7D+SVqenm+bVgdU30KIUQQgghhBBiwui6zqYWH+9m2n9ZTQd3gJhoEnCPhG//+D+nxQGWWkglINQJO18ARwEUz4XCmSobLtPNhRBCCCGEENPMro4gb+/tpchpnfD2X8OZXPn2ye693/f/vvYBNd1bH6dek0YzuCtVP2/NAPvWqH7eO5+HngYVkAshpg3pczt1yXt35OTfbuqS904IMdr29YRZs7cHm9mIxz55l91OztMAk1VeBbjKIdgGe/+lNmcx1J2hNnfl2I9BM4CjSG3xIHTvgu6dau13yXw13dw2/VrJCDFdWCwWDAYDLS0tlJSUYLFY0GSWy5Sg6zrxeJzOzk4MBgMWy8T3Bp0q5HM/dcnnXggxFjoCUVbv7iaZ0qnKP3zhzGQ6zeNrmjhtdvE4jG4wCbhHYsVnoHIZbHgcevZA05sQ6oLNf1Zb0SwVeNeuBOs4BL0WFxS6VHY73AW7XwSbB4rmQGG9OjkwyYoGCCGOjsFgoL6+ntbWVlpaWiZ6OOIIOBwOampqMMjf55zJ537qk8+9EGK0eMNx3tjVTSCWoKbAcdj907rOg6/v5b1mHzs6AnzurFnjmhGXgHukNIPqkT3nPDjhWmh+W2W6W9+F7t1qW/9bFZjXnQ6VJ4BpjM/mGs2Z7HuZqm7evB7aNqqMe8l88MxQa8GFEMcEi8VCTU0NyWSSVCo10cMRI2A0GjGZTJKdPQLyuZ+65HMvhBgtoViSN3Z30xFQvbYP93dF13Uee6uJtxp6MGhw9Sl14z79XALuo2Gyqmx27UqIeKHxDRV89zaoQLz5bTDbofpkqD0dSheObcZZM4C9QG2JKATaVIVze4FqK1ZQK0XWhDhGaJqG2WzGbJ68a5aEGG3yuRdCiOkrmkjx1p4e9vWEqR2i1/ZQ/ryhmZd3dKIBHz2xmoWV47/0VgLu0WLPh/kXqc23P7PG+3U11XvPy2qzF0LtaSrznV8ztoGv2Qb51ZBOQ6QHmt6A1g0q2100R/00H369gxBCCCGEEEJMpEQqzbq9PexsD1Bd6Mip1/Zzm9r4v41tAHzilFoWVkxMnSsJuMeCZwYs/Tgc91Ho3K6C76Y3VeC77a9q88xQWe+601TWeawYDKqwm7MY4qFMT+9dquha0dxM1rtYst7HmvSA6ZaNb8Css8Ew+foSCiGEEEIIcSjptM47TV62tPipKrBjMR0+2H5lRyd/Wq9aOl+xvIoz55bQGYiN9VCHJAH3WNIMULpAbSdcCy0bYO9r0LJeZcHf+53aSuapzHfNKWNbbM3iVFs6CeGBWe8qyXofS7Y8Dc9+rf/yo1eq9fwX3AULL5u4cQkhhBBCCDECuq7z3n4vG/b1Uuq2YTMfPoG0ek83j7zZCMCFi8u5cHHFWA/zkCTgHi9GC1SvUFs8BPveUlPOO7aoLHjndnj7Yag4TgXfVSeOXfBrMKk2Yq5S1VqsL+tdqLLe+TUq6y6VRKeeLU/DH64G9MHX+1vV9R/5jQTdQgghhBBiStjeHmB9k5cipxWX9fCh6/qmXh58vQEdOHteKR86vmrsB3kYEnBPBItTTfGddbbKNDe+AY2vq2JrLe+ozWiBqhNU8F2xVFUiH5OxuNSWTmXWeq9WGXh3JRTPBXcVWF1j89xidKVT8NzNHBRsQ+Y6DZ67BeZfLNPLhRBCCCHEpLanM8iaPT04LcacKotvavbxP6/uIa3DyllFfGxF9aTojiAB90RzFMKCS9Tmb+4PvgNtKvhtWg1mJ1SfpILv0kVjk3k2GFVW21kCibDKiPY0qGJwhbNU1juvAozykZm0Gt8A/6H60+r9n7H6M8ZtWEIIIYQQQozEvp4wb+7pxmjQKHJZD7v/9rYA9768m1Ra58TaAq49tS6nKubjQaKnycRdBUs+DIuvhJ49KvBuWg2R3v5K5zYPVJ+iWpEVz1HrxEeb2QH5DtDTqt1ZyztqrberTGW9PTNUq7FJ8iEWGcH20d1PCCGEEEKIcdbmi/LG7m4SKZ2qfPth99/dGeSnL+4knkpzXJWHT59ej8EweeIUWaQ7GWkaFM2C5VfDZb+Ac74Fs88FSx5EfbDz7/DCt+Hpf4d3fgvdu0Efahrx0Y7DkFnXPQvcM9Rz73kZNv8ZdvwDunZBPDz6zyuOjKtsdPcTQogBXn31VS699FIqKyvRNI2nnnqq77ZEIsHNN9/MkiVLcDqdVFZWcvXVV9PScqhZN0IIIcRgXcEYr+/qIhxPUuk5fD2rvV0hfvzCTmLJNAsq8vj8WbMwGSdXiCsZ7snOYIDShWo74Vpo26Sqi+9fq9Z/b3tGba5SqD4Vak+F/NrRzz6bLGpdN0AsqNabd+3ITDmfKVPOJ4Paleo98rcy9DpuTd1eu3K8RyaEOAaEQiGWLl3KddddxxVXXDHotnA4zPr16/mv//ovli5dSm9vLzfeeCOXXXYZ69atm6ARCyGEmEq84Thv7OqiNxyjttB52PXX+3rD3PPCDiKJFHPLXPz7WbMxT7JgGyTgnloMJqhcprZUXLUZa1oNzesh2AFb/6K2vAqoOVVt+dWjPw6rS23pNER7+6ecO0uheLbKhktv7/FnMKrWX3+4GtAYHHRn3osL7pSCaUKII3LhhRdy4YUXDnmbx+Ph+eefH3Tdz372M1asWEFTUxM1NTXjMUQhhBBTlD+a4PWdXbT5o9TlEGy3eCPc8/wOwvEUM4udfPHsOVhzaBk2ESTgnqoGthlLRlXQ2/iGCsIDrbD5SbW5q1R/75pTwDPKwbfBAI4itaXiKuPe8C8w2yGvHIpmg9UDP1qg9v9Gi6rQLsbOwstU669nv6Y+B1nuShVsS0swIcQ48fl8aJpGfn7+RA9FCCHEJBaKJXljVxf7vRHqipyHXX/d6ovwg39sJxBNUlPo4MZz5+TUn3uiSMB9LDDZ+jPaiQg0v60y363vqqrUm55Qm3sG1Jw8NsG30aKC7Lxyta47kKlyPjCbuutFmH+RZFjH2sLLYOZZcGfmPf63P6kWdPLvLoQYJ9FolFtuuYWrrroKt9s97H6xWIxYLNZ32e/3j8fwhBBCTBKReIrVu7to7A5TW+jAeJhgu80f5Qf/2IE/mqS6wM5N583FYZncIe3kHt2kpEEqBr59qoiZNW9yBTJmO9SdrrZ4GJrXQdOb0PYu+PfDpv0HB9/uGaM7/dviUFvTW/D2g/3X/+ET4CiGVV+H4z8JpsOX+BdHaOBnsnbl5PqMCiGOaYlEgo997GOk02nuvffeQ+57xx13cNttt43TyIQQQkwm0USKtxq62dUZorbQcdhiZ+3+KD/4+3Z8kQRV+SrYdlknfzg7+Uc42RTWg+E88O2HUCf09gApMDlU8G1xTp7gxuKA+vepLR7KZL7fhLb3Dgi+K6H6ZNVuLL9mdILvfWvg9R8dfH24C575T+jcptqfuatUVtx4+Gb2QgghJrdEIsFHPvIRGhoaePHFFw+Z3Qb4+te/zk033dR32e/3U109BrVHhBBCTCrxZJo1Dd1sbw1QXWg/bLGzjkCUH/xjO95Igsp8G195/1zybFMjfpCAe6TsBWqrWKqC2HAPhLtVxjvUrYJwHbDYVABudqm1zhPN4hwQfGcy3/veykw7b1Gtvjb/GVzlmbXhJ6vq40cSfKfT8PZDh97nvT+Cp0adnHAUQeEs8FSpwmtS6VwIIaacbLC9c+dOXnrpJYqKig57H6vVitUqs52EEGI6SaRUsL21NcCMAjtW06GTlR2BKN//+3Z6wwkqPDb+87x5Iw62Y8kUvmiCivzDtxobbRLZHA2LU2351apyeCyogu9wjwrAw90Q7AR0MA/IgGsTHIAPzHwnwqrK+b63VKXxYBtsfVptzmKYkSnMVjw393F3boVIz6H3iXpVobWCORDxqsy70aSmnBfNUpXWXaWTZ7aAEEJMc8FgkF27dvVdbmhoYMOGDRQWFlJZWcmVV17J+vXr+dvf/kYqlaKtrQ2AwsJCLBbLRA1bCCHEJJJMpVm3t4fNLX6q8u2HrSze7leZ7Wyw/ZX3z8NjH1mwHU2kaO6NML8ij1NmHv5k8GiTgHs0ZdtlFdSqADyeCcBD3eBrgkivat8FKui15oHZObHts8yO/jXfiYiqdr5vjfoZ6oLt/6c2Wz7MOEkF36ULVIuy4US8uT13xKuKrblK1ZaMq0C98TUwmMFZojLfeeUSfAshxARbt24dq1at6rucnQp+zTXXcOutt/L0008DsGzZskH3e+mllzjrrLPGa5hCCCEmqVRaZ31jLxubfVR4bIetLD4awXYknqLFF2FBZR4r6osmpJq5BNxjRdNUQG3Ng4I6qFoOMf+AAHyfCsD9bSpzbHWqImxm+8QF4Ga7KrBVuxKSMTXdfP8alQGPemHX82qzuNTrmbECyo8D0wGZC3t+bs934H6mTKVzylWrs4gX9r4KRis4M9PO8ypUIC7TzoUQYlydddZZ6Lo+7O2Huk0IIcT0lkrrrG/qZcN+L6V5tsNWFh+NYDsUS9Luj7JkhocTawuxmCZmlrFELeNF08DmUVvhTKg6AWI+Nf081DkgAG/JBOAusLrBPP7rDABVQTzb5zuVhPZNKvjev06dOGh4VW0mq1rPPmMFVB6vpsyXLAB74aGnlTuK1H7DPr+tv81YX/D9L5URtxepf0N3Ztq5FFwTQgghhBBiUkqndd5p6uWdJi+lLtthK4urPts78EUSVHps/OcRBNuBaILOYJyl1fksry04bFG2sSQB90QxGPoLsBXNgvQKlUUOd6tp5779EO6ERFRN385myyeilZbRpKbIVy6DEz8NXdvVtPP9a9R4961Rm8EIpYvU1PMlV8KaXw7/mMuvyb2Y3KDgO6ZOTDStVs9nL1SV490V4CqTVmNCCCGEEEJMEum0zrv7vKxv6qXEZcVlO3T42eyN8IN/bCcQTVKVbz+iauTecBxfJMGJtQUsrc4/bG/vsSYB92RhMICjUG3FcyCdUoFluBsCbSrzHWxXAbjJmgnAXSrjO97jLF2gtuVXQ29DJvheC/5m1XKs7T21r6sCYl61NjzLUaSC7eoVR/b8Jmsm+EYVXYt41XNrmlpnXlCn2py5ytQ6eSGEEEIIIcS4S6d13t3v5e1MsH24wHlfb5gf/mMHwViS6gLVZ3ukwXZPKE4wluSk+kIWV3owTHCwDRJwT14Go6oS7iyGknmQSvS3IAu0gr8VfC2QTqgMcDYAP1Qxs9GmaWpqd+FMWPoxdVJg/1o17bx7JwRbB+9ffTLMvUC9ntEwsOBaKqlmCLRsUAXfbG7wVINnhrrd5hmd5xRCCCGEEEIcUjbYXt/YS6HDctjAeW9XiB+9sINQPEVtkYMvnzv3sFPPD9QZiBFLpTh1VhHzy/PQJrIw9QAScE8VRjPklamtbKGaWh3ugXBXf/bb2wTpZKYFmVsVNxvPHuDuSlh4udrCPZle32vU+m9Qrcf2vQVWT6bo2olQtuTgomtHwmjqP0GRTql15h1boW2TKkjnKlfZb1epmoY+GXqjCyGEEEIIcYwZGGznOyy4D7P+eldHkJ/8cyeRRIqZxU5uPHfOYYuqHajVFwENTp9dzOzSvKMZ/qiTgHuqMlnVumV3BZQvUdO2w92qlZdvn6qEHuoCPZ1pQeZWP8erB7ijEOa8X23xsOrxvX8dtL6jisXteUltRouqdF51giq6lmuF80MxGPvXx+tp1Z7Ntx+6d6lK7I4iKKhXJy+cJVJ0TQghhBBCiFFwYLB9uGJnW1v9/PylXcSSaeaWufji2XNG1LpL13X290awW4ycOquI2iLn0b6EUScB97HCbFfTpz0zVHGzWFBlvwf2AA+0ZdqVuTIF2MapBZnF0d9uLJWEzq0q+G5+W42xeZ3a0KBotgq+q05Qr+Vox6cZ1MkGq1tdToQz1eD3g2ZSQXl+jTpx4SxV/zZCCCGEEEKIERlpsL2x2ce9L+8ikdJZWOHmC6tmYTXlHmyndZ19vWE8NgsrZxdRmW8/2pcwJiTgPlZZXWrL9gCP+jIZ8E7w7oNwLyRbQDP2tyAbjwrfRpPKyJcvgROuVdPgmzPBd88etfa7eye89zsVAFctV5nv0oWjk4k2O9QGquha1N+/7tvqUlPP82tk6rkQQgghhBA5ylYjf7tJrdk+3DTydY09/OpfDaTSOktnePjcmbNG1LormU6zrydCSZ6VlbOLKM2boFbKOZCAezrQNDVV256vWpDNWNFfAT3YrqZbB9vVunCjpb8F2VhPtdY0KKhV2+Ir1LrvlvUq+G7fBKEO2PGc2kw2qDgOKjMB+GgUQTNaBqz7TkM8AN5G6Nqh+p/bCyG/DvJK1dRz8+Q8ayaEmBjheJKF3/o7AFu+c/6I15sJIYQQx4JUps/2+hyrkb++q4uHVu9F1+HE2gI+fXo9phEE24lUmqaeMNUFDlbOLiLfMc5dm0ZIvh1MRwYDOIvUVjJ3iAroLSoI15Mq0LVkAnBD7lM8joijEGafq7ZkVBU8a1kPzetVBfJsv280deKg8ngVgBfUHf3Uc4NBBfHZQD4RVtnvptWZlmMecFepwnDOEjUVXbLfQgghhBBiGkulddY39fJOkzenYPufW9t5fO0+QBU4u/qU2hG17oolUuzzRphV4uSUmUUjbhs2ESTgFgdXQE9EIdKTKcC2X2Wae7tB18evAJvJpqqYzzhRFT7raVDBd8s7mannu9S28Y8q+K1YpgLw8iWjk4nOTj3PQ1V+j/qha7vKvJsd6uRAfi24SiT7LYQQQgghpp1kKs36xl427PdS6rLhsg0fWuq6zjMbW3lqQwsA5y4o5aMnVo+odVc4nqTVH2V+eR6nzCwaUXG1iSQBtziY2QbmSpXNrTgO4iEVfIe71ZTroQqwZddFjwXNoDLaRbNgyYdVNr51gwq+295T48lWPTcYoWRBJvt9PORVjEL226QCbEehOumQiKiMe2MLaKie33kVqsibo1jtN9azAYQQQgghhJggiVSadXt72NjsozTPdsie2Wld54/r9vP81nYALj2ugsuWVo4o2PZHEnSFYhxX5eGE2kIspqkz01QCbnF4FqfaCmpVEJstwBbsUBnwcA8kmlVgas3LFGAbw7UUjkKYdbbaUgnVb7tlvSp+FmxTWej2TfDOb1XhtcplKgNetujoC8NpmsruWwZkv2MB6N6txmG2gTUfCjKF1xzFKiAfbxYn3Oob/+cVQgghhBDHtHgyzZqGbja3+Knw2A5ZwySV1nl49V7e2N0NwEdPrOa8hWUjer6eUJxANMlJdYUcNyMf4wimoE8GEnCLkTmwAFs6BRGvau/lbwV/MwRaVCBssmZacrlUMD4WjGaVha84Dk5ArUFvfkdlvzu3qunwO/+hNoMZShdkpp8vG73sd7bnN6jp+DGfanuGrgJfZ4mqfO4oVj3AzZO3iqIQQgghhBDDiSZSrGnoZmtrgKp8+yGndSdSaf7n1T1s2OfFoME1K+s4bVbxiJ6vzR8lldZZObuI+eV5I8qKTxYScIujYzAOKMA2L1OArVtNQfc3q+rnvU1qHbbFnln/7Ry79d95FTC/AuZfpILfjs0q+G7ZoE4KtL2ntnd+o7LfFUvVVrZ4dAJhs01trjL1muNBCLSrNegGo3r97ko1TmexqoRulP+GQgghhBBicovEU7y5p5sdbQFmFNixHiLYDseT/PylXexoD2IyaHzuzFksq87P+bnSuk6LN4LVZGTlnCJmlrhG4RVMDPmmL0aX0Qx55WorXwzxsArAw12Z/t9dKggHsLjUdGuT/egzzUMx26DqBLXpuqq+3rpBBd/Z7Peu59VmMELxvP4APL/26MekGTIZ/syU8lQSYn7o2gntmzMzADyQP0MF6I4isOVL9XMhhBBCCDGpBGNJVu/uYk9niBmFdqym4YNtbzjOT/65k329EWxmA/++ajbzy3NfYplK6zT1hih0WDl1VhGV+VO7OLEE3GJsZdc751erqdyxQCbo7gRfE4R7x2f9t6aBp0pt8y/uz363vquC8GAHdGxR27uPqzZg5cep4Lt8ySj1/R5QfA1U67NYAFreBT2lCs/Z88FTrbLfjiL1vFNw6owQQgghhDg2+CIJ3tjdRVN3mJpCB+ZD9Mxu90f50Qs76ArGcdtM3HjOXGqKci+unO2xXZVv59RZRRS5jrL+0iQgAbcYP5qmMto2NxTOhPRJqsJ4X//vA9d/Z/t/j8HHdGD2G1TV9dZ31daxWRWG2/svtYHq9V1+nNpK5qlM/tEy2dTmLOmvfh7zw/61gA5mp1ob7qlWU/YdRerfQwJwIYQQQggxDnpDcV7f1UWLL0JtkQPTIWZi7u0O8ZN/7iQQTVKSZ+XL586hNC/3JZvRRIrmTI/tk6dIj+1cSMAtJo7BMGD999z+9d/hbvA1q4rj3qb+7K81T01DH4v139lp8HPPV+Po3N6/3rt3b/+29WkwWlXxtfIlKgD3zBiF6ecDqp9DZv13GKK9qhJ89nZ7kZot4ChUAbjFJQG4EEIIIYQYdR2BKG/s6qYrEKO20HnI6uCbmn3c98puYsk0NYUOvnTOHDz23APmQDRBZzDGoko3J9YVTpke27mQgFtMHgPXf5ctUhnfUNcB6787UdW/x3D9t9Gs1p+XLwauUlXY2zZmtvdUD+7WDWoDlYUuW6wC8LLF/VPGj4ZmyPQ4d6n2Y3pa9UMPd6mTEJohE4AX9gfg9kLJgAshhBBCiKPW7I3wxq4u/NEENUUODIf4fvn6ri5+s7qRlK6zoDyPG86ajd2Se8DcHYwRiqc4sbaQ42Z4MB1iyvpUJAG3mLzMdhVMDrn+e9/4rf+250P9GWrTdfXcre+pALxzq5oWP3D6uXtGJmBfojLh5tzXrQxLM/RPsQdIpyERHBCAZzPgBeCp6V8rbnVLAC6EEEIIIXK2tyvE6t3dxJIpagocw7bi0nWdZza28tSGFgBOri/kupV1OQfMuq7T6ouiabBydhHzyqZm26/DkYBbTA05rf9uhVQcjBa131is/9Y01VM7vwYWXKKer3OHCr7bN6r2X/79atvxnAqUi2apzHfZYiieOzrrvw0HVEDvC8B7wLtfXWd1qqrn7hlq2r69QKqgCyGEEEKIIem6zs6OIG/t6UZDY0bB8EmjVFrnsTVNvLKjE4ALFpXzoeVVh8yED5RO6+zzhsmzmjllZtGICqtNNRJwi6npsOu/2/vXf5sGrP8e7WDTaBkw/fzjEAtC+ya1tW1S69C7dqpt85/V/iXz+gPwgvrRGdOBAXjfGnCvaoem62rGgNWtKrU7S1QAbs8fnRMAQgghhBBiykqndTa1+Fi3tweHxUTxIaqDRxMp/ufVPWxs9qEBHzupmnMWlOX8XNlK5BUeG6fMKhpRYbWpSAJucWwYav13uFutAfftUz+DHWpfq1MFnmbH6E+3trqg5hS1AYQ6M9nvTar3dtTXvx4c1BhKF6gxly5S0+dHoyjcwDXg0F8FPR5Qfcj1tJp+b3GBuxJcpZkAvEAF5kIIIYQQYlpIpNK80+Tl3X29FDqthyx25g3H+emLu2jqCWMxGvjMGfUcX1OQ83OF40lavVFmlR5blcgPZVIH3MlkkltvvZVHH32UtrY2KioquPbaa/l//+//YZBpseJQzHZVPdwzAyqXqfXfoS61eZvUdHR/qwq4s+u/zWNwds1ZArPOVpuuq6nmbZngu2MLJMLQ/LbaQI2ldGF/AO6uHJ2TAgOroGdicNUHPAid29QJgOxaeEeRel57vgrAZR24EENKpfW+39c09HDGnJJDVnAVQgghJptoIsXavT1sbfFT6rbhsg4fHjZ7I/zknzvpCcXJs5n4j7NnM7PYNez+B/KG4/SEEyyp9rC8puCYqkR+KJM64L7rrru4//77efjhh1m0aBHr1q3juuuuw+Px8KUvfWmihyemkmzBscJ61Xs76lXrnYPtqgJ6qAOSMZUpz+5rHOUCbJqmemp7qmHehWrddW9DJvu9RQW+sQDse0ttADbPgAB8IeRVjF7w29cHvFhdTiVUJXR/M3Tv7g/SbfnqeZ3F6neZhi4Ez21q5dtPb+67fO2Da6nw2Pj2pQu5YHHFBI5MCCGEyE0gmuCtPd3s7gxRlW8/ZAC8ucXH/a/sIZJIUe628aVz5lCSN/y08wO1+6Mk0mlOmVnIokrPtDpBrem6rh9+t4lxySWXUFZWxgMPPNB33RVXXIHD4eC3v/1tTo/h9/vxeDz4fD7cbvdYDVVMZalkpgBbl8p6B1oh6od0AkzWzNpo1+gXYBtqHD27M9nvzdC1QwXBA2UD8NIF6qe7auyyz+m0ysDHgyoQ19Pq38PiUlPQ88r7A3DpBy6mkec2tfL5R9Zz4MEz+z/gvk8sP+Kge7ofs6b76xdCiPHSHYzx5u5u9nsj1BQ6MB+isvgrOzp59K1G0jrMLXNxw5mzcdly+16cTuvs94ZxWEysqC9kZknuGfHJbCTHq0md4T799NO5//772bFjB3PnzuXdd9/ltdde48c//vFED00cS4wmcJWorXSBynSHe1QA7mtW2e9xKcBmUgXVSuYBH1LBdveuTAC+VQXgUR80rVYbqJMBpfNV8F2yYPTWgEOmENuAdeCgpqHHQyoD3rkVMGay4J7MNPRCFYDb8semRZsQEyyV1rntr1sOCrYBdFTQfdtft3DewvJpdfZeCCHE1NHijbB6dzc94Rh1Rc5hj1fptM4f1+/n+S3tAJw6s4hrTq3Nue1XtjhaucfGKTOLKHMf28XRhjOpA+6bb74Zn8/H/PnzMRqNpFIp/vu//5uPf/zjw94nFosRi8X6Lvv9/vEYqjiWmKzgrlBb+RJV7buvAvo+CGWKsZFWRc+sbhV0jlagm2U0ZzLZC9TlVFwFuh1b1Na1E2J+2LdGbQBmpwrASzJbYf3oZuaz09AdRepyOgWJUKYaemvmpIRVjcNVAq6y/gDc6paWZGLKW9PQQ6svOuztOtDqi7KmoYdTZxWN38CEEEKIHOzuDLJmTw/RRIraQuewbbyiiRS/+tce3t3vA+ADyyq5eElFzn2yQ7Ekbf4os0qcrJhZhHsaFEcbzqQOuH//+9/zyCOP8Nhjj7Fo0SI2bNjAjTfeSGVlJddcc82Q97njjju47bbbxnmk4piWLTaWX91fgC3crQJvX6YAW7Ats69LZcDHogK60TIgAL+ifwp6xxbo2AZd21XwO7AIm9EKxXP6A/DiOSogHi0G4+B2ZJDJgoeht1Fl5dFUETtLHuSV9a8Ft3nA4pSp6GJK6QgMH2wfyX5CCCHEeEindTa3+FjX2IvFaKC6cPi+193BGD99cRfN3ggmg8b1p9Wzor4w5+fqCcXxRxMsq85nWU0+VtP0KI42nEm9hru6uppbbrmFL3zhC33Xfe973+ORRx5h27ZtQ95nqAx3dXW1rAcTY0PXVZY5WwHdtw8iXkhGVMbb4lQBuMk+9oFlOgW9e1UA3rkNOrer9dcDaUaV9S6ZlwnA54FtjP9f6OlMS7KQ2tJJFaibM1PR8yrAUah+t3mkLZmY1Fbv7ubjv3rzsPs9/plTjijDPd3XME/31y+EEGMhnkyzvrGH95p9FDos5DuGX/a3qyPIL17eRSCaxGM384WzZuW87lrXdVp8UQwaLK8tYEG5G8MxurzqmFnDHQ6HD2r/ZTQaSafTw97HarVitY5iBk+IQ9G0/kCxaBakTxpQAb0DfPvV78kokF0TPUYtyAxGNYaiWbDgUhXo+pvV+u/ObWoL96h14d27YNsz6n55lf1rx4vnjm4ldOg/8WBx9l+XTqqCbFEv+FsAHTTT4Kro9vwBQfj0XPMjJp8V9YVUeGy0+aJDruPWgHKPbUSZACGEEGKsBGNJ1jb0sKM9QLnbhvMQbb9e393Fb1c3kkzrVBfY+Y+z51DozK0mTzKVZl9vhEKnhRX1hYfMoE83kzrgvvTSS/nv//5vampqWLRoEe+88w733HMP119//UQPTYihGQwqW+sohOLZKusc8WamoGcD8E5IxDLTsV1qqvVYBJSaob8N2Zz3q2x8qFMF3l071E/ffgi0qG3PS+p+VrcKvLMBeGH96LdIM5gOnoqebUsW7lLj0tOqkJzFqfqBO8sGBOFuyYSLCWE0aHz70oV8/pH1aDAo6M6epvr2pQulYJoQQogJ15WpRN7sjVBd4MBiGrqWTiqt86cBxdGOr8nn06fVY82xT3Y4nqTVF6W2yMHJ9UUU5BikTxeTekp5IBDgv/7rv/jzn/9MR0cHlZWVfPzjH+db3/oWFktub6RMTxOTSjqVaUHWncmAN0Pcryqja2McgA8lFlRrvzt3QNc26N6j2qENZDBBQX0mCJ8LRXPUCYXxkIqr9eCJsJqWrusqCDc7VNCdV5FZD54J3mVNuBgn2T7c7f7+JUyj0Yd7uh+zpvvrF0KI0dLYHeKtPT0EYglm5DuGPREciiX55at72NyqCk1felwFly6tHLaY2oF6w3F6w3EWVXo4obbgkL28jyUjOV5N6oB7NMjBW0xq2R7gkZ7+ADzmUwG4wZhpQTaOAXgqAT17VAa8a4cKxGO+g/dzFKsCbMVzVCCeX6cC4XEZ4xBBeHZNuNWlKqM7CtW/nTUvUx19evzxF+MrEE2w5NZ/APDQdSdxxpySo85sT/dj1nR//UIIcbTSaZ2trX7ebuwF1Mng4SqLt3gj/OKlXbQHYlhMBq5fWceJdbklVdK6Tqs3isGgMuILKjzTanbXMbOGW4hj3sAe4CXzhg7Aw52QiKpMs8WpgsqxKsJmNA/oBY4KZoPtqgVZ1w7109eopn03dfX3AzeY1dTzokwQXjRbtQ4bkzFawG5R08uzUklIhlUF+WCHWiOuGdS0c7NDjcVVkpnGngnEZUq6OEoDv1isqC+cVl80hBBCTD7RRIoNTb1savHjtpkPuf76naZeHni9gWgiTaHTwr+vmk1NjuuuE6k0+3rDFDmtsl47BxJwCzGZDBWAZ4uwhbIBeLYImzZgCvoYBeCaBnnlaqs/Q12XiKh+4N0DgvB4sD8rvj1zX3uBCryzW+GsscvUG01gPGBNuJ5WJyoSYVW9vSszMKNF9RK3usFVqgJ3a15/Szfj9O0TKYQQQoipyRdJsLahm92doUMWR0vrOk+/28Lf3msFYG6Zi8+9bxZue27ff4KxJO3+KDNLnJxUV3jIiudCkYBbiMnMaFJ9q53Fav10tghbpAeCnaoKeaRXVfrWtEzP8Dz1Uxu6MMZRM9uhfLHaIJMFb1OBd/cuFXR7M/3J969VG6jxuav7K6kXzVYF3cZqurdm6O+hPlAynqmQ3quKxelpQFNBuNmuAnBHSWZduKs/EJdp6UJMKfFkmrf39jCr1EWpWzodCCGOXa2+CG/t6aEjEKWm0IHZOPR3wHA8yf++1sB7+9VywXPml/LhE2dgMuT2nbEzECMcT0p/7RGSgFuIqcRgBGeR2ornQDqtMuCRXgh1g3+/uhxoUyWTzfZMAO4cw8BWU8XL8iqg/n3qumQMehv6g/DuXapQnK9JbdmK6EYLFNSpALwwE4i7yse28JnJojby+6/T02rWQCIK/lboaUC1KjOo6fsma6b6fHFmSror0+rMJRlxISapWDJFQ3eIxp4wJ9YVMqvEOew6RiGEmIrSaZ2dHUHWNfaQSKapK3IOW+xsX2+Ye1/eTWcghsmgcfWptaycVZzT86TSOvu9YRxmE++bW8KsEtcx2197LEjALcRUNrANWdEs0E+CmF9NO4/09vcBD3WBnlJZ3Ow68NFu9TWQyQol89WWFentD767d0PPbjU9PTsVPcvshMKZaiuapX6O1XrwLM2g1nqbD8iGp1OZQDyi/i27d6MaQQ3IiNvcKhC3ufuDcLPj4Gn+8RDcXql+/0bL4L7kQogxoaMq8P5rRyeBSIIlMzyYhsn8CCFEVjieZOG3/g7Alu+cj8My+UKmaCLFu/u8bGr24bSaKCsYfh31m3u6+c3qRuKpNEVOC58/axZ1Rbl9D4kmUjR7I1Tl21lRXygzho7A5Pv0CCGOnKZl+lR7gHqoWq5af0V61RZozRRja1Htvwym/mnTJtvYBrX2AphxktpAZZUDrZnge48KxHsbIRGC9o1qy7K6VVG2bCBeUD/2QTioWQEW58HBcTqTEU9G1b+nt0m9Hp1MBt2WKdZWqF63xdXfpFkIMa5K8qwkUzprG3vwRROcVFc47NpGIYSYCrzhOGv39rCnM0SZ24ZrmL9pyVSaP7y9nxe3dQCwqMLNZ86YicuW29/AnlAcbyTBgoo8TqwrnJQnHqYC+VcT4lhndaktvxoqjlPTpiO9mann7Wr6ebhbXd+3DtylMs05ruk5IpoB3FVqy05FTyXBt09lv3v2qL7gvn0qa9/6rtr6XlcmCC/IBOIFdeAsGZ8+3IZh1ofrumpbloyqEwdd3arVmgYkB/Q33/K0KkRnz+/PrJszjzfWJz6EmIbcdjMWk4HtbQGC0SQrZhZSmidZGiHE0FLp/q7Jaxp6RqXt42jZ1xNmTUMP3aHYIddrdwdj/M+re9jTFQLgkiUVXLa0Mqep4Om0TosvgtGocdqsIuZXuCfN65+KJOAWYrox28BcAe4KKF2QqYTuU0F4uFsVYot6VeaWdCZbOw7T0EEViSusV1tWKq4yyNkAvHePmt49VBBucanAu6AuE4jXgatibE8cDKRpajq9yQp4Bt8WD/f/HvWpLZUJwjXUv7PRotaM29yZzLgz09rM3t/izGQdn9cixDHGZjZSV+RkvzfMi1s7ZF23EGJIz21q5dtPb+67fO2Da6nw2Pj2pQu5YHHFhI0rmUqzpdXPO01egEOu197U7ONX/9pDKJ7CYTFy/Wn1LKvOz+l5ookULd4IZR4bJ9UVUpkvbVSPlgTcQkx3RlN/ITZmqyxtLDB4GnqoS1VCTyUz2d3sWmX72FVD7xufpb+12JzMdck4eBtVYbaeBvXTt0+1J2vfpLa++1uhoEYF4Pm1Khj3VGcKp42jgUF/XpkKsLP0tHpNqRgkI+DzqSn2ZCqoawb1OkzWTEuzPJUdtzjV5ex68uzvRvnTLsRQjAaN2kIn7f4or+7oxBuOc9yMfCwmWdcthFDB9ucfWY9+wPVtviiff2Q9931i+YQE3YFogrcbe9nRHqDQYRm2FVc6rVp+PbOxFR2oLXLwuffNoiQvt5P1agp5nLnleZxQW0CeTQrDjgb5ViaEGEzTVIbV5oaCWmCZmm4e9aqWZOEutQY86lMVvUFlzbNrncc6Cw4qWC6eo7asVEJlvnsbVN/t3ga1JjwVU9XSu3YOeI0GyKtUry+/tv+nPX/sxqyn+3/v2ArlS/uDcM2QmXkwzBTXdDIzVX1AS7NsQK5rKkNutPRvZnumnZkbLNlA3Dogi565LK3OxDRV5rb1fYH1RhKcVFuIxyFfLIWYzlJpndv+uuWgYBv6yqVy21+3cN7C8nGdXt3ijbB2bw9tvigz8u1YzUMfu73hOL/81x52tAcBWDWvhI+cWD3slPOB0mmdZl8Ek1Fj5awi5pe7pcDkKJKAWwhxeGYbmMvVumNQRcNivkxPcK/Kgoe7D86Cm51j2xN8IKP54Ono6Uxhtmzw3bsXvHtVBt+/X22Nr/fvb/OowDu/pv+nu+roM8b71sDbD/ZffuUusBfCCddC9YrD399gUtuBVdSz9LQ64ZBKqMA86lMnRpLxzLcEXf00mNS/U/Zndpq6NTNbIZtFN5ozwfvA380SoItjSp7NjNVkZE9nEH9EFVOrLhy+yq8Q4ti2pqGHVl902Nt1oNUXZU1DD6fOKhrz8SRTaba1qSnkqbROfZFz2PXXm5p9PPB6A4FoEqvJwNWn1nJyfW5jzFYhr/DYOFGmkI8JCbiFECNnMKg1xvaCzBXHH5wF97dCPJBZC55SwVs2C24ap2JFBgN4qtRWd7q6TtfVVHlvNgBvhN4mFZhHfdD2ntqyNCO4KzNBeGbzVOdeJX3fGnjtnoOvj/So60+/Kbeg+1A0w4C144eQSqrq9OlMcB71qRMlqYRqG5elo/7tDCYwZAJtg6m/ArspE6ibrep2o7l/v2xAbzD13y+7acbxW08vprVwPMmSW/8BwPevXDJsZV2LyUBdkZNWX5SXtnWwrCafhRWS2RFiOuoIDB9sH8l+R2PgFPICh4WCYaaQJ9Npnt7Qwv9tagOgusDOZ8+cRXmOrbu6gjECUVWFfHlt4bDVzsXRkX9VIcToGCoLHg+oADxbET3UqbZETM3N6qvO7VSB2njQtP7e5ZXH91+fjIJ3nyrQ5m1Sgbi3SU3h9u1T28BsuNmhAu/8avDM6A/ErXn9+6TT8PZDhx7P+oeh6sTxCUSNpky2Poez1+mUmso+cIuHIOofcFvqgJMOmYl4mkm9nmyArRn7fzdkM+ymwcF6X6Ce3d9wwJZZy47W/5yaNvjywN5rmqZOrhw4Nl1Xv+sDLuvpzHXpobdU9vVmTlRkf48lgMxJDn8rFFfn/FaIycOgaVTl2/GG47y5p5ueUJzltQW4Ze2iENNKrp0LxrrDwb6eMG839tLuj1KVb8c2zBTyzkCMX/2rvwr5WXNL+OhJuU0hT6bTNHsjOMwmzphbwpzSPKlCPoYk4BZCjA2DYUBP8FqoQAUrEW9/VXR/iwrGfd5MX3BjfwBudozvFGaT7eB14bquMsB9QXgT+JpUcJUIQ9d2tQ1k86gA3FOtAsRIz6GfN9wNnVuhbNHov6ajYTBm/v1HWBVd11W2PJ3K/MwGrpnrUokhglp98O+QW9/y7KK6gXH1QffTDnjM7A5D3XngYw+4LRvsH3gCIGUAStU+ibHPeIixle+wYDcb2d4eoDeU4MS6ApliLsQ0sqK+kAqPjTZfdMgjgwaUe2ysqC8ck+ePJ9NsbvHx3n4fun7oKeRr9/bwm9WNRBIp7GYj15xay4l1uY0rGE3S7o9SXeTgxLoCaZE4DiTgFkKMH6MZXCVqy4qH+9tkhbvV1O6YH4KdKkgzmgcE4eNQFX0gTQNnsdqqlvdfn0qq9mnZzLdvv/oZ7Oh/Le2bh3/cA0W8oz70CaNpmQz3sX94cQB7r0MVsLPMn+jhiFFgNRupL3LS4o3w0rYOllZ7WFjpySljdEyIh+D2SvX7N1rU310hpgmjQePbly7k84+sH/Zc7rcvXTgmmeDeUJy3G3vY3Rmi2GXFYx96hk00keJ3a/fx2q4uAGaVOPnMGTMpdh3+5Hha12n3R0mk0hxfk89x1fnDZs/F6Dr2vxEJISY3i0Nt7kybjWxbsmzgGuqCYJv6PdCmsqBGS2Y9uENlpsczCAc1HbogU918oER0cCDesQ16dh/+8bY8BR2bVYE2d5VaM+4sHv/XJYTAoGnMKHDgDcd5q6GHrmCcE2oLhm3DI4Q4dlywuIL7PrGcbz+9mXZ/rO/68jHqw51O6+zpCvJ2oxdfJE5NoWPYE3wNXSF+9a89dARiaMBFSyq4bGllTicAYokU+70Ril1WltcWUFfkQMulDo0YFRJwCyEml4FtycisiU2nVda7LwjvUBnwcC8kIqoKt9GayYQ7VFGviTiQmG1QNEtt2XE//e+Hn1aeDdAHMlpU6zJ3hQrA3VWQV6G24dqHCSEA1d4na3dHkOU1lmGnZg4n32HBYTGxuzNIbyjB8tp86oud8iVViGPcBYsrOG12cV/hxYeuO4kz5pSMemY7FEvyTlMv29sC2DKza4b6+5JO6/zfplb++m4rKV2nwGHmU6fXM7/cndPzdAdj+KIJ5pXncXxNwbDZczF2JOAWQkx+BoPqkT2wT3Y61R+Ax/wQ6IBwNghvUfuYLAOC8AnIhBsMqvXXUFXKs5b9m6r27m/ObC1qWn0qrlqYefcefB97oQrEswG4u1L9dJZI6y4x7T23qZX/99Smvsv3v9pAvmM/Hz+phhNqCw5xz4NZTAbqi5y0+2O8vL2TzkCMpTINU4hj3sDgekV94agG27qus7830lcYrcJjG7aTQmcgxq9fb2Bnh+qtfWJtAZ88pRZnDtXEE6k0Lb4IdrOR02YXM68sTzowTBAJuIUQU5PB2F9tHDJF2ZL9mfCDgvBMJtxgUQG42TE+a8KrV6jWX28/qArFZTmKYPk1Q7cES6cg2K4Cb39L/xZoUdPtIz1qO3CduGYEV6mqFJ9XroJwV+Z3R7G05BLHvOc2tfL5R9YfVPDIG05w3yu7+fyZs0YcdGuaRrnHRjCaZMM+L12BGCfUFVLukZkmQhyrHBYTe++8eNQfN5pIsanZx+YW/yELo+m6zmu7uvjd2n3EkmmsJgP/dnINp84symmWjS+SoCsYo7bIwfJaKYw20STgFkIcO4ym4YPwmF+1tAp1QLCrf004adWWyjwgCB/tLHH1CihfDH+6Xl0+82YoXzp8AGzI9P52V0LVCYNviwX7A/FA6+Atlej//aDHNIGzFPLKMkF4Gbgym7M00y5MiKkrlda57a9bhqs7D8BDb+xlaZUHk2nkJ59cNhM2i4MWb4Tnt7axbEY+8yvc06egmhDiqLR4I7zT2Mv+3gilbit5w7Qe9EcS/GZ1Ixv2ewGYU+ri+tPqKck7fGG0VFqn1RfBoGmsqCtkYZUbq0lm5Ew0+YYlhDi2HRiEg8ogZwuzxfwQ7lF9wuMBFZCnU/0tyrJB+NH2CR+YSS9dcOTZZqsLrAe0LwNVTC7co04iBFrVz2Bb5me76h0dyGTJDxqbpjLuAwPwvMxPVylYXBOzJn6yS0bhj9eq32eumtChCFjT0EOr79Dt2SKJFN95Zgs3rJpNuXvkGR+TwUBNoZPecJzVe7pp90c5vqaAohwqBAshpqdoIsXWVj+bmn0kUjq1xQ5Mw3wHWNfYwyNvNhGMJTEZNC5fVsn5C8tzqkERiCboCMSozLezvLaAqnz7aL8UcYQk4BZCTD8G4xBrwtMQD/ZnwiO9KlDNBuR6EtBUwbJsEG6aRFO0NEN/C7PyxYNvS6ch3KVeT7BdnVwItmV+tkMqpqrBh7qGbmdmsqvA25lp6eYsUcF49rJZehWLidcRyK0Xeosvynf+uoUPLa/i7PmlGI7gZFKBw4LTYqKhK0xXMM6ymnzmlOaNSbsgIcTU1eqL8E6Tl3094UO2+wpGkzy2pok1e1WR1RkFdj51ej3VBYc/vqbTOq3+KGld5/jqfJbMyMdukaz2ZCIBtxBCgMo4Z6ujezLX6TokwioAjwVUv+xQu/oZ7IBkXO1nsqoA3OxQAflka+dlMKiA2VUKLBl8m66rTH+wXb2mgT9DHerEQzIC3ka1DcXizAThJWqtuLMkE/yXgLMILHnHZoZcT/f/3rw+M3NBvuRMlFzXKNYU2mnqifC7tftY39TLtSvrjmh9o8VkoK7IQVcwzr92dtHmi7KsOl/ahwkhVFa7xc+mFh+JVJraQsewBcveaerlt2824o8mMWhw0eIKLjmuIqcCZ8FYkjZ/lHK3jeU1BVQX2qWTwiQkAbcQQgxH0zL9vp2oBeEZyVgmCM9swQ4Id6vgNBAF0qCZMsXZ7GCaxBlgTevP9pfMO/j2VBxCneo19v3MtGULdapZAfGQ2nr3Dv0cRqsKvB2ZDLyj6ICtWFWUn0r2rVGF8LL++h/wyh1wwV2w8LKJG9c0tqK+kAqPjTZfdNh13AUOM9+8cAGv7uriT2/vZ0d7kFuf3sIHj6/inPmlI24dpmkaJXlW3AkTO9oDdPhjLKvJZ1aJS7LdQkxDuq7T7I3wbpO3r+/1cFntQDTB42v29WW1Kzw2rj+tnvpi52GfJ5vVTqXTLJ3h4bgZ+TlVLhcTQ9N1/VD1RaY8v9+Px+PB5/PhdufWr04IIUasrzhbQG3hbhWcxoOqQno6pYLbgVPSjdapn/lNhDPT0TMBeHZqeqhTTWOP+nJ7HEteJvjOrLd3FKl2aY4i1QbNUTB5pq7vWzNMq7fMe/mR3xxx0D2Zj1mvvvoq3//+93n77bdpbW3lz3/+Mx/4wAf6btd1ndtuu41f/vKX9Pb2cvLJJ/OLX/yCRYsW5fwcR/v6s1XKgSGD7oFVyjsDMR5evZdtbQEAZpU4uXZlHRWeI1v3qOs6ncEYoViSOWV5UzPbHQ/B7ZXq92+0ZE42CiFyEYol2dTsY2ubH3Qo99iGXKut6zpr9/by2Bq1VlvT4PyF5Vy+rDKnIowDs9rH1+RTU+iQrPYEGMnxSk6FCCHEaBiqOJuuqy+w2UA84uufkh7qhEQM0MBkzkxJz2TDp1L7LrMD8mvUNpRUXK2BD3WqkxDhbhWQZ38Pd6kZA/GA2obqO55lsqkgPBuA2w/YbPnqp2kMC1il0/D2Q8PcqAMaPHcLzL/4mJteHgqFWLp0Kddddx1XXHHFQbfffffd3HPPPTz00EPMnTuX733ve5x33nls376dvLy8cRnjBYsruO8Ty/n205tp98f6ri9wmPnYAX24S/Ks/Od5c3l1Zxd/fHsfuztD3PbXLVxyXAUXLCofcb9aTdMozbMRs6XY0R6gzR/l+OoCZpU4pfetEMewdFqnsSfMhiYvHYEopXnDVyDvDcd59K0mNuzzAlCVb+e6lXXU5ZDVTqV12nxqrbZktacWyXALIcR4S8YymfBMgbZwl2pVlgirTU9nqqTbVcEys2PqTbnOla5DIqSC8nB3/89Ij/o9+zMRzv0xzXawFahp8rb8A3561O82D1jzRh4Ut2+GF797+P2u+RvUnzGyx2bqHLM0TRuU4dZ1ncrKSm688UZuvvlmAGKxGGVlZdx111189rOfzelxR+v1B6IJltz6DwA+9756ltcUHnK6eHcwxm/fbGRTix9QX4KvWVnLzGLXET2/rut0BeMEYklmljhZOiM/p5Y+E04y3EKMSG8ozrv7vezuCGE2apS7bUP+rUnrOq/s6OTJ9c1EEimMmsZFS8q5eElua7WzFcgrPDaWVcta7clAMtxCCDGZmaxqcxb3X5dOqwxv35T0XpUNjwX6e2wDmK39QfhkLNA2Upqm2o5ZXMNnyUG14Ar3qHXy4R6IelUwHulV/1bRXjVzIBVXU/gTkaFboA1+chV029yZANyTCcjdYHX3B+XZy2aHeo5cBNtz2+8Y0dDQQFtbG+9///v7rrNarZx55pm88cYbwwbcsViMWKw/E+33+0dlPAPXT88qdR12bXaRy8qXzpnDWw09/G7tPpq9Ee54dhvnzC/lA8uqsJlHdmKmb2233cTezhAd/ihLqjzMLc+b3D1x06n+3xvfgFlnH3MzNYQYDfFkmp3tATY2+/BHE1S47cNWBm/xRvjN6kZ2dQYBmFns5JpT66gqOPzylWQqTas/ikHTWF5bwKJKNw6LhG9TjbxjQggxGRgMmWDPM/j6RCTTMzxToC07NTtboE1Pg8E0oEr6KPQMn4xMNnBXqm04uq7+vbLBd8SbCcx71VryqFf9jGT6r6P3F77z7T/8GDRj7q3gXGW57XeMaGtrA6CsbPDrLisro7FxmOr2wB133MFtt902pmPLlaZpnDKziEWVbn6/bh9v7unhha0dvN3Yy8dOqmF5Tf6IM0pWk5G6Yic9oThv7O5mX2+E42Z4qMqfhNmpLU/Ds1/rv/zoler/mxQCFKJPtijae/t97O8J47GbqS9yDvn/OZZM8czGVv6+uZ1UWsdqMnDF8hmcNbckpwKNveE4PaE41YUOllbnU+mxTb6/GyInEnALIcRkll3b7Srtvy6V7M+G9/UM71DXRXrU7RoqOOzrGW6d+tnww9E0VRne4gB31aH3TaczU/ozgXgskPk9c102EM9O+09GQU+p6e+HHoQKUmpXjtarmlIO/DKo6/ohvyB+/etf56abbuq77Pf7qa6uHrPx5SLPZubTp8/k1JlFPPJmE53BGPe9spvjZnj4txU1FLlGPjW80GnBbTPR6o/ywtYo88vyWFTlGXad57jb8jT84WoOKjXnb1XXH0UhQCGOFb5wgk0tPna0q0KL1YWOYYucbWr28chbjXQFVfvQpTM8/NvJtRQ6D788LJZM0eKL4LCYOLm+kPkV7hHPshGTiwTcYkyFE2FOfuxkAN666i0ck6XKsBBTmdHUXygsK9szPDslPepTQXh2CnYiAugq+z0wG26YpocBg6G/HRq1h98/Fe8/wbF/LWx+coidMoHlBXdOu2m45eXlgMp0V1T0t9Dr6Og4KOs9kNVqxWqdnGubF1V6uO2yRTyzsZXnNrfx3n4f21o3c8lxFbx/YdmIC6GZjAaqCxwEo0ne3e+j2RvluBke6osnuKhaOgXP3czQdd2P7UKAQuQilkyxqz3IphY/3kic8jzbsMXKekJxfr9uH2839gKqYONVK2o4vqZgyP0HSus6XcEYwViKmcVOjqvOpzQvx1lVYlKbpt+0hBDiGDOwZ3heef/1qUR/gbZYAELd/f2zQ50q03sstisbbUZLf9/wwnooqCO19kGMsd7+fdyVKtiehpnA+vp6ysvLef755zn++OMBiMfjvPLKK9x1110TPLojZzEZ+ODxVZxcX8gjbzWyoz3Ik+8088bubq5aUcPCypEXdnPZTDisTjoDMV7e0cne7hBLqvIp90zQF+vGN8B/qHoHOvib1X5HUAhQiKkqndbZ1xtm434fzd4IHruZmcNMH0+m0jy/tZ2/vtdKPJlG0+Dc+WVcvqwyp+x0KNPqq9Bp4ax5hcyc6BNxYlRJwC2EEMcyo3mYdmXB/mx4xAuhDvUz2AHJOFO+XdkY85ccz6aFFax856sAdK76ASVnXH9MZwCDwSC7du3qu9zQ0MCGDRsoLCykpqaGG2+8kdtvv505c+YwZ84cbr/9dhwOB1ddddW4j9VhMbHx1vfz9Lsto1KkrDLfzlffP483G3r447p9tPmj3PPCDk6sLeDDJ8wY8TRzg6ZR5rYRT6Zp6gnT6o0yvzyPBZXu8Z9mnmuBv2lWCFBMbx2BKFta/OzpDGHUNGqLHEP21AbY0uLnsbVNtPmiAMwpdXHVyTVUFxx+Vme2KBo6LK7ysGSGB/dkWWoiRo0E3EIIMd1omerc1gN6Iw/XriwagEQ7kFaFw7KZcLPj2CzQdhjRRIodbQEiif6KzvGyZcd0sA2wbt06Vq1a1Xc5u/b6mmuu4aGHHuJrX/sakUiEG264gd7eXk4++WT+8Y9/jFsP7gMZDRpmo4HOYIxKj2HYtZa50jSNU2cWsXSGh79saOHF7R2sa+zlvf0+LlxczvmLyrGYRvYcFpOB2kIngWiCd/Z5aewJs2SGh5nFrhE/1hHLtcDfNCsEKKYnfzTBthY/29sDxBJpyj22YTPUnYEYf1i3j3cyPbXzbCY+fMIMTp1ZdNjiZrqu0xtO0BuOU13gYMkMDzMKJmExRTEqpA+3GFOyhluIKS7briyamZIe6VWZrphfrQvvK9Bm7w/CTcfulPRkOs3WVj/NvRFK81S/1UjbDqpPuYIZsxcf9eNP92PWaL9+VU3Yy76eME6LiZI8K4ZR+mzu6w3z+JomdrSrVj/FLgsfPqH6iKqZg1q/2R2ME4glmFHgYHGl+gKeSzXjo5JOwY8XqwJpQ67jzhQCvHHjMX9SSUxf0USKXR0BNrcE8IbjlLisuO1Dn1COJlL836ZW/rG5nWRax6DB2fNLuWxpZU4tu8JxNX3cbTOzuMrNnLJJ3i5QDEn6cAshhBgdw7Uri4cHZ8OD7ao4W7hLZcpJg8GignCLQwXkU/zLejqts6crRHNvhCKndewDIXHUqvLtlOZZaegKsXG/j4auEMUuK55hvkiPRHWBg6++fx5r9/byx7f30RWMc98ru5lb5uIjJ1ZTV+Qc0eMZMr27CxxmWv1RWn0RZpW4WFjpHtvCSQajav31h6tRZ88GBt3TtxCgmB7iyTSN3SE2NfvpCEbJt5mZWTz0Ou20rvPG7m7+/E4zvkgCgAUVeXz8pBoq83PoqZ1O0+aLktZhfnkei6vyc6paLqY+CbiFEEKMXLb9Vt6AaabZAm3ZtlqhbrU2PBaAQHumZ/jUnZLe4ouwtzNEvt2Cebym+4qjZjYamFuWR2W+nW2taqpod1eMcrctp2zUoWiaxor6QpbO8PDc5jb+vrmdHe1B/vuZrZw6q4gPHV9FvmNkX6iz1cwjcVUZeV9PmHllecyrcI/KiYIhLbxMtf569msQaO2/fhoXAhTHtlRaZ19PmC0tfpq9YewWE3WFTozDnEjd3hbg9+v20dQTBqDEZeXDJ87g+OrDz2jRdZ2eUBxvJEFVvp3jZuSPz+wVMWlIwC2EEGJ0DFWg7VBT0sO9oCeBTJV0UyYbPgmrpHcGYuxsD2A3G7FZJNM3FbmsJk6sK6Su2MmmZh8NnSG6tTjlbttRr++2mo1cvqyKM+aU8MT6/bzV0MMbu7tZt7eX9y8s44LF5SPuo2u3GKkr7l/fvac7xMIKN7NLXUd9omBICy+DmWfBnZk+6P/2J5h1tmS2xTElndZp9kbY0upnf08Yk8HAjILh+2m3+iI8sb6ZDZl12nazkUuOq+Ds+aU5/d0IRpO0B6J4HGZOm10k08enKQm4hRBCjJ2hpqQP7Bke9Wd6hrdngvFslXTUWvC+Kek20CYmq+yPJtjRHiCtQ95YZRjFuCl2WTlzbgmzSlxsbvGxrzeCzWSgNM82bHYrV4VOC585YybnzC/l9+v2sbszxN82tvLKzk4uO66SM+YWD1vpeDh5NjMuq4meUJzVu7rZ2R5kYaWb+mLniIP4wxoYXNeulGBbHDPSaZ1Wf5StrX6ausNoGpR7bMMGv75IgqffbeFfOztJ62DQ4H1zSrh8WWVOnQTiyTSt/ggmg4ElMzwsqvDgccjxY7qSgFsIIcT4Gq5neLZKenZKerADwt0qE56MqinpRkv/dHTz2Lcqy1YkD8YSY7uOVowrTdOoLnRQ7rHR2B1mU7OPvd0hPHYzhU7LURdWm1ni4pYL5rO+ycuT6/fTHojx6JomXtjazgeOr+KE2oIRPYemaRS5rBQ4LHSFYvxrRyc72gMsqnRTU+gcv4rmQkwx2UB7R1uAvV0h0uiU5Q1feTwcT/KPze08v7WdWDINwLLqfD50fFVO67RTaZ2OQJRoIkVdsZPFVR7K3TapPj7NScAthBBicjBZ1eYs7r8ulVTBdywzJT3UrQLxeCDTFzgNmqk/E252gGF0Dm2JVJod7QG6gjFK8qzyhekYZDYamF3qYkaBnd0dQTa3+GnoClHotJBvNx/Ve65pGifUFrC02sOrO7r463sttAdi/M+re6gpdHDF8ioWVrhH9BwGg0Zpno1CZ5rOQIwXt3VQ6bGzoNJNTeHw02KFmG6ygfb21gCN3SrQLnXZsA+zJCieTPPS9g7+b2Mrobhq+Vhf7OTDJ8xgbtnhWxsOXKdd5rZx6qxi6oocmOT/pEACbiGEEJOZ0ZTDuvAeVZQtG5CnUyqLns2EWxwqMz4C6bTOns4QLd4IRS4rxjHOpIuJZTMbWVTloabIwa72INvaAuzpDlHqsuY0ffRQTAYDZ88vZeWsIp7f0s5zm9to6gnzoxd2MrfMxQeWVeX0hf7Ax6zw2Emm0nQEYvxzazsz8h3Mr8ijWgJvMY2l0jot3gjb2/zs64mQ1nVK84YPtJOpNK/v7uZv77XQG1aVx8s9Nj64rCrnFn/+SILOYKxvnfbs0rzRX+4hpjQJuIUQQkwtw60Lj4f625RFeiHYpn73ezP9wjPF2bLT0U3WYZ9iX2+Yxu4Q+Q6LBC/TSJ7NzPG1BdSXONnWFmBne4DOYIzSPBsu69F9ZbKZjVy6tJKz5pXwzMZWXt7eyY72IHf/fTuLKtxcfnwlM4tdI3pMk9FAZb6dRCpNhz/Gfm+YKo+deRUq4y1TzaeGcDzJwm/9HYAt3zl/bIriHeMSqTT7e1Wg3dwbRdOgNM86bOCbSuus3qMC7a6gqhtS6LBw2bJKTp1ZlFM9h3A8Sbs/hs1i4Pjq/LHtJCCmNPkfLYQQYurTNLC61Oau7L8+2y886oOIF0Lt6mewvb84WzYIz1RIbwvE2NURxGE1SZZimsp3WDhlZhGzSlxsb/OzuzNEZzBKWd7RtxLLs5n52Ek1vH9hOc9sbOW1nV1sbvWzudXPkioPly6tGHHgbTYaqCpQgXd2qnmFx8b8cpXxls+xOFZFEymaesJsbwvQ7o9iNGiUe6zDFkNLpXXebOjm/95rpT0QA8BtM3HRkgrOnFuS0wnWWCJFeyCKpmnMLXexsMJDSd7wJ3CFkIBbCCHEsWuofuGJaH8mPFshPdwDoU4CwSCtHUFcWHCZ3aRSdtKGydemTIyPkjwrxa5i5pTlsbXVz97ukMp4H2ItaK4KnRY+eUotFywq56/vtbB6Tzcbm31sbPaxuMrNZcdVMrNk5IF3NuPdFYzx0vYOil1W5pe7qSt2SOZUHDP80QSNXSF2tAfpDsawW4xU5duHDZiT6TRv7u7hmY2tdAZVoO2ymrhwcTlnzSvJqVVXIpWm3R8lldapKXKwoMJNVb5d6nuIw5K/vEIIIaYXs01trtL+65Jx/N5u3traQNjdTY0lDLFuLNFeDKkYoJM2WkiZ7KSMdtJGW18QntYn5mWI8aFpGmVuG6V5Vub589jeFqCh8/BFmHJVkmfl+tPquXhJBc9sbOXNPd1savazqdnPgoo8Ll5SwbyyvBF9qTcbM2u802m6g3H+tbOTTS0W5pS6qC92ku8YWU0DISYDXdfpDMRo6AqxpzOEP5rAbTNTW+Qcdgp4IpXmtV1d/H1zW9/U8TybifcvLGPVvNKcZn8k02rmSCSRZkaBnYUVbqoLHUfdRlBMHxJwCyGEmPYiaSNvtEGTXkZd7Uy6NQ0tncCUCGBKBDElAlginZhjPZjjXgypGJqu88/eYp7cP48fH59ixkS/CDGmNE2jwmOn3G1jblke2wZUPy5xWY86e1zmtnH9afVcclwFz7zXypt7etjaGmBra4CZxU4uWlLBcTM8I2onZjIYKHPbKNF1ekNx1jT0sLXVT32xk5klLkql+r6YAuLJNC3eCLs6gzT3RoglUxQ6LMwsdg77+Y3EU7y8o4MXtnbgi6hiaHk2ExcsKuesuSVYcwi0U2mdrmCMUDxJudvGqbPc1BY5pa6HGDEJuIUQQkxriVSaNXu72dsdpq7Q0RfQ6AYzCWshCWumQnoBaOlkJggPsKnZyw92xUjpGk9tj7Bo8QS+CDFuNE2jMl8F3m3+PHa0B9jbHaIjEKV0FNZ4l+bZuO60ei5bWslzm9v4184u9nSF+PlLu6j02Dh/UTkn1xeOqN2QIdPHu9BpwR9NsrHZx472IFX5NmaV5lGVb5cCa2LS8UUS7OsJsasjRGcgilEzUJxnwWEZvh+2Nxznn9s6eGVHJ+FMe69Cp4ULFpVz2uyinKaOp9M6XaEYgWiS0jwbJ9UXUlvkyOm+QgxFAm4hhBDTVjqt8+4+L9tbA8zItx82iNENJhLWArb5zfzw7S5SusbCijw+/j6Jtqcbg0EF3hUeW99U88buMO3+GMUuy1G3EytyWfm3k2u55LhKnt/Szss7OmjxRXnwjb08taGZc+aX8b65xSMK8DVNw2M347GbicRT7OuJ0NAVoiTPxpwyFzOcOp7DP4wQYyaRStPmi9LYHaKpJ0wgmsRlNVFdcOie1q2+CH/f3M6be7pJZtb5lLttXLgkc4Iqh9aOAwPtYpeV4+cWUF/slKKD4qhJwC3GVCqd6vv97fa3WVm5EqNB/nAJISaHrW1+3t3npTTPlvOXqhZvhJ/+cyfxZJpFlW4uXVo5omm+4tgycKp5ZyDGzvYge7qCdAZjFDmtuG2mo5q27bGbufKEGVy0pJxXdnTywtYOesMJ/rR+P399r4XTZxdzzoJSSvNsI3pcu8VIdaGDZCpNdyjOazu7yLOZqP233dSVOCkzWuVLohg33nCcZm+EXR1BugJx0HTy7RZKiodf9qDrOlta/Ty/tZ1Nzf6+62eVOLlgUTlLq/Nz+tucSut0h2IEYkmKnVaWzVGB9tHWZxAiS/6WijHzQuML3LHmjr7LN/zzBsocZdyy4hbOrT13AkcmhBDQ0BVi3d5e8mxmXLbcDofdwRg/emEHoXiKmcVObjhzFi3+6BiPVEwFmqZR6rZR6rYxvyKPXR1BdncG2dMVI99upsBpOaoTMw6LiQsXV3DugjLe2tPDP7a20eKN8s9tHby4rYNl1fmcPb+U+eUjK7BmMqp13qW6jj+aZGubj23tfkrzbMwqcVGVb8fjkN7CYvRFEylaM9ns/b1hQrEULquJynzbIddJx5Ip3trTwwvb2mnxqr+/GrCsOp/zF5UzuzS36v7ZooLBWJKSPCvLqiXQFmNDAm4xJl5ofIGbXr4JncHlezvCHdz08k3cc9Y9EnQLISZMmy/KW3u6MRo0Cp25VWz2RxLc8/wOesMJKj02vnjOnJwK74jpp8hlpSjTjmtPV5Cd7UEaukK4rCaKXJacprcOx2w0cPqcYk6bXaSye1va2dTi5519Xt7Z56XSY2PV/FJOnVk0oqmwA6ebx5NpekKqunmezURVgZ26Iidl7txngggxlEQqTUcgRos3wt6uEN5IAqOmUeiwUJZnO+TJoo5AlJe2d/L6rq6+9dlWk4Ez5hRz9vzcZ3lk2+ZFEilK82ycUFdAXZFMHRdjRwJuMepS6RR3rrnzoGAbQEdHQ+OuNXexqnqVTC8XQow7bzjO6t3dRBIpqgscOd0nHE/yoxd20B6IUeS0cOO5c3FZ5RAqDs3jMHN8TQFzy/Jo7A6zoz1AU08Ei1GjxGU9qhM2mqaxqNLDokoPLd4IL23v4I3d3bT4ojz6VhNPrm/mlJmFnDm3hBk5fs6zLCYD5R4buq4TjCXZ1aFOGhQ4LNQVOagqcFCSZ5W2SCInqbROdzBGqy9CQ1eY7lCMdFotl6gpOHR7rVRaZ2Ozj5d3dLC52d/3zbLEZWXV/BJOn517HYNYMkVnIEY8labcbeOUmUVUFzok0BZjTr4tiFG3vmM97eH2YW/X0WkLt7G+Yz0nlZ80jiMTQkx3oViSN3Z30xWMUVuUWxAST6b52Yu72NcbIc9m4qbz5uacFRcCwGk1sbDSzaxSJ/t7I+xsD9DijaADhY6jL7BWmW/n306u5YPHV/HG7m5e2tZBeyDGS9s7eWl7J7NKnJw5t4QTagtGVGlZ0zTybGbybGaS6TS+cIK3m3p5b7+PIpeF+mInZR4bxU4rBgm+xQDZddHtvigNXSG6Q3HiqTQui4lKj/2wrbV6QnFe29XFv3Z20htO9F2/uMrN2fNKWVyVe4u8cDxJVzCGrmtUFtiYV5ZHdaFD2nuJcSMBtxh1neHOUd1PCCFGQ3bd376eMLVFjpy+rCXTae5/ZTc7O4LYzUa+fO5cytwjK04lRJbVZGRWiYu6Iidt/ii7OwI09YTpCGTWeTssRxW4Oiwmzl1QxtnzS9nWGuCVHZ28s6+X3Z0hdneGeHzNPlbUF3LGnGJqCx0jW+ttMPRNlY8lU3jDCVbv6cZqMlLsslBX7KQ0z0aR8+heg5i6Eim1JrrdH6GxO0xvOEEsmcJpMVGaw4yOZCrNhv1eXtvZxeZWP3omne2ymjhtdhHvm1Myor+//kiC7lAci8lAXZGLOWUuKvPtMjNDjDsJuMWoK3GUjOp+QghxtFJpnXV7e9nZEVDtZXJpEaPrPPj6Xt5r9mExGvji2bOpKRzZ1FwhhmI0aFTl26nKt9MTitPYHWJnR5C9PSEVwDotRzXd3KBpLKx0s7DSjTesMoWv7eqiKxjnlR2dvLKjkxkFdlbOKuLk+iI89pFl2K0mI2VuNb5oIkVPKM7+3gg2s5FCp5p2Xuq2Uei0SBYxB6l0/xK8NQ09nDGnZMoEhZF4iq5gjHZ/lKaeMN5wnGQanBYjRU7LYadr67pOU0+Y1Xu6eXNPD8FYsu+2uWUuzppbyvE1+Tl/jtJpnd5wHG8kgctmYlGVm1klLkrzhq92LsRY03RdP3ih7STS3NzMzTffzLPPPkskEmHu3Lk88MADnHDCCTnd3+/34/F48Pl8uN3uMR6tALWG+/wnzqcj3DHkOm4NjTJHGc9d8Zys4RZCjDld19nQ5GVtYw8VbntOFWh1XeeRt5p4ZUcnRk3jC6tmcdyM/CH3begOcd6CMuqKnUc91ul+zJrOrz8ST9HsDbOzI0ibN0oqrVPgtBx1W7GstK6zvS3Av3Z2sb6pt69XsUGDRZUeTp1ZxNJqz4imnB8omkjhiyQIxZKYjQbcDjM1hQ7K8mwU51lG1DN8unhuUyvffnoz7f5Y33UVHhvfvnQhFyyumMCRDS2d1vFGEnQHY7T4IrT6ogSjSdDV0gmP3YzFdPjguCcU562Gblbv6e6rNA6QbzezcnYRp80qHlE2O55M0x2KEY6nKHBamFOqZpIUyPIfMUZGcrya1H/5ent7Oe2001i1ahXPPvsspaWl7N69m/z8/IkemjgEo8HILStu4aaXbzroNg31peHmFTdLsC2EGBfb2gKsb/JS4rLm3O7lyXeaeWVHJxrwqdPrhw22hRgtdouR2aV5zCx20R6IsrcrxN6uMHu6QjgsRoqc1pwCmeEYNI0FFW4WVLgJxpKs3dvD6t3d7OkKsbHZx8ZmH1aTgeU1BZxcX8iCCveIs6w2s7EvoxlPpvFHE2xo6gUgz2amzG2jIt9GkdNKgcOMaZpnv5/b1MrnH1l/UGqizRfl84+s575PLJ/woDtbOK83lKArGGN/bxhvOEEkkcJiNJBnM1F9mMJnWcFokrebenmroZud7cG+120yaBxfk8+pM4tYVOkZ0ecuGE3SHYoBGmVuKyfPzKO6wCGtvcSkMqkz3Lfccguvv/46//rXv474Mabz2fKJlu3D3RHu6Luu3FHOzStulpZgQohx0dAV4tUdndgzU11z8X8bW3nynWYArj6llvfNPfTyF8lwj57p/voPFIgmaPZG2NUepD0QJa3rFNgtuO3mo+rpPVCbL8rqPd281dBNVzDed73LamJ5TT4n1BYwv3zkwfdAqbQK2gLRBPFkGqvZiMtmoirfTkmelUKHBY/dPK3WfqfSOqff9SKtvuiQt2tAucfGazefPa7Ty3VdJxRP0RuK0xuO0+KN0BNSvaoNaNgtRtw2c84BbTCWZMM+L+sae9jaEiA1IOyYU+ri1FlFnFhbMKLZD8l0Gm84gS+SwGE1Ul3gYFaJiwqPbdqfxBHjZyTHq0kdcC9cuJDzzz+f/fv388orr1BVVcUNN9zAZz7zmZwfQw7eEysQC7DydysBuPece1lZuVIy20KIcdHijfDK9k5Suk55jlMTX9rewaNvNQHw4RNmcP6i8sPeRwLu0TPdX/9wkqk07YEYTd0hGrvD+CIJtV7aYRm1TJ6u6+zpCvHWnh7WNvYQiPavpXVZTSyrzmd5TT4LKtxHvS47lkgRiCUJxZKk0jp2i5E8m5kKj40il8p+u+3mY3r99+rd3Xz8V28edr/HP3MKp84qGrNxpNI6/ogKXr3hOC2+KN5wnFA8ha7r2M1GXFYTTosp5xMivkiCd/d7Wd/Yy9bWwUF2TaGDFXWFnFRXQJHLOqKxhuNJuoNxEmmdIqeFmSVOaouc0jVCTIhjZkr5nj17uO+++7jpppv4xje+wZo1a/jiF7+I1Wrl6quvHvI+sViMWKx/HYzf7x+v4YohDAyuTyg7QYJtIcS46A7GWL27m2giRXWOhc5W7+7uC7YvXlKRU7AtxHgwGQ19RdaWzEjS4o2wuzNIhz9G1J/CbTUf9RRtTdOYVeJiVomLj55UzY72AOsae1nf1EsgmuwrvGY1GVhS5eH46nwWVXmOqB+91WzEajZS7LKi6zqRRIpQLMWmZh/JtI7NbMRpNVKSZ6XEZcPjMOO2jSzom+w6AkNnto90v1xkp4f7o0lVwTsYoyMQIxRLEk2kAA175t9+pK3e2vxR3t3n5Z0mL7s7g4OmyVfl2zmxroATawuo8NhHNOa+bHY0gd1kpLrQzswSVW1c+meLqWJSB9zpdJoTTzyR22+/HYDjjz+ezZs3c9999w0bcN9xxx3cdttt4zlMIYQQk4g/muCN3d30hmPUFuaWdX67sZdfv9EAwDnzS/nAssqxHKIQR8xlNTG3LI/ZJS66QjGaeyM0dIXY740AOvl2C27b0U3PNhr613tftaKGHe0B1jf1smGfl95wgnWNvaxr7EXTYHaJi+NmeDiuKp/KfNuIC7xpmobDYspMKVYZz2giRTieYk9niO1tAQyamsrstJjUFHSnBZfVRJ7NhMtqmpLTiEvzcpt1k+t+B4on04RiycxU/iS94RidgTjheJJwPEVaV2unHRYj+XYLNrdhRO9dIpVmZ3uQ95q9vLffR0cgNuj2uiIHy6rzObG2kHLPyF5D37rxcIJkOk2R08qKukJmFDgodlmk2riYciZ1wF1RUcHChQsHXbdgwQKeeOKJYe/z9a9/nZtu6i/W5ff7qa6uHrMxCiGEmDzC8SSrd3fT4o1QX+TM6YvZpmYfv/zXHnQdTptVxEdPqpYvdGLSMxg0SvNslObZWFTpod0fZX9vmMaeMI09IYyagXyHGZfNdFTrvQcG3x9fUcPe7hAbmry8u99HszfCzo4gOzuCPLG+mQKHmUWVHhZXuplf7sZlO7Kvmdnia9mpwqm0yoJH4im2twZI6jqaBjaTAZvZSL7DQpHTgstmwmk14bQYBxVwm4xW1BdS4bHR5osO0c+lfw33ivrCYR9D13WiiTSheJJIPEUoroLr7mAMf0RlrWPJFDqqj7rdbMRhNlHktI54Xbiu67T7Y2xq8bG5xc/29gDxZLrvdqNBY26Zi+OrC1hWnX9E07xjiRQ94TjheAqXzcTMEid1RU7KPbZJ/V4KcTgj/ksYCoW48847+ec//0lHRwfpdHrQ7Xv27Bm1wZ122mls37590HU7duygtrZ22PtYrVas1pGtCRFCCDH1xZIp1jT00NAVoq7QkVOGb0d7gHtf3k0qrXNibQHXnFo3asWoJloqleKhhx4a9nj94osvTtDIxGizmAxUFzqoLnSwtDpJm0/1RG7xRujsimExGSiwW3BajUd1MsmgacwsdjGz2MWHls+gKxjjvf0+3tvvZXt7gN5wom/quQZUFzpYUJHHgnI3s0tdRxw0GQ0aLqtp0PT1tK4TS6SJJFK0eiPs7QoCKmNuNRmwmIzYzQbyHaq1msNqwmYyYjMb1JR2kwGL0TBhU9SNBo1vX7qQzz+yHg0GBd3ZEf2/ixdkguY00UQqs6UJx5N4Iwn8EVWELppMZYJfDQPZExYGCp0WLCbDEf9N6w3H2drqZ1tbgK2tfnrDiUG3e+xmllR5WFLlYVGl+4je30RKTRn3RxNYTAZK86ycWOei0mPH4xhZf3ghJqsRB9yf/vSneeWVV/jkJz9JRUXFmGYBvvzlL7Ny5Upuv/12PvKRj7BmzRp++ctf8stf/nLMnlMIIcTUk0ylWbe3l21tfqoLHDlNMd3TGeQn/9xJPJVmSZWHT59ef8ysDwX40pe+xEMPPcTFF1/M4sWLJWs/TTgsJmaWuJhZ4sIfTdDhj7K3O0y7P0p7MIrFaCDfbsZlPfr+3sUuK2fPL+Xs+aXEk2l2dgTY1OJnc4uPFq8K+pt6wvx9czsGDWqLnMwtczG3LI9Zxa4jzoADfdPMDywal9Z14sk0sWSaUCxFTyhIIpXuC2iNBg2L0YDZaMBs1LCbTThtRhwWFZCbTRomg7rNZDRgMmgYDRpGTcNoVD8NmoamgabRF8wO/JfUAV1XY8mOKZXWSachpesk02lSaZ1FlR5uvWwRP31xJ90DKsTnO8x86PgqwvEUf9nQTCKlk0ilSeugoaOhYTEZsGa2PJsJi3FkU8IPpOs6ncEYO9uD7GgPsKMjSOcB08RNBo3ZpS4WVbpZXOlhRoH9iJ4zmU7jjyTxReMY0Mh3WlhRUUhlvp1i18iz70JMdiOuUp6fn88zzzzDaaedNlZjGuRvf/sbX//619m5cyf19fXcdNNNUqV8Cgknwpz82MkAvHXVWzjMuRUvEkKIXKXTOuubVHGnCrc9p6rNTT1hfvCP7YTjKeaX5/HFs+ccUY/jZCpNU0+Y9y8qn3RVyouLi/nNb37DRRdddNTjGi9yzB47vnCCjoAKgtv9UYLRJCajAY/dTJ519IuRecPxvszotrYA3aH4QfuUe2zMLnExs8RJfbGTSo99zIOtZCrdF8AmUmmSaZ1kSgXBup4JltHJhtEGgwrSDWhoBvoCblDZdE3t1iebrVaPpR4wreukdT0ThKu/WanMdZqmEY0n+eHzOwH4+EnVzCvPw2oyqqA/E/ybjyJTPZRoIkVjd5g9XUF2d4TY3RUcVJlevT6oLXSwoMLN/PI8Zpe6sJqObJZCNsj2R+OAhttupq7QQUW+nTK37ah6zAsxEca0SnlBQQGFhcOvJxltl1xyCZdccsm4PZ8QQoipQ9d1Nrf4eHeflxKXNadgu8Ub4Z7ndxCOp5hV4uTfV80+oi97iUywXVvkoNQ9+ZYyWSwWZs+ePdHDEJOEx2HG4zAzpywvk/mO0ewN0+qN0tgbxqCBy2IatXZc+Q4Lp8ws4pSZqqVVdzDGjo4gO9oC7OwI0uaP0uZT22u7ugA1Nb6mwEFdsYOaQrWVe2yYDKMXjJmMBkxGsHP4vxW6ngmM0/1Bc1pX1/cF50PkrTRAM2iAhkEDLRO4ZzPjRk3DYOgP3GOJVN99T59djHWU1ytH4in294bZ1xthb3eIvV0hWodYO24yaNQNnIVQ4jqqtnPJVBpfJIE/lkBDw21Ta/yr8tXfTFmXLaaLEQfc3/3ud/nWt77Fww8/jMMh2UohJiOZWSCmi50dQdbt7VVZOtvh1/u1+6P88PkdBGNJaoscfOmcOUe87rCpJ0x9sZOVs4szFZYnl//8z//kJz/5CT//+c9lOrkYxG0z47aZmV3qIhxP0hmI0eqL0twbocUXIZnScVpNuG0m7OajW/edVeSycqrLyqmZADwQTbCnK8TujiC7O0M09oSIJtLs6gyyqzPYdz+TQaMy386MAntfa7TKfDsFDvOYf641TcOkaTBFkq/Zfu3Z97HFG2Ffb+SgqeFZBQ4z9cVOZpW4mF3qoqbQMSo91n3RBMFYEqNmwG03sbQqn3KPXYJsMW2N+BvCD3/4Q3bv3k1ZWRl1dXWYzYO/4Kxfv37UBieEEEIMZ29XiLf2dGO3qCrFh9MVjPHDf+zAF0lQlW/ny+fMPaJAOZ5M09QbZnapi5WziiZlsA3w2muv8dJLL/Hss8+yaNGig47XTz755ASNTAySToM+YEPP/K4PcVnPXB54mz74Jxzm9yz1uwOo1aA2H+IuHW8kTk8oQYsv8v+z995xcp31vf/7nDO9l+1F2lWXLNmybMu2bFywAIdmCOkk1BQuBBNMEpPcG4jvTTBOcQgl5OeEa+CSmAQcDAmxAQM2Ni6yJctWs9XLrrbvTm+n/f54ZmZnpa3Sdj1vvZ7XOdOfmdXMOZ/n+/1+viSHdAZ0E01VCbiFA7hD06oJ1ygiigtgV/YVtXy7KHK2K9cpKqCU76cScqpsbfFzRWsIULCA3mSBk0NZTg2J2u8zIzkKulWtBa/F7VBpDHloCnloDLlpCHpE3+6gm5Dn4uvTFyuGZTGSFeUBg5kSfakCvakCfckCA5ki1gSFolGfk/aYj5UxHx11wv077L14UzLLtsmWe3sXdROXUyXidbGxKURD2ENdwHXBaegSyXJhxmcJ73jHO+ZgGhKJRCKRTJ/uRJ5njw2hoFAXmDqdezhb4m9/eJjhXImmkIe73rDuggybirpJVyLP+sYg16+OL+poTSQS4Z3vfOdCT2PpYNtgmWCbYmsZ5X1r9DrbFELXqt2ec51tgll+vGWApdc8rwFm+Xltu/waZff4MeIawBqdV1U022Mv24xeX7lvdR/G2F+f6+pVS1mcuoAG26YBWAcUNJOcaZAq6KRGDIqGhWXZODQFl0PD7ShHv8uPt6svpFTFuF0VvmUhrlSEuDoqyFGwVQfNisoVbgd2qwOr3YGFg56Cg1NZjdMZjdNpOJ226M3aFI3xhTiAS1OI+53E/C7ifjdRv5uw10nE5yTsdRIq160vxv7dg5kiOd0kmddJ5nRGcjojuRLDWTFGcqUJRTWAx6nSEhZZAJWMgPaYd1oZQNOlqJukiwbZkoFliWyI5oiHtoiPuqDrgtqOSSTLmRmfbXz605+ei3lIJBKJRDIt+tMFnj06RMEwaY9OXS6RzOv87Y9eYyBTpD7o5hNvXHdBkZ2CbtKdyLO+Kch1qxa32AZ48MEHF3oKC4ttw8gJMEqj4tc2xWWzBKYOZrG81UfFb0U8YwmxXdmOiUAzVsCCuMK2q+ITRS2Pivis7KujkeHafVU7/7oJt+XXm2h/FqK7KiL67QPqEGUUmYJBqqgznC2RzBsUSgaWZeHSVLwO0W5LU0fFv1ITeVcYu3CglKP2SnmRQTV1sG00LBS7fDs262yLdS4LJWphR8X70y3oLbo5k3fRlffQXXTTU3TRU3AxUHJSMqEnVaInVQIy47w7gc8BQbdKwKXic2nV4XE6cbscuBxiW2te5tBUVGW0HltVlKpBWsWZvNaIzTDF4kDREO29Kq3MciWDXMkkVzIp5dOc9PwWABv/8/+SxzPp38apiYXG+qCbhqC7GulvCnuIeGc/1V43LTJFg0zBQDct3E6NgMfBlrow9SERxZ5NQS+RLDcuOA9u9+7dHDp0CEVR2LRpE1deeeVszksikUgkkvMYyZZ45ugQyUKJFdMQ2+mCENt9qSJxv4s/fMM6otNIPz+XXMmgJ1ngspYQ2zvjS8pRd2BggNdeew1FUVi3bh319fULPaX5oZSBkz+H3DBUTbcqEVZNXFcVxdrovuoAh6vmtnHGJYhTU4n6XUT9LlbG/BQNk3TBIFs0GMoUyRRN0jkDCxunqope0A4VbY6+K3XlcSWUhbyOYhcxTJPBvMJAQWGgoDJQUBkuqgyXNIZLGkMljaTuwEIhZ0DOsOjLWoAx2cvNKV50KhrbqSn4vS4Rkfe6CPucxP0uYjUj7HXOqmP5uZQMi2zJIFM00A0Lh6YQ8DhZ1eCnKeQl5ncR9TkXZYaARLIYmbHg7u/v59d+7dd44okniEQi2LZNMpnk1ltv5Zvf/OalcyCXSCQSybySKuj8/Oggg+kiK+K+KaM4mYLB3/7oMGcTBaI+J5944zri00g/P+95igb96QKXt4W5uiM2Kw7O80E2m+WjH/0oX//617EskZ6saRrvec97+MIXvrD8jU9tW6Rzh1vBdfEt2yRjcTs03AGNuoCblXEhwDNFk0xRJ5HVSRUMRnI6hmWhqgpuTUTA3ZpadvCeRRQF0LAVDU110uiExvO69JjlIVpzZQ1IllSSJYWsoZDRIatDVrcpGFAwK1sRUR8dChaKaO9lK5g1TuQimUHFUY6IOxwamiret8uh4XY6cDmdeN0uvG4nPqfoIx5QivBzMcv73rkFp2/+WuJZtk1BN8kWRdTdsG1cmorf7aCzzk9jyEPM7yLic8pabInkApmx4P7oRz9KKpXiwIEDbNy4EYCDBw/y3ve+lzvvvJOHHnpo1icpkUgkkkubbNHgmaODdCfydMT9U0Z3skWD+x8/TNdInrDXySfesJ6G4ORpmuORLugMZEpsbYuwbWV0SUV07rrrLp588kn+8z//kxtuuAEQRmp33nknn/jEJ/jyl7+8wDOULCfc5ZruuN/FyphIQ86WDHJFk1TBIJkrUdBNUnkdC9Eay6WpuB0qLoc6633AJ0NVIOiEoNOi7WLWYmwLxTZRLAPFNlAtA8XSxdY2UGwT21ZQFBtb0bAVB5bqxFYdmJoPw+nHcAYpmKNF2a5SEsXlwNI8s55NYdsivT1XMsmXTEqmCYqCx6kSdDvpqPMRD7iJ+ER0fSll8kgki5kZC+7HHnuMxx9/vCq2ATZt2sSXvvQl3vjGN87q5CQSiUQiKegmzx0f4uRQjo6Yb0oznlzJ4O8eP8zp4RxBj4NPvGEdTeGZi+1kXpgVXb0yyhXtkSVnAvTwww/z7W9/m1tuuaV63Zvf/Ga8Xi+/8iu/IgW35Dxyus2mbwjxd/A3FXzOC/8/79SEW3XECy0IsZfXTfK6Ra5okC4apPI6Rd0kVdCxsFFRcGpCgDs1UTO9qN3Gy+7rtirql83J7mubNYJcx6EncRUHUSwdr65X71Z/9nEcbh+W6sR0BjCcQQxnEEvzYDo8mJpX7Guect3/+BiWRUG3KOomOd1ENy1Awe0Q9ertcS8NQQ8hj7PcVtExr4seEsmlxIwFt2VZ57UWAXA6ndWUNYlEIpFIZoOSYfHc8SGO9mdYGfNNGWEu6CZ//+MjnBzKEXALsd0S8c74dUdyJVJ5g6tXRrm8LbIkT0RzuRyNjY3nXd/Q0EAud76zs0QylyiKgs/lwOeCuF/4KFiWTcEQIrygm+RLBsm8Tq5kkSno6JaNXRbiDlWIcadDxakqaEso2wQARcPSNNDc5wnzUmm0T3bJHUVxqKhWCVdxCHeuF8XWyx59CpbixFKdWJoLwxkgr4XIqz7ytpuc7SaHC13zojhceJ0aHqfG6oiouw55nAQ8DoIex5IpjZFIlgMzFtyvf/3r+djHPsZDDz1ES0sLAN3d3Xz84x/ntttum/UJSiQSieTSRDctXjg5zGu9adoi3ilPECti+9hAFp9L4643rKNtGsZq5zKUKZIrmVy3KsamltDijrBNwvXXX8+nP/1pvv71r+PxiAh/Pp/nnnvu4frrr1/g2UkWI2ZNv6ldvTava2VOMztUdVSE16Kbws27YJgUdIu8Lhyy8yWTom6SMW0Mu9KEzBb10qpwENdUBaeqoKqLPDo+AZbmxnQKUW7bNpZlo1s2pmVjGCaWWcIuFdGsHKqVxMUpIopNvUPB43Ti8XpxaT5c7hDuYBxPMIbqDggfA6cPXE6QYlsimVdmLLi/+MUvcscdd9DR0UF7ezuKonD69Gm2bNnCN77xjbmYo2QJ43P62PfefQs9DYlEssQwLZuXTo1woDtJS9iLe4oWXEXd5PM/OcKR/gxep8ZdO9exIjZzsd2fLqCbNjvW1LGuMbAkT9gr/P3f/z233347bW1tXHHFFSiKwt69e/F4PPzgBz9Y6OlJFhmPnbT59POjl9/3ODT7bD59LdzeMb/fA5FOrhI45zTVsmyKpmixpRu2aLWlW9UWWyXLRtdNMmWBCqJdl2jKpqKpQuRrioKmKqhKeZQ7sYlWX3PzXm3bLrdQtzHL7cMsS+xTk1KeyuUxC5X2aeW5auDQNDwuB363G68rWq6ZF+n3HqeKS1NFKzWzCEYRjCwkhmGo/NyqCg6PGJ4QeONi6/KDKwDugLhtCf/mSSSLlRkL7vb2dvbs2cOPfvQjXn31VWzbZtOmTezcuXMu5ieRSCSSSwzLsnnlTIK9XUkaQx68rinEtmHy+Z8c5XBfWWy/YR0ddTN3QupJ5kGBG9bUsaYhcKHTXzRs3ryZI0eO8I1vfKN6vP61X/s13v3ud+P1zjzNXrJ8eeykzf/4qY19zvW9OfgfP7X58q3zL7rHQ1UVvKqGd4IFOMOyKBkWuil6YeuGWd0XPbBNSqaFbliYtoikW7ZVdhwv99HGRkGpCvWxDdcrDdjP/aTG3v/cx1YeVRH1WkXcqwoORcHpHI04r6oP4nB5cWoihd6hCXM5l0PFoU4RmVY0UH0ikn0ullkW4gXI9EPitOhLjwKaS4htlx98cfDFhAivCHGnTwpxieQiuOA+3G94wxt4wxveMJtzkUgkEskljm3b7D+bZM/pEeoDLvzuyQ9TRcPkCz85ymt9aTxOlY/vXEvnDMW2bducTRRwOVR2rImzMr58Wkh5vV5+53d+Z6GnIVnEmJbNPc+fL7ZhVCjes8vmDSvmNr18NnCoKg7X1OnSIrJsY9k2hlneL0ebK7fZtvhMLEuIcRC/FWJ7/nMqCqLNe7lNmKooUBXYIsVdVahG1rVypN2hKqhWEV4Uz7Oqzi/E72yjauDyiVGLbYNZEkK8lIHsIJi6+MOrDnB6hfD21YEvCu4guEPiOucczFMiWYZMS3B//vOf53d/93fxeDx8/vOfn/S+d95556xMTCKRSCSXFrZtc7AnxYsnR4j4XAQ95xt01lIR26/2pnE7VD6+cx2r6mcWmbZtmzMjefxuBzesiU+r5tuyLdKlNKliikQxwXBhmMvqLqPOWzej154Lvve97/ELv/ALOJ1Ovve9701637e//e3zNCvJoqHSm9wolKOdJXb1KfTkmiZ+CNCThV3P/pTr/T1gGSJaalvlbXm/OmyxrbzeGClfFuyiYTVQzuVW1HJ0Vq3ZdwiRqFb2naA5xb7mFFFZzSmud7jLUdqarcMDmls85zmoqoJanssUa3rzw0J6DitK+fNyA+Gxt5kl0GuEuFUCWwGHS0S93UEINII3UhbiQXAFx/3MJZJLmWn9zPzd3/0d7373u/F4PPzd3/3dhPdTFEUKbolEIpFcEIf7Muw6PkzA7SDsnZnY/oOda1k9Q7Ft2TZnRnJEvC5uWFM3YeuwolkkWUySKqYYLg7Tn+0no2coGIXy81h0hjthEWRpv+Md76C3t5eGhgbe8Y53THg/RVEwzUmbGEkWG7Yt6nOLGShlhQgqZUHP1WxzYqvnQM+LYeSFaDLyQmTbY9Vdv3k98NEpX77/xD7Qnp2jNzeHVNKlnR5weMXW6RORW2c5/bpqKFbeVkzGXAFw+i9dAam5xCA0el3l/6FegNwQJLvFoouiiui5wweBOvDXi0i4OyRqxbXJf9MlkuXMtAT3iRMnxt2XSCSLE9MaPZHe3bebHS070Cbp1ymRLDRH+zM8d3wIn0sj5ndNet/xxPbahuCMXs+0bE4P56gPurlxbR11AXf5epOMniFVTJEsJunP9ZMoJsgbeXRLR1M1vA4vYXeYBl8DqqJyKnnqgt/3bFPbnlO26lzk2JYQzYUkFFJiW0yJ/WIKiunRUcqIrWXM3uuXI8MNtgX61HdvaFsLodjYqHMlGq2oNdHpsjhVakVqJRW9HO2uRL5rI+KVUYmaVyLplimi8pYBpiH2zfKwSmJrlMpmYSUwC2JbeS2zJEYxdeGfldNfjuAGRiO5tWLSHQJPuDxCZZG6TFGUUfM1b2T0esssL+7kYfAo9B0Sf3aHW3x+vpiIhnvCo5+XYxl/ThJJDTNOpPnf//t/84d/+If4fGPT7vL5PH/913/Npz71qVmbnEQimTmPn3qce3fdW7384R9/mEZfI5/c/kl2rpTmhpLFx4nBLM8eH8SpKcTLwnciZkNsG6bFqeEcrWEP21b5MZQRDo+kGM4PM5AfIKtnq9Frj8ODz+GjwdeAc4lFaL7+9a/zq7/6q7jdYz/TUqnEN7/5Td7znvcs0MyWOZYFhQTkhyE/UjMS5evL20LyvGjztFC1sqGVvxyR9ddEaH2jUVunVwyHZ3RbifRqbvE8wHbLpvlbNr25863AQGimJj9sv+kXYJHXcFex7bIQL4wOPT+6rWYAlLMBSnnQsyJDoJQFPQPFrBCQIG7Ts5CZ5us7feCJCEFa2XqjY4cvNje12gtF9f9lACo2GLYtsir0HCS7hBBXEAsSTp8waKukpFcWLJbY76xEMh0U2x7P+mFiNE2jp6eHhoaGMdcPDQ3R0NCw6FLUUqkU4XCYZDJJKBSa+gESyRLm8VOPc9cTd3Gu/Y1Sji7cf8v9UnRLFhWnh3I8fXQAy4am0OQnn6L1lzBIuxCxrVsl0qUUx4YGiQRLNMd0DHLkjByWbeFQHHgdXnxOH27NjapMnkZaNIv84ZN/CMDDb3uYdbF1057LRMzmMWupHa9hlo/ZhRTs/3bZ4GmWjPBsSzxvdkCk0+aGIDdYsz8ChZHxXbUmwhWoifrVRk0rUdRg2S26vHW4Z90xuuJSDuNWXPPlW5VF4VI+71hGTQp/emzWQTUToZKVkBSLKNYMvldOnxDengj07RfXXf1BCDaBv04I0uUYLTcK5fKHckQcwFmOhPvrRiPhlSEz9CSLkJkcr2Yc4bZte9wehS+//DKxWGymTyeRSGYJ0zL57K7Pnie2odKHVOG+Xfdxa/utMr1csijoGsnxzLFBDNOmJTJ5AXSh3Gf7cF9mWmLbsHQKZpa8mSFnZEjpQySLCfqzaaJ+lTpvgJLtx+vwEnVHl+V3YqLjdVdXF+FweJxHSLBtIZqy/aJ1UnZAjEx5mxucXlq3ogoR5YuCNzY2ylkb+XSHQFt4167bOxS+fCt8+nmbvtzo9U1++PT2S1Rsg0ib90bGpk5Phm2LSHghWc5kSI5mN+TLizG5EZH9YBTKkd9y9LfCi18Z+5yesBCh/vqa0QCBBrG/FCPClWyLCpW68FIOEqdg4AhgjzqkVxYgKt8bl1+2KZMsKab9Kx+NRlEUBUVRWLdu3ZiDuGmaZDIZPvShD83JJCUSydTs6d9DX65vwtttbHpzvezp38M1TdfM48wkkvPpSeb5+dEhirpFa3Rqsf33Pz7Ckf5MufXXujEGaaZlkC+L67yRIa2PkDESlKwChiWKU23LQa6osTbewmXNcVyO5WuCdOWVV1aP17fddhsOx+ih3jRNTpw4we23376AM1xgLFOI53QvZPrOGf2i3ncyFKWcElxXHnHwx4Ww9sVHRfUSM9q6vUPhhmabLf8qLn91J7yuVVn0rcAWFYoymlYdap38vnpOiO/cEKTPwu6viuujHaIGPTckRGihHDkfOjbeC4pFnUAj+Bsh2Cj2g01ijNePezFSWxdOOXhnW8KYTc/CwCHo1UWk2+kHbxiCrSI7oCLCF8HClUQyEdP+3/m5z30O27b5wAc+wD333DNmddzlctHR0cH1118/J5OUSCRTM5AbmNX7SSRzRV+qwNNHBsmXDFqniGznS0JsHx3I4HVq3HlbJ40Rg4FCN3kjTVpPkDGSlKx8VVw7VCcuzUvAGcWhOCnqFkm9xPoGP2sbAji0pSWEZkrFnXzv3r286U1vIhAYXZyoHK/f9a53LdDs5gnbhnQPDB4R6b+5IXE53SOi1fYkab+KAt44BOqFiKlGF8tbX0xEPpchQlyLLKntTVJszylOH4R9kOqGg98dvX7kpFi8ue7D0HjZaJZFdlBkXlQzLvpEfXRuWAwOnf8a7hAEm8UINY/uBxsXf6p6xfXc5RPfOxDZJaWceL/JbvE9d7rFAkegSUT9vVEhwmerjEQimQWmfcR473vfC0BnZyc7duzA6VyCKSwSyTKm3lc/q/eTSOaC/rLYThcM2qPecVOeKyQKOb7w42OcGiriccLbr8szpDxL73AR3SqhoNSI6wgOxXXe8+WKBumizqq6AKvq/WhLLOp4IXz6058GoKOjg1/91V/F41lGxkzTJdMPX9o+8e2aU0QCA03liGA5MhhoFFHrSzRa5nMqnHy/FNnzxpld8PT951+fH4af/x3ceBe0b4dY5/n3sW2xmFSboZGubHtFTXmlxnzwtbGPVRQhYkOtEGyBcKvYD7UKJ/bFiuoQ/gaecr1sxZStlIHBw6IOvmLe5ouJ91MxqXOHllzWiWT5MK0jSiqVqhaDX3nlleTzefL5/Lj3lcZkEsnCsK1hG42+Rvpz/ePWcSsoNPoa2dawbQFmJ5HAQLrI00cHSeRLrIj6quLYsi1KVp6CmROp4Uaa/uwwjzzvYjDpxOU0uXVbL14/KIqnGrmeTKwDpPM6BcNiXWOQlTE/6ixH66wah+n9g/tZHVm9qGrBKwvllySBhnKaqVNE9MJtEGoRAjvYJE7GpzDFk0jmFMsaTSOfiD1fg9arxxeKijIqPuvWnn+7nhMCvJLZke6BVHmr58SiVKYfeGns4zxh8X0JtwvBGmkX+4sxYqwo5b7qHpGBAqNGd5k+GD4prnP5xecUahULDZUo+CL6vZYsb6blUl7rdKqq6rgnORVzlsXmeipdyiWXEtKlXLJYGcwUeerwIAPZDHVBKFk5ilaOtJ4ko49QsgqUrAK2bVPUHfxkdxPDaScel827rjeon6HHVyJXwrJgbWOAtiki6RfC3v69fPvwt0mWktXrZqP93sUes2KxGIcPH6aurq7qvTIRw8PDFzzPuWJWj9m5ETj4ndl1KZdIZou+A/CT/zP1/V7/ZyK1fLaoGAOmuiF1tjy6xOXcJL8JvpgQ3pEVEF4htqHWxZ8NYltigaGYEenotiUEujso5h9oECn83sjSNKCTLBiz7lL+k5/8pOpA/tOf/vTiZyiRSOaEnSt3cv8t93Pvrnvpz/VXr2/0NXL39rul2JbMG5ZtkdWzZPUs3ckRnj7eRU+mD7/XoHukWK63tlFVBy7Vg7ucFp4vavxgt4PhtILPLcR2fCa6y7YZzuqoKmxsDtI8RY34hbC3fy9f2f+V867vz/Vz1xN3LejC1t/93d8RDAar+7O90LBkKGXhrzrE/h3/IAW3ZPGRT8zu/aaLoow6r58r5PWcEODJrppxptzyrlwr3vNyzXNpQrRGV0JkpdhGO4SYXSwo6qiRHZTT0AsiHb93n/Bz0Fw19e6NZQPEmBTgklljxn24lxoywi25FEkX0+z45g4A/uG2f2BHy45FleoqWT7Ytk3eyJPVs2T0DDk9x1BhiGQxSd7IM5zLcnQgTa5o0BAI4tI8OFX3uCnhmTw8/KyDkYyC323zrh0GsRmct9m2zWCmhMepsbEpSF3QPcvvViwkfPqZT5MoJsa9vVK68di7Hrug79ylfsyatfdfysJnWsT+Hf8gTp4lksXEQkW4L4RSTgjvxOnRbeK0EOjj4YsL4R3tgNgqiHaKNO7FugBoFEQEvJgWKekO96jTfLBxtPuAFOCSGua0D/djjz1GIBDgxhtvBOBLX/oS//RP/8SmTZv40pe+RDQavbBZSySSWaP2RP+qxquk2JZcNBVhnTNy1ch1ophgpDBCXs9TMAsYlgEKuFQXHocHxfIwkgSn5WFtzDNptDWVg4efcZDMKQS9IrIdmYF3j23Z9GcKhDxONjSFiPrnxoH3WOLYhGIbFlf7vT179uB0OtmyZQsA3/3ud3nwwQfZtGkTf/7nf47Ltchdii8Gq6a8bfAwtG2XhkmziWWJyKBtihTdyrBq9rFFNLF2f8yWmsvTQFEABVEhVdkv/6Yoas3t6ujl8/a10e1C/3+o3ygiqfnJ0rjj4n4LjcsH9evFqGDboi/9yCnROztxSuxn+soR8SHo3j16f09YCO/YqtGxWBbCKi3JKnXgRlGI7/6D0PuKEODukPCBCDaNCnB5biWZJjMW3H/0R3/EfffdB8C+ffu46667+MQnPsFPfvIT7rrrLh588MFZn6REIpFI5gfLtqoR65yeI2tkSRQSJIoJ8kaeolFEt3QURcGhOnBrbjwOD2FPGKc6uvqfKRgc6E+SLlg0BCYX24msENvpvELIJyLb4Rm0j7VMi4FskYjXxabmEEHv3EUhksXk1HdicbTf+73f+z0++clPsmXLFo4fP86v/uqv8ou/+It861vfIpfL8bnPfW5WX88wDP78z/+cf/mXf6G3t5fm5mbe97738b/+1/9CnU9xc/B78Ogfj17++eeEsLnqfcLxWSKwjNFhlre2KRYrLKO8NREitiyKbcritSxgVQ1QhXitCFkUcb2igOIQztK1t1dEcEWsVC6LC+dMsvK61ui2IuIrYr8yz8rcq+LfBAyxCIBVs0hQszgw3kui1MxZK++fs1Uco+/xQlFV8X9yPJfyCtveu/ALAxNRcTr310Pb1aPXl3JCfA+fEC3ORk6IGvFCEnr2ilHBGxXCO76mvF09mvq9kDjcYlQFeDkC3ndApNQ7PeAum8sFGoQA90QW799KsuDMWHCfOHGCTZs2AfDwww/ztre9jc985jPs2bOHN7/5zbM+QYlEIpHMPrqlk9NzImqt58joGRKFBMlSkoJRoGAWMMtRQqfmxK25cWtuwq4wzinS6jIFgwNnkyTyOg0BN8ok7uDDaZFGni0oRP02v7jDIDiDsmvDtBjMFGkIulnfHMLvmlsDn7B7eu5ti6H93uHDh9m6dSsA3/rWt7j55pv513/9V37+85/za7/2a7MuuO+77z7+8R//ka997WtcdtllvPjii7z//e8nHA7zsY99bFZfa0IOfg/+/T1wbqeG/LAQNpU2S8sV2yqL5xKYuhiWLq4z9VFxaSMEo1YRxOWheUWkz+kFh1f0OFadIpV2jPAsj0qkuLq/CCLIVUFunSPETSGyqwsLNYsKlj66+GCURITTKJRHEcySGHr5MWb5OaoLAuXIu+oof6blz0tzlj8/x/i929u3i/+Tux+E/Mjo9b64ENtL8f+qywcNG8WoYBRFCvrwcSHEh49D6ox4z927x0bCg80QXwt1a8Q20r7wfe/PjYDrBdFu7ezesgmbV9TEh1dAoE60FnQHF28KvWTemfH/YJfLRS4najYef/xx3vOe9wDCGTWVSs3u7CQSiURywVi2RcEokDNy5HWRDp4qpUgUE2RKGYpmkaJZrHaZcKku3A43PqePqCeK4wJOcmYitgeS8B/POsiXFOJBm1+83sA/g5bRumExlCnSEvGyvjmI2zH36X2rI6uJuCNT1nAvhvZ7tm1jlaN4jz/+OG9961sBaG9vZ3BwcNZf79lnn+WOO+7gLW95CyD6gD/00EO8+OKLs/5a42KZ8NjdnCe2a5mszdJSoCIIzRKYZSFolABrVPRprlGh5/QJAeQKiP7Kmlvc7nCN7mvO8ta1dD+XWhSlHGnXZq/m1jLLCxilckZA5W+g14jxgqhpLmVBz5f7Q2fL99fLAh3xd1KV0b9RfA3svAf+805x+813Q9MVy+NvUcHhFq3LatuXGQURAR86BsPHxDZT08bs5M/E/TQXxFYLAV63TgzPDNtWzDaVVmSBBrHAo+eFAO/aJS67/UJ0R9rF1l8nRLnkkmXGZ1M33ngjd911FzfccAO7du3i3/7t3wCxkt7W1jbrE5RIJBLJxNi2TcEskDfyYuh5MnqGVDFFspSkaAhRbdgGtm2jqdpotNodxq25UWepH/FMxHbPiMIjz2kUdYWGsM07rzPwzsDjrKCbJHMlVsR9rGkI4nLMz8mpqqi8a+27xnUpr7Tfu3v73YvCN+Hqq6/mL/7iL9i5cydPPvkkX/7ylwGRqdbY2Djrr3fjjTfyj//4jxw+fJh169bx8ssv8/TTT08aSS8WixSLxerli1q4P/WMcFiejNwQDBxaeBOqibDtsogrR1YroyKoVU2IF81VFtEhIT5cvtEonMNTTon1CGEtuXjUcvTeOYMVQVMfjY5XIuZmSWxLOVEjXMoIsabnRx+nuWHkOKCUF0Zqh3vxt+GaLg4P1G8Qo0IxJYT30FEYPCq2elZ8ZwcOjd4v0CSEd/068fhQS01ZwjyjKOVFrXIdlG2Jv2u2HxInxeKPOyRqv0OtQnx7Y8vn7yiZFjP+a3/xi1/kwx/+MN/+9rf58pe/TGtrKwCPPvoot99++6xPUCKRSC51bNumaBZHRXU5DTxZSpIsihTwklmiaBartdIu1TVaX+2eOg38YqmI7eQ0xHbXkMJ3n9PQTYXmqMUd15l4ZjC9XNEgXdTprA+wqt6PY54jQVsbtvLBzR8ctw/3Ymq/97nPfY53v/vdPPLII/zP//k/WbNmDQDf/va32bFjx6y/3t13300ymWTDhg1omoZpmvzlX/4lv/7rvz7hY+69917uueee2ZlApm9695vtNksXgmWCkRdRUbMIekVUMxp9dnpEfaw3JtqaOb0iYl3ZSjG9uNGc04uwm4Zot/XY3eLy2jeKTIVSDgopIUL1HOgpIdxto/xAZWy2gsMttks5Mu4OQcuVYoAQr6keYXw4dERsk12Q6RWjEgV3+aGubOpWv0FExBdK0CqqeB/usmu1ZYjFlaFj0H+obMAWFtHvigGbJyzTz5c5si2YRLIMyek5rv3XawF4/jeex+ecgQOVZEGopH9XBHUlFTxRTJAupauiumSWxAMUcKpOXJoQ1i7NhUt1LUjf5XTB4GBZbNdPIbZP9iv81wsahqnQVmfx9u0mMym7TuV1SqbFmvoAK2I+1Elea67JG3n++GfCnOue6+/hjjV3XHRkez6OWYVCAU3TcDpndxHmm9/8Jn/0R3/EX//1X3PZZZexd+9e/uAP/oD777+f9773veM+ZrwId3t7+4W9/xNPwdfeOvX95rPNUq2wNsppxiBOyh1ecfLtjZRrPgNlYe0vR6y9S1s8SaZPbRu7Pz17ft94o1T+f5Qvi+9y+no+AYXEaAq7UaBaUqE6R82/HG7QPMvj/1MpI6Lfg68JAT54VCxa1aKVU/Xry7XkdevEZ7AYMApiIaWUEZ4Cbj9446KHub9c/z2TTArJgjGnbcEATNPkkUce4dChQyiKwsaNG7njjjvQtIVPoZNIJJLFim7pVTFd2Wb1LMlSckxNtW7pIj3ZBpfmqpqWBVwBnKpz1lLAZ4N0XudAT4pkviTcyCcRwEfOKjy6W8OyFToaLN56jclMyq5HsmKxYWNziJbw5M7n80Ht32Fz3eZFkUY+Hrt37x5zvN62bW7qy//oj/6IT37yk/zar/0aAFu2bOHUqVPce++9Ewput9uN2z1LJ8Ird4jU0lQPE9Zxz1WbJdsuR6rzNSnC9qiwdvog0jBqplQR166AbC0kmRpHOZI9Ue1yRYDrOfF/r5QVruC5YSHsciM1YrxcPz6mBGEJZUu4AtCyVQwQEeSRUzDw6ugopkU0uf8QHEB8x2KroWGTGPXrF06AOzwQ8AAN5fTzLOQGRPq56ii7n7eK3zJ/vXQ/XybMWHAfPXqUN7/5zXR3d7N+/Xps2+bw4cO0t7fz/e9/n9WrV8/FPCUSiWTRUxulLpgF4fZtFEiVUqRKKXJ6TkSprRKWbWFjo6KK6LTmwqN5CLlCOFXngovJ6ZDK6xysiO3g5AL44GmFH+3VsFFY22Jx+zYTbZrnELZtM5Qt4dJUNjQHaQgu7Oq/ZVtk9SzDhdH+uSOFkUkesTD09/fzq7/6qzz55JNEIhFs2yaZTHLrrbfyzW9+k/r62XVSz+Vy57X/0jStatw256ga3H5f2aVcYVzRPRttlmy7XIdbY44FQrQ4fcJIyd8gxFFVXEthLZlDKiZejNPX2iiJOuhSVqSplzJCiOeGy1HykbKDvS3anTlrnOo11+JPdVYdop1YfDVseIv4fqbOiprviujOD5ej4Yfh4CPiuxhfAw2XiWyXurXivc43ilr+jQiKy6YhSgj6D0HvfvE38MUgshIC5RZs0nxtSTJjwX3nnXeyevVqnnvuOWIx8cUeGhriN3/zN7nzzjv5/ve/P+uTlEgkksVARVAXzaIQ1qaIUldMyrJ6Ft3UKVpFdLMcpVbAoTpwqUJUh9whXKpr0UZDp0syr3PwbIp0YWqxvfeEyhP7xPu9bIXFbVeYTDcT3LJsBjIFgm4nG5pDxPxzc1JUMkukS2nSepp0KU2mlBGXa66rXJ/RM9jniLmjiaNc23LtnMztQvnoRz9KOp3mwIEDbNwooroHDx7kve99L3feeScPPfTQrL7e2972Nv7yL/+SFStWcNlll/HSSy9x//3384EPfGBWX2dSNr0dfuXrog93umf0+otps1QxudKzoJeEMHF4hLiOrhQCu2Je5g4untRViQRGo+Pe6NjrbXvUVb2UEX2m8wnIDYrLmZQwecMuO95XWsV5Z8/9fS5QFBEhDrfCmp3ifWb6yuL7IPQfEIsNA6+JceA/xPupWw+Nm6FpM0RXLUxUWXMIge2LjbqfFxJw6qx4X56QiHyHWsXvjox+LxlmLLiffPLJMWIbIB6P89nPfpYbbrhhVicnkUgk88m5groSpc7qWVIlIaiLphDTJatUbaelKmpVUHudXkLq0olSXwiJXIlDPSkyRYP6ScS2bcOuIyrPvirE9tZVJjdfZk07YGKaFgOZInG/mw1NQYLe6Z/kVdzbq6K5lCZVSk0oogtmYdrPXcHn8JEzRJtMj2Px1dw99thjPP7441WxDbBp0ya+9KUv8cY3vnHWX+8LX/gCf/Znf8aHP/xh+vv7aWlp4fd+7/f41Kc+NeuvNSmb3g6rboHPtovLN/wBtG2f3ompZYxGAfW8SPl0uEVddbhscuQJixNdd3BxCw+JZDIUpVzW4Acaxt6m54UAL6XFNjcshHgxI6LFpiGSSBzuUSM/h2fhnMInQ1HE9zbYBKtvFQembD/0HRgdhQT07RfjFcT3vXGTEODNlwtX9Pk+nte6nwcRv02FlIjS9x0Qn7svBtEOEfn218va70XMjAW32+0mnU6fd30mk8HlWkI1IBKJ5JLDtEwhpivp3jWCOl1MkzEylMxSVVBjg63YaIo2xqAs6Aouulrq+WIkW+JgT4pcyaAu4J5UbD91QGXPcSG2r11nct366Ytt3bAYzBZpCnnY0BTE63KcJ6IrArpWSNfu65Y+o/fmUBwEXUECrgBBV5CQK0TAKfZrR8AZIOAMVLMUTiVPcU3TNTN6rfnAsqxxjdGcTuecpHkHg0E+97nPTdoGbN6ozSCpWzex2DaKo9E9qwSoIv3bF4NgK/iiQlx7wkurzlUiuRic5Ug2NWUnlYh4MS1GISWEa254tEbctsQilNM3OhZbBFZRINAoxurXj6ag9+0bFeB6FrpeEAOEmVnT5eWxWfxGzDfqONHv/Agku8Vn7A5DuE1E9v114ndrmS76L0VmLLjf+ta38ru/+7t85StfYft2kZr1/PPP86EPfYi3v/3tsz5BiUQimS66pY+NUJf3M3qmGqE2TIOiVcQwDWzFBhs0VQrq6TCcLXHwbIq8blIfcE94MLds+PHLGgdOi8/v5s0mV66aWOAZlk7ezJAz0uTNDOliipFCEoezyKmRAj/pHxXSMxXRbs1N0Bk8TzRXBbUrQMgVIugK4tEW3ohtNnn961/Pxz72MR566CFaWoQDcnd3Nx//+Me57bbbFnh2c4zLD588A/u/PZriXam9LqZFGq1liNtcAWGoFGoSabeeiHj8Mvq/IJFcNLUR8WDT6PWVuuNiSny3skOQ6RfR8UwfYInacJdPRI4XmwivTUFfd7voLDByAs6+BPsfFvfJDsKxn4ihKBBbIyLfzVeI/fl+P+f2/jYNKCZFynzvPvE38teJ6HegbNYo+34vKDP+9D//+c/z3ve+l+uvv766cm4YBm9/+9v5+7//+1mfoEQikcBoL+pz073zRp6MniFTypA38uimjm7p6LYuTIIVBU3RhNu36qymfDtUhxTUM2AwU+RgT4qSYVEfmNhIxzDhsT0aR3tA1VJcd1mS+vo0h1Np8kZmjLDOG2lyZgbdKo77XBNRWRSpCOXa/XOvcy2EEc4i4Ytf/CJ33HEHHR0dtLe3oygKp0+fZsuWLXzjG99Y6OnNH7lhSPeBbYqonSsITatECqYvJgS2jF5LJBdGbd1xBcsSmSOFpBDi2cGxIty2hElZVYQvonT0iqFauG1UcN94lzBh69kHqS7RE3zoiLjd5ReR7+YrxDi3Vn4+0BzCp8IXFwuLpaz4vEdOiowDT1T4TQSbhAA/t+2cZM6ZseCORCJ897vf5ejRoxw6dAjbttm0aRNr1qyZi/lJJJILwOf0se+9+xZ6GjPCsIyqmK5N+87qWdKlNFk9K9K9LSGoTcsERGsmh+qoRqgDrgBOzYlDcSyraOVCMpAucuhsCsOyCfsUUvoIOTNdFcyVbVZP05fKoAfSBDZkURSbfTrsOzv1a2iKA7cawK36iXnDNPqjhN0hQu7zhbRbk6ZU06G9vZ09e/bw+OOPjzle79y5c6GnNj+oDhG9tm0RvQo0gjcm+l4vcdNCiWRRo6rC4MtT05u4VoQXkmUR3ivSolN5QAGnq9yHPrC4FsGaLx81XMwOiihyz8tiW8rC6WfFAIh2ipZlzVshvnZhot/ugBggymYKSejeLS67g8J4LdwuxLc3KrN55oFpC27Lsvjbv/1bHnnkEXRdZ+fOnXzqU5/C45EF+hKJZHLOjU7XCup0KU1Gz5DX8+iWqJ0eN927bErmd/pxqs4l7/K9mLBtm7yRJ1lKkiqKFmbJYpJUKUVfZpj+bIKCmaZoZ6eORjth9PRCwav58WoBvI4APi2I1xHAqwXxOvzVyz41QDqvomoK6xqDi6LH9lLnW9/61pjj9Uc/+tGFntL84/KJNkEOjxTYEslCM0aElw0NLXNUgBeSorNAdlBsLR1QwV1OY3f6FkcU3F8nzNdW3yrmP3RUiO+evTB8XKSjj5yAA98R2TQtV0DLNhH9XojIssMthHWgQcy3mIahY8K13ekT7yfWKVoZ+utl6vkcMe1P9b777uN//a//xW233YbX6+X+++9ncHCQBx54YC7nJ5FIlgC6pVM0hIgumsXqflbPVtO9a6PTlm1VHb6dqlMMzYnP6SOshpe1w/d8Yts2OSNHspgUoyyoz92mSqkZ1UZrihNfVUAHcdgBjneHyeZCOJUAt2z00R4N4NF8qMrkQse2bQYzRTxOjQ1NQeqDMnp9sTzwwAN86EMfYu3atXg8Hh5++GFOnDjBvffeu9BTm39k6qREsnhRtXPS0beKiGw+IZzDs0OQ7oZCGlK94i5Or/heuwMii2UhUTWoXy/G5b8i5t37iqj/7nlFpNCffFoMRYX6DUJ8t24TUeaFmK83IkbFBC83CInTIvXcGxV138FmIdBlz+9ZQ7Ft2576brB+/Xo+9rGP8eEPfxgQ7Ube8Y53kM/nF/WJcSqVIhwOk0wmCYVCUz9AIpGMwbItSmbpvNrpglEgradHa6ctvVo/jcJ50Wmn5qyKaxmdvjjOFdKViHRVSNfsG7Yx7ef1OXyEXCFCrhAOxU+p5MGvBYj6IqPRaC2IUx11Jx9Ow3eec5DOKwQ8Nr94vUEsOL3Xs0yLgWyRsNfFhuYgEe8iSiGcAaeSp7h1xa2sCK246OeajWPWli1beMc73sH/+T//B4CvfvWr1Z7cix15zJZckpSy8JmyAPvTs3KhqBbLEnXg+ZFy+vlZyA2J9HTLHDU+dAdEXfhsYRTgW+8T+7/8VZEpM6N5m6KF19k90P2SqP2uJdgMrVdD21UQn6STwnxhlMQiR7F8nPBUXM/byj2/wws6vcXITI5X0xbcHo+Hw4cPs2KFOKGwbRuPx8Px48dpbW29+FnPEfLgLZFMjm7qY1K8K/vZkqidzhk50Xu6HJ22bRvbtsfUTlfEtEt14VBl7fTFUDSKJIoJkqXkmMh0db982bCmL6T9Tj8hV4iwO1zdhl1hcdktBHbYFcapObEsm9PDOY4OZHBr6qS9r3tGFL77vEahpBAN2LzzOoOQb3pzqrT9agy6Wd8Uwu9eumlsi01w+/1+9u3bx6pVqwAwTROv18vp06dpamqa4tELizxmSy5JpOCeGaVcWYAPi8h3plcIcFMXotsdEOncF1MHfrGC+1wyfdC9R4yBg0KQV3AHReS77Rpo2jLaWWGhqPT8LiTFPN1+0Ys8unLUC2OhFwgWATM5Xk37DKdUKuH1jqYWKIqCy+WiWJyZu6xEIpk/LNuqiuja+um8kSdVSpEpZYSYrnH2VmwFW7FxKKNiutJayaE6ZHT6AjEtc4xwThQT44rpglmY9nOeK6Qj7sh5ojroFi3OpoNl2ZwcynKsP4PP7ZhUBJ/sV/ivFzQMU6ExYvGOa0280zxHKOomI7kSbVEv6xqDuB3y/9Rsks/nCQRG+8Rqmobb7SaXyy3grCQSyYS4/PDnyYWexdKh0hIr3CoEqlEUAjw3DOleUQOePlsjwIOzHwGfKYFGWP8LYug5kXLe9aJIPy+m4cSTYmguUe/dejW0XjVqfjafjOn5XTa7S3bB4BHxufvqINYhRLis+54WM/qE/uzP/gyfbzR8USqV+Mu//EvC4dE0g/vvv3/2ZieRSCbEtm1KVmlUUNfUUGdKou90zshhWAa6KczIxAMZrZ0uR6als/eFUzEcqwjocbelJJlSBptpJRTh0TxCMFeGK3ze5ZArhFObnpCeDqZlcXwgy/HBLCG3A+8kYvvVLoUfvqRh2Qor6i3eeo2Ja5pHk2zRIFPU6awLsLrej0OTq+RzwT//8z+PEd2GYfDVr36Vurq66nV33nnnQkxNIpFIZheHW7S8CjZB4yaRHp0fLgvwHkj1QPKsMGJzeEYF+ELVgDt9sOI6MSwD+l8VLuLdLwjTuK4XxFBUaNgkIt9t14xtvTZfKCq4Q2KAWCzID8OJM+W675hwZg81iUWFhY7OL1KmnVJ+yy23THkirigKP/nJT2ZlYrOFTE+TLFVqU71rBXVOz1VrpytCumJEVqG273StsJZ9p2eGaZnV+uhEMTFGRNfuT9dwTFO080R0JSpde53nYlPXZohhWhzpz3B6OEvY68LjnDjivOeYys8OiNvXtVq86UqT6WrmZK6EbtmsqQ+wIuZDVZfH4s5iSynv6OiY1vH6+PHjF/T8c4k8ZkskklnHKArxnRuEZDdk+4URm22JiK07JLa150h6Dr79AbF/893QdMXcp1HbNiROjQruxOmxt9ethfbrhPgONMztXKaDURyt+1ZU8ERE2nmoRYjvZV4aMSc13EsVefCWLEYqPafPjUwXjMLYVO8aIzJFUbBtu2pEdm7ttEz1nhm6qZ8noMeMQoJUKTXtqLTP4auK54m2fqd/0S16lAyLI30pzozkifpcuCcQ27YNTx9U2X1M3L610+Tmzdb02nfaNoPZEk5VtP1qWmZtvxab4F7KXOrvXyKRzAOlnDBeyw4KgZsfhmJWCGpXQKRO7/2GSFOv4I3BVe8b7cc9H6R7y+J7l5hTLbFV0H6tiJIHGudvThNhGmXxnRJGd96w6PUdbhPz8yy/33MpuGuQB2/JfGNYBiWzRMEsiG1N3XRGz5DVs2N7TlsG2GAjjMhqhXRlSCOymVE0iyQKo+J5pDAyRkwni0kyemZaz6UqKmFXjXj2RMS+a2x02rWQtWEXSNEwebUnTU8yT9zvxukYfzHAtODxvRqHusTtN2w0uXrN9MS2ZdkMZAoE3U7WN4eI+5fe5zQVUnDPHpf6+5dIJPOMbQtzsNwQpPvg4COw6/+b+P433jW/ortCblgI7zO7YOCQmHeFaAesuF4I8OAiMMa0LCgmRZs02xSLGMEWEf0ONopI+DI4p50T0zSJRCL6TVdEdKVV1nhi2rCMaqo3MGnPaYfqWHRRz8VM0SgyUhwZV0gnCglGiiPkjfy0nsupOom4I9URdoeJeqJi6xbboCu4LP8+uZLBqz0p+tNF6gLuCWupSwZ8/wWNUwMqimLzhitMNq2Y3jqtYVoMZorE/W42NAUndTyXSCQSiWTeUZTR3tTRDnj4g5Pff/dXhaHZfLt0+2Kw7nYxCkkR+T79HPQfgJGTYrz8UDnyXa4PX6i0c1UVPb29UZG2X8zAyAkYfK0svhvFZx1oEu9rGYjvqZCCWyJhrAFZRUhXtnkjT6aUIaNnxrTHMixDCGkUUBgjpr1OLyE1JMX0DCmZpaqQHimOVAV0rbierpj2aB4hpD2RMaI64olUxbTP4bskMwfSBSG2h7JFGgJu1AnEdrYA333eQX9SwaHZvOVqk87G6YntihN5c9jLuqYg3knqwiUSiUQiWXBOPSPczScjPwxHfwSNl4ne1K7A/AtGTxjW7BSjkKoR3/th+LgYL/8rxNeKyPeK6xbGcA3Ktd0hMWxbtMBLdcPgUVHj7a8TiwTBJuF+vkzbjUnBLVnW2LZdjUrXiujKyOpZsnpWuHmbRjXF27ANIaQBhbGO3n6nv5rmLcX09DEsY0wU+lxRPVIYIWdMr22RR/NUhXTUHa2K6FqB7XV4p36iS5BErsShnjTpgk5D0DOhcdlIBr7znINUTsHrsrnjWpOm6PTEdq5okC4arIz7WdMQwCmdyOeVrq4u2traFnoaEolEsrTI9E3vfpEVQiBmB0SdteoQItgThvn20/GEYM1tYlQi36eehf6DMHREjJf+HzRsgJU3iLRzd3B+51hBUYQ7fKXVWSknjOwSp8HpKbcb64Rgs2g3toy8iaTglixJLNuiZJYoWSWxrRHUJbNEzsiRLWXJGll0U0SjdVtsQdRLK7aCpgo3b4fqwKE58Dq9VTEtmT6WbZEpZRguDpMoJBguDI+JVI8URkiX0tMyIHNr7vNEdNQjxfRsMJgp8mpPmrxuUB90Txjd7xlW+O4ujUJJIeyzeed1BpFptgJN5krops26xgArY/5l40S+lNi8eTNf+MIX+K3f+q2FnopEIpEsHaZrPtZ2DXTcKARupl9EbJNdMHIKsMsR3fD89/2ujXznR+DM8yJqP3gY+g+J8eKD0Hy5EN9tV4s2aQtFpZ86gJ4Xcz7RJVqL+eIQWy0WNpZBr+9pz/5Tn/oUn/rUp3A4xn/I6dOn+eAHP8iPfvSjWZuc5NLiXBFdaXlVuS6v58kZOfJGnoJRECLa0jEtU6R3Y4NCVUg7VEc1zdvj8AhRLaPSF0TBKIwRzyOFEYaLwyLNuxyhNm1zyudxqI5qVDrqiY4R1hVR7XV4L8k077mmN5nntd40pgX1AfeEKXBHexQe3a1hWgqNEYs7rjXxTaOtpm3bDGdLOFSFy1pCy86JfCnxmc98ho985CM88sgjPPDAA8Tj8YWekkQikSx+Vu4QLa1SPTBugEARt6/cMbb2u36diNZm+8VjR06K9mOWKaK53sj8C1tvdLTmOzsgot6nnoHESTj7khgON7ReAx03QNPlCxtRdnrFADAKQnyf/JlYtPDViV7f4RbwNyxJ8T1tl/IVK1YQj8f5+te/zpYtW8bc9sADD/CHf/iH3HDDDTz66KNzMtELRTqeLhwVQVzb2qq6Lad55w0hogtGgYIpRHRFQBu2cO9GERFpTdFwKI6qcB4zFOnifaFYtkWymGSkOMJwfnhcUT2dumkFpdoCK+qJEvPEqvsVQR1wBuTfaZ6xbZuukTxH+jKoKkR8E6+47z2h8sQ+FVDoaLB489Umrmkc1yzLYiBTIuRxsL4pRGwZOpFPxmJ0KT9x4gQf/OAHOXjwIA888ABvf/vbL3pu84E8ZkskkgXl4Pfg399TvlArkcrnLr/yddg0xe+pqYvId7oXRo4Lh3GjKGqWvdFRYbkQJLvh1M/h1NNijhXcYVh5PXS8TtRUL5ZzNaMoxHcxI1L3fTER+Q41C1M4beHMWOekLVgqleL3f//3+fd//3c+/elPc/fdd9PV1cUHPvABXnzxRf7mb/6G3/7t356VNzAR9957L3/6p3/Kxz72MT73uc9N6zHy4H3xGJYxdtjGaJp2jYFY3shXe0kXzIK4j21URbRpm6MpxWUhrSkiEl3Z1gpoTdVkNHoWKJrFUQFdGB7dFkeqqd+WbU35PF6HtyqeK2I65okR8USIuWOE3WHZC3yRYVk2J4eyHOvP4nVpBDzjq+dze2xvXmny+i3WpN4ltm1hY1MyTAazRer8LtY1BvC7HdiVf+XDS+V7f+7l6nNNUGpQ8VGovVy7YFN7ubJf/aecv50rFqPgrvDFL36Rj3/842zcuPG8DLU9e/Zc9PPPNvKYLZFIFpyD34NH/xjSPaPXhVrh9s9OLbbPxTJHa72Hj4uaZb0gUqm9UXD6Znfu08W2YegonHwaTj8r+mdXCLZA5+uE+PbXLcz8xsMoQWEECmkRjffFxeJAqGVBxPectAULhUJ8/etf513vehe/93u/x7/9279x4sQJrr/+evbt20d7e/tFT3wyXnjhBR544AEuv/zyOX2d5YZhGZi2KaLG9qjwrYjn2v2KkC6aRYpGUYjmclTatM3RUX6OCjbCqVtV1KpwVhUVh+rArbrxO/1SQM8Rtm2T1bMMF4aroyKkK8I6q2enfB5VUUcFdHkb9UTHRKdl3fTSwbRMSqbB0YE0p4YyBFwqmkMla1jYtoWFhW3b2FgYhsVT+6Oc6vUDcMWaYS7rSDJUFAvcEy7JKgq6YZEumDSGPDTFFIp2ilKxRgCXHfxr96sPr1w3CVWhXivI7dHbKqK+VtDXCn0La8x9FJEuU90/d6soYqiKiooqtoqKoihoila9XPmtq2yn402wEJw6dYqHH36YWCzGHXfcMWFJmEQikUhq2PR2WHULfLasbd79bVj9+gtLuVY1UYccbBJp27nBsvg+JoR4qQvcfvDG5jfyrShQt1aMbb8FvfvgxFPQ/YJwan/l38RouEyI7/ZrFzYyD+BwiTr7QOOo+D79vHA2X2DxPRUzPvpee+21bNmyhR//+Mf4/X7++I//eM7FdiaT4d3vfjf/9E//xF/8xV/M6WvNF5ZtiYivbWPZ1ujAwrLKW9vCtMzqfcfdltOvK+7aY1K2rZJ4rvJzn/tYC6t6AgpUT4xVRUVTNTSlPFQNl+qq7leul6nBc49lW6RKKYbzw2NEdVVcF0YoWaUpn8ejeapp3tWtO0rMG6u2yJKLIYsD27bPW9wybRPLsjBsY+x32LKqIta2hYcBNliWwunhPANpnYjXhepwYtoqCkIguhQ3muKgVHLywz0Ozg4rqAq8dZuLrR0rUSpis7xVUMuR4splhUTOIKeYXNYRYXNLBJdDq/5+ANX7VSLMFWovnxutHvM51IjYc0V15faqwK7s23bNYsLob2vl+jG/tfb5v42VrJ3q1hw1WzQs8dnrln7e4zwOz5SLB/PNP/3TP/GJT3yCnTt3sn//furr6xd6ShKJRLJ0qBXXK3fMTn2zqgoxGGiAxs2QGxJR9Ir41gsi7dwXm9+ab9UBLVeKoefgzC4hvvsPjI4XH4T27dB5MzRuEu2+FpJa8W2WRNr5GPG9elHVfM9oBg899BC///u/z9atWzl06BBf+cpX+IVf+AU+9KEP8dnPfhavd25WPj7ykY/wlre8hZ07dy644O7P9dOX7RMncbUndNjnncBhI6LKlZPjmtsqQrs2IlM5UaycGGJT3a+NzkA5QlNzslqJtIwXiamkbJ8bmZECa+ExLZNEMVEV0EOFIUYKIwzlh6omZdMxIwu5QlUhXRXV7lFx7VuolKVLnNqMknO3FYFXEYwwKjodigNVVUcXvRQNp+bEr/nxaB5cmgu35q467FdLMhQHed1i7+k0YavIphY/XqcTtbpIpqGWxXNfqsDnnzxCX7qI16nxkVtXs6Fp6hRe27bpSRbwqHDjhhjrG4OXhBN55bf73L9p5XLcs3iMyW6//XZ27drFF7/4Rd7znvdM/QCJRCKRzC+qCoF6MRo3i8h36qxIO0/3gVkEd0iI7/l0O3f6RHR/1S1iEeDk03DiZ2Jh4ORTYvjqoPMmWHXz9J3d5xJtvMj3s+Wa73LkO9wCTj/cVy79+tOzYnFjnpi24P6lX/olfvCDH/CZz3yGj370owD81V/9Fe985zt53/vex6OPPsrXvvY1rr/++lmd4De/+U327NnDCy+8MK37F4tFisVi9XIqlZrk3jOnP9fP091P43P6xkRpzt2vrRk8N9JT2VZSFSspjJXbKvtjtjKavCQxLZORohDQ50anh/JDJEvJKeuna9O9a0dtpNq5yFJnlisVkVxbhlE1+itHn6u2GGWPgorZn6aKDBGf5sOjefA4PXg0D26HG4fiEH3eFdGSzqk5xzUInIrBTJGXzgwykvKyoT4+Yf/ro/0ZvvjTo2SKBnG/i4/dtpaWyNQLpqZlc2YkS9jr4trOOCvil85CTmWR0qku/u+aaZq88sorshe3RCKRLAVqI99NW4TQTZ2FwSOi3ZhljTqiz2fbWn89XPZO2PQOUe994knhdJ4bhAP/IUbDRui8BVZcu7Atxiqcm3aeH4bTz4gU84XqP84MBHdPTw8vvfQSa9asGXP99ddfz8svv8zdd9/NzTffTKk0dXrrdDlz5gwf+9jH+OEPf4jHM70/4r333ss999wza3MYD5/Dx8rQyjl9DcnSYDxBPZQfYqggLieLySnrOx2KY0x0ujq8Yht2STOyueTcVOJzxXQF27arJRWVaLJDcxBwBvA4PPgcPrwOrxDOas045/Jc/S27E3meOzbESK5IZ3zi/tfPnxjiwZ+fxLBsOuI+Pvr6tYS9U4vIomHSNZKnLeLl2tVx6gLT6BUmWRBke06JRCJZooyp+d4i6r2TXSLyPXJKpHJ7o6LX93xlqtbWe1/5Huh+EY4/Ieq+K/29d39VuJyvuhXiaxaHy7nDNfpZGkWxiFHh1DMXXpd/AUzbpdyyLNTJLGuBn/3sZ9x0002zMjGARx55hHe+851o2uiHYZqmiAKrKsViccxtMH6Eu729fdYcT/cP7md3725WhqXgvhSoTfkeKgwxnB+uiumh/BCJYmJKQe1UnUQ9UeKe+BhBHfeKy0FXUKb3zwGmZY5x0a+MSg0uUM0wqUSWK8Pn8OFz+vA5fLgdblyqC6fmxKW6cGkunKqzul3o7BPbtjk2kGXXiSGKhkVbZPw+5rZt8/19PTyyVxxwrmyP8Ns3duJ2Tn2wyRQN+lIF1jUGuaYzRsC98PVQy5VL3aX7Un//EolkkVDKwmdaxP48px+Pi14QZmYjp8QopkRE2RcXjucLQXZQpJgffwIyfaPXh9uE8O58nUiLXwyc2QW7HxS13hVCLXD7fTN3ni8zJy7lU4ltYFbFNsBtt93Gvn37xlz3/ve/nw0bNnD33XefJ7YB3G43breMvEimh2VbpEvpalT63O10WmY5VIcQ0DWCuiKm4544QVdwwUXZcqKSvl0xCKwV0rWu1pqi4VRHhXTIHcLr8FYj0m5tVEhX6qFdqqiJXip/L8uyOXA2yYunRnA7VNqj4x90DdPi68+d4pljQwC8cVMjv7StbVq110OZIpmiwZUromxtj+ByyMUhiUQikUjmFadH1CLHVkEhJaK1Q0dFbXWyS0S8ffH5def215VTzu+AgVfh2E/hzPNiPi/9P3j5IWi7RkSSGy9bOKO1M7vg6fvPvz7VI3quT6e3+kWyqMMUwWCQzZs3j7nO7/cTj8fPu14iGQ/btskZuQkF9XBheEza8HhUUr7jnnhVSFdEddwTJ+AKyAj1LGDbdjWNu9Ztv2JOVaFiBFgR00FXEJ/TR9AZHBXSmmuMsZhLdS27tHzdtNhzaoRXuhJEfS4ivvFNVTIFg3948iiH+zKoCvzG9hXcsr5hyue3bZuzyQKqAjvW1F0y5miS5cVAboCIJ7Ikau8lEolkWnhCYtSvF1HmZJeo906cEd1KvLF5TjlXoWGTGFe9H049LaLew8eFednpZ0V9+qrXCzM2b2R+5gWi/n33Vye40QYUeOyTsOEtc5pevqgFt0QyHUpm6XwxXbNfMAuTPl5BGSOoa7cxb4yQKyQF9UVi23Y1Cl07Km7dlch01TSsnLId9UQJuAL4HX7cmrsqoGu3y01IT4dcyWDXiWFe603TGPJMmOLdmyrw+R8foT9dxONU+dBNq9ncGp7y+Q3L4sxIjqjXzbWrYrTHLh1zNMnyIatnebbnWXwOH5vrNtPkb1roKUkkEsnsoSijTudNm0XUe+QkDJ+AoWOib7avTkTH5wuXD9a+UYzhE3D8p8LpPNMPr3wT9n0LWrfBmp2iRn2uz68HDgnjtAmxIdUtaro7Xzdn01hygvuJJ55Y6ClI5hnLtkgWkwzlhxgsDFYFdWU/VZraiT7oCo4rqOPeOFF39JIUbbNJtXexKfq/nyembcYYiPkcPgLOAH6Xv1onXSuoPZpnUdRHL0ZGsiWePT7EmeEcbRHvhDXYr/am+IcnjpErmdQFXHz01rW0Rqd2Ii/oJl2JPCtiPq7tjBGX5miSJYpt2xSMAoO5QQZyA6yNrmVDbAMBV2ChpyaRSBY7Lj/8eXKhZzF9NCdEV4rRcqUQkQOvCdM1Uy+7nMeEI/p8EesUY+u74fRzcOzHMHgYul4QI9AAq28TUW/P1MGACyKfmN79amvQ54AlJ7gly5O8kRciOj9YjUxX9ofzwxj25GnfHs0jRPQ4gjruieOazx6GywzLtsYI6WrttG2g2Aq2YuNUnNUUb6/DS4OzAZ/Th9/px+1wV3tHezSR8i3bmF0YPck8zx4bYihTYmXch2OCA+fPDg/wL8+fxrRtVtf7+cgtawhNw4k8ldcZzBbZ2Bzkmo4YPpc8REiWPk3+JizbYt/gPrrT3VxWdxkrwytlmrlEIlmeVFLO69YLIZk4JVLOh4+Dww3+uOi3PV843KJn96qbRdr7sR+L3t6ZflHnve/foe1aWLsT6jfOrsP5dNPX57ifuDybkswLlm2RKCaqQroyKuI6o2cmfbyqqMQ8Meo8dWOEdZ1XXPY5fDIaeoHUiuiSWaqme9vYKLaCoirVllYuzUXYFSboCuJ3+asCulI7XYlQS2aXihP5CyeGKRgmK+M+1HH+v1uWzb/vPsPjh/oB2N4R4/03dEzYj7uW/nSBomFxzcoYW9rCOKbxGIlkqRBwBfA5fQzlh3i6+2lOp0+zKb6JRl+jPHZIJJLliapCqFmMpsvLtd6vidRzo7QwUe9IO1z1Prji10Vt99EfifT308+IEWoTwrvjptlxX6/fKN7jhGnlinArX7nj4l9rEqTglswaRaPIUGGIgfzAGGE93Si13+kXArpGSNd566jz1BF2y17UF4Jt21UBXRHTJbOEaZvYtg0K1ei0U3Pid/oJuUMEnAG8Dm9VSHs0TzXtW9azzy+mZbOvK8FLZxK4tImdyHMlgweeOs7+blFiccfWFt66pXlKMWFZNl2JPF6nxuvW1rG6PiAFiGRZoioq9b56ImaE7nQ3fdk+1kTXsCG2gaAruNDTk0gkkrnD5YP6daJHdrZf1HoPHoHhY6LG218v2ozNFw63SCVfdYuo9T76Izj5c0h1CZOzlx+CjteJWvDIigt/HVUVAn88l3LK5zq3f3bO+3FLwS2ZNrZtk9bTQkjnRqPUgwWxTZfSkz5eUzQRpfbWjRHUldRvr2Pq+lLJWCYS1IZtUGkPXtszOuKOEHQFCbqCVRHtdXirolqmei8uCrrJntMj7O9OEfe7CE+QFj6QLvKFnxzhbLKAS1P5wA0dXN0Rm/L5ddPi9HCOprCHazvjNIXn8WArkSwQTs1Je6idTCnD/oH9nEmd4bK6y1gVXiV/AyUSyfJGVSHYJEbTFpHiPXhY1Hxbpmgt5gnPblr3VMQ6YfvvwtbfhJM/gyOPC+F99HEx6tfD2jdB+3ZQL0C6tm+HG++aoA/3Z+e8JRhIwS05B9MyGSmOjEn7HsgNVIV1ySxN+nifwzc2Ol0ZnjoinoiMjl4AlZTvklWiZJaqglqxFVBEH/BKP+moJ0rIFSLgCuDVvNX66Uqk2nEhP1SSBSFV0Nl1fIhj/VmaI54J66lf7U3x5SeOkS2ZRLxOfv/WNXTU+ad8/kzRoC9VYHVDgO2dMUIeKTQklxYBVwC/089QYYhnzj7DydRJNsU30RpolccqiUSy/HH5oWED1K0T/byHj8HQcRH59oSEw7k2j+eNLh+su12I6/6DcORH0LVLmL8NvAbeqHA3X33bzFuLtW8XTu7f/oC4/O5vi/7g85Q9K8++L0EqbbQGc4MM5AfOq6m2bGvCxyooRNyRsWK6Zvjm04RhmWDZlhDSNYJat3RARLAr6d4u1UXYHa7WUHscQkhXBLVH88i0+2VCX6rAc8eH6E0WWBH3TViD/cRr/Ty06wymbdMR9/GRW9cQnaAfdy1DmSKZosHW9ghbV0RwO+T/G8mliaIo1HnriLgj9OX6ePLMk3SGO9kQ20DcG1/o6UkkEsnco6oQbhWj6XJInIb+V4XZmuoQbcfm8/xeUaDxMjFyw8Jk7eiPRXR637fgwH9A+3VCnNetncHz1pxLrdwxb2IbpOBetuSN/HkR6oq4ThQTkz7WoTqo84wvqGPemHR2vQAqqd7VYZVEyyzbRlVVXKoLl+rC6/DS6Gsk5Arhc/rwODyilrosqmWEenlj2zbHB4U5Wq5k0Bn3o6rnp3UZlsW/vXCGn742AAhztPft6MDlmDwqZ9k23Yk8Tk3hhrV1rGsIjvv8EsmlhkN10BpoJW/kOTJyhO5MN+ui61gXXScXkiUSyaWDNyJG/QZInhEma4kzwmTNHwdPZH7TzX0x2PLLsOmdcOZ5OPIDkQJ/6udixFYL4b3i+qmj8Q4PvO3zYvHANXUm4Gwiz96XMFk9K0R0OVJduz+V67dH81Dvq68K6Xrv6H7YHZbpdDOkUktdEdRFq0jJLAljMkZ7ULs0F3FvnJA7RNAZrArqikGZS3VJw6plylAuzS3fEi6YT/zyM8R9Y02azjVHWxEb/2CQLuj845PHea0vjQK888pWfmFz05T/b3TT4sxIjvqAh+2rYrRGpGeCRHIuXoeXjnAHyWKSl/pf4nRKuJnLNmISieSSwuGC+GqIrRKtxYaOiVTzwcOixttfd2H11BeK5oCOG8QYPg6HH4NTz4g0+Oe+BHv/Bda+QaScz1VP74tACu5FjG3bVVE9kBuoRqgrl3NGbtLHB5yBUSHtE6K6ctnv9EthN0PGE9W6Kdpn2YjU70prrJg3RsQdwevw4nP48DpFlNrr8Mq0b8l55Esmu08Nc7AnRdzvntAc7cxwji89cZTBTAm3Q+V3XreKre2RKZ8/WzToTRVYVe9ne0ecsE8KB4lkMsJuUbozlB/i6bNPczx5nI3xjbK+WyKRXFooSo3J2mbhKD7wKgyfFE7jgQaxnU9iq+C6D8PWd4tU86M/qkk3/w6svAHWvxmiK+d3XpMgBfcCY9s2GT3DYH6Q/lz/mO1AfoC8kZ/08SFXiAZfw5i078pl6fp9YRiWQdEUEerKtlLX7tRGRXWdt46QO4Tf6a9GqSuRanlCJpkuI9kSz58Y4uRQjtawF69r/AWZ3adG+MrPT1AyLOqDbn7/1jXTilLX1mtf0R7B45QLPhLJdKi2EbMi9Of66T/TT0e4gw2xDdR56xZ6ehKJRDK/eMLQslWkmydOw8AhSHaDbUOwAVyB+Z/P5l+EjW+HM8/B4UdFJP7Ek2I0XAYb3gwtV46t314ApOCeB8aLVM9EVEfdUZH27RMR6so27o3j1uZ5VWmZUDEqK5rF6jBtE+yy67fmwq25afA1EHVH8btGRbXP4ZOiWjIrnBnOsevEMMPZEh0xH45xzNEsy+a7L5/l+/t6ANjUHOJ3b1pFwD35z3dtvfaONXWsb5T12hLJheBUnbQGWikYBY4ljtGV7mJNZA1ro2sJuxdf6qJEIpHMKU5Puaf3atFObOA10dc71StSzee7rZjmgI4bxRg8Aq99H87sgv4DYgSbRMS786b5m9M5SME9i+T0HP35fiGqa4T1TER1g6+hWlvd4G0g7o3j0qZ2HZaMj2mZFMxCVVRX6qpVRcWluarO31F3lKAriM/pEyngZXEt078lc4Fl2RzoTrLn9AiWDR1x37glHrmSwT89dYJ93UkA3rCpkV/a1oY2hXCW9doSyezjcXhYGVpJupRm/+B+TqVOsSG2gc5wpzRWk0gklx6qBpEVEG6HTD8MHRU13oN9wuzMF5//yHLdWqj7A8gOwuEfCIfzdC+8+H/hlX+HFTtg7Rvnd05IwT1jCkaBvlwfQ4WhqpgeyA3Qn+8nq2cnfWzEHRkToa5s67x1UlRfJLqlUzRGo9UlqwQ2aKpWTQFv8bcQdocJOAPVNHCf0yc/e8m88+KpYbqGTMJeFzH/+P//zibyfOmnR+lLF3FqCu+9voPrVk3dpihTMOhLF1hd7+caWa8tkcw6QVeQgDNAopjg+d7nOZY4xsb4RlaGVsrjiUQiufRQFAg2itG4SfTy7j8Ig0dFP+/5NlgD8ZpXvhs2vwtOPAGv/bdYFDj6Qzj1NGz7LRGpnyek4J4B9+26j28c+sak96nUVNcK6kpNtTwQXzyV+uq8kadoCtMyEGngldZZjf5Gop4oPoeIVlfEtYxWSxYLh86mWVMfw+ca/yd4z+kRvvL0CYqGRczv4iO3rGZlfOoWFgPpIrmSyZUrolzRHpb9tSWSOUJRFKKeKGF3WBirdT/NscQxNsQ20BZsky0cJRLJpYk3Cm1XQf16GDkBfQeFwZrTKwzWtHkOAjg9om3YmjdC94tw8BGIdMyr2AYpuGdE3CuiS16HlyZ/U1VM14prj2N+/4DLFdMyKZpFkQ5uFClaxWp9dUVYN/ubq8La7/Tjd/plbbVk0dI9PFpW0hbzjiu2Lcvmkb3d/Pf+XgDWNwb50M2rCHomP0BZlk1XIofHqXHTujrWNARkFwLJJc/J5ElMy5zT16gYq0WtKAO5AX7W9TPagm2si66jJdAij0cSieTSxB2Api0QXyvqu/sPwsgp0W4s0CS284mqQvt2iHbAAgRApeCeAb+87pfZXLeZ14ZeY2V48VjNL2Vs26ZklSgYBQqGqLW2bRtFUUQbLaeXukAdMU8Mv0uI6oAzIIW1ZMlgWjYHzyZ58nAfZr4Z23byfPdu3tB5Iw5t9Cc4UzT4p6eOc+BsCoA3bGzkl66aul67qJt0JfI0hz1cuypOY0gu+kkkuqXz8Sc+TtbIcnPbzdzSdgvuOWxd41AdNAeaKZklejI9nM2cZUVoBeui62j0NcoFMIlEcmni9EDDBmGwNnJKmJglukT9d7ARFiJQuQAZSFJwz4BK/a/kwqhErfNGnoJZQLd0sKnWWMe9ceKeuKiPc4k6a5/DJ1PBJUuWXMlgz6kRvvziI7yS+xqaV5if/XDkL/jhQJibYr/DO9ffzumhHP/wpOiv7dJU3rtjJdd2Tl2vnczrDGWLrG8KcnVHbErnconkUuF06jSGbZAupfmv4//FT07/hJvbb+bmtpvxO6cuz7hQXJqL1qBwND+VOkVXuouOUAfrYutkKzGJRHLpojmhbo2IMCfPQP8hEfkG4SLunHtz15xZ4tr9fwPA8xvfMq9ml/LsTDIn6JZejVrnjTyWbaEqKh6Hp5qSH/PEhIGZS0StZY27ZDkxkC7ywslh/mXff/Fy6fOgQW2My9aSPJn8G7qfz3Hg6Ep006Y+4ObDt66mPTr5QcC2bXpTBUzb5pqOGFtaw+O2FJNILlVWR1bz8Nse5q9e+Cue63mOocIQj554lB+f+jE7WnZw64pbiXlic/b6HoeH9mA7OT3H4cRhTqdP0xnuZG107Zy+rkQikSxqNAfEOiGysiy8Dwrhbdsi4r1MOz5IwS25aHRTJ2/kq5Fr27ZFrbXDQ9AVpDPcSdgdrjq7+pw+mQ4uWbbYts2xgSwvnhwmWSjwSv5rQmyfk1GqKOL4csT8F3Tzbi5vjfLBGzvxTxGl1k2LrpE8UZ+LqzuidNTNXbROIlnKuDQX2xq3cWPrjRweOcyPTv2IrkwXT3Q9wc+6f8ZVjVexc8VOWgItczYHn9NHh7ODTCnDoeFDnEqeYlVkFWsia4h4InP2uhKJRLKoUVWIrhQtxVLdMPAqDB0D2xQ13q7lJbyl4JbMCN3UyZt58vqouHaqTrwOLzFvjHpvPSFXiIArQMAZwOvwyto1ySVD0TB5pSvJvq4kbofKqfQBcCSZ6BugKKA4k1yxZpiPXH8N6hTflUzRoC9VoKPOz/aOGNEJWopJJJJRVEVlW+M2rmy4kleHX+Xx049zeOQwL/S+wAu9L7ApvonbVtzG2sjaOTteBVwBAq4AqVKK/YP7OZE8wZrIGlZFVhF2h+fkNSUSiWTRo6oQaYdwGzRsFKnmw8chYywr4S0Ft2RCTMskZ+RE5NooYNnW+eLaHRICu2xkJpFcqiRyJV48OcyxgSwNQTdBj5Mnzw5O67GNsdKUYlu0/DLY2h7hivYIHqf0NpBIZoKiKGyMb2RjfCOnU6f50akf8fLAyxwcOsjBoYOsCK7g9Stez9b6rXPmHRJyiWNmsphkb/9ejiWPsTq8etEI75ye49p/vRaA53/j+XmtcZRIJJcwiiJEd6gVUmdFqvnQMciY5Rrvpf1bJAW3BADLtigYharANi0TTdXwOryE3WGR/uaOEHQFCbqCUlxLJDWcGsry4skRhrJFVsR8OMv11HWeOkhP/fg6z8RmSma55ZfP6eB16+pZUx9AncK5XCKRTM6K0Ao+uOWDDOQG+OmZn/Jcz3OcTp/mqwe+SswT49b2W7mu+bo5O9aF3WFCrhCpUqoqvNeE19AZ6VwUwlsikUgWBEWBcCuEWkYj3kNHyzXe82OuNhdIwX2JUjJL5IwcOT1HySqhoODVvPicPlaEVhB1Rwm5QgRdQZkWLpFMgG5a7O9O8nJXAhWFzrh/zHflpvbt/GdPGFtLnlfDDeL4oZgRbmrfPu7z50sm3ck87REv13TGaJAtvySSWaXeV8+vrP8VfqHzF3iq6yme6n6K4cIwDx95mP8+8d/c0HIDN7XdRNQTnfXXVhRljPB+qf8ljiaPLmjEu7Zv+e6+3exo2SE7hUgkkvmnEvEOtkD9Bug7IFLNUSDUtDDtxC4CKbgvASzbIm/kyenl6LVt4tJc+Bw+WgOt1PtE3XXILVLDpaGZRDI1ybzO7pMjHO1PEw+4CXud593HoTnY4nkPr+hfEOK6RnTbttjeFPvtMf24KwxnSyTyJTa3hNi2MorPJX+uJZK5IugK8uZVb2bnyp3s6t3FT8/8lP5cP4+ffpyfnPkJ2xq2cWv7rawIrZj11z5XeL888DJHE0fpDHeyOrJ6TsT+eDx+6nHu3XVv9fKHf/xhGn2NfHL7J9m5cue8zEEikUjGUKnxDrUKV/O+AzByAhQNQs2wRDocyTO4ZYhu6eR0Eb0uWkURvXZ4CTgDrAqvIuqNVuvIZCsuiWTmnB7K8eKpYQbSRdqiXtyO8yNAlm3zwwN9PLe/FTXwm7gb/xPFmazerpgRbor9Nu9cf/vYx1k23ck8Tk3hhjV1bGgKockUcolkXnBpLm5svZEdLTs4MHiAn575KUcSR3ix70Ve7HuR1eHV3NJ+C5fXXz7ri9O1wjtdSrN/cD/HE8fpiHSwKrxqTvt4P37qce564i5s7DHX9+f6ueuJu7j/lvul6JZIJAtH1dW8DRKnoXef2DpcEGgW7cYWMYt7dpJpUTSKZI0sOT2HYRk4VAc+h4/mQDMNvobqATzgDMjUcInkIqikkL/SJYRzZ51/XLOzTNHgwZ+f4OXy/a6pu4m3bn479+79GLbt5M2t7+ENnTeeF9ku6CbdiTzNYQ/XdMZoDi/NWiWJZKmjKipb6rewpX4LZ9Jn+Onpn7K7fzfHksc4ljxGzBPj5rabub7leryO2f2eKooiDEndQngfHDzI8cRxVoZWsiq8igZfw6wey03L5LO7Pnue2AawsVFQuG/XfdzafqtML5dIJAuLqok+3uF20b+79xWxdfkg0ChuX4RIwb3EsG2bglkgqwuBbdomHs2D3+lnTWQNcW+csDtM2B3GrbkXeroSybIhkSvx4qkRjvdnJkwhBzg2kOH/e/I4w7kSDlXh17ev4Ka1dWSKOTRvDwA3tl1zntiupJCvbwpydUeMwBT9uCUSyfzQHmznPZe9hzvW3MFTXU/x9NmnGS4M852j3+H7J77PtU3XclPbTTT5m2b9tStGpVk9y+GRw5xInqA92M7qyGqa/E2zEmXf07+HvlzfhLfb2PTmetnTv4drmq656NeTSCSSi0ZzQN0aiKwQtd09r8DwMfCEwV8Pi6w8Vp7RzYCcnuPXv//rAPzNzX8zL4K24h6e1bPkjBw2Nh7NQ9AVpCPUQcwbq7qHO9XxBYBEIrlwbNvm5FCO3SdHGM4VaYv6cDnO/yGvpJB/56VuTNumMejm925ezYrY5K0sLMvmbDKPpirsWB1nQ1MIh7a4DhQSiUQ4i7919Vt5Y8cbeaH3BZ7sepKebA9PdQuztY2xjdzUdhOb4ptmPd3c7/Tjd/rJG3lOJk9yMnWS1kArayJraA40X9TxfyA3MKv3k0gkknnD4YKGDSLdfOioiHgPHhGi2xtlXMfaBUAK7kVGxeAsq2fJG3ls28bn8BF0BVkbXUvUE60KbGluJpHMLQXdZF93kn1dCZyaep4LeYV0QefBn5/klW6RQr69I8ZvXbcSr2vy1KZKCnlT2MPVHTFaIzKFXCJZ7Lg0Fze03sCOlh0cHjnMk11Psn9wP4eGD3Fo+BB13jpe1/o6rmu+btb7WHsdXtpD7RTNImczZ+lKd9Hga2BtdC1twbYLCgTU++pn9X4SiUQy7zi90LQFop3Q/yr07YehIxBoAk9ooWcnBfdCY9t2VWDnjFxVYIfcIdZF1xHzxIh4IgSdQVl/LZHMIwPpIrtPDXNqKEdD0E3QM34E6dXeFP/81AkSeX1MCvlU31eRQq7LFHLJsqK7u5u7776bRx99lHw+z7p16/jKV77CVVddtdBTm3UURWF9bD3rY+sZzA/ys66f8VzPcwzmB0W6+fHvc03TNbyu7XW0Blpn9bXdmpu2YBu6qTNUGOKprqeIeWKsiaxhRWgFAVdg2s+1rWEbjb5G+nP949ZxKyg0+hrZ1rBtNt+CRCKRzD7uALRfDfFVwtF84DXIDkCoGbMmUDnfbQ/lGd48c24NtoWFV/MSdodZG11L3BMn7AlLgS2RLBCWZXOkP8OeUyNkSzorY75xU7wty+Y/XznLf+3rwbahKezh925aRXt06ohWVyJP1Kdyw+o4G5qlC7lkeTAyMsINN9zArbfeyqOPPkpDQwPHjh0jEoks9NTmnDpvHb+49hd5y6q38GLvi9V085+f/Tk/P/tzVoVX8brW17G1YSsOdfZOvZyakyZ/E6ZlMlIc4fne5zk4fJBV4VWsDK0k5olNeS6hqRqf3P5J7nrirvNuUxCPvXv73dIwTSKRLB18Meh8HdStg95XePzED7h34OnqzfPd9lAK7nmgZJbI6Blyeg7d0vE4PASdQVaFVxH3xmWKuESySMgUDV46PcKrPSkCbicd8fGjRMPZEv/89HEO92UAuGF1nN/YvgK3c3onpLGAk9evb5Qu5JJlxX333Ud7ezsPPvhg9bqOjo6Fm9AC4Nbc1XTzo4mjPNX9FC8PvMzx5HGOJ4/zH0f+g+taruOGlhuIe+Oz9rqaqlHnrSPuiVd7eR8eOUx7sJ3OcCeNvsZJBfPOlTu5/5b7uXfXvfTn+qvXN/oauXv73bIlmEQiWZoEG3l8yOaunh+cl78zn20PpeCeA0zLJKNnyOgZdFPHqTqrNdj1vnqibtEHW64WSySLhzPDOXafGqE3VaA17J2w/vql0yN89ZmTZEsmbofKb123kutWTX3iPJQrVfdft7Zeim3JsuN73/seb3rTm/jlX/5lnnzySVpbW/nwhz/M7/zO7yz01OYdRVFYG13L2uhaksWkiHR3/5xUKcWPTv2Ix089zqb4Jm5svXFWTdYqvbzD7jBZPVsV+o2+RtZE1tASaMHj8Iz72J0rd3Jt07Xs+OYOAP7htn+Y15RLiUQimW1My+SzL/zVOMUy89v2UAruWaBidJYpZcibeVRUAs4A7cF2mvxNxDwxwu6wdBGXSBYhRcPkQHeKfd1JbNtmVdyPOk6Kd8mw+PcXz/DEYeHU2xH38TuvW0VjaPyT1wqGZdGdEAaIFfyyXluyDDl+/Dhf/vKXueuuu/jTP/1Tdu3axZ133onb7eY973nPuI8pFosUi8Xq5VQqNV/TnTfC7jBv7nwzb1r5JvYN7uPp7qd5beQ1Dgwd4MDQAaLuKDtadnB9y/WE3eFZe92Ks3nJLDGUH+Js9ixRV5TVkdW0BduIeCLnPab2hPOqxquk2JZIJEuaxdL2UJ71XSAls0S2lCWjZ7Cw8Gk+Ip4ImwObiXliRD3RCVeRJRLJ4qDWGK0+4CY0QW/trpEcDzx1nLOJAgBvuqyRd25tnbJ9V6Zo0Jcq0B7zcXVHC7/zun2z/h4kksWCZVlcffXVfOYznwHgyiuv5MCBA3z5y1+eUHDfe++93HPPPXM2J03RGMwPErWj+J3+BS3d0lSNrQ1b2dqwlf5cPz/v/jnP9TzHSHGE75/4Po+efJTN8c3saNnBxvjGWZurS3PRHGjGtEwSxQQv9L3AwaGDtIfa6Qh10OBrqAprn9PHvvfK3ymJRLI8WCxtD6XgvkAGc4PU+erYFNok0sQ9UWl0JpEsEQzT4rW+NC+fSZArGayI+XCOI55t2+bHr/bz7d1dGJZNyOPgAzd0srl18iiUbdv0pYuUDIut7RGuaI/gmWZ9t0SyVGlubmbTpk1jrtu4cSMPP/zwhI/5kz/5E+66a9SsK5VK0d7ePivz8Tv9XNV4FWfSZ+jL9jGYH8SpOgm7wwScgQU9Xjf4Gnjn2nfy1lVvZe/AXp7ufprjyeO8MvgKrwy+QtQd5bqW67i++XqinuisvKamasS9ceLeOOlSmiMjRziaOEqDr4HV4dW0BFpmvY2ZRCKRLCSLpe2hFNwXyM6OnTT5m2SauESyxEjmdPacHuFIf5qwZ2JjtGRe58FnTrC/W6S4Xt4a5n07OiaMglcoGRZdiRxRn4vrV8dZVTd+726JZLlxww038Nprr4257vDhw6xcuXLCx7jdbtzumfeOng6KotAR7qAj3EGmlKE/18+ZzBn6s/2LRnw7NSfXNF3DNU3X0JPt4Zmzz7CrZxcjxREePfEoj514jI3xjVzffD2b6zbPmsN50BUk6ApSMksMF4Z5KvMUYVeYjnAH7cF24t64NHKVSCRLnsXS9lAK7gsk7olLsS2RLCEsy+b4YJaXTo8wkivRGvZO6Cq+90yCrz17knTBwKkp/PJV7dy6vn7Kk/JErsRwtsSqhgBXr4wS8bnm4q1IJIuSj3/84+zYsYPPfOYz/Mqv/Aq7du3igQce4IEHHljoqRFwBQi4AqyKrCJdSjOQG6iK76H8EA7VQdgdXtC082Z/M+9a+y7evurtvDzwMs+cfYYjiSMcHDrIwaGDBJwBtjdt57qW62j2N8/Ka7o0F03+JizbIllMsm9wH68Ov0qTv4mOcAfN/ma8DmnwKJFIliaLpe2hYtc6+SxDUqkU4XCYZDJJKBS6qOfK6Tmu/ddrAXj+N56XqVcSyRIhXdB5+UyC1/rSeBwaDUH3uOK5qJv8++4uniwbo7VFvfzOjatojU5+wmlZNmeTeTRVYUtrmMtaw+OmqEskUzGbx6yF4L/+67/4kz/5E44cOUJnZyd33XXXjFzK5/v914rvgewAaT1djXwvdM03iLrCZ3ue5fme50mVRg3lOkIdXNd8Hdsat826IM4beUYKI5SsEmFXmM5wJ62BVhn1lkgkS5bHTz1+XtvDJl/TRbU9nMnxSgruGZAupmW7DIlkCWHbNieHcrx0eoSBdJGWSdp9HR/M8JWnTtCXFo7Jb9rUyDuubJ1SOOdKBmeTBVrCHq7qiNEakdEgyYWz1AX3xbKQ7z9dSjOQH6A73U1fro9MKYOmaoRdYQKuwIKKTdMyOTR8iGfPPsv+of1YtgWAU3VyRf0VXNt8Leui62Z1jpZtkSgmSJVSuFQRCe8IddDkb5IBB4lEsuSYbR0nBXcNs3XwHm9lpNHXyCe3f3LOm6VLJJKZky0avNKV4NXeNJqi0BT2oI4T1TYsi++/0sP39/Vg2RD1OfnADZ1sbJ7898K2bfrTRQq6yYbmEFeuiOBzySodycUhBffieP+ZUoaB/ABnM2fpyfaQ1bOoqITcIQLOwIIutqdKKV7ofYHnep6jN9tbvT7qjnJ109Vc23Qtjf7GWX3NStS7aBYJu8KsCK2gLdhGnbdu1urKJRKJZC6Z7UxlKbhrmI2D9+OnHueuJ+46r9i+kvt//y33S9EtkSwSbNvm9HCOl04n6E0VaAp5CEzQ97o3WeCfnz7OyaEcANs7Yrz72hVT9smuGKOFvS6uWhlhVV1g3N7dEslMWSyCc6FYjO8/p+dGxXemh5SeQlM0As4AIVdowcS3bducTp/m+Z7nebHvRfJGvnrbytBKtjdt56rGq/A7/bP2mpZtkSqlSBaTqIpK3BNnVWQVTb6mcft6SyQSyWJBCu455GIP3qZl8qaH3zRh0/SKu91j73pMppdLJAtMrmSwryvJwbMpVFWhOeQZVwhbts1PX+3n4T3dlEwLn0vjN69dyfbO2JSvMZIrMVI2RrtqRZSoXxqjSWaPxSg455PF/v7zRp7B3CC9uV660l2kS2lsbIJO4frt1BbGTFU3dfYP7ef5nuc5NHyomnKuKRqb4pvY3rSdy+oum1Wz15JZIlFMkNWz+Bw+mgJNrAiuoNHXKFPOJRLJomMhBbfMA5qCPf17JhTbADY2vble9vTv4Zqma+ZxZhKJpEJtVLsvVaBxkqj2UKbIg8+c5NXeNAAbm4O8f0cnsSmEs2FZnE3kcTpUrl8dZ0NzSBqjSSSXGF6Hl/ZQO+2hdi6vv5zB/CD92X7OpM/Qm+vFtE38Dj8hdwi3NjftzsbDqTm5suFKrmy4klQpxYu9L/JC7wt0ZbrYN7iPfYP78Dq8bK3fyjVN17A6svqi671dmosGXwMAWT3LmdQZTiRPEHKGaA+10xpopd5bv2CLEBKJRLJYkIJ7CgZyA7N6P4lEMrtkKrXaPSk0VaUz7h83qm3bNs8cG+KbL5whr5u4HCq/tK2NW9bXj1vbXUu6oNOfLtIW8bKtI0pzWBqjSSSXOm7NTWugldZAK5vrNjNUGBK9vtNnGMwPUjJLeB1ewu7wvLbWCrlCvH7F63n9itfTk+lhV+8uXux7kUQxwbM9z/Jsz7NE3BGuaryKqxqvoi3QdtF9yP1OP36nv5pyfnDoIIeGDhH1RFkZWkmTv4m4Jy4zASUSySWJFNxTUO+rn9X7SSSS2cGybE4N59h7OkF/WtRqT1R7nciV+Ppzp3ilKwnA6no/H7ihk8aQZ/LXsG16kwVMy+bKFVEubwvjmaB3t0QiuXRxak6a/E00+Zu4LH4Zw4VhBvODnE6fZqQwQl+2D5fmIugKzmu7seZAM3esuYO3rX4bxxLHeKH3BfYO7CVRTPDj0z/mx6d/TKOvsSq+KxHrC0VVVCLuCBF3BN3SSRaT7O7bjUt1EffGRcq5v5GoJypbjEkkkksGKbinYFvDNhp9jfTn+s8zTYPRGu5tDdsWYHYSyaVJMq+zryvBa70ZnJpCZ51/3Ci1bds8d2KYh3adJlcycagKd2xt4U2bmqY0OcuXTM4m8zQEPWxbGWFFzHfRUSCJRLL80VSNel899b561sfWkywmGcwP0p3pZiA3wFB+CIfqIOgKzpvjuaqorI2uZW10Lb+87pc5MHSA3X272T+0n75cH/994r/57xP/TXuwnW0N29jWsI2Yd2pPi8lwqk7qvHXUeesomkWSxSTP9z6PR/MQ98ZZGVpJva+eqDsqf1slEsmyRgruKdBUjU9u/yR3PXHXebdVXMrv3n63TJOSLCpyJYNNn/oBAAf/95uWTbsq07I5PpBh75kEw7kSzSHPhO8tmdf5f8+dYu+ZBAAdcR/vv6Fzyj7Z1XZfhsllLSGuaI8Q9MgaRIlEMnNURSXqiRL1RFkbXUu6lGYwP0hvtpeeTA/dmW5sbALOAEFXEJc29yaMTs3J1oatbG3YSt7I88rAK+zu281rI69xJn2GM+kzfPfYd+kMdXJl45Vsrd9K1BO9qNd0a+5q9Dxv5BkuDHM2cxaPw1ONfDf4Goi4I1J8SySSZcfyOAufY3au3Mn9t9w/bh/uu7ffLVuCSSTzwFCmyCtdSY72p/G5HKJWe6Ko9vFhHnpBRLU1VeHtV7Rw+2VNaFNEtYu6SXcyT9Tn4tpVcVbVjV8PLpFIFjez7UY7WwRdws28M6ViT88AAE/ISURBVNxJ3sgzlBd135Xot27peB1eQu7QvNR9ex1erm2+lmubryVdSvPywMvs6dvD0cRRTqROcCJ1gv848h+sCq/iyoYruaL+iosW316Ht/recnqOwfwgXekuvA5vVXzXeetk2rlEIlk2SME9TXau3Mm1Tdey45s7APiH2/6BHS07ZGRbIpljSobF4b4U+7pSZIoGLWEv7gnqqEdyJf5fTa32ipiP99/QQXt08pNt27YZzJTIlAzWNQbZ2h4h4pPtviQSydzhdXhpC7bRFmxjS/0WhvOi7rsr01Wt+3Zqzmrq+VyLz6AryI2tN3Jj640ki0n2Duzlpb6XOJ48Xh0PH3mYjlCHiJDXbyXujV/Ua/qcvupiSE7PMZQfoivdhcfhIeaJ0R5sp95bT8wTk+dbEolkySIF9wyo/bG/qvEq+eMvkcwxZxN5XulKcHooR8TnorPOP+79bNvm6aOD/PuLXeR1Uav9titaeNNljTjUyU9Si4bJ2USBoMfB69bWsbYhOGUkXCKRSGYTp+qk0d9Io7+RjfGNJItJhvJDnM2eFc7nhTMoKNXU87lutRV2h7m57WZubruZRDHB3v697O3fy/HkcU6mTnIydZJHjj5Ce7CdK+qvYGv9Vhr9jRf1mrXiO2/kSRQS9GR6cKpOIp4IbcE2GrwNxL3xeUm9l0gkktlCCm6JRLLoyBYNDnQnOdSbxrQs2mO+CXteD6SLfO3Z0b7anXV+3rejY8pabRBp6smCzqr6ANtWRKfsxS2RSCRzTW3d95rommrkty/Xx9nMWfpyfRiWgcfhIeQSqedzWfcccUe4pf0Wbmm/hWQxycsDL7O3fy9HE0erNd//dfy/aPI1cXn95Vxefzkrgisuak61aedFs0iqmOKlvpdQVZWQM0RLsIVGXyNxT5yAKzBbb1UikSxDbNsmUUzQn+vn/lvux6W55r3MSApuiWQZYlqjjvq7TgzzurX1SyJqa1k2J4ayvHwmwUC6SEPQPaFhmWXZPP5qH4/sPUvJsHBpKndsbeENGxunrLsuGRZnE3n8bgc3rKljXWNwQkEvkUgkC0kl8tseake39DGp54lCgr5cHw7VQcgVmnPX87A7zE1tN3FT202kS2n2De5jb/9eDo8cpjfXS++pXn546odE3BG21G3h8vrLWRNZg0O98NNNt+YWru/UY1gG6VKaV4de5eDgQQKuAHXeOloCLcQ9cSLuiMw+lEgkWLZFophgIDfA6fRphvJD5I08lm3R5G+a9/lIwS2RLDMe29/Dp793oHr5fQ++QHPYw6fftonbNzcv4MwmZzBTZH93kmP9GdwObcJWXwBnhnN87dmTnBzKAbC+Mch7rl85ZV9tqIlq1/nZuiJKXcA9q+9DIpFI5ora1PNN8U2kSimG8kP0ZHvoy/bRnenGsi38Tj9BVxCPY+rfxAsl6Aqyo2UHO1p2kNNzHBw6yCuDr3Bg6ACJYoKnup/iqe6n8GgeNsU3saVuC5vimy4qsuRQHdXov2VbZPUsZzNnOZE8gUfzEHKHaA20UuetI+aJLRqzPIlEMveYlslIcaQqsocLwxSMAh6Hh7ArTJO/icH84ILMTQpuiWQZ8dj+Hv7HN/ac1zG+N1ngf3xjD1/+zW2LTnQXdJNXe1Ic7EmRLZo0hz14JjBFKxkW//XKWX5woA/TtvE6NX7pqjZet7ZuQnFe+9juZA6/y8ENq+tY1ySj2hKJZOmiKAphd5iwO8yqyCoKRoHhwjAD+QG6092MFEYomkVhvOYM4nf65yz663P6uLrpaq5uuhrd1Hlt5DVeGXiF/UP7SZfS7Onfw57+PaiKyurwajbXbWZz3eZqq7ALQVXUqus7QNEokiql2DuwFxUVv9NPva+eJn8TMU+MiDtyUZF2iUSy+NBNnaGC6PbQle5ipDhCySzhc/iIuCN4/XPf7WE6yF8eiWSZYFo29/znwfPENoANKMA9/3mQN2yauj3WfGBZNqeHc7zSlaAnWSDmd9FZN3E05lBPim88d4q+dBGAbSsi/Mb2FdNyE6+Nal/RHqU+KKPaEolkeeFxeGgJtNASaGFL3RZGCiMMF4bpyfYwkBsQ0W8s/I65jX47NWdVUFu2xanUKfYN7mP/4H56sj0cSRzhSOII3zn6Heq99Wyu28xl8ctYHVl9cannDjf1DpF6blomWT1LV7qL44njuDQXQVeQZn9zteVYyBWSPb8lkiVIVs9WfS26092k9TSWbeFz+Kjz1uHWFt853qIW3Pfeey//8R//wauvvorX62XHjh3cd999rF+/fqGnJpEsOnadGKYnWZjwdhvoSRbYdWKY61dfXCuXi2U4W+KVrgTHB7JoisLKuG9CN/F0QeffX+zi2eNDAES8Tt597QquXDF1L9iKA3lA1mpLJJJLCFVRiXvjxL1x1kbXktNzDBdE7Xd3ZjT67VAd1bZjcxH9VhWVznAnneFO3r767QzmB9k/uJ99g/s4ljjGQH6An575KT8981Pcmpv10fVsim9iU3zTRfX71lSNkDtEyB0ChPFappTh4NBBLCx8mo+QO0RzoJmYJ0bUHcXv9EsBLpEsQkzLJFFMMFQYoifTw0B+gEwpg6Zq+J1+mvxNONW57dxwsSxqwf3kk0/ykY98hGuuuQbDMPif//N/8sY3vpGDBw/i94/fHkgiuVTpT08sti/kfnNBQTc53Jdmf3eSTNGgOeTF6xr/JM+2bZ45NsS3dneRKRoowC3r63nnla34XJP/dFX6aqeLBqvq/VzZHiEua7UlkksG0zKr+7v7drOjZcclbaZVMV5rC7axpW4LiWKC4cIwfdk++nP91dpvn9NHwBmYM+fzOm9d1fE8b+R5bfg1Dgwd4MDQAdKlNK8MvsIrg68A0OxvZlN8ExtjG1kVWXVRJ9RuzY3b6ybujWPbNnkjT6qUorevF0VR8Dv8hD1hmn3NRL1RIu4Ifqc8z5RIForaRcKzmbMki0mKZrGarRILxVCVpRNAWdSC+7HHHhtz+cEHH6ShoYHdu3dz0003LdCsJJLFSUNweumB073fbGJZNieHsuzrTtKbLBD1uVhVN3Erl7OJPN94/hSH+zIAtEa8vOf6layun7r9S0E3OZvME/a6uHldPavr/ThkVFsiuWR4/NTj3Lvr3urlD//4wzT6Gvnk9k+yc+XOBZzZ4kBTtTHR77yRZ6QwwlB+iO5MN4niqPN5wBkg4AzMSd9vr8PL1oatbG3YimVbdKW7ODh0kANDBziVOkVPtoeebA8/Pv1jXJqLtZG1bIxtZENsAw2+hgteEFAUZUzP74r52lB+iLOZs2CD3+Un7BYCPOwJywi4RDLH6JZOoiAWAnuzvQzkB8jqWWxs/A4/UU90Tk0g55pFLbjPJZlMAhCLxSa8T7FYpFgsVi+nUqk5n5dEshjY3hmjOeyhN1kYt45bAZrCHrZ3Tvz9mQv60wX2d6U4MZjBqal0xP0T1pAXDZPv7+sRpmiWjUtTedsVzbxhU+OEKecVLNtmIF0kr5usawyytT0yrfpuiUSyfHj81OPc9cRd2Of8Cvbn+rnribu4/5b7peg+B6/DizfgpSXQwmV1l5EqphguDtOf7ac321vt++12uAk4A/id/lmPLKmKyorQClaEVnB75+1k9SyvDr/KwaGDHBo+RLqUrkbCAaLuKBtiG1gfW8+66LqqcdqFvnat+VqtAO9Od6MoCl6Hl5ArRJO/qVr/HXKFLumsCYnkYrBsi2QxyUhxhMH8ID2ZHjKlDCWrhFtzE3AFiLqjy+Y7pti2Pd65+aLDtm3uuOMORkZGeOqppya835//+Z9zzz33nHd9MpkkFArN5RQlkgWn4lIOjDndrMjb+XQpTxd0Xu1N82pvioJu0hzyTug+DvByV4KHdp1mMFMC4PK2ML+xfcW02nZliwa9qQJ1ATdXtEdYVeefshe3RLIYSaVShMPhS/aYdTHv37RM3vTwm+jL9Y17u4JCo6+Rx9712LI5iZtrdFNnuDDMSHGEs5mzDBeGx0SdAq4AHs0zp5Ffy7Y4mznLq8Ovcmj4EMcTxzFsY8x92gJtrIuuY11sHWvCa3A7Zq+EyLIt8kaerJ4lb+QBkaLud/qp99YT98aFAHeH8DoWhyOyRLLYsGyLdCk9xswxVUpRMAo4FAd+l5+AM4BLm9tAyWB+EK/Dy1tWveWin2smx6slI7g/8pGP8P3vf5+nn36atra2Ce83XoS7vb39kj15kVx6VPpw96VGvwfz2Ye7ZFgcH8ywryvJULZEfcBN2DtxOuJAusg3XzjNy10igyXqc/Ib21ewtT0y5Umcadn0pgqYlsWG5hBbWsMEPYvbOEMimQwpuC/8/b/Q+wIf+MEHprzf/33T/+WapmsudIqXNFk9y3BhuJp+XTlh1hRt3k6YS2aJo4mjvDb8Gq+OvCrSwGtQFZWOUAfroutYG11LZ6hzVlPibdumYBbI63myRhbTMtFUDZ/DR9gdptHXSMgdqkbNF7uZk0QyF5iWSaqUIlFMMFIYoTfbS6qUomgWURBlHX6nf84X7M5loQT3kkgp/+hHP8r3vvc9fvazn00qtgHcbjdutzRHkly63L65mRvW1LHlz38IwFfffw2vW1s/563ALMumayTP/u4kXYkcQbdTRJon+CHVTYsfHOjl+/t60E0bTVF4w6ZG3np586SR8ArJvM5gpkhz2MPW9ijtsbkx+ZFIJEuDgdzArN5Pcj5+px+/0097sJ3L6y+vpp8P5Aboy/YxkBtAt3ScmrOafj7bva9dmqvqZA6QKqU4PHyYwyOHeW3kNYYLwxxPHud48jiPnXwMh+qgM9TJmsga1kbXsjK08qIWBSop5l6HlxiiRMuwDHJGjsH8IF2ZLgDcqhuvw0vcG6fOW0fAFSDkCs3JZyKRLDQls0SymCRZTDJcFIaMGT1D0SiiqRoezUPYHZ53gb1YWNTfeNu2+ehHP8p3vvMdnnjiCTo7Oxd6ShLJkqBWXG/vjM252O5PFTjYk+L4QBZVgfaob9L2W690JXjohTMMlHtqr2sM8JvXrqQlMnU6nm5anE3mcWkq13TE2NgcmtDpXCKRXDrU++pn9X6SyVEVlYgnQsQTYVV4Fbqli5Ptgqj/7s/105PtwbTMak2mz+Gb9XT+kCvE1U1Xc3XT1YCIYB0eOcyRkSMcHjlMqpSq9v5+9OSjOBQHK0MrWR1ZzZrIGjrDnRdtxuRQHdW6bhDnryWzRM7IcSZ9hmPJYwB4NI8Q6p4YcW+coDNIwBUg4ArISLhkyWDZFhk9Q6qYIlVKMZAbYLgwTE7PoVt6NeMj6o7i9rkvSYF9LotacH/kIx/hX//1X/nud79LMBikt7cXgHA4jNcr62QkkoUmmdd5tSfF4b40BWPqOu1z08fDXie/fFUb13bGpvxBtm2boWyJVEFnZdzPFW0RmsJL17FSIpHMLtsattHoa6Q/13+eaRqM1nBva9i2ALNb/jhVJ3XeOuq8dayLrqNoFhkpjJAoJqr13yOFESwsPJqnGi2fbQO2yhx2tOzAtm36c/0cSRzhaOIoR0aOkCqlOJY8xrHkMX546ocoKLQF21gdXs2qyCpWhVcRdocvag6KouB2uHE73EQR/cQt26JoFskb+VERboPb4careQl7wsQ98WpfdL/TP2ft2SSS6WLbNjkjR7qUJl1KM1wQGS05PUfezGNj41bd+Jw+GnwNc9LRYDmwqGu4J/qRefDBB3nf+943ree41OvhJJcmuZLBpk/9AICD//tNU/atnin5ksnR/jQHzqZI5nUagu5Ja6cLusl/7+/hhwf6MCyRPr5zUwNvu7xlWunj+VK51ZfPyeWtEdY2BiaNoEskS5VL/Zh1se9/IpdypWwdKV3KF46cnqvWc57NniVZSJI1sti2jdfhJeAS/b/nsreubdsM5Ac4ljjG0cRRjiWOMVQYOu9+dZ46OsOd1dESaJmTeVUi4XkzT8EoUDSL2LaNQ3XgcXjwOXzEvXHC7jB+h3+07nUJt0eSLF4s2yKn58joGdKlNIlioiquc2YOy7bQFA2vw4vP4cPj8CypXtgga7jHZRGvBUgklyQlw+LkUJb93UkG0kUiXlGnPdHimG3bPH9imG/v7iKR1wHY1Bzi17e30xyeOktl1BTNZmNzkMvbZKsviUQyMTtX7uT+W+7n3l330p/rr17f6Gvk7u13S7G9gFR6X7cEWtgU30RWz44V4MUkA/kBsKkKy9kW4Iqi0OBroMHXwPUt1///7d15lBzlYS78p6p635eZ7lk1WpGEhAzIbCKAFxnjgI0PnC/E5iNxjE+MiR0SkhyDk2uwkxh8fINJ4ouNY0fHPjc3EG+fieMLgQDCRNjCEsLCsgTakDSafXp6r/39/qjpmhmtM63pnhnN8zunT/dU91RXvWrN20+9GwAgp+ZwMH8QB8YO4GD+II6XjmNYHcawOoxXB14F4MxK3hPrwbLYMiyNL0VPrOecliKbfDy1lnBMmn7IsA1opoaKWcFobhSm7czK7lW8CCpBhLwhd3mysNcJ4gs1ANHc0CwNZaOMsl5GySghp+UwUh1B1XQu/tjCdsdeBz1BJAPnzxJdc2Fet3DPhsXeWkA0Gyxb4MhoBXt68+jNVxHyeZCJ+M+49Nah4TKeePUIDgyVAQAtER9ue2f3tGYfB4Cxio6Rko62RADv6EpgSSrEpb7ovLfY66zZOv+iVsSmJzYBAB5772PY1LGJXxbnMSEEykYZOS2HMXUMx8vHUdAKqJgVCCEQ8DSuC/qJqmYVh/OHcSh/CIfyh3C4cBiqpZ70unQgjZ5YD3piPVgaW4quaFdDZ2gXQsCwDaiWCs3UoFkaLGFBQMAreeFXnOAe98WRCCQQ8jgXOGoTvPkVjqVdjFRTRcWsoGJUUDbKKOpFjKgjKOtlqJYK3dIhSZLbch3wBBBQAuft30u2cBPRvCOEwPG8ij3H8zgyUoFHls86IdpYRccPdvbilYNONz2fR8aNF7Xj+guz0+oGrhkWjheqCHoVXL4shTWcFI2IZmjyl8WN2Y3n7ZfH84UkSe7kYd3RbqxvWe+2gI+pY+ir9CGv5t0x4LV1sMOe8Kz/2wY9QaxNr8Xa9FoATjfb/nK/G74P5Q9hoDKAEXUEI+oIdg7uBOBMItcWbkNPtAdLYkvQHe1GR6Rj1iZDkyQJPsXnhPoTcr1hGdAsDbqlo7fUi0OFQxBCQMLE7/gVv7teeMgbQlAJIugNIqAE4Pf4OWnbAmZYBipmBVWz6t4KWgE5NYeqWYVmadBsDRDO30a/4kdACSDtS8Mn+3ghpgkYuInoJEIIDBY1/KavgENDZQgItMUC8J9hvLVmWnh2zwD+7xv90EwbAHDV8jRuubQTyWl0A7dtgcGShqpuYllrBBu64shEOU6NiGixmRzAu6JdWCfWoWJWkNfyGNPG0F/ud7qia8dh2iZ8is/pWu0JzXorsyzJ6Ih0oCPSgas7rwbgtIK/XXh7yq2gF3C8dBzHS8fxSt8rE78b7kBXtAvd0W43hPuVqcvXapaGP9/65wCA/3nd/zzp+bPxKt5TTlZlCxuGbUC3dGiWNiWMA87s6j7FB6/sRdATdNcOr7Vy+hU//IofPsXH7upzyLRNd8I9zdKgmipUU0VBLyCv5VE1q86/sa1B2AICzjwAtV4PYV940QZrIQRG1BEcLR7FseIxHMwfRCqQmpUW7plg4CaiKYZLGvb1FXFgqATNstAWDZ6xhdkeH6f9w53HkKs447RXtIZx22XdWN4SmdZ75qsGhkoaMlE/rlyewrKWSMOXMiMiooVBkiS3S3ltDHjVrLrr/g5WBjFcHXbWARcGFElxu1Q3Yt3foCeINak1WJNa424b08bwduFtHCkcwdHiURwtHkXJKOFY6RiOlY7h530/d84FElpDreiKdKEz0onOaCdag41Zqk6WZDc0n4phGzAsA4ZtuDNQG7bhtI5LEmRJhkf2wCt73VBe+3cIeAJO67nsm3LvVbxsLZ+m2gWRWu+E2oUR3dJRNasoGSWU9BJUU3UvnBjCgCQkQBq/YDJe7jF/DD7Zt6h78+iWjv5yP3pLvVNuVbM65XUJf6Lpx8bATUQAgFxZx5sDRbw5WERVt5CJBhDxn3liszcHivi3Xx7F4ZEKACAV9uHWSzpx+TSW+QKcVvH+ggqfIuOdPUmsbY8h7OefJSIiOrPa2OS2cBtWp1bDsAzkdSeAj6gjGCgPOGHccibPCygBd3KxRoSShD+BRGsC72h9BwCnZS2n5nCkeATHSsfcFraCXsBgxVmnvNYdfbIf7/8xuqJdaA+3oz3c3tAZyWtB+nQs24Jpm04wtw2MaWMYrg7DsJ2L67XVABRJcYK55IUiK1NmWa+NH/fIHieMS154ZM+UmyIp8MrO7y7EVnQhBCxhwRJOedXKbHLZGZbzc9WsomJWnFZqS3W3124uaeLfx6t4EfKGkPAn4JE9i7KlejJb2BipjqCv3Ie+ch96S704Xjp+2iUhPZIH7ZF2dEW6kAwksTS2tOnHzG+2RItcvmLgrcEi3hwooqiaaI340R47c9Duz6v4/s5j2HV0DADgHx+nvXltFj7P2StL2xYYKKpQDQvLWsLY0JVAJsbu40REVB+vMrEO+AqsgGVbKOpFFPQCcloOg5VB5LU8cloOtm3DI3vcAN6ICcUkSUIqmEIqmMLFmYvd7QWtgN5SL46VjjktcMVeDFYGYcMZivWz3p9N2U8qkEJbuM0N4G3hNmRD2aYsDabIijPmF2fu4l4L5qZwQmOthXbIHoIlLNjCdoNQbYk+RVLcmyzLzv2kFvXJ3d1r2xRZgQwZsuTcFEkBJLjbJDgtvxKkiZ8nkSTJ7U5fOx4BAVvYgJh4bMOGEOOPJ92mBGjbgGmZ0G0duq3Dtm03dNvChmVPPIYEQGCi14DkcS9M+BQfQt4QPJKHYfoEtrAxqo6iv9yP/nI/+sp97mPd1k/5O2Fv2B3G0RnpRFe0C9lQFh7Ziby1SdOajYGbaJHKVw0cGCxhX38RBdVAS8SPTOuZK/BC1cC//+o4tr45BFsAsgRcs6oVH3pHB+LB6XUhG6voGCnryEQDuGpFC5a1hNl9nIiIZpUiK0gEEkgEEliCJQCctcBr415H1BEMV4aR03LQLefLu1/xuyG89gV9tsX8zsRltUnZAKBklHD/z+4HAFzbeS0GK4POTO16AaPqKEbVUewZ2TNlPwl/AtlQFtlwFplQxnkcyiLhn95KILNpusG8ZnKLcC2c2sIJrFWzioqouM/Vwrot7Ek7gBtiheRMDlfbJoRwn6s5sTymLNA0KQxP7F643bbd9xpXC/snBn9Zlp0u3bWLCJK8YFvsm00zNQxWBzFQHsBgZRADlQEMVJzHtd4UJ/LIHrSF2tAeaUdHuAOdkU50RDoQ88Xm5UULBm6iRaYWtN8cKCJfNZAO+864ljYAqIaF/9wzgGd+PTEh2ju64rj10i50JKZ3pbCqW+grVBH2e3D50hRWt0cR8vFPEBERNUdtLfC2cBsAZzKqWit4bSx4XsujT+uDZVuQJXnK0lqNCk+KNNHF/cKWC3Fr6lbIkoyyUUZfqQ/9Fad1r/a4qBedGdy1MezL7ZuyL5/sQ0uoBZlgBq2hVmSCGbQEW9Aaap03YUSSJKdFt4kxpBay58P5L0aapWGkOoKh6hCGKkPu/WBlEHk9f9rf88geZIIZt5dHW7gNbeE2tAZbF9R4dX7bJVok8hUDB4YmgnZqGkHbtGy89NYw/v1Xx1FUnbFFS9Mh/D8bu7G6LTqt9zUtG/0FFbYALshGsb4zjpbIzGZgJSIimm0e2YNkIIlkIOluqy2pVNSLyGk5DFWGUDJKGKmOwBZOV/RaAJ+Nmbt3De7C99/8vvvzN17/BhL+BG5ddSsuzlyMlcmVWJlcOeV3KkYFA5UB9Jf73ZbAgcoAhqvD0G3dnS39RF7Z6XafDqbREnDu08E00oE0UoFUU7qpzxUG7cayhY0xbQyj1VFnybzqCIbVYee+OoyCXjjj70e8EWRCGbe3Rm3oRDqYPi96CUhiSr+K889MFiUnOh+NVXTsHyzhrYESCqoTtBNB7xkrH1sIbD80ih/vOo6hkgYAyET9uOWSTmzsSU6r4rKFwEhJR1E10JkI4qKuBLqSQcjsPk50Wou9zlrs50/zjxACZaM8MR5czWGoOoSq4ax3XFuCqZ4QvmtwF779xrdP+/yd6++cMv77bCzbwog64rQcVgfd2duHK8MY1Uandss+hbA3jFQghaQ/6V6IqD1O+BOI++PnRfihmauaVYypY8hpOeTU3MS9msOoOurMjXCWz1fIE3LnWciEMmgNtjr3oVaEveGmnEdtDPdsLAs2k/qKLdxE56mRkob9gyUcGCqhqJrT6jouhMCvevP44c5e9I45yyjEAh58cEMHrrmgBR55ehVtYXyZr1TYh2suaMXy1jD8noXT9YeIiAiYuiZ4O9oBOK15JaOEol5ESS9hVB3FcHUYJb2E4eowbGFDkRUElIAbxE/s/moLGz946wdnfO8fvPUDbGjdMO2Qq8iK20q4DuumPGfZlnucI6rT6jhSHXFbIytmBWWjjLJRxtHi0VPuX5ZkxHwxxP1xxP1xJPyJiZ99cWd8ui+GsDfMYL5AaJbmXEzSCsjrefe+tuZ9bek91VLPui9FUpAMJJEKpJyeFAGnB0UtZDcrVM9HDNxE5xEhBIYmBe2KZqEl4kdry9lnYP1NXwH/365eHBgqAwCCXgU3rG/D5jUZ+L3TC8uqYaE/r8Lvk3FpTxJr2qKIBrgeJxERnT9qwTPmm2jVsoWNslFGSS+haDhjrIcrw6gYFeS0HCxhQYIEv+JH0BPEsdIxjGljZ3yfMW0MB8YOYFVy1TkfsyIraA21ojV06jW/q2bVaamstViO349pY8ipOeT1vNtt+GzHLUsyIt4IYr6Yc7HCG0HUF0XE61y4CHvDiHgj7prejVqqbbERQkCzNPfCSdkoo2SU3M9l7SJR0Sg693oRmqVNe/8hj7M0WSKQOKknRDqQZg+IM2DgJjoP2LZAf0HFmwNFvD1SgWZa01reCwAODJXwo9d6sbe/CADwKTLesyaDG9a3ITLNNbGN8XHaQgArsxFc2BFDJnr+jgUjIiKaTJZkRH1RRH1RtyVcCIGqWUVRL6JslFHQCxiuDqOoF9FX6pvWfvPa6SeUmk1BTxCdkU50RjpP+bwt7CmTtU1uAS3oBRS0Agp6AWWjDFvYzrazjNudbPI66UFPEEFvECFPCAFPAEHF6apfW9Pb7/EjoAScx4ofPsUHn+KDX/EvyMAnhIBpm9AsDbqlQ7M1aJYGzdSgWqp7r5oqqmYVquXcV4wKqmbVfVw2y2ft1n0qXtnrXEDyx9yeCnFf3B1GEPfHkfQn4fdw/p16MXATLWCmZaN3rIq3Boo4OlqFDYGWsB9h/9mD9uHhMn78+nHs7nUqc0WWcN2qVvz2RW1IhHzTen/bdlrUK7qJzmQI6zviHKdNREQEpzt6bWb0yXRLR9wfx48P/Hha+ykbZXdN6rkiS7IbvnrQc9rXWbaFklFyA/eUllW9iIpRmWh1NUqoms7wNdVSoVoqRjF6TsfpkTzwKl54ZS98sg8eZXxd7/F1rhVZcdfBnryE14k3SZKmrOMtQXLX7gacpcNqa3XXHrvLnAnLXYfbEs4a5ZZtOWt3j6/lbdrOGt6G5azpPXnf58ojexDxRhDyhtyeBCf2Moj5Yu4FooAS4KRyDcbATbQAqYaFY7kK9vUX0ZdXIUsSMlE/AtPo+n1kpIKnXj+OXcfGADhraW9a0YIPbmhHepqzhwshkKsYyJV1tMb8uGxZCstawvAqC+/KMhERUTP5FB+u67oO2VAWg5XB04atpD+JVclVqBpV5NQcTNtZLcQjexDwTLTweuUzT4TaTIqsuMF8Omxho2pW3S7Qk1tsa49rLbqqqUKzNPfebRG2NLcMTWHCNE1UUW3kaTaMR/bAJzut9bV/44ASQMAzcau1+Ic8IbcnQNATdLvo+5TpNZpQ8zBwEy0gRdXAkZEK9g0UMVzSEPAo6EwEpxV03x4p499/1YddR8cAAJIEXLksjZs2tCMbm37376JqYKioIRb04qqVaazMRLieNhER0QwosoL7Lr8P975470nP1VpWP3/V5/GeJe+BaqooG2V3YrO8lkdOzbnd1XVbB4TTCl3rWl3rZj2XreLTIUuyGxTrJYSAYTstxbqlw7ANaJYG0zbdFuVaq3Kt5dmwDbc12hY2LNuCDRtCjLdcjz8GMOWCyORW71pLuAznfnJruSIpJ7Woe2UvPLLT4u7eFKclvnbPseznJ35LJprnhBAYKes4NFzGgcES8lUD0YAHS1Khac0afnikjH9//TheP+Z0HZcAXL4shQ9u6EBbfPpBu6KbGChoCHhlvKM7gTVtMcRD87siJyIimq8292zGI+96BA9tfwiDlUF3ezaUxWcv/yw292wGgFN2S69NkFUxK6gYFSeM62XktJzbdTunOpO1CSFODuOyDx7ZM29axs+FJEnuBYbFPBM2zV8M3ETzlGnZ6MurODBUwtHRCiq6hXTYh2UtYcjTqCD3D5bwk93H8UavM2mJJAGXL03hpg3taI+ffYx3jWZY6C863dZXt0Wwtj2O1ignziAiIjpXm3s244q2K7DpiU0AgMfe+xg2dWw6a0unJEluF+NUIDXlOcu23O7YtVtJLyGv5VE0iqgaVYxZYzCE4bbY1lpca63iPsUJ5ER07vg/iWieqegmjuWcidD68xogCaTD/mmFZCEE9g0U8ZNf9bmzjksScMWyFG66aGYt2rWZx21boCcdwtqOODrinFiDiIhoNk0O1xuzG8+5W7EiK+7a4SeybMttGVfNiZmvC3oBRb3ohnPd1mHaplvnn6ortFf2LshZwYmajYGbaB6odRs/MlLB/sESxio6Al4F7fEAfJ6zV2a2EPjVsTx+ursPB4eddbQVWcKm5WncsL5tRmO0TdvGYEGDZtnoTASxriOGrmQICmceJyIiWtAUWUFIPrmLeo1hGe4SVO69qbozjVfMClRLRVEvOrNrCwEBAQkSFFlxW8ZrAd0je+CRzo+u60T1YuAmmkO6aaMvX8Wh4bLTbdywkAh4sTQdntbSWpYt8OrhUfzfN/rRO+bMyOmRJVyzqgU3rGub9qzjtX0NlzSUdRNtsQAu7IijJx3izONERESLhFdxWq+jvugpn6+1kJ90MzWUjJK71JdpmagaVXfiMgEBSIAknGBeC+Ue2eNOMFabXIyt5nS+YeAmmgNjFR3HchW8NVDGSFmDLGHa3cYBZ1z1z/YP49k9Axgp6wCAgFfGu1dnsHltFvHg9Cczs22ndb2gGshEA3jn0hSWtoTg93CmTCIiIppwthZywOm1p9u6u2xX7aZZGgzbcCd5qxgVZ7utoWyUYdkWTGGO7wSoTQiuSIq7bvaUNbQnraXN2b1pPmPgJmoSw7LRN6bi8EgJR3NVlFQTEb8HXYkgPNNsRS5UDbywbxAv7BtCSXMqpWjAg/euyeA9azIzWp7LFgKjZR35qoGWiB/XrGrF8tbwtNbyJiIiotkR8oaw+/d3z/VhzBpJktw1ws/Gsi3otu4u6WXapru0V22bO9bcqkKzNFi2s6yXZThLfFnCgmVb7gRwtdZ0GRNLdMmS7LaeT16+61Q/08JhC2f5ttps/LVl3mxhw4YN27anbKuaVQQ90584eLYwcBM1kBACuYqB3lwFB4bKGC5pkACkwj5kIv5pj2nqz6t49jcD2HZgGIblrAfZGvXj/RdmsWlFy7TGedfYQiBX1jFWNZAM+3D1yjSWt3ItbSIiImouRVYQlIMIYnohSAgBU5gwLAOmGF9ne9LjWhivvUa3dKiWCsMaX5tbOK8xbdNdh1sI4TyGBdu2ne9m40tvC4gp39VkSYYE6aQ1uE+3XYI05V6G7HStn7z9hNcsFLawAcAdxy8g3McQmFjXfNL22r0t7In7ydvG10Cf/BhwyksIMbEOugR3ubtamSuS4lxkkWX33qt4EZbD8Mged+m4hD/R9LLiN2yiBlANC8fHqjg8XEHvmLOkV8TvQWciOO0x0bUZx5/bM4jXj43V/vZjaTqE969rw8YlyWmN866ZHLQTIR+uWpHGitYIwn7+GSAiIqL5T5IkeCVnhvR61AK7LWwnoI+3jltiUgi3J7Wcj7eO1l5XG5Nu2IbbBb62zRKWExxtJ7wLezwwniJ81rYLnBBWxfi3PQmAwEQAFxPbhDQpeIqTLwrMtDymhNjxb5uSkNz3q10gsIU9sQ3OsU25aOC8cMpFBffCw6TXTQ7Jk4cIeGQPZEl2J9ur3dfCdO1W+z1ZlqcMKag9liXZnRtgvgw14Ddtolli2QKDRRXHcs4kaGMVAx5ZQirsm9G616ZlY/vhUTy7ZwBHc1V3+8VdCVy/LotVmciM/rCeGLSvXJ7G8tYwooH6KisiIiKihagW2AFMq8v7TNVay90uzbWW2vGfJz9/Yotv7fcntwBPCeW11mNMBOPa87XfPe1xYVKwnqT2fbIWlt3HOLkVHtJEC/+JrfJuC/4ZWvoVWZnSI2Axdd9n4CY6B7Uu4335Kg4OlTFUVGHaAvGAFz2pmS2lla8a2PrmELa+OYR81QAA+BQZV61I431rszNaQxtg0CYiIiJqJrc1FvOjZZXmBwZuaqiKbuLCzz8DANjzxfefN+OEi6qB/ryKwyNl9OdVVHQLYb8H2VhgxrN7Hxou47/2DuDVwzlYtnN1MhH04j1rMrh2VSsigZmVmTvreNVAMuLDphVpLGuNIMKu40RERERETcVv4ETTVNFN9OdVHBmtoG9MRUE1EPAoSIS8M+oyDjgzlr96eBTP7x3E4ZGKu31FaxjvXZPFpT0JeOSZdbWpraNd0kykw35cvSqNZS0co01ERERENFf4TZzoDCq6iYGChuO5Ko7mKiioBjySjETIi2UtYcgznKRiqKhh65tDeHn/sLusl0eW8M6lSbx3TRbLWsIzPkbTsjFc0lHRTbRE/bhkSRJLW0LnTW8CIiIiIqKFit/IiU5Q1kwMFsdD9lgFhaoJRQbiAS+WpsIzmhkccFqed/fm8eK+Qfz6eMGdbTwV8uFdq1vxWytbEAvOfFy1btoYKmnQTBvZmB+XL09hSSrEdbSJiIiIiOYJBm4iOBOWDRU1HMtV0J93uosrsjQeskMzDtkAMFLS8PL+Yby8fxi5iuFuX9cew7tWt2JDV2JGk6rVqIaFoZIG2xZoTwSxui2K7mRoRmtxExERERFR4zFw06Jk2wKjFR1DRQ1HcxUMFTWUNRMeWUY8WF9LNgCYto3dx/J46a1hvNGbd1uzI34Prl6ZxrWrWpGNzWy28ZqSamK4rEKRZHSlglidjaEjEYBnmut6ExE100MPPYTPfe5zuOeee/Doo4/O9eEQERHNCQZuWjRUw8JIWcdgQcXR0QpyFQOaYcHvVRAPeJGJ+Ge0vvVkffkqXn5rGNsOjqComu72NW1RXLuqFZcsScBbRzAWQiBfNTBa0RH0KrggG8WqbBTZaKCuCwJERM3w6quv4pvf/CY2bNgw14dCREQ0pxi46bxl2wJjVQOjZQ19eRV9YyqKqgFLCIR9HqTDvnMa71zRTfzycA7/fWAYB4bK7vZowINNK9K4ZlUr2upszbZsgdGyjoJqIBbw4uKuBJZnImiJ+Os+XiKiZiiVSrj99tvxT//0T/ibv/mbuT4cIiKiOcXATeeVkmZitKRjuOSMx85XDVQMC15JRjToQWcyOOPltiazbYHf9Bew7cAIdh7JwbCcTuOSBFzUGcc1K1twUVe87vfQTRvDJQ2qYSEd8WPTijR6WsKIBWY+qRoR0Vz4oz/6I9x4443YvHnzWQO3pmnQNM39uVAoNPrwiIiImoqBmxa0im4iVzGQK+voHatiZHwdagkSQj4FiaAPbTG57q7iNUdzFfz8wAh+fmgU+erEBGgd8QA2rWjBlctTSIR8de+/rJkYLmuAkNAeD2BVNoJuzjhORAvME088gZ07d+LVV1+d1usfeughfOELX2jwUREREc0dBm5aMIQQKOsWcmUd+aqB4/kqRks6ypoJSwABj4xowIOWsH9WxjePlDT84tAofnFoFL1jVXd72Kfg8mUpbFrRgqXpUN1h3q6Nzy4747NXtEawojWC9jgnQiOihefo0aO455578J//+Z8IBKY3nOb+++/Hvffe6/5cKBTQ3d3dqEMkIiJqOgZumrcsW6BQNTBWNTBW1tGXVzFW1VHRLVi2QNCrIOz3oCsZqmt5rVMpVA3seDuH7YdH8dZgyd3ukSVs6IrjquVpXNQZP6dAbFg2RsrOhYJ4yIuNPUn0pMNoifjOuSWeiGiu7NixA4ODg9i4caO7zbIsvPTSS/ja174GTdOgKFN77fj9fvj9nJuCiIjOXwzc1FCWLdzH2w+N4ppVracMx7YtUNZNFFQT+YqB4ZKGoZKGsmpCNS1IAIJeD8J+ZdZasGtKmoldR8aw/fAoftNfgBg/ZAnABdkorliewsYlSYT95/bfpaSZGC1rsAWQifrxzqVJdCVDiJzjfomI5oP3vve92L1795Rtf/AHf4A1a9bgs5/97Elhm4iIaDHgN31qmKff6MMDT/3a/fljW15FezyA/3Hjhbh6VQtKmomiamCk5KyHXdZNVHULthDwyjJCPgWpsA9+z7mPwT5RSTXx2tEcfvl2Dnv7irDExIWBpekQLluawmVLU0iF6x+XDTgXHMYqOsaqBkI+BctbI1jeEkF7IlDXMmFERPNVNBrF+vXrp2wLh8NIp9MnbSciIlosGLipIZ5+ow+f+t87IU7Y3pdXcff/2YnfvbwbK1sjsAXgkSQEfQrCXmf89Wx1Dz9Rvmpg55Ecdh7JYV9/EZMa39GVDI6H7CQy0fqW8ppMNSyMlHRoloVUyI/Ll6bQnQ4hHWa3cSIiIiKixYKBm86ZZlqo6hYq47d8Rcf9P9x9Utie7Ok3+vHwhy+Cx9PYVt6BgorXjoxh19ExHBgqTTmm7mQQG3uSeOfSVN3rZU9mC4GxioGxqg6fR0Z7PIAVmSi6kkHONk5Ei9KLL74414dAREQ0pxi4Z8i2BXTLbkg35/lICOd8VcOGZlhQDRuqaaGijY+3rhqo6BZ004Jm2hACeHukhFzFOON+xyoG9g+XsKYtNqvHa9sCB4fLeP2YE7L78uqU55e3hHHpkiQuWZJAdhZCNjDeml3WoRkW4iEfLlmSxJJUCK2R2R1rTkRERERECwsD9wzt7S9id28eXkVC2O9BxK8g4vfC55Gdm+LcexUZXkUav5cb1k26HpYtYFg2TFvAMG3olg3dtGFYzmPNsFHWTJQ0ExXdCdK6ZcEwbZg2AAhIEuCVnXP1exSEQz74FBmyLGGwqJ7tEABgynrW56Kim9hzvIDXj+WxuzePkma6zymShNVtUVzSncA7uhPnPCa7xrYFxqoG8lUdXo+MbCyAla0RdCaDCPn434qIiIiIiBi4Z8ywbIyUNKTDPgxpGo5bNkzbBgC3u7IiS/DIMjyKBEWWoEgSPIoEv6LA750I5L7xMC5Jzu8osgQnlzv3klT72SFBGn8fASEm3s8WAkII2MJ5bNkCtu0cq2nZ0MYDtW7a0EzneE1LwBICliVg2LY7m7gECZAEFGnqBYOg1wufIk9rOax40Dutspzu604khMCxsSre6HUC9v7B0pTx2EGvgos643hHVxwXdcVnNQCXNROjZR2GbSMxqTW7ha3ZRERERER0AgbuOngVCenI6dcNNW0b1nigrQVbzbBR0Zz1o23hBGJnZuzJo4onBzYBSBIgpo6EFpAg1X5Hkib9uhj//an7kyVAHg/9TqB37n3jre6K7FwM8MizN5b6gkwUyZD3jN3KkyEvLshEp73PompgT18Bvz7u3E5sHW+LB9yQvTITmdXzMSwbuYqOomoi5FPQnQ5hWUsYHfEggj6OzSYiIiIiolNj4G4AjyyjwXOBzWuyLOF3L1uCr289cNrX/O5lS87YIqybNt4aLOI3fUXs6SvgyGhlyvM+j4zV2Sg2dMaxvjOO1ujpL4DUwxYChaozAZoEGemID+s74+hMBJHiTONERERERDQNDNzUEBt7kvjUdSvwr9uPYGxSa3Qy5MXvXrYEG3uSU15vWDYODpWxt7+AfQNFHBwqw7Sntu53JYNY1xHD+g6nFbsR61iXNBO5ig7DshELeLGuI47uVAjZGNfNJiIiIiKimWHgpobZ2JPEhW1RfObJXQCAe96zEus64pBlCZpp4eBQGW8OFE8bsJMhL9a2x7CuPYY17bG6x3yfjWZYyFUNVHQTQa+C7lQIS9NhtMcDCPv5X4SIiIiIiOrDNEENNbnbeEW38L2dx7B/sIQjI5XxMewTogEP1rRFsaYthjVtUWSi/oZ13TYsG2MVA0XNgFeR0RLx45IlCbTHg0iGvOwyTkRERLRIVYwKrvg/VwAAfvHRXyDkDc3xEdFCxsBNs860bBzLVXFw2GnBrvmnlw9NeV0y5MUF2ej4LYK2WKChQde0bRSqJgpVA5IkIRH24rK2FDqSQbRE/PNq6TYiIiIiIlr4GLjpnNi2QF9BxdsjZRweqeDwcBlHRisndQ8HgI54AKuyUazKRLAqE2nK5GO2LVBQDeRVA7YtEA/5sKErjo5kEJloAL7FPLsdERERERE1FAM3TZth2egbU3FktDJxy1Wgm/ZJrw37FCxrCaMnHcJ/7O4HAPzlb6+F39v4ZbSmhGwBxALOWPDORBDZWACBJhwDERERERERA/cMVHQTN/+v/wYA/K+PXNKU8DgXhBAYLes4nldxLFfBsVwVx3JV9OfVk8ZdA4DfI2NJKoSe8fWpl7WE0Rpxxl9rhuUG7kaaHLItG4gFPbggG0VXMoS2WIDrZRMRERERUdMxcM+ANamb9JsDRXfG7YXKsgWGSxr68ir68yr6CyqOj1VxPF+Fapzcag0AIZ+CJakQulMhLEk6IbstFpiTcjBtG0XVRL5qQMCZdK0WsrMxP0I+fryJiIiIiGjuLIhE8thjj+ErX/kK+vr6sG7dOjz66KO45pprmnoMT7/Rhwee+rX7898/v/+0a0rPJ6ZtI1c2MFTUMFTSMFBQMVjQ0F9UMVzUTjnWGgAUSUI25kdXMoSuZBBdySA6E8GmjLs+E8OyUagaKGgGJEiIBby4sCOGjngQGYZsIiIiIiKaR+Z9OnnyySfxJ3/yJ3jsscdw9dVX4/HHH8cHPvAB7NmzB0uWLGnKMTz9Rh8+9b934sRomqsY+PrWA/jUdSvmLHTrpo1cRcdoWcdoRcdoScdwScNI2bkfLes4TaYGAHgVCW2xANriAbTFAuhIBNGRCCIb9cOjzI8JxTTDQl41UNZMyLKERNCHd3Qm0J4IojXq55hsIiIiIiKal+Z94H7kkUdw55134hOf+AQA4NFHH8UzzzyDr3/963jooYca/v6WLfCFf99zUtie7IlXj+CS7sSsdau2bYGybqKoOreCaiBfNZz7ioGxqoGxirOtpJln3Z9HltAa9aM14kcm5kc2GkA2FkA25kcy7IM8z9acFkKgrFsoVA2ohgWfV0Yy5MPathiy8QBaIn7OLk5ERERERPPevA7cuq5jx44duO+++6Zsv/7667Ft27ZT/o6madA0zf25UCic0zFsPzSKvrx6xtfkKgb2DRSxMhOBaQnolg3dtGGM36umBdWwoY3fV3ULVcNy78uaibJuoqxZKI0/PsXcZKfl98hIhn1IhrxIh/1oifiQjviRDvvQGvUjHvTOu1B9ItO2UVJNFKomTCEQ8slojfnRkwqjJepDOsx1somIiIio8Szbch/vGNiBTR2boMjsUUn1mdeBe3h4GJZlIZvNTtmezWbR33/qma8feughfOELX5i1Yxgsnjls1/zds2/O2nvWhHwKon4PYkEvYkEv4gEvYkEPkiEfEiEvEkHnPuRT5nRc9Zn4vQq+9XvvPOVzqmEhXzVQ1k3IkoRowIuV2Qg6EkG0RvyIBT3z9ryIiIiI6Pzz3NvP4aHtE71o7/6vu5ENZXHf5fdhc8/mOTwyWqjmdeCuOTF0CSFOG8Tuv/9+3Hvvve7PhUIB3d3ddb93Jhqo6/d8Hhk+RYZXkRDwKvB7ZAS8CgIeBUGfgqB34j7sVxD2exD2eRD2K4gGvAj7FXjk86vbtGULlDSni7xu2Qh4FCRCXlzYHkNrzI+WCMdjExEREdHceO7t53Dvi/dCnDCYdLAyiHtfvBePvOsRhm6asXkduFtaWqAoykmt2YODgye1etf4/X74/f5ZO4bLl6XQHg+gP6+edhx3IujF/7hxLbweGV5FhkeW2DIL58JI1bBQVE23FTsS8GBpOozOpDPjeTLkY1dxIiIiIppTlm3h4e0PnxS2AUBAQIKEL2//Mt7d/W52L6cZmddNqD6fDxs3bsSzzz47Zfuzzz6LTZs2NeUYFFnCAx+8EABwulj4kcuXIB7yIeTzwKvIizpsa6aFkZKGt0fLODRSQb5qIB704vKlKbx/XRtufkcn3r0mgwuyUbREOC6biIiIiObezsGdGKgMnPZ5AYH+Sj92Du5s4lHR+WBet3ADwL333os77rgD73znO3HVVVfhm9/8Jo4cOYK77rqracdww/p2fP3/vRQPPPVrDBQmJmRbCOtwN5pp2ShpJoqaCcOy4VVkZ23s9hhaowGkwz5n0jYGayIiIiKap4YqQ7P6OqKaeR+4b7vtNoyMjOCLX/wi+vr6sH79evz0pz9FT09PU4/jhvXtuHplCy568D8BAPe8ZyXWdcQXXZA0bdudTV0zLCiKhIjfi2UtYbTFA0iFfEiGffDOkzW8iYiIiIjOpjXUOquvI6qZ94EbAO6++27cfffdc30YU7o/X5CNLoqwbVo2yvp4wDYtKJKEcMCDzkQQ7YmAOw6bk50RERER0UJ1aeZSZENZDFYGTzmOW4KEbCiLSzOXzsHR0UK2IAL3fBHyefDjP7oa2w+NwH+eBkxjvIt4WTOhWzYUWULY7wTstngAybAPqZAPQd/5ef5EREREtPgosoL7Lr8P975470nPSeMzOX328s9ywjSaMQbuRUwIAdWwUdadgG0KAZ8sIzw+k3gmFkAy7GULNhERERGd9zb3bMYj73oED21/CIOVQXd7NpTFZy//LJcEo7owcC8ipm2jolmo6BZUw4INMb4OuAfdqRhao34kgl7EQ174PQzYRERERLS4bO7ZjCvarsCmJ5wVkR5772PY1LGJLdtUNwbu85QtBFTDCdcVzYIlbMiyhLDPg1TEh/ZYAImwD4mgF7Ggl8tzEREREREBU8L1xuxGhm06Jwzc54Fa1/CqYaGim9AtAQkCAZ+CiM+L7lQILRE/YkEP4kEvQj7+sxMRERERETUak9cCU2u5ruoWqoYF3bIBSAh6ZQR9Cpamw2iJ+hEPehELeBENeBbFbOpERERERETzDQP3PGZatttyXTUsmLYNCUDAqyDkU7A05oTrWrCOBjzwcP1rIiIiIiKieYGBex6wbQHVtKAaNlTDgmZZEMJZ9zvoVRDyebAkHUIy5HODdcTPcE1ERERERDSfMXA3kWULaOPBWjMtaKYNIQQkSYLf43QJb08E0RLxITreah3xexDyKZAkdgsnIiIiIiJaSBi4Z5kQArplQzed7uC6aUO3LAgAiiTB55UR8CjIxgJIh32IBr0I+z2I+DwI+xW2WhMREREREZ0nGLjrIACohjUepm1opg3ddEI1APg9ykSLdTyARMiLSMCLsN/pHh72MVgTERERERGd7xi4Z0iSAFmSMFrW4fPICHgVZGJ+JIM+hAOe8THXTrAOeGV2BSciIiIiWkBC3hB2//7uuT4MOk8wcM/Q8tYI0hE/Ql4FQZ/Tks1QTURERERERCdi4J6hiN+ZyIyIiIiIiIjoTDiQmIiIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBGLiJiIiIiIiIGoCBm4iIiIiIiKgBPHN9AI0mhAAAFAqFOT4SIiKiM6vVVbW6a7FhnU1ERAvBTOrr8z5wF4tFAEB3d/ccHwkREdH0FItFxOPxuT6MpmOdTUREC8l06mtJnOeX0W3bxvHjxxGNRiFJ0jnvr1AooLu7G0ePHkUsFpuFIzz/sczqw3KrD8utPiy3+sx2uQkhUCwW0dHRAVlefKO+ZrPO5me6Piy3+rDc6sNyqw/LrT6zWW4zqa/P+xZuWZbR1dU16/uNxWL8gM8Qy6w+LLf6sNzqw3Krz2yW22Js2a5pRJ3Nz3R9WG71YbnVh+VWH5ZbfWar3KZbXy++y+dERERERERETcDATURERERERNQADNwz5Pf78cADD8Dv98/1oSwYLLP6sNzqw3KrD8utPiy3+Yv/NvVhudWH5VYfllt9WG71matyO+8nTSMiIiIiIiKaC2zhJiIiIiIiImoABm4iIiIiIiKiBmDgJiIiIiIiImqARRe4H3roIVx22WWIRqPIZDL48Ic/jH379k15jRACDz74IDo6OhAMBvGud70Lv/71r93nR0dH8ZnPfAarV69GKBTCkiVL8Md//MfI5/NT9rN06VJIkjTldt999zXlPGdbM8sNAP7jP/4DV1xxBYLBIFpaWnDLLbc0/BwboVnl9uKLL570WavdXn311aad72xp5uftzTffxM0334yWlhbEYjFcffXVeOGFF5pynrOtmeW2c+dOvO9970MikUA6ncYf/uEfolQqNeU8Z9tslBsAfPKTn8SKFSsQDAbR2tqKm2++GXv37p3ymlwuhzvuuAPxeBzxeBx33HEHxsbGGn2KCxLr6/qwvq4P6+v6sL6uD+vr+izY+losMu9///vFli1bxBtvvCF27dolbrzxRrFkyRJRKpXc1zz88MMiGo2KH/zgB2L37t3itttuE+3t7aJQKAghhNi9e7e45ZZbxFNPPSX2798v/uu//kusWrVK3HrrrVPeq6enR3zxi18UfX197q1YLDb1fGdLM8vt+9//vkgmk+LrX/+62Ldvn9i7d6/43ve+19TznS3NKjdN06Z8zvr6+sQnPvEJsXTpUmHbdtPP+1w18/O2cuVK8du//dvi9ddfF2+++aa4++67RSgUEn19fU0959nQrHLr7e0VyWRS3HXXXWLv3r1i+/btYtOmTSeV7UIxG+UmhBCPP/642Lp1qzh06JDYsWOH+OAHPyi6u7uFaZrua2644Qaxfv16sW3bNrFt2zaxfv16cdNNNzX1fBcK1tf1YX1dH9bX9WF9XR/W1/VZqPX1ogvcJxocHBQAxNatW4UQQti2Ldra2sTDDz/svkZVVRGPx8U3vvGN0+7n3/7t34TP5xOGYbjbenp6xFe/+tWGHftcalS5GYYhOjs7xbe+9a3GnsAcaeTnbTJd10UmkxFf/OIXZ/cE5kijym1oaEgAEC+99JL7mkKhIACI5557rkFn0zyNKrfHH39cZDIZYVmW+5rXXntNABBvvfVWg86meWar3F5//XUBQOzfv18IIcSePXsEAPHzn//cfc0rr7wiAIi9e/c26GzOH6yv68P6uj6sr+vD+ro+rK/rs1Dq60XXpfxEtW4XqVQKAHDo0CH09/fj+uuvd1/j9/tx3XXXYdu2bWfcTywWg8fjmbL9y1/+MtLpNC6++GL87d/+LXRdb8BZNF+jym3nzp3o7e2FLMu45JJL0N7ejg984AMndQVZqBr9eat56qmnMDw8jI997GOzd/BzqFHllk6nsXbtWnz3u99FuVyGaZp4/PHHkc1msXHjxgaeUXM0qtw0TYPP54MsT1QhwWAQAPDyyy/P+nk022yUW7lcxpYtW7Bs2TJ0d3cDAF555RXE43FcccUV7uuuvPJKxOPxM5Y/OVhf14f1dX1YX9eH9XV9WF/XZ6HU14s6cAshcO+99+K3fuu3sH79egBAf38/ACCbzU55bTabdZ870cjICP76r/8an/zkJ6dsv+eee/DEE0/ghRdewKc//Wk8+uijuPvuuxtwJs3VyHI7ePAgAODBBx/EX/3VX+EnP/kJkskkrrvuOoyOjjbidJqm0Z+3yb797W/j/e9/v/uHYyFrZLlJkoRnn30Wr732GqLRKAKBAL761a/i6aefRiKRaMwJNUkjy+0973kP+vv78ZWvfAW6riOXy+Fzn/scAKCvr68Rp9M051pujz32GCKRCCKRCJ5++mk8++yz8Pl87n4ymcxJ75nJZE5b/uRgfV0f1tf1YX1dH9bX9WF9XZ+FVF8v6sD96U9/Gr/61a/wr//6ryc9J0nSlJ+FECdtA4BCoYAbb7wRF154IR544IEpz/3pn/4prrvuOmzYsAGf+MQn8I1vfAPf/va3MTIyMrsn0mSNLDfbtgEAf/mXf4lbb70VGzduxJYtWyBJEr73ve/N8pk0V6M/bzXHjh3DM888gzvvvHN2DnyONbLchBC4++67kclk8LOf/Qzbt2/HzTffjJtuumnBV0SNLLd169bhO9/5Dv7u7/4OoVAIbW1tWL58ObLZLBRFmf2TaaJzLbfbb78dr732GrZu3YpVq1bhd37nd6Cq6mn3cbr90FSsr+vD+ro+rK/rw/q6Pqyv67OQ6utFG7g/85nP4KmnnsILL7yArq4ud3tbWxsAnHT1YnBw8KSrJcViETfccAMikQh+9KMfwev1nvE9r7zySgDA/v37Z+MU5kSjy629vR0AcOGFF7rb/H4/li9fjiNHjsz6+TRLMz9vW7ZsQTqdxoc+9KFZPovma3S5Pf/88/jJT36CJ554AldffTUuvfRSPPbYYwgGg/jOd77TwDNrrGZ83j760Y+iv78fvb29GBkZwYMPPoihoSEsW7asQWfVeLNRbvF4HKtWrcK1116L73//+9i7dy9+9KMfufsZGBg46X2HhoZO2g9NYH1dH9bX9WF9XR/W1/VhfV2fhVZfL7rALYTApz/9afzwhz/E888/f9KHbdmyZWhra8Ozzz7rbtN1HVu3bsWmTZvcbYVCAddffz18Ph+eeuopBAKBs773a6+9BmCiklpImlVuGzduhN/vnzLFv2EYOHz4MHp6ehp0do3T7M+bEAJbtmzB7/3e7531C+V81qxyq1QqADBlbFPt51rrzUIyF3/fstksIpEInnzySQQCAbzvfe+b/RNrsNkqt9PtW9M0AMBVV12FfD6P7du3u8//4he/QD6fP+t+FiPW1/VhfV0f1tf1YX1dH9bX9Vmw9fWMp1lb4D71qU+JeDwuXnzxxSlLMlQqFfc1Dz/8sIjH4+KHP/yh2L17t/jIRz4yZTr5QqEgrrjiCnHRRReJ/fv3T9lPbTr5bdu2iUceeUS89tpr4uDBg+LJJ58UHR0d4kMf+tCcnPe5ala5CSHEPffcIzo7O8Uzzzwj9u7dK+68806RyWTE6Oho08/7XDWz3IQQ4rnnnhMAxJ49e5p6nrOtWeU2NDQk0um0uOWWW8SuXbvEvn37xJ//+Z8Lr9crdu3aNSfnfi6a+Xn7x3/8R7Fjxw6xb98+8bWvfU0Eg0Hx93//900/59kwG+V24MAB8aUvfUn88pe/FG+//bbYtm2buPnmm0UqlRIDAwPufm644QaxYcMG8corr4hXXnlFXHTRRVwW7DRYX9eH9XV9WF/Xh/V1fVhf12eh1teLLnADOOVty5Yt7mts2xYPPPCAaGtrE36/X1x77bVi9+7d7vMvvPDCafdz6NAhIYQQO3bsEFdccYWIx+MiEAiI1atXiwceeECUy+Umn/HsaFa5CeEskfFnf/ZnIpPJiGg0KjZv3izeeOONJp7t7GlmuQkhxEc+8hGxadOmJp1d4zSz3F599VVx/fXXi1QqJaLRqLjyyivFT3/60yae7expZrndcccdIpVKCZ/PJzZs2CC++93vNvFMZ9dslFtvb6/4wAc+IDKZjPB6vaKrq0t89KMfPWn5kJGREXH77beLaDQqotGouP3220Uul2vSmS4srK/rw/q6Pqyv68P6uj6sr+uzUOtrafzgiYiIiIiIiGgWLbox3ERERERERETNwMBNRERERERE1AAM3EREREREREQNwMBNRERERERE1AAM3EREREREREQNwMBNRERERERE1AAM3EREREREREQNwMBNRERERERE1AAM3ER0Sg8++CAuvvjiuT4MIiIiOgvW2UTzlySEEHN9EETUXJIknfH53//938fXvvY1aJqGdDrdpKMiIiKiE7HOJlrYGLiJFqH+/n738ZNPPonPf/7z2Ldvn7stGAwiHo/PxaERERHRJKyziRY2diknWoTa2trcWzwehyRJJ207sXvaxz72MXz4wx/Gl770JWSzWSQSCXzhC1+AaZr4i7/4C6RSKXR1deGf//mfp7xXb28vbrvtNiSTSaTTadx88804fPhwc0+YiIhogWKdTbSwMXAT0bQ9//zzOH78OF566SU88sgjePDBB3HTTTchmUziF7/4Be666y7cddddOHr0KACgUqng3e9+NyKRCF566SW8/PLLiEQiuOGGG6Dr+hyfDRER0fmLdTbR/MDATUTTlkql8A//8A9YvXo1Pv7xj2P16tWoVCr43Oc+h1WrVuH++++Hz+fDf//3fwMAnnjiCciyjG9961u46KKLsHbtWmzZsgVHjhzBiy++OLcnQ0REdB5jnU00P3jm+gCIaOFYt24dZHniOl02m8X69evdnxVFQTqdxuDgIABgx44d2L9/P6LR6JT9qKqKAwcONOegiYiIFiHW2UTzAwM3EU2b1+ud8rMkSafcZts2AMC2bWzcuBH/8i//ctK+WltbG3egREREixzrbKL5gYGbiBrm0ksvxZNPPolMJoNYLDbXh0NERESnwTqbqDE4hpuIGub2229HS0sLbr75ZvzsZz/DoUOHsHXrVtxzzz04duzYXB8eERERjWOdTdQYDNxE1DChUAgvvfQSlixZgltuuQVr167Fxz/+cVSrVV49JyIimkdYZxM1hiSEEHN9EERERERERETnG7ZwExERERERETUAAzcRERERERFRAzBwExERERERETUAAzcRERERERFRAzBwExERERERETUAAzcRERERERFRAzBwExERERERETUAAzcRERERERFRAzBwExERERERETUAAzcRERERERFRAzBwExERERERETUAAzcRERERERFRA/z/gqHPx4dTtRIAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize_fit(t, xs, ys, xes, yes, x_model, y_model, xe_model, ye_model, mm.name, t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "f7ae3e7f", + "metadata": {}, + "source": [ + "## 1.3. Example: Parallax Model Fit" + ] + }, + { + "cell_type": "markdown", + "id": "08eceab5", + "metadata": {}, + "source": [ + "Parallax model requires some fixed parameters: `ra`, `dec`, `pa`, `obsLocation`, and `t0`.\n", + "- `ra` and `dec` are required parameters. \n", + "- `pa = 0` by default\n", + "- `obsLocation = 'earth'` by default\n", + "- `t0 = np.average(t, 1./np.hypot(xe, ye))` by default\n", + "\n", + "We need to provide the fixed parameters in the `fixed_params_dict`:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "018fc13a", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 1 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 2 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 2 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 1 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"taiutc\" yielded 1 of \"dubious year (Note 4)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n" + ] + } + ], + "source": [ + "mm = Parallax()\n", + "fixed_params_dict = {'ra': 0., 'dec': 10., 'pa': 0., 'obsLocation': 'earth'}\n", + "params, param_errs = mm.fit(t, x, y, xe, ye, fixed_params_dict)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "73dafb1f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 20 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 40 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 40 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 20 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"taiutc\" yielded 20 of \"dubious year (Note 4)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_model, y_model, xe_model, ye_model = mm.model(t_test, params, param_errs)\n", + "visualize_fit(t, x, y, xe, ye, x_model, y_model, xe_model, ye_model, mm.name, t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "5be8fb7e", + "metadata": {}, + "source": [ + "# 2. Fit Motion Model in StarTable" + ] + }, + { + "cell_type": "markdown", + "id": "3bd8dec7", + "metadata": {}, + "source": [ + "Examples on `flystar.StarTable.fit_motion_model`. Prepare the data with invalid values:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "aa698e86", + "metadata": {}, + "outputs": [], + "source": [ + "t = np.array([0, 1., 2.2, 3.5, 5.]) + 2025.0\n", + "\n", + "x = np.array([\n", + " [0., 0.5, 2.1, 3.2, 8.0], # Increasing 5 Epochs\n", + " [10.0, 8.9, 9.2, 7.4, 7.0], # Decreasing 5 Epochs\n", + " [2.5, np.nan, 5.2, np.nan, 5.0], # 3 Epochs\n", + " [np.nan, 6.2, np.nan, np.nan, 9.2], # 2 Epochs\n", + " [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch\n", + " [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs\n", + "])\n", + "\n", + "y = np.array([\n", + " [10.2, 8.5, 9.1, 10.5, 13.0], # Increasing 5 Epochs\n", + " [8.0, 9.9, 8.2, 7.4, 7.0], # Decreasing 5 Epochs\n", + " [5.2, np.nan, 4.7, np.nan, 6.0], # 3 Epochs\n", + " [np.nan, 1.2, np.nan, np.nan, 3.2], # 2 Epochs\n", + " [np.nan, 2.0, np.nan, np.nan, np.nan], # 1 Epoch\n", + " [np.nan, np.nan, np.nan, np.nan, np.nan] # All NaNs\n", + "])\n", + "\n", + "xe = np.array([\n", + " [0.2, 0.5, 0.3, 0.4, 0.6],\n", + " [0.5, 0.2, 0.7, 0.3, 0.2],\n", + " [0.5, np.nan, 0.6, np.nan, 0.3],\n", + " [np.nan, 0.6, np.nan, np.nan, 0.3],\n", + " [np.nan, 0.4, np.nan, np.nan, np.nan],\n", + " [np.nan, np.nan, np.nan, np.nan, np.nan]\n", + "])\n", + "\n", + "ye = np.array([\n", + " [0.3, 0.2, 0.5, 0.2, 0.4],\n", + " [0.2, 0.5, 0.6, 0.4, 0.2],\n", + " [0.7, np.nan, 0.5, np.nan, 0.2],\n", + " [np.nan, 0.4, np.nan, np.nan, 0.5],\n", + " [np.nan, 0.5, np.nan, np.nan, np.nan],\n", + " [np.nan, np.nan, np.nan, np.nan, np.nan]\n", + "])\n", + "\n", + "x = np.ma.masked_invalid(x)\n", + "y = np.ma.masked_invalid(y)\n", + "xe = np.ma.masked_invalid(xe)\n", + "ye = np.ma.masked_invalid(ye)\n", + "mask = np.ma.getmaskarray(x) | np.ma.getmaskarray(y) | np.ma.getmaskarray(xe) | np.ma.getmaskarray(ye)\n", + "\n", + "tab = StarTable({\n", + " 'x': x,\n", + " 'y': y,\n", + " 'xe': xe,\n", + " 'ye': ye\n", + "})\n", + "tab.meta['list_times'] = t" + ] + }, + { + "cell_type": "markdown", + "id": "9201897f", + "metadata": {}, + "source": [ + "There are a 2 ways to specify the desired motion models:\n", + "1. Let MotionModel automatically determine which motion model to use among the given `motion_models` list based on the number of valid observations. MotionModel will choose the motion model that has enough observations, i.e. $n_\\text{fit} \\geq n_\\text{params}$. \n", + "2. Specify a motion model for each star in the `motion_model_input` column. In case there is not enough observations, MotionModel will \"downgrade\" to a model with less parameters until $n_\\text{fit} \\geq n_\\text{params}$ among all the unique motion models specified in the column.\n", + "\n", + "Note that when `absolute_sigma=False` and `n_fit == n_params`, we don't have enough degree of freedom to rescale the uncertainties, so the uncertainties will be set to infinity -- the same behavior as `scipy.optimize.curve_fit`.
By default `motion_models = [Empty, Fixed, Linear]`. `Empty` and `Fixed` will always be added in the list to handle 0 and 1 point cases. See examples below for details. Let's start with the most basic usage." + ] + }, + { + "cell_type": "markdown", + "id": "e58f429d", + "metadata": {}, + "source": [ + "## 2.1. Example: Default Fitting" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "02642d3b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Empty: 0%| | 0/1 [00:00StarTable length=6\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
n_fitn_requiredmotion_model_used
int64int64str20
52Linear
52Linear
32Linear
22Linear
12Fixed
02Empty
" + ], + "text/plain": [ + "\n", + "n_fit n_required motion_model_used\n", + "int64 int64 str20 \n", + "----- ---------- -----------------\n", + " 5 2 Linear\n", + " 5 2 Linear\n", + " 3 2 Linear\n", + " 2 2 Linear\n", + " 1 2 Fixed\n", + " 0 2 Empty" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tab['n_required'] = 2\n", + "tab[['n_fit', 'n_required', 'motion_model_used']]" + ] + }, + { + "cell_type": "markdown", + "id": "20470c6e", + "metadata": {}, + "source": [ + "Next, let's try `absolute_sigma=False`. As mentioned above, we don't have enough degree of freedom to rescale the uncertainties for the forth star. In this case, the parameter uncertainties will be set to infinity, which is the same behavior as `scipy.optimize.curve_fit`. The same `OptmizieWarning` as in `scipy` will be raised." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "26b11593", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Empty: 0%| | 0/1 [00:00\n", + "0.2398025689409276\n", + "0.07197698078673948\n", + "0.26723109004421475\n", + "inf\n", + "inf\n", + "inf\n", + "" + ], + "text/plain": [ + "\n", + " 0.2398025689409276\n", + "0.07197698078673948\n", + "0.26723109004421475\n", + " inf\n", + " inf\n", + " inf" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tab['vx_err']" + ] + }, + { + "cell_type": "markdown", + "id": "241ab6d6", + "metadata": {}, + "source": [ + "## 2.2. Example: Specify Motion Models" + ] + }, + { + "cell_type": "markdown", + "id": "220922c5", + "metadata": {}, + "source": [ + "Alternatively, one can specify a list of motion models to use, and the function will also automatically determine which model to use for each star depending on the valid observed epochs. In the following example, we specify `Acceleration` model, but **the function will always implicitly add `Empty` and `Fixed`** to handle the 0 or 1 epoch stars." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "a596c8e8", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Acceleration: 0%| | 0/3 [00:00StarTable length=6\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
n_fitmotion_model_used
int64str20
5Acceleration
5Acceleration
3Acceleration
2Fixed
1Fixed
0Empty
" + ], + "text/plain": [ + "\n", + "n_fit motion_model_used\n", + "int64 str20 \n", + "----- -----------------\n", + " 5 Acceleration\n", + " 5 Acceleration\n", + " 3 Acceleration\n", + " 2 Fixed\n", + " 1 Fixed\n", + " 0 Empty" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tab[['n_fit', 'motion_model_used']]" + ] + }, + { + "cell_type": "markdown", + "id": "188290a9", + "metadata": {}, + "source": [ + "## 2.3. Example: Specify the `motion_model_input` Column" + ] + }, + { + "cell_type": "markdown", + "id": "99624463", + "metadata": {}, + "source": [ + "One can also specify a motion model for each star as a column in the star table. However, the function will \"downgrade\" the model to one with fewer parameters until $n_\\text{fit} \\geq n_\\text{params}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "04db5f9e", + "metadata": {}, + "outputs": [], + "source": [ + "ra = np.zeros(len(x))\n", + "dec = np.zeros(len(x))\n", + "pa = np.zeros(len(x))\n", + "\n", + "motion_model_input = [\n", + " 'Acceleration', # Will use Acceleration\n", + " 'Parallax', # Will use Parallax\n", + " 'Linear', # Will use Linear\n", + " 'Acceleration', # Will use Linear, as n_fit = 2 < 3\n", + " 'Linear', # Will use Fixed, as n_fit = 1 < 2\n", + " 'Fixed' # Will use Empty, as n_fit = 0 < 1\n", + "]\n", + "tab = StarTable({\n", + " 'x': x,\n", + " 'y': y,\n", + " 'xe': xe,\n", + " 'ye': ye,\n", + " 'ra': ra,\n", + " 'dec': dec,\n", + " 'pa': pa,\n", + " 'motion_model_input': motion_model_input\n", + "})\n", + "tab.meta['list_times'] = t" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "2b61fbcf", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Acceleration: 0%| | 0/1 [00:00StarTable length=6\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
n_fitn_requiredmotion_model_inputmotion_model_used
int64int64str12str12
53AccelerationAcceleration
53ParallaxParallax
32LinearLinear
23AccelerationLinear
12LinearFixed
01FixedEmpty
" + ], + "text/plain": [ + "\n", + "n_fit n_required motion_model_input motion_model_used\n", + "int64 int64 str12 str12 \n", + "----- ---------- ------------------ -----------------\n", + " 5 3 Acceleration Acceleration\n", + " 5 3 Parallax Parallax\n", + " 3 2 Linear Linear\n", + " 2 3 Acceleration Linear\n", + " 1 2 Linear Fixed\n", + " 0 1 Fixed Empty" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all_mm_map = motion_model.motion_model_map()\n", + "tab['n_required'] = np.array([all_mm_map[mm].n_params for mm in tab['motion_model_input']], dtype=int)\n", + "tab[['n_fit', 'n_required', 'motion_model_input', 'motion_model_used']]" + ] + }, + { + "cell_type": "markdown", + "id": "d4f96fcb", + "metadata": {}, + "source": [ + "## 2.4. Example: Infer Positions" + ] + }, + { + "cell_type": "markdown", + "id": "c660ec98", + "metadata": {}, + "source": [ + "Continuing from the previous example: Once we fit the motion models and the parameters are added into the table, we can infer the positions at arbitrary times with `StarTable.infer_positions`" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "095be28f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 20 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"dtf2d\" yielded 40 of \"dubious year (Note 6)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 40 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"utctai\" yielded 20 of \"dubious year (Note 3)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n", + "/Users/weilingfeng/Software/miniconda3/envs/main/lib/python3.13/site-packages/erfa/core.py:133: ErfaWarning: ERFA function \"taiutc\" yielded 20 of \"dubious year (Note 4)\"\n", + " warn(f'ERFA function \"{func_name}\" yielded {wmsg}', ErfaWarning)\n" + ] + } + ], + "source": [ + "x_model, y_model, xe_model, ye_model = tab.infer_positions(t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "a4df5458", + "metadata": {}, + "source": [ + "As in `MotionModel.model`, `StarTable.infer_positions` is also vectorized and returns positions and uncertainties in shapes of $(N_\\text{stars}, N_\\text{times})$" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "2f7e8b7a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(6, 100)" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x_model.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "7aab0868", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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UtTbG0pGserpp06ZxH3f//febhxxyiGmz2cy5c+eaa9asMe+7775hVS9Nk6ptnnPOOaMe4y9/+Yt55JFHmna73ZwxY4b5wx/+0Hz++edHVP1Mterpz3/+c3POnDmmzWYzDz30UPP3v//9iIqV//zP/2w6nU5z69atw56brDZ6xx13jPu+h1Y9HctoVU9N0zRff/1187TTTjNdLpfpcDjMpUuXmn/5y19GPP/OO+80GxoaTEmShh1ntK9DOBw2f/SjH5mzZ882FUUxa2trze985ztmX1/fsMeN9X1ItTIoElVPx3Ng1dOk//u//zOPOOIIU1VVs7i42DzvvPNGfP2Tj1uwYIGpqqq5cOFC8/777x/1PcfjcfO//uu/Bn523G63+bnPfc688sorzZ07d6b93ib6no5W9bSpqck844wzTI/HYwIYMUbGGMs1Pl/fMe775vP12Ph8zaYrwTSH5F4wxhhjjDHGGGPMEryHmzHGGGOMMcYYywEOuBljjDHGGGOMsRzggJsxxhhjjDHGGMsBDrgZY4wxxhhjjLEc4ICbMcYYY4wxxhjLAQ64GWOMMcYYY4yxHJALPYB8MgwDra2t8Hg8EASh0MNhjDHGhjFNE36/H3V1dRDFg3dOnM/XjDHGJrN0ztcHVcDd2tqK+vr6Qg+DMcYYG1dzczNmzpxZ6GEUDJ+vGWOMTQWpnK8PqoDb4/EAoC9MUVFRgUfDGGOMDefz+VBfXz9wvjpY8fmaMcbYZJbO+fqgCriTaWlFRUV8AmeMMTZpHexp1Hy+ZowxNhWkcr4+eDeIMcYYY4wxxhhjOcQBN2OMMcYYY4wxlgMccDPGGGOMMcYYYzlwUO3hZoyx6UTXdcTj8UIPg6VBURRIklToYTDGGMszPmdPPaqqWtKikwNuxhibYkzTRHt7O/r7+ws9FJaBkpIS1NTUHPSF0Rhj7GDA5+ypSxRFNDQ0QFXVrI7DATdjjE0xyRN3VVUVnE4nB25ThGmaCIVC6OzsBADU1tYWeESMMcZyjc/ZU5NhGGhtbUVbWxtmzZqV1feNA27GGJtCdF0fOHGXl5cXejgsTQ6HAwDQ2dmJqqoqTi9njLFpjM/ZU1tlZSVaW1uhaRoURcn4OJOiaNqaNWtw7LHHwuPxoKqqCueffz62b98+7DErV66EIAjDbkuXLi3QiBljrDCS+7+cTmeBR8Iylfze8V4+xhib3vicPbUlU8l1Xc/qOJMi4N6wYQOuvvpqvP3221i3bh00TcMZZ5yBYDA47HFnnnkm2traBm5/+9vfCjRixhgrLE5Jm7r4e8cYYwcX/rs/NVn1fZsUKeUvvPDCsI8feOABVFVV4f3338cpp5wycL/NZkNNTU2+h8cYY9NSPBLBby/9CgDgmgf/HxS7vcAjYowxxtiB+Hw9tU2KFe4Deb1eAEBZWdmw+1999VVUVVVh4cKFuOKKKwYKzzDGGGOMMcYYY5PNpAu4TdPEddddh5NOOgmLFy8euP+ss87CH//4R6xfvx6//vWvsWnTJpx22mmIRqNjHisajcLn8w27McYYI4YxuCdp/7ZPhn2cC0NrcSiKgurqaqxYsQL3338/DMNI+Thr165FSUlJ7gbKGGOMTSL5Pl8DfM620qQLuL/73e/i448/xqOPPjrs/osuugjnnHMOFi9ejHPPPRfPP/88duzYgeeee27MY61ZswbFxcUDt/r6+lwPnzHGpoSd77yFtdddNfDxUz9fhd9f/S3sfOetnL5ushZHU1MTnn/+eZx66qn4/ve/jy996UvQNC2nr80YY4xNNYU6XwN8zrbKpAq4v/e97+HZZ5/FK6+8gpkzZ4772NraWsyePRs7d+4c8zE33XQTvF7vwK25udnqITPG2JSz85238OzttyHQ1zPs/kBvN569/bacnsSTtThmzJiBo48+GjfffDP+/Oc/4/nnn8fatWsBALfffjsOP/xwuFwu1NfX46qrrkIgEABAW4suu+wyeL3egZn3VatWAQAefvhhHHPMMfB4PKipqcHFF1/MW48YY4xNWYU8XwN8zrbKpAi4TdPEd7/7XTz11FNYv349GhoaJnxOT08PmpubUVtbO+ZjbDYbioqKht0YY+xgZhg61q/93biPeeXB3+UlXS3ptNNOw5FHHomnnnoKACCKIn7729/ik08+wYMPPoj169fjxhtvBACccMIJuPPOO1FUVDTQseKGG24AAMRiMdx666346KOP8Mwzz6CxsRErV67M2/tgjDHGrDIZz9cAn7MzMSmqlF999dV45JFH8Oc//xkejwft7e0AgOLiYjgcDgQCAaxatQpf/vKXUVtbi6amJtx8882oqKjABRdcULiBB3sARykgTop5C8YYm1DLtq0I9HaP+xh/Tzdatm1F/WFH5GlUwOc+9zl8/PHHAIBrr7124P6Ghgbceuut+M53voN77rkHqqqiuLgYgiCM6Fpx+eWXD/z/3Llz8dvf/haf//znEQgE4Ha78/I+2CQVjwBaBHCUFHokjDGWksl6vgb4nJ2uSREp3nvvvfB6vVi+fDlqa2sHbo8//jgAQJIkbNmyBeeddx4WLlyISy+9FAsXLsTGjRvh8XgKM2hDB5reAPoaC/P6jDGWgUB/n6WPs4ppmgP9Ll955RWsWLECM2bMgMfjwSWXXIKenh4Eg8Fxj/Hhhx/ivPPOw+zZs+HxeLB8+XIAwL59+3I9fDbZ9e8Fdr8CRLyFHgljjKVksp6vAT5np2tSBNymaY56S6YVOBwOvPjii+js7EQsFsPevXuxdu3awhZBM00gFgC6d9D/M8bYFOAuKbX0cVbZtm0bGhoasHfvXpx99tlYvHgxnnzySbz//vu4++67AQDxeHzM5weDQZxxxhlwu914+OGHsWnTJjz99NMAKG2NHeRMgybI970D6GP/HDHG2GQxWc/XAJ+z0zUpUsqnLNMEvM1AoBPwVBd6NIwxNqEZhx4Gd1nFuGlqnvIKzDj0sLyNaf369diyZQt+8IMf4L333oOmafj1r38NMbFd509/+tOwx6uqCl0fvmfts88+Q3d3N37+858PTMa+9957+XkDbIoQgK7tgLMcmPkPhR4MY4yNazKerwE+Z2diUqxwT2nBHk4rZ4xNGaIo4bSV/zLuY0699F8gilJOXj8ajaK9vR0tLS344IMPcNttt+G8887Dl770JVxyySWYN28eNE3Df//3f2PPnj34wx/+gP/5n/8Zdow5c+YgEAjg5ZdfRnd3N0KhEGbNmgVVVQee9+yzz+LWW2/NyXtgU5QkA64KoPV9oJfP24yxya3Q52uAz9lW4YA7WzY30L0TiI2/T4ExxiaLBcedgH+87ma4S8uH3e8pr8A/XnczFhx3Qs5e+4UXXkBtbS3mzJmDM888E6+88gp++9vf4s9//jMkScJRRx2F22+/Hb/4xS+wePFi/PGPf8SaNWuGHeOEE07Av/7rv+Kiiy5CZWUlfvnLX6KyshJr167FE088gUWLFuHnP/85/uu//itn74NNUcmiafveBsL53/fIGGPpKOT5GuBztlUE0zx4NiD7fD4UFxfD6/Vm3yJM14CPHgMEAKFeYMEKoOpQS8bJGGNjiUQiaGxsRENDA+x2e1bHioaCuOuyiwAAF/7bKsw+cklOZ8oZGe97aOl5agqz/OvQuQ3Y9RJQPp/2c/fsAao+B8w7DeCfecZYjlh1zubzdWFYdb7mFe6sCYDiBLo+o8rljDE2RQw9Wc88dDGfvNnBQRCB4plU9LR3T6FHwxhjE+Lz9dTGRdOs4KoAfK10Kylg5XTGGEuDYrfj+sf/WuhhMJZ/ih2QbUDLB0BRHaC6Cj0ixhgbE5+vpzZe4baCbKOK5T27Cz0SxhhjjKXCXQv424C2jws9EsYYY9MYB9xWcZVTtfJwf6FHwhhjjLGJiCLgqQE6tlKGGmOMMZYDHHBbxVYERANAcOxeeYwxxhibROzFgB6j1HI9XujRMMYYm4Y44LaKIFAhFn9boUfCGGOMsVQVz6C+3N07Cj0Sxhhj0xAH3FayFwHeZkCLFXokjDHGGEuFpAJ2D61y87YwxhhjFuOA20r2IiDiBUI9+X9tXytfKDDGGGOZcFUB4V6gdTMVQWWMMcYswgG3lSSV9oAFu/L7uj27gR0vADv+Dvjb8/vajDHG2FQnCNQerGsb0L+30KNhjDE2jXDAbTXFAfTvy9/r9ewG9mygGflQN7BzHdDXlL/XZ4xNGvFYFNFQMG+3eCxa6Lc8wquvvgpBENDf35/yc+bMmYM777wzo9dbuXIlzj///IyeyyYZ1Q1AoNTyeKTQo2GMTWN8vj64ztdyQV51OrMV0Qp3xEcp5rmUDLZh0sy8aQK+FmDXemD2CUDlITRrzxib9uKxKHZvehuRYDBvr2l3uTDv2KVQVFtKj1+5ciUefPBBXHnllfif//mfYZ+76qqrcO+99+LSSy/F2rVrczDazK1atQqrV68ecf+6devwm9/8BuaQFOTly5fjqKOOyviCgBVY8QygZw/QuQ2YsaTQo2GMTUN8vs6dyXq+5oDbajY3EOykoDuXAXdvI9A4JNgGKLgungkEOuhzih0onZO7MTDGJg1D0xAJBiGrCmRVzfnrabEYIsEgDE0DUjyBA0B9fT0ee+wx3HHHHXA4HACASCSCRx99FLNmzcrVcLN22GGH4aWXXhp2X1lZGdQ8fK1ZHoky4KoA2j6k86m7stAjYoxNM3y+zq3JeL7mlHKrCSIAEQh05u41dA1o/ZD2iyeD7aHc1YChU1DOGDuoyKoKxWbP+S3Ti4Sjjz4as2bNwlNPPTVw31NPPYX6+nosWTJ8RTEajeKaa65BVVUV7HY7TjrpJGzatGnYY/72t79h4cKFcDgcOPXUU9HU1DTiNd966y2ccsopcDgcqK+vxzXXXINgmisLsiyjpqZm2E1V1WEpaitXrsSGDRvwm9/8BoIgQBCEUcfDJjlnGRALAc1vc2o5Yyxn+HzdNOI1p+v5mgPuXLC5aR+3ruXm+P42Ko7mrhn7MY5SoG8vpbYzxqY10zQRj0Sgx+PQYvm76fH4sPSsVF122WV44IEHBj6+//77cfnll4943I033ognn3wSDz74ID744APMnz8fX/ziF9Hb2wsAaG5uxoUXXoizzz4bmzdvxre//W3827/927BjbNmyBV/84hdx4YUX4uOPP8bjjz+ON954A9/97nfTHvdEfvOb3+D444/HFVdcgba2NrS1taG+vt7y12F5UDKLtm21vAcYRqFHwxibJvh8fXCerzmlPBfsRbTCHe4F3FXWH79nN+3XlseZsbIX0eN8rbnfS84YKygtGsX/fufSgrz2IcefBLjcaT3nm9/8Jm666SY0NTVBEAS8+eabeOyxx/Dqq68OPCYYDOLee+/F2rVrcdZZZwEAfv/732PdunW477778MMf/hD33nsv5s6dizvuuAOCIOCQQw7Bli1b8Itf/GLgOL/61a9w8cUX49prrwUALFiwAL/97W+xbNky3HvvvbDb7SmNecuWLXC7B9/nokWL8O677w57THFxMVRVhdPpRE3NOBOibPKTFNrP3fYR4CgDqhcVekSMsWmAz9cH5/maA+5ckO2AFqV93FYH3OF+oG8P4Cof/3GCSOPo3c3F0xhjk0pFRQXOOeccPPjggzBNE+eccw4qKiqGPWb37t2Ix+M48cQTB+5TFAWf//znsW3bNgDAtm3bsHTpUghD/r4df/zxw47z/vvvY9euXfjjH/84cJ9pmjAMA42NjTj00ENTGvMhhxyCZ599duBjmy31fXBsilLdgJpILXeUjL6FizHGpjE+X1uDA+5ckW1AfzNQfZi1x+3fB0QD46eTJznLAF8bEOqhIjCMsWlJttlw5b0PYvvGN2BzuaDYUpsFzkY8GkE0GISc4Yns8ssvH0gTu/vuu0d8Ppn6JhwwWWia5sB9qaTHGYaBK6+8Etdcc82Iz6VT9EVVVcyfPz/lx7Npwl0F9DYBe98C5n+BAm/GGMsQn6/HNp3P1xxw54qtiKqFx4KA6rLmmHoc6NpOe8RTWbFWXdQmzLufA27GpjFBEKDY7ZAUJVH1VMn5a5qmDi2mjDjBpurMM89ELBYDAHzxi18c8fn58+dDVVW88cYbuPjiiwEA8Xgc77333kC62aJFi/DMM88Me97bb7897OOjjz4aW7duzdvJV1VV6Lqel9dieVIyi7LFdrwIzFoKlM4u9IgYY1MUn68HHUznay6alis2D61EB7utO6Z3P7Ucc6YRPNs8QM+u3BVwY4yxDEiShG3btmHbtm2QJGnE510uF77zne/ghz/8IV544QV8+umnuOKKKxAKhfCtb30LAPCv//qv2L17N6677jps374djzzyyIieoD/60Y+wceNGXH311di8eTN27tyJZ599Ft/73vdy8r7mzJmDd955B01NTeju7oYxDQturVmzBsceeyw8Hg+qqqpw/vnnY/v27cMeY5omVq1ahbq6OjgcDixfvhxbt24t0IizJIpA+Twg4gV2vgjsf58mwBlj7CDA5+vsccCdK6IEwAACXdYds2c3AIGKuaTKUU5jCHRYNw7G2KSlxWKIRyM5v2mJ2e5sFBUVoaho7KKOP//5z/HlL38Z3/zmN3H00Udj165dePHFF1FaWgqAUsyefPJJ/OUvf8GRRx6J//mf/8Ftt9027BhHHHEENmzYgJ07d+Lkk0/GkiVL8JOf/AS1tbVZj380N9xwAyRJwqJFi1BZWYl9+/bl5HUKacOGDbj66qvx9ttvY926ddA0DWecccaw1i2//OUvcfvtt+Ouu+7Cpk2bUFNTgxUrVsDv9xdw5FkQRKCkHlA9wN43gV0v0zk52DP6hLauUVCuxai1mJb97wtjbHrh8/XBc74WzExqxE9RPp8PxcXF8Hq94/7QpETXgI8eo9RuZ9noj/G3AfYSYNH5NEOejWAP8OkztGJt86T33J5dwMxjKRWOMTalRSIRNDY2oqGhYVjFzngsit2b3kYkzX6V2bC7XJh37FIoauELkkwlY30PAYvPU3nS1dWFqqoqbNiwAaeccgpM00RdXR2uvfZa/OhHPwJAPVqrq6vxi1/8AldeeeWEx7T869C5Ddj1ElBuQaqiFgN8+6ldmGKn7VvOSsDUAS1CRVMNDTCTqyUmIEgUsBfXA55aeh5jbNob7e89n6+nDqvO17yHO5dsxUCoF4j0jx2Up8q7D4gFMquSai+hmfjao/gkz9g0pag2zDt2KQwtf9tHRFnmkzeD1+sFAJSV0XmusbER7e3tOOOMMwYeY7PZsGzZMrz11lujBtzRaBTRaHTgY5/Pl+NRZ0FWgbK51J5Ti1Ctlr5GmoAXJUCUKcAWJQCJPZOmDrRvAdo+pnNy+Tygbgmfkxk7CPH5+uDDAXcuKQ7A30r7uLMJuA2dAuZ0V7aTHCVU3TzQwcVeGJvGFNUG8AmV5ZFpmrjuuutw0kknYfHixQCA9vZ2AEB1dfWwx1ZXV2Pv3r2jHmfNmjVYvXp1bgdrNUGg87ziSO3xznJa+Q73A83vApE+YPZJgH1qZDIwxqzD5+uDC+/hziVBoFluf1t2xwl0Uk9vR4ZBuygDhkmr7YwxxphFvvvd7+Ljjz/Go48+OuJz47WIOdBNN90Er9c7cGtubs7JeAtOlKlrSNkcoHsnpblbWVyVMcbYpMMBd67ZPFRdPJuKpr5WwIhTb+9MqXbac8YYY4xZ4Hvf+x6effZZvPLKK5g5c+bA/TU1NQAGV7qTOjs7R6x6J9lstoGiPBMV55kWJBUom0fn951/B/qn6QQDY4wxDrhzzl4ERH2Zz2DrGqWTqxmmkyepHiq8Fg1kdxzGGGMHNdM08d3vfhdPPfUU1q9fj4aGhmGfb2hoQE1NDdatWzdwXywWw4YNG3DCCSfke7iTlyjRXvCID9jzKp2jGWOMTTsccOeapNLqdijDgDvQAYR6Mk8nT1JdVHQtzGnljE0H07G/88Fiqn/vrr76ajz88MN45JFH4PF40N7ejvb2doTDYQCUSn7ttdfitttuw9NPP41PPvkEK1euhNPpxMUXX1zg0U8yggCUzErs636H24cxNk1N9b/7Byurmnlx0bR8UOyULlZzePrP9bVS0TRZzW4Myb7goV46uTPGpiRVVSGKIlpbW1FZWQlVVcfcF8smF9M0EYvF0NXVBVEUoapZ/l0vkHvvvRcAsHz58mH3P/DAA1i5ciUA4MYbb0Q4HMZVV12Fvr4+HHfccfj73/8OjyfLbK3pSBCA0lnUwtNVCdQfW+gRMcYswufsqcs0TXR1dUEQBCiKktWxOODOB1sRFT6LBgCbO/Xn6XGgdzdgt+gCRXYAvhag7ihrjscYyztRFNHQ0IC2tja0trYWejgsA06nE7NmzYIoTs0ks1Rm/AVBwKpVq7Bq1arcD2g6kFQKtts+BNxV3FGEsWmCz9lTmyAImDlzJiRJyuo4HHDng+qhPdyh7vQC7mQ6efHMiR+b0jjcNI5YCFCd1hyTMZZ3qqpi1qxZ0DQNuq4XejgsDZIkQZZlXuFgIzlKgKgf2PcO4CjldmGMTRN8zp66FEXJOtgGOODOD1EETBMIdAGlc1J/nnc/YBo0820Fm5v6cYd7OeBmbIpLpjhlm+bEGJtEimdQodT97wFzl9P1A2NsyuNz9sGN/5Lni80N9O+l/dip0GJAbyOlo1tFlOn1892POx7hQjCMMcbYRAQRKJoBdG2nawbGGGNTHgfc+eIooRVuf1tqjw+0U2DsKLV2HIqd9nHnSywI7FoH7H6JUtkZY4wxNjbVSYXU2jYDWrTQo2GMMZYlDrjzRbYDpg5075r4saaZeJwJSBanniT3ccfD1h53NFoUaHqT0uO6dgJNb9BqN2OMMcbGVjSDupt07yj0SBhjjGWJA+58clUCfXsmTukOdFJ1cne19WNQPUDUl/u0cl0D9r0NdH5K+9ZL59D/N73BM/aMMcbYeCQZsBcDrZupRzdjjLEpiwPufLJ5gIgP6JtgX1bnNkCLpFfRPFVSYh93OIcBt2EALe8BbR8DJfWAbKM+4qWzgc6twN63eE83Y4wxNh5XJRDuA9q3UOYbY4yxKYkD7nwSBNqT3fXZ2KnVgS6gZxf14cwV2Qb4UtxLnonuHUDL+4CnClCGVEOX7UDxLLp46N6eu9dnjDHGpjpBADw1QNc2wMf9exljbKrigDvfnOW0h7p/3+if795O+6utrE5+INVNPb5zsZ/aMGhCQbKN/h4UOwXhvY08Y88YY4yNx+ahLVqtH9K/jDHGphwOuPNNlGiFueszCk6HCvXS6rCrIrdjsLmBaIBS1awW7KJg3lk29mMcJbRPPRevzxhjjE0nRTOAvibKfmOMMTblcMBdCO5Kas11YIuwru1A1E8BaS5JKmDEgUi/9cf2tdD+c8Ux9mMUJxAPAv5261+fMcYYm05klVqFtX5Ik+WMMcamFA64C0G2U+Gyzm1Ax6cUaHd+Rqversr8jEGUaZXZSnoc6N5JlVXHIwiA7KAZe8YYY4yNz11N2WMdnxR6JIwxxtIkF3oABy1PNQXcXduG3CnkphXYaGxuKpxm6JTmbgV/GxDqBopnTvxYRzEQaKd2J7le0WeMMcamMkGk64OOrUBpA11DMMYYmxI44C4U1Q1UzC/g67toz3i4H3CVW3PM/mbANChlfcLX9wD+Dpqx54CbMcYYG5+jBAj1AG0fAa4vACInKTLG2FTAf60PVrKD9lpbtY87FgJ691Dbs1QIAgXmY1Vrz5e+JqBrR2HHwBhjjKWiaAZt3erdU+iRMMYYSxEH3AcrQQAgAMEea47nb6Pg3Z5iwA3QXm9vCxWKK4S+vcDu9UDja7yfnDHG2OSn2AHFBux/h7LUGGOMTXoccB/MVCdVFbeiH3bvHkCQ0ktxsxdRsO3vyP710+VrpUDb0AAYwN6NfPHCGEudFqU6GB1bgd2v0JYaxvLBUwcEe4F9bwNarNCjYYwxNgHew30wU120Kh0LADZP5scJ9wPeZsCZ5l5wQaSCbd79+d3PHugC9rwKxIJAySwAJtCzh4Lu+afTCgJjjI2lYyvQ8iFNGBpxQI8mOkzUF3pk7GAgCEDpLKBnJ+AsA+qPS2StMcYYm4wmxQr3mjVrcOyxx8Lj8aCqqgrnn38+tm/fPuwxpmli1apVqKurg8PhwPLly7F169YCjXiaUNwUdIb7sjuOvw2I+DML2u3FFKzHQtmNIVXhPgq2w30UbAsCBf6ls4HeXUDL+4Bh5GcsjLGpJx6molVaGCiuAyoWUKtHxvJJUgF3DU389Owu9GgYY4yNY1IE3Bs2bMDVV1+Nt99+G+vWrYOmaTjjjDMQDAYHHvPLX/4St99+O+666y5s2rQJNTU1WLFiBfz+Au3/nQ5EkaqKZxtw9+0FZFtmM+z2YiDipWrl+dC9m9LJS+cMH6+kAEV1QNtmoGdXfsbCGJt6+vYCwW5K602lIwNjuWIvAmQV2LcRCHQWejSMMcbGMClSyl944YVhHz/wwAOoqqrC+++/j1NOOQWmaeLOO+/Ej3/8Y1x44YUAgAcffBDV1dV45JFHcOWVVxZi2NODbAf87UDtkZk9P+qn52fa2kuUaA95uA9AQ2bHSJWuAX2NdJEijDLXpLoBsY/S9CoX5nYsjLGpR9eAzk8Bxcktmdjk4KkFehuBHS8AM48FKhbSeXUi8Qidd8N9tLXMVkRdRhwltN2MMcaYZSZFwH0gr9cLACgrKwMANDY2or29HWecccbAY2w2G5YtW4a33nqLA+5sqC6aGdeitEqdrkAnBd3uyszHoDho1XnG0ZkfIxXBLiDUTRcoY7EXD76nbPa1M8amH28zFUormVnokTBGBAEoawCCncCul6nzx8x/GNmi0zSpMGiwkwr8BTqAaIBqEAiJbDdRomsCdzXtC3eWFeY9McbYNDPpAm7TNHHdddfhpJNOwuLFiwEA7e3tAIDq6uphj62ursbevXvHPFY0GkU0Gh342Ofz5WDEU5zNTcFuuA/w1KT/fF8rnaxHWzFOleqi149HcluwzN8O6LHxJxZsbrogCXZxwM0YG2SaQNcOCnA4lZxNJoJAQbKtmDIwAh00sSyrgKgAokyTRcFuIB6in197EdUgGPqzbGgUhHfvon8bTgE81WO/LmOMsZRMuoD7u9/9Lj7++GO88cYbIz4nHLBH2DTNEfcNtWbNGqxevdryMU4rkkppkpkE3FoU6N9HJ+5sqE4K3CP9gJJB0J8KQwd6d08cRAsiAJFalZXNzc1YGGPpMU0g6kts+0ghXTYXAh2Ady/grirM6zM2EcUOlM+nCeOenbRqbeiDn3OUUK2Ssa6bRJkeYy+iWgW7XwLmnAKUcPV9xhjLxqTahPa9730Pzz77LF555RXMnDmYsldTQ0FYcqU7qbOzc8Sq91A33XQTvF7vwK25mfukjkqUaOY7XYFOCpLtJdm9/kDQ35/dccYT7AZCPYC9dOLH2tw0kaBruRsPY2x8yRTYjk+B7X8DPnka6PikcOPp2QXEo7y/lU1ugkCTQiWzqDho+Ty6Fc2gn91UipsKIj03GqA0da6CzhhjWZkUAbdpmvjud7+Lp556CuvXr0dDw/DiWQ0NDaipqcG6desG7ovFYtiwYQNOOOGEMY9rs9lQVFQ07MZGobpohTk5E54qfwdgmIBkQaKEKNL+6lwJtNOKfCop6/ZimkgI9eRuPIyx8e3bCHzyFLDrJcDXQntN2z4GIgXYGhTuB7p3Aq6K/L82Y4UgCBS0mzrQ+DpXQWeMsSxMioD76quvxsMPP4xHHnkEHo8H7e3taG9vRzgcBkCp5Ndeey1uu+02PP300/jkk0+wcuVKOJ1OXHzxxQUe/TRgc1O6ZjrtwQwd6G8CbBat9qguKkaUix7YhgH07El9ZUq2UXAe7LJ+LIyxiYX7ga7t9LtYsQAorqcVunAv0LE1/+PxNtPfSHtx/l+bsUIqqgNiAaDlPc76YoyxDE2KgPvee++F1+vF8uXLUVtbO3B7/PHHBx5z44034tprr8VVV12FY445Bi0tLfj73/8Oj4cLW2VNcQLxMBUVS1WoJ5GiXWLNGFQXVQaP5mD1KtQDhLrSa10m2ymtnDGWf95mIOIFnOWD9wkC4KoCOrflf7Wtfx/9nUwlHZex6aa4HujeDXRvL/RIGGNsSpoURdNM05zwMYIgYNWqVVi1alXuB3QwUhzUo7r6sNQuKpOtxKyqKq44KUU90p95T++xBNoTFdCdqT/HXsTtwRgrBF2jauA2z8i/RY4SqsfQ9jEw//T8BMDRABDgrgXsICYnqpq3vE/Vz7ldGGOMpWVSrHCzScBRQgFvKmnlpgn077W2hZcg0nGtLpxmmkBvY3rBNgCoHgq2Oa2csfzyt1JFcOcY+6WL6qgCszdPRTBDPUAsSH8TGDtYuSqBsBdo+SA3W78YY2wa44CbEcUFxIOppZVHvHRBbFU6+cAYbIC/zdpjhnpppTrdVXNRpNUzf4e142GMja+3kSbK5DF6XatOAALQujk/e0qD3QAM+pvA2MFKEIDiGZRW3rOr0KNhjLEpha8gGBEEQE6klU+U4u9vAyJ+69vjKC66uNWi1h0z2AVo4czGavNwezDG8inipYB7opTVolpa4c71Krdp0t8AbgXGGG09k+1A6wdALFTo0TDG2JTBATcblEwrj/SP/Rg9TkWLVBelgVtJdVPqZsRr3TGDXYAgZfZce1Hh24OlUN+AsWmjvxmIeieuBi6p9LsRyHEGSqSfKqPz/m3GiLuGrhN4lZsxxlLGATcbpLqp/cd4adT9+6h9l7vS+teXVUCPWbeP29Cpf2+mq1OynVbbc9kffDxtHwM719EkB2PTna4B3Tvo71AqxdBsHqCvKbcZKKFeWslTeIWbMQC0tcJRDHRsoQlyxhhjE+KAmw0SBFo56msa/fOGQb1xRYkel5MxiNatKIf7E1XG3ZkfQ5TpojvfenYD+zYCnZ8CHZ/k//UZyzd/G9WQGKtY2oHsxVTkMZcTYv4O+rvI7cAYG+SqpMr93TsKPRLGGJsSOOBmwzlKqUrwaGnd/laqTu6uzt3rqy668LYilTrcR+3AZEcW43FS2mo+U7t9rUDT6xTsuyqBlg8pq4Cx6ay/GTD1sYulHUi2UfZHrnpyGzrtEed0csaGE0Sqs9D+CU1qM8YYGxcH3Gw4m5v6zh6YVm6atLptGNa2AzuQ6qJ9k1acxINddGGQzeqU4qCxxALZjycVoV6g8XUgFqb2R84yQIsA+zfR5MFk4WsD9r1LQQlj2TIM2v6RbnCrOCkjJxcTYuE+2k9uK7L+2IxNdc5yykbr3F7okTDG2KTHATcbThABSaGV7KG9NoNdVD3YXZXb11dctGdyvMJtqUhewKtp9t8eMR4nEA/lZxY/FgKa3gCCnUDprMH7i+vpa9++JfdjSIWvDdizHmh+hwvnMGtEvUDUR/u302Evps4G2f69GE2wmya5cjnByNhUJYiAqwLo3GptoVPGGJuGOOBmIznLaTV7xwtA9y4qHNa9C4iHs9sPnQpRBEwj+8JpUR8Q8WU/XlGm8eTjgsLbTKt1JXOGV4CXZJroaNtMabeF5G+nYDvso8mMlg8oI4KlbrK2mTN0wNtSmCJ94T6a2FLS3P6huij7JNBl/Zj8bTT5yBgbnaOMJrt4lZsxxsbFATcbyeahPrf9+4AdzwOfPA10bwdc5fl5fUmlVd5shHsTF/BZrnADAETrKqePx7ufLvAleeTnHCUUCHVszf04xuLvAHavB8JeoHQ24Kmh/bOTZeV9sjN0oONT4NNncrfvOBOmST97O18Etv+NJtvyLdQHmEi/1aAg0KSYr8Xa8WgxqqXA+7cZG5sgUJHDzq2FKS7KGGNTBAfcbHSKk4Kq0jmAHqF2XfaS/Ly26qLgLpuVtlAfBRJW9ApXHbSym0vxcOICf5z9oo5SmoiIh3M7ltFEfMDuV2jioXROonKzSEF3x1YaOxtbxAfs2UATFn17qdjQZOixHuoF9rwKfPYc0NtE97V/nP92P9799HuWCXsxPd/KGgehnkSGDAfcjI3LUUq/K4WcDGaMsUmOA242PlGmquQls/LXGkd1A/Fg5mncyRW7bPdvJylOSlGPhaw53miCXfR+7eME3DY37SW3qm1aOvztib3ls4f/HNiLaDKmdfPkTZUutN5GWjnu2EKF8EpnAz07rV+VTZeu0QRA+xYqzlfWAHjqaPU9n+1+ogFKKVczDG7tRfS7k21WzFChHsCI5679IWPThSDQxGvX9pHFVhljjAHggJtNRrKN9o1nGnDHkhfwFu03VxyJwmk+a443Gn8nAJMmOMYiypSWXIiA29dCrz9axkDRDKB3NwWRbLhogArhRXxA+Xz6WVJd9H1s3zK8MGG+BTtp73PJ7MHfFVGkGg7tn9CY8yHcRyvqqiuz54syANPai31/GwfbjKXKXkTdNNq3TI7MHcYYm2Q44GaTT3IFNdM9YeE+CrozvYA/kKTSamCuAhDDAPqbUpsgUOxU2Cqf4hF6TXvx6J+XVcoCaP+ksAHkZBTooKJCRTOGT1Z4amnlu39vwYYGbytgaCP7Xg+0+/ksP+MI9wHQAVHK/BiqmwoOWtGmTovRKj+nkzOWOk8tda3w7i/0SBhjbNLhgJtNTooz833BoV4ARnYX8AcShNwVTgv3UtAxXjp5kuqh9PNcprcfKNQ9cT9iewllJOSiPdNU5msFINDK8VCKnQLw9i2FScXXNaB3D2AfJagUBMBVmb9CSP42QLJldwx7Cf0eWTHecB9t3bAqQ4axg4HqpI4eHVusmfhijLFphANuNjkpTiDSl1lg6WsFZIt75yp2IJij/WnBrtQrqtvclKacz7TyQBdg6qNXT09SHFTMLdyXv3GNxTTzlw49Hi1Klf7HygwoqqUCan2N+R0XQCvvoR7AXjr65x2ltIWic1tux6FF6ecr2+BWsdPKdKg7+zGFe6kuwYEr/4yx8RXVAj2NlG3CGGNsAAfcbHJS3RRsp7tiGg/TRXemBZjGojhphVuLWntcgHprp7rCJ8qAqeUv4DZNSndXJkjPFwRAABAswP7yoUyT+pVvfz43vZnTEeikn9+xqvtLKgWKbR/nv/e1b4x08iRBoGKJXdtzu8od7gdifppIypYkW9NNINA5fi0FxtjoZDu1tmz9kLJEGGOMAeCAm01WkkwBQbpp3KHe3KSDKk5ahbZ65TQWpJTasVZBxxpLvipch/voa5pSursL8O0vXNEc0wTaPgL2bqR9hG0fFbaAj7+d9rSPlxngqqLiZfnMWNDjY6eTD2Urop/PoAWrxmMJ99J4rChQZvPQRIIWy/wYugb42qyZAGDsYFQ0g34P972T/XYZPU5/y/0dNAHPBdkYY1MUT+OzyUuU0w9EQt20f2y8ICcTso3STKM+wF1p3XGDXZQiXjo79efYkvu4s6jsnKpgN000eGonfqzqoRXdqC+9CQQrmCb1j977Fr22u5qqplcsSO9raxVDp7TKiQI3WaWLynAftdbJh0AnTaIU1Y3/OEGgOgj+NqByYW7GEuyybjU5GXCHeii1NRORfiDmA5wV1oyJsYONKAIl9bQdxVkOzFiS/jFCvVRQsmsnEOqieheKgyYB3dVAzeL8n2MYYywLvMLNJi/VRatN6VS+7t9HJ+ZcMJF5q7KxDLQDS6PAm5rHfdy+VkCQUuvBrjqBaDA/hbYO1L5lMNh2liV6sAu0yp3vdG2AJirCvYCjZOLHSoo1qdCpmiidfCibh7IpcvE1NHQai6XdBOLZ/V6E+2jbSK7+hjB2MJDtgKscaNmU3n7uYDewaz2w9Rlgz2tAPAgU19PkoGyn8+/+94BdLxfmPMMYYxnigJtNXqqL9ndGUwxyIz46YY9XTTsbio2KTVkl1VXQA4kSVYPN9QWHFqVgK5V0coBWIQTk/0Io1Au0vEcTEc6ywfuLammVpHdPfscD0M+JFkmteJ/qpsAzHxMDqaaTJ9k89HuVi+9pxEsTR1amb8u2zLsbALTijhQmlxhj43MkCjLue3vivx+xELD/fWDbX4COrYDNRVk1nhqakJRUmkz11ADl86hN5e6XC1+ngzHGUsQBN5u8FAediFPdxx3qoQv4XLXzUZx04WBVYBTqBaL9gC2D1DjFCXibrRnHWILdlGKbzgSG4sh/H9ZgN6XXO8uH3y8l+oO3bs5vGzXTpImUiQrNJdnc1Dc+HxXeA4n94o4xqpMfKLmVworq3wcK9wFaGJAtXE22eWiyIx5O/7mGQRfyud6mwdjBomgGBcWf/Y0C6qF/40yTzoGdnwGfPQfsfYP+ZlfMH/+cI0pA2VzKDtv9cn6zgxhjLEMccLPJS0j8eKaaxh3opMWpA3seWyVZOM2q6quR/kT6agYtzGweqggeDVgzltEEOyn1WFJSf47qGexjnC/+trHT3t01QKCdqm3nS7iPVkodKU6kyHb6OchHZoCvNVHILY0iZZKa3arxWJLvN5XtCqmyeaiGQCZp5VEvPddmcYcDxg5WggiUzwVgAE2vU6p405tAywfA1qeBT54Cdq2jc3zZvOEZSuMRRaBsDv0N2b2e08sZY5MeB9xsclNsFFBNxDBo/3auVreBRGAUsW4fd6gPGaevqi5aFc3VPm7TpB7R6a72JceVr37cWoxW1McKkkSRVnM7P81NS7fRBDppxT3VFW6ACodZuV1hNKZJWRG2FPq9D2Xz0CpSPGLteALt1u+VFmXaqpHJ70WolybUeP82Y9YRRMBVCVQspHNo64dA01t0jnCUUKBdPCO9OibJ45bOoQynQnekYIyxCXDAzSY3xUUruRO1+gn3JXoe52j/NpBYiTOtW731t2V+cS9Kgyl5uRD1UdGvdNPdRQlAHvaXJ4V6ElXRx/m+24sT7ydPkwDeZloVTmfl1uamAoHZttEZTyxIk0XpTqLYihKrxhamlccjtFVESTP4T4XioN726Qr1UmFEgU+LjFlOECjALp8HVMyjQmiqK7sMF0Gg43R+ll5xNsYYyzO+smCTm+pObSU31E37NnNxAT+UqFoTTMZCNEGQzXgVG6V950LER2PMZHyyI399wkPdE/dxTlavzkfArcWoZ2y6acmqh9pRRfpzMiwAFGzHM/ieSlmsGo8l6kuMJQf7pW0eWvVKZ7uFaVIPeTXHfz8YY9ZKBu2tH1qfhcMYYxbhgJtNbrJKRZsmKsTla7Wun+94FDvtz802fS3ipYA2mwJNsoPS0g09u7GMJuoDYGS2H151JwqZ5aFQWX9zanvgRZlSvXMt6ge0UPqBm2Kni8VcZgZEvPSzksnvSaarxmOOxUeTE6m0JkuX6qHV/HQmCKJ+mpCxsmI6Yyw/imdQZlHXtkKPhDHGRsUBN5v8HCVAz86xZ6+1KFUXzmU6eZLioBX3WDC740S86RckGzEWO60SxnJQOC3cDwgZTmAMVN3OcVp5NEBBdCpV1Ad6uudgcmLYmLz08yjZ0n+uICXaUuVIqCfzSSlbUfqrxuOJeHPXfUsUqW1eMI0U+HBvIqODA27GphxRBhxltJebC6gxxiYhDrjZ5OcopZPoWGnKyX28ueq/PZTspNT1bPdxh3qz3ysqO6itUi4qlQc6sthfLgOmnvsU7lA3BfZqCunbyUkAqwrejSXqT+wDziCatLlp4igXkwKmSYXPMk2ZVt2JVWOL9nH726xtB3Yg1Ql496WeieJNVGHPVYcDxlhuOcuBiJ/aQBpGoUfDGGPD8NUFm/xEmVb/eveM/vlgN2BmuVqcquR+1mwCbtOkCs3Z7hcVJVrJs7oFVyxEExjZVGuWbIAvx/1RA4nU/lSCpOTkRK4nAYLdmf8c2tz0dc/FpEDUD8T8me+ZFkUABhUwzJYWpe9DLquB24pou0Uqe+LjEaCvkYrrMcampmQBte4dqXU2YYyxPOKAm00NrnLaQzpaulj/vtyulh1IQHZBbnKl1ZICTQLth7VS1J8oQJfF11RxAOGe3K00GAbQvzf1PbeCAECwJmAcb0zBrsy/r7KDvu65SIlM1gzI6nvqpK951vULEgXTclmgTHXRBIM3heJ9gXbaQuEoyd14ppnXXnsN5557Lurq6iAIAp555plhn1+5ciUEQRh2W7p0aWEGyw4eqpMmxDu3cZswxtikwgE3mxpsHgpUDyyeFuqlVcV8pJMnyfbsqoMPVIu2oEKzbAdCFu/7jfoS+8uzKGglO+g9xrPc6z6WSD8FSens21edVIk6VxdiMX92fZwFgbYZ5GIfd8RL2RDp9rodylZEX/NsV+CjPiqEKKdQ7C5TgkBBd/eOiVP0k39T8lF0cZoIBoM48sgjcdddd435mDPPPBNtbW0Dt7/97W95HCE7aHmqKGMl0FHokTDGJhNDpwLL+94Fdq7LfU2fA/AVBps6bG6geztQtYhSu8P9QONrdAHvrszfOBQHBfq6RuNIV8RLe5yzCX6GjiXcn2iNZVFKfcRH+5CzISequUcD6bfISkUw0QZOrkv9OaqbAvWoPzcF9qJ+WkV2VWd+DNVJtQqMDCvEjyXUk/3Ph+qkfeDhvuxWgyPe7H++UuEsp/EGOijVdDTxMNDbCDg4nTwdZ511Fs4666xxH2Oz2VBTU5OnETGWoLqpNWPXdsDDP3+MHfT0OND1GdC9k64HYiGKGQzNmuvwFPEKN5s6nOW0b9ffShf9u9dTOnlZQ/YFyNKRTP2NZZhWHuzOvAL4gRS7NUXchgp2Uo/vbEiJwmnZVnMfi6+V/lCmU5xMcdEf2lzt4474AKS4p3wsamIft5WV5w2DLkCz7VEviKAtDP3ZHSfQkVort2zJdjqh9u0d+zH+NpoAsJfkfjwHmVdffRVVVVVYuHAhrrjiCnR25qEtH2MA4KoEenal16mAMTb9aDGg6U1g9yt07eepGXsCPsc44GZTh6RSWmz3Tvrl8bYAZXPznwqq2AEtklmQmwx+sum/PZScGItVAZqu0ep9tsFZUqaTEuPR47QKnO7KebLwV64C7nB/9hM/isP6CZRkAG/FnmnFRu3VMqXFaB+9VT9fE7GX0IX3WD3hvftp0iaPs9wHg7POOgt//OMfsX79evz617/Gpk2bcNpppyEajY75nGg0Cp/PN+zGWEbsRTTZ27Wj0CNhjBWKFgX2vgm0fwQUz6BAO5db2SbAATebWpxllCo2EGwX4EJZSARumQRFVgY/w8ZiUcAd9WVfMC1JUimV2WrRxF7pTCYtZDutjudCNq3UknJReT6aKFImW/Azp7roexqPZD4WLccF04ZylNFEyGgtBWMhWv3m1W3LXXTRRTjnnHOwePFinHvuuXj++eexY8cOPPfcc2M+Z82aNSguLh641dfX53HEbNpxVdIWNO7LzdjBJx4Bmt4A2j4CiuvzN8k/Dg642dRiL6H9o2VzC9szV5DoQj5dAwXTLPzlz3Qso4n6acXcillA2Q4Ee60vUhb10cylnEHau+rOLmAcy0ArNasqz/dbcJyEiBeARXvCVRdN7mQ6vogXiEepbVw+iCLtXe/ZNfLncCCdnPdv51ptbS1mz56NnTt3jvmYm266CV6vd+DW3NycxxGyacdeTNt8uncVeiSMsXzS40DT60D7FqB0dm5bkKaBA242tQgC4CgtbLAN0C9wIIM9iclq0VbuOc+2avpQUR8Ai8an2KlKudX7uKMBZDxG1U3PtzqtPJplhfKhFAdtO7BKoAsQs6g4P5SkAkY8869f1Edt9dLZe58tZzllxBy40tXfTD9DnE6ecz09PWhubkZtbe2Yj7HZbCgqKhp2YyxjggC4KoCubdl3VmCMTR1tH1NrwNLZBU0hPxAH3IxlQnYk2kCluVIa7Myu3dZoFGdiZXrs/ZEpC/VaV9BNdiT2l1sccIf7Mh+jpGQXMI4l6s++lVqS4kykgVuwCm/oNDFkZQq3KGdejCjQmVlmQjZsbpr48e6jGgpRP+3d7t/LvbczFAgEsHnzZmzevBkA0NjYiM2bN2Pfvn0IBAK44YYbsHHjRjQ1NeHVV1/Fueeei4qKClxwwQWFHTg7uDhKKfura+zMCsbYNNLfDLR+SJNtkyjYBrgtGGOZURxAwEcX76lWXNY1Wm20qmDawFiSLbj82QUzpknHsSo4kxR6z7EAgCxaZR0o2JXdSrKkUOBXvci6MUW8oKVbCygO2g+ezs/WWJI1Axyl1owNoJ9fX1v6rcv0OAXqhdhLZSsCOrZS/Yd4mCYzzDhQOi//Y5kG3nvvPZx66qkDH1933XUAgEsvvRT33nsvtmzZgoceegj9/f2ora3FqaeeiscffxweTw5aBDI2FkFI1H3ZBlQuzE07SMbY5BALAs3v0uKHldc8FuGAm7FMyDaquJxOD/Coj/4gOC3+QyDZaHU76qdZvUzFgpRurVq530WwtgBYLJQIRLMYo+oCAu3W9roOWrhyK6np/2yNJeKlALNo7FTetKluyhCI9NPFbMpjSRRvc5ZbN5ZUuSpoEkNU6PvvrKDWdSwjy5cvhzlObYYXX3wxj6NhbBzOMqrh0LMbmLGk0KNhjOWCYQAt7wPeZqB8fqFHMyq+4mAsG+kEk+E+Cn5ki3sACgKtTmfbGiy5D9nKgEiSra0SGwvQ1zCbytLJ7QCxgDUrHnrc2lZqggDLJioiXkAwra0ZoNgBfzj9gDvqta4gX7pEGSiakf/XZYwVliDSalfHJ0DFAtpiYpVgD50zAQAmAIH6/EqKda/BGJtYz06gbQtQPHPS1mXhgJuxTElKem2vgj25KxglKdkHtlE/YOrWrvwpdvoamaY17zvqpz3YchZ7peVECn4saE3AHfXTJEA6wedEZCXzfdJDBS0smJaUDN7TrYwf7k9ck+axYBpjjDnLge6ddFFeZ8Eqt2FQmnrzuzRxm0z2EEWgahEw+4T816pg7GAV6qXfRdVp/ZZNC3HRNMYypTgoKDKMiR9rmtQLOFd/DJJBZDYtuML9sGwfcpLsoMB2YBUgS1E/YGY5RkmmYmLZZgQMjCnRu9zKC6x0frbGYhh0jFz0vJYdo/e2HotpUjGTfPXfZoyxpOQqd+en2RfxjIeBvW8Au1+l45bNAyrm081TB7R/DDS+bn3rScbYSLoGNG+i61e3hbWCcoADbsYypTgTba9SCNyifiDSl7uAW3EMpltnKtiZfZGuAyl2ayuVh7pp9dcKVu0tj/oBWJ227aBJilgWY4wF6BhyDnpQqi6aVY6lOJESCwDhXmvTORljLFXOCiDQTXu5MxXsBnauA1o+ADzVgLtqeMaOYgdKZlH6etPr2Z2PGWMT69oGdO8ASmZO+uw5DrgZy5RipxNqKgF3pJ+CEyVHAYfioLFkGkRqMZohtDo4k1Ta42xFcJtcsbViD7BsoxR/KwR7rG/1JjspWI74Mj9GMtXdit7gB1LdNIkS6U/t8cngPFc//4wxNh5RpDaAbR9ltv0q0AXsegno30er2mNNnst2oHQOdUXY8xqvdDOWK4EuYP/7gKN40rUAGw0H3IxlSkykJqdy8g71ArCwKvaBJHVIC64MxAKAlqPgLHl8K44RD1lTnEy2AeGe7FK2AUqVDnVbnxkgioBpZDdREfXTMXJRQESSqfVGqvu4k/v4c/XzzxhjE3FV0t+s5rdpIjhVoV5gz6v0d6ysYeI6J7INKG0Auj+jfeOMHSwMHfC1Upr39udpgsvbYv3EkxYD9m+i60JXlt1c8oSLpjGWDdkGePcDNYvHf5y/LT8zcJkGaFE/tRbLRaEXSUm/wNZokinzVvxxHUjBDwK2LHoDJ9Plc/G9FcTsvm6Rfli+J38oUU69n7l3P6BO/hloxtg0JghA6SygayfgqgZm/sPEzwn3AbtfobaCZQ2pbx2SVcBeTHu6Sxt4Ow2b3uIRSu3u2UW/K7oGKDYqVihKgK2Ifn9qj8zumiupYyu9Vuns7I+VJ7zcwFg2bEX0x2W8PcrxSKJ4VY5PuNlUKo8FYfk+5CTZln1BN2DIiq0F84SyA4hHqe94NmLB3LW6Up1AsCPz5wc6c5exANAFpL+dTqzjifppZUi14CTLGGPZkFTAXQm0fkDp4eOJeGll29dKQXO650dXJZ37Oz/LeLiMTXpaFGh6gyamwn3UGq9iPlBcT634iuvpd2f/+8Bnz1EdhWyuB7t2APvfpe4DGWznC8V19ARjmb9+hjjgZiwbNvdgQDGWcB8FdrkOuIe24EpXxIucrYYqjsHANBtRPywboyQDZhYp+EmxAKU2Wb2HG6BJgeQ+7HRpUfqe5jTg9lAhwGDX+I8L9dL3P9c//4wxlgpHKaW+Nr87+qSraVJQsP1F6q5Q1pDZdhhBpKCg8xO6DmBsutFiQNObQOdWyh4pqhu5ACEp1Da1Yj79vu14kYoKZpKR2dtIwb2kpt2KNa4b2NcbwpYWL5q6gohqevqvn4VJE3C/9tprOPfcc1FXVwdBEPDMM88M+/zKlSshCMKw29KlSwszWMaSRJl6cI7XMzncR72jJYuqa48lmxZcwa7cBWdyolJ5tqvJgU5rV5JNWBBwJzMDcjBZoTip0FgmJ6WoP7d78gH6Xugx2i4xnlAvfa15/zZjbLIorqfWhntepfTUYGKyOuIDGl8Ddv4diHqpQFo2dTAcZUDYC3Rss2zojE0KehzY+yZV5S+eNfH1mSACxTOoun/LB8Bnf0tvtdvXSoG6qdMqeqrDNEy0+yL4cF8/Pm31IhzVoWWbcZmBSbOHOxgM4sgjj8Rll12GL3/5y6M+5swzz8QDDzww8LGq5mBVibF0qQ6gfy9Qt2T0wCvQmftgG6AV7nBvYjU9jfZjWowuMnK1x1xS6TVifgAZ7r/WNZq4sLI4maxmX6k84stNGj5A40tWeHdXpffcqI9WuaUc7MkfylYE9O6mfVljXZT6eP82Y2ySEUWgZDbgbwV699AEp6uCMooCnRQYWNHGUxDo73fXZ5Re654aBZ4YG5euAfs2Au1bgOKZ6V2bqS76XfC1ATv+TjWQZhw9/u9boBPYs4EWIVLct22aJvpCcezrDaHTF4EkCqj02GCEwjD0LAvmZmDSBNxnnXUWzjrrrHEfY7PZUFOT+qwGY3lhKwJCfVSkylE6/HO6RiuA+UinHVapvDr158UCtAKdZnpOygQBgJldL+6ojy6EnKUTPzZVsp1WX40sqseHeqyvUD6UAHrv6Uquiue6L6WjlH6+A51AUe0o4wjQpAbv32aMTTayjVa6ATo/hboBQaLUVysnUh0llAXX8QngWj7p+wUzNqHu7VSBvGhGZpl0ydXuaABoeZ/qwdQeATgr6LpCFGnlO9BBq+DdO+l3tKwhpcP7Ixqae0No84ahmyZKnSoUmX6n8x9qk0kTcKfi1VdfRVVVFUpKSrBs2TL853/+J6qq0lz5YcxqqpP+WIR6RwbckX5a2XXmcVY73TTpZMCdiwrlSaKcXcXtgTFaGNwqQ1LwM6kgq2u0TzqX1eclGwWz6Qr2AGIesipkG22X8LeNHnCHexNtOypyPxbGGMuU6rJmRXssnhqqqly1CPCkMSHO2GQT7KEg2VZE17/ZsLmB8gWAv4X2ditOqu5fPJNqxPQ3U4akq5wyRSaYrArHdbT2hbG/L4SwpqPEocKu5KA1agamTMB91lln4atf/Spmz56NxsZG/OQnP8Fpp52G999/Hzbb6IFCNBpFNBod+Njny2CliLGJCCLNxvk7gPJ5wz8X7qPU3lyugg6VSQuuaACAkbvUaIACs/EKy00k6oflY5TtdOKIBTILuONB+t7ai6wb04EUB62M6NrEvV+TDIOek8v920OpHpqBrjli5BiT+yJz0QucMcamCpubJib7GjngZlOXoVOwHUnUN7CCKFKmiWlS7Zmon/Z4ixJtwVAmDupjmoF2XwT7ekPwR+IosiuocU6ubcdTJuC+6KKLBv5/8eLFOOaYYzB79mw899xzuPDCC0d9zpo1a7B69ep8DZEdzFQ34G0eGRgFu5HTXsgHGtqCK9W0tYgXQI4DItlOgb2eYfG4sJdS/awkKVSpPBoAMsl4jgXp5CDnMHtBddJ2hagv9ZT/eBCI56EqflIyrTzYSRVKh/Ltz1/gzxhjk5mzjFJjaw7P7Wo6Y7nStZ36bRfPtH5rhCBQcK04gRQvXzTDQKc/in09IfSHYnAoMmqK7BDGGZtmAH2x/Ie/U7ZsbG1tLWbPno2dO3eO+ZibbroJXq934Nbc3JzHEbKDiq2I0sfDQ/pgGwZVQc3niTWTFlyh7tyvwMt2QI9mvo872JG7wC2WQRVwgN6LYVFf8LHIDgrqI97Un5NsJZavQFe20USKt/WAcST2b2eSPcAYY9ONo5Sy3ibq/83YZBTqTaSSu3O7lS4FhmGi0x/B5n392LLfi3BMQ6XHhmKnMmawrRnAuhYF13w0A3fuqoGZ50rlU2aF+0A9PT1obm5Gbe0o+wYTbDbbmOnmjFlKsVN6caiH9pnocaDlw8Te1rqJn28V2UHBWTSQWsClx2n1ONd/PGUbTQLEQ1RAJh1alN5PLsYoKpmnuscCuU9eEARqqZVuwJ3riYAD2TxU6bfuqESPc5MuKnn/NmOMEUGk1buuz4CKhbzVhk0dyVTycP/IrZN5ZJomekNxNPeG0OmLQhSBCpcKSRp7/Vg3gFfbFfyp0YaOMD0upgvo8EUx25G/BbFJE3AHAgHs2rVr4OPGxkZs3rwZZWVlKCsrw6pVq/DlL38ZtbW1aGpqws0334yKigpccMEFBRw1Y0NIKvUJLJ4J7Hsb6PiUCqWksP/EujEo6bXgivoTFcotrP49GlGiIDCTFe7kir2z3PpxKQ4g2JteCn5SqC9/hckCHak/PuzN7X780TjK6Gc/2EkFT1o+oIq8qpMvKhljLMlVSZlvvhagZFZuX0uLUrZTPEznUHcVp7JPF+F+wLsfiEeAsjm5n9ju2Z27VPIU9YdiaO4LocMXhWmaKHGqUOWJA+3/16iiLUzXIcWKAW9chFeTUeTIw/XbEJMm4H7vvfdw6qmnDnx83XXXAQAuvfRS3HvvvdiyZQseeugh9Pf3o7a2Fqeeeioef/xxeDzcboZNEjYPBR07/k57V0tn57by92gEgVZdUw1sc1H9eyzpjGuoWIAuHHLxtVTsNKZYML3UZ9Ok7QP5KIanOtMrnBbsBJQ8/9zJKmBoQNcO2qLgbaHMDk4nZ4yxQbIKwKQAJlcBtxYD9r5FdWW0KKDH6O9zySyg4ZTctQBluWXo9D3tbaTiexE/XVe1fwSUzaXe1p66zNucjiUaAFo/oOvEfBUAHsIXiaOlL4x2bxhx3USxQ4FtnMrjmgG82qbgiabBFe0ixcAFs2NYVhvD5a9Todv39vbjtMPckMT8TCBMmoB7+fLl4+bTv/jii3kcDWMZsBUBPTvpj1LZfOv/6KVKkGj1NRXRAAAzPyuiYgYV1AEKhs0cVVGXHbQvKd1K5VqExpWPiQrFSWnvqRRO02L0NZYLUKjMXgS0f0wTI+UF/PlnjLHJzFlBAVPoSOuDXz0O7H2TeiS7Kil7TUpUa+5rAna9DMxdRqvdbOowTcoc2/8ubTNzlQPuGlpkifopo7LrM6DiEGDOidYuULR/TF14KuZbd8wUBKIaWvvCaPGGENUMFNsVlLrGDlvjBrC+VcGTTTZ0Ruj6o1gxcP7sGM6cGcPmXhk3vDt4nXfFHz9GbfEO3HLuIpy5eOztyVaZNAE3Y1OeJNMfu0IHGoqDVhlTEfUhb1XUZdvwonKpivhzNyEgKbRynO7KezLNPZctwZJkO6WNRfonvjiLBajImrMA+6ZdlfT1KHAxFcYYm9RsHsDfDvTvtTbg1uPAvo0UIJXUj9zOVjY3EXSvAxqWUXowmxq6dwIt79HWOnvx8M/ZPHSLh4D2LXTfnJMS2RRZ8rYAHVtpe2SetqoFYxra+yPY3xdGOK6hyK6g1Dn2BEJMB9a1KniqyYaeaCLQVmlF+8yZMdglYGOnjF98PHIhot0bwXce/gD3/vPROQ+6OeBmzEqFDrYBCnhiAQrSJkr/CXblL0VITqRvp5seHu7JfWp+NM1K5bEArSZLeUjdTu6XivgmfmzES9/3fG9lAGicHGwzxtj4BAFwFAOd24HKQ605B+sa1Y5p3UyB9Gi1YwQRKG2ggpa7XgYWnAEU5X5lj2XJ10ZbBGT7yGB7KMVJ2wasCrr1OBVK0+N5WVwIxTS0eSNo6QsjFNPgsSuodozd4iusAS+2qPjzXhV9Mbr2LrNRoH3GjBhsiaxz3QT+b3vyd2z4sczEPav/8ilWLKrJaXo5B9yMTTeKHQj6KSgc70SuxymIy1f6sWwDQon90qkGhIaRSJHOYSAnKZRWno5YkP5K56t4iJJi4bSoH7RFoDBFTRhjjKXAWQ70NlHwW7kw++O1vA+0fki1M8Yr1CoIVF+mdw/QthlwV0+OhQI2uoiPtgjEQ0BZw8SPV+yDQbcgALNPzDzo7toO9O2ln5ccCsd1tHvD2N8XQTAah8umoHqcXtqBOPBcs4q/Nqvwx+lnt8Jm4MI5UXyhLg71gO3dn/ZJAyvfozEBtHkjeLexF8fPy0Fx3gQOuBmbbiQbEI9S8DVe5cpkv+ZcVygfOi4tTMFqqml08SA9R81hcUTFQXuk06lUHvUDyONFipIsnBanCYKx+NsKs7rNGGMsdaJME6mdn1KqdyoFMcfi3U9p5K7K1KuQF9VR0N3fRK/PJh8tBuzdSBXty9LYP63YaUtB28f08ZyTxr9uGI2/nVLY7UXpPzdFFGhT6ngwGodLlccNtPuiAp7dp+KF/SrCOj2m1qHjy3NiWFYbhzLGJVlfLLXruk5/JKP3kSoOuBmbbgQBEMyJ9yUn9yHnKw1YFGkqMR5K/TmxIE0eOFNocZYpJZGCn06l8lBPfiuBKy4g1EWz3a4xZmBjITpJ2vKwr5wxxlh2XNXU0cS3Hyidk9kx4hFg/3uUUu4oSf15sp2C/raPgeL6nAVVLAvdO+hWMif9LATFMRh0izIw6/jUJ3UiPqDpDbqmSGVVPU3pBtodYQFP77Xh5VYFcYMeM8ul46sNUZxQrUGaIJ4uVccuyD1UlSe318IccDM2HQky7ecdTyyQu+rfY0m3NVgsSO1Mspn9n4ic6MWdaqVyQ899mvuB5ETWQqR/7IA71E0r7zlO/2KMMWYBWQUg0F7uktmZbQVq/4TSfsszWKX21NJze3YDVZ9L//nTWSxIe6f791LAWnN4ftupRQPU7svmzjwlXHEAxTNoX78oAfXH0b/j0aK0XzzdVfUUhGIaOnyRwdTxCQLtRr+Ip5pseLNThmHSYw4p1vDlOTEcU6Eh1e3Wi0p1lNsM9EQFjFYkWABQU2zH5xty+/3lgJux6UixUz/m8UR8+Q22AWpPEk6xZRlAQXCuq6hLCmBqdIJLJXM92RfcnsM09wMl+6uPVzgt2E0ZBCL/WWeMsSnBXU1p3YEOqgSdDl8bBWXuysz+7ksKoDqphVjJLPr/fNKilJXlb6NiYJOhy0uwh/Y/e/cBYS8FqIZObdxqj7SuyN1EOrfROb08y6BXddHPVcv7tBAz85ixv8aGQdkSXdsp48Ki70WyGFpr/8SBtmkCn/RJeHqvig96BrMujirT8OU5USwu1dOal4rrBnzhOL5Sb+B/dxVjsEwaSf7fLecuynk/br4yY2w6ku0UQI5XETyfFcoHxmWjAmWp7pcO9+d2dTvJBBBLsVJ5LLGvXM5hmvtoZBsQaB/9c6ZJM/FqAfpvM8YYy4zqBPxxSh1OJ+DWYsD+TXSOL6rL/PXd1bTC3b0DqDsq8+OkI9hDr9e3Bwj1JTLtJLo2mPEP+b8uSYoFgcYNgLeZ9sOXzU1shTNpG1nj60DPHmDWUlo5zpVQL9DxCbX3tGJRxOYGzCr6edEjQNWikfV9tCjVE2jdTD9PFrQUC0Q1dHgjaOmnquPjFUPTTeDtThlP77Vhl49W4UWYOLFawwWzo5hbZKT12pGYDl80DgECSp0KLj3CgcUzBPxsE9AxZFdjTbGd+3AzxrIgJ3pxj1URPB6hleZ8VShPkmy0h1uLULrTREJ5aAkG0Mkl2JPaY2NBukDI90qy4qIxjlY4LdJPFy756AvOGGPMOs5yoGcXUL049bTl9i1Ab2P2e2xFiQqntm+hADPX55BYENjzKhV6c5ZRKr0kU+ZYy3s0yT77+PymbwOJtmrvULBdNm946rUgUIDqKAH6m4HG14CFX8zNGE2TvhdRP1CxwLrj2osoeG/9COjeBVR+jrYR6HF6Tz076PrCWZp6LZsx+CJxtPsiaOsLIxzX4baPHWhHdGB9q4I/77OhI0yTC6po4rS6OM6bFUWtM7X91wBgmiYCUR3BaBw2WURdsR21JU6UOBRIooC6YuDsOSbe3RdAZ9hA1aJl+Pz83LYCG4oDbsamI1mlGcuof/STQrALiPqA4ln5HZdip5XkWGjigDseoZNwPvZKy3aaoDCMidOo0tmDbiXVSd+3iHfk7HSwhyq6p5uSyBhjrLDsxUBPJ62ephLE9e0FWj+gVHIrip05K4DunUBfE1B7RPbHG0syZdnbTKnSQ4Na1U09wnv30DXC3OX5PZ+1bwE6ttI10Vj7nEWZaqT07AGa3wbmnW79goC/DejeTvvrrWZzA7b5NKnRsgno/oxq5MTDgL0EKJuT8UKCaZrwRuJo64+g3RdGNG4k+mgrowbafVEBf2tW8UKLMtDay6MYOHtmHGfXx1CcYqEzANB1A75IHFHNgMumYEGVB5VFNhTZR/5uSKKA46t1wIgDc8uQ8kZwC3DAzdh0JIi0ChvuHb2IVqATMMz8pGsPJamUChcPApig32GyirorD3ulFSed5ONBwDbB64V6AbEAFV2T7d5GC7gDHQAE7r/NGGNTjSAAjjJKIy6ZOX6gGfEC+96mlVCHRS09BYFWQDs/o5VPC9KJR9W9nd5jcf3oQa2kUPG33kYKzBeemZ9rlN5GCkBd5ROnswsiUDoL6NoJ2Espvdyq865h0H56PZ71KvO4HCU0yRP109d3vL7tEzAME33hOFr7Q+jyRREzDBTbFZQ6R5+I2BsQ8ew+FRvaFGiJQmjVDgP/OCuK0+visE9Q022oSFyHLxIHTAElTgULqh2o9KiwyWkcJI844GZsurK5aW9WzRHDT26GQQVAbCn267RSciIglVXiZHEyKUcn/6EUe2LV3z9+wG0YVIwulXR4qyVP6gdWn9c1SgmbaKKAMcbY5OQspxXmpjeABSsoIDqQrgHN71Itj2yLaY14/Qqgf19i9XmetccGgEAX0PwOFfEarzibIFJA3tcE9O4GKg+xfixDhXqBfW8BEFKfwJBUoKgGaNtM37fKhdaMpb+JVvg9WezJT1VykiVDumGgNxhHS38Y3f4oDJgosisoU0YGu6YJfNgj4dl9NmzuHQw7DynWcN6sGI6rmri118CxDBOBqIZgTINNFlFbbEdNkQNlLgVSoQvuTYADbsamK0cpVQANdAJFQ9KTwr10c06wwpwrgphiwB0EYOankrooA6ZOhebGE/VROnyh9korDrooqlo0OBMf6gGiXsBdVZgxMcYYy44g0H7m3t1A05vAvNNGrrZ2bKFV6JJZ1p8XJZmO2b2L9nJbmS0VjwD7NgLRYGrty2SVznWtHwLFMylIz5WOT2hLVroTGLYiukZpfpuutdxZFlHV44M9swtVNC4Fcd1AVyCK1r4weoMxCIKAYocCVR758xjVgVfbFPylWcX+4GAhtKVVGv5xVgyfK9FTf12N0sbjxvC0cY9NHrOt2GTDATdj05Vspz/i3pbhAXegE4iFgeI8twAZGJdKQeJEon4AeZ6xjE5QqTzqo6Jv7ur8jOdA7spEut27wOwTKXMh1J2oRj95T9KMMcYmIIrUjql7J6X5NpycqJDdTZPn+9+nPd65+lvvrqR2WMEuaydwO7fRinVpGgXe3DVUSK5jG1B/jHVjGcrfAXTtADzVmU0wuGtoRbr5HSqils1++p7dlKk22hbASSAS19Hlj2J/XxjeSAyKKKLMpUKWRl6jdUUEPN+s4u8tKgIafV0dkokv1MXwpVkxVDtS259tmibCMR2BqAZBAEqdKupKHSh32WAbJcCf7DjgZmw6sxfRjHndkYMng/59hZ1BlWxUtGOi1mCh7vwGkbKNXnM8ER+AFAqr5YqkUrpd20eUQl63hCZU8pF2zxhjLLckhfZxt2+hglbBbiDSR5Pn9uLcVu9WXYCvlYJIqwLuqJ9WkR2l6e3HFkWqVdLxMRXzOrBuSbZMk9pgxcOZt/gSBKCknibBOz+lPt2ZiIXonK46rSmCZ6FAREOHL4JWL/XQtisSKt22Eenbpgl82i/hr80q3umSYQzZn/2l+hhOr4vBmeK3X9cN+KMaInEdDkVGfZkTVUX2gWrjUxUH3IxNZ45SCsgCHZSaFfXTTPlo+8PyRbbTSS4eGjtVzNBpr3I+WoINjMtBrbUMfewqpaGewhRMG0p10naA5ndpLIF2bgfGGGPTheKkgLfrM5pY9dTm71zoLKMV9prDrUnl7tpBW9gy2XPuLKMU97aPgXmnWpvm7m8HenZmXwldUqkIWcsHtPc6k9Ty7h00nlzsnc+AYZjwhqm1V4cvgoimw6XIo7b2iurAa+0KnmtW0RQYvG46vFTDl+pjOKYytf3ZpmkiEtfhj2gAgCKHgrmVblS4VTjV6RGqTo93wRgbnaTS3mTvfgq4A51UjduV5X6jbMh26hsdGyfgTlYoz2chMMVOExKxwOgTEoZBKWhZVPS0jKOUJi1a3qd956V5bu/GGGMsd+xFhZlIdZQm0pv3AVWHZnesiI9Wfh1lme85L6qj6uYV82nvuhVMk1bdtZg11cBdFZT+3rIJmL8ivVXqiI+yGZylY0/054lmGOgJxNDmDaM7EINhmHDbZJQ4R2bQtYcEPL9fxcutg2njqmhieW0c59THMNttpPSaum4gENUQjuuwKSLqSuyoLnKg1KVAnuRF0NLFATdj0529mFKe6o6mgBFi4VKiAToZDbQGGyPwjwWo0Eo+JwZkB01IRMcIuGMBIB4A1ElSDbyojvqxCkLGvTMZY4yxAYJIk8qdnwHlC7Jry9W9M/PV7STVCQRM2stdXG/NKrevhSYVrOx1XTwL6N4NFM1Mr5d556eUOVexwLqxpCm5P7u1PwxvOA5REFBkV6Aqw68TdRP4sEfG35oVfNgjw8Rg2vhZMylt3JPCXMPAanZUA0zAY1cwu9yFCo8Nbtv0vZaZvu+MMUbspYPtPvr3AvYCB4yCAAgYv1J5LEQr8/kMJEWJVrFjY1Qqj3hpXK5JVA18khZYYYwxNkW5Kiko9bVkfo6xYnU7yVNNLbP8bTTRnA3DANq3UnvS8dqTpUtWAUcx0PoBpamnsge+vxno2EpFWPPRjWUI0zThi2jo9EfQ5o0gFNVgUySUu1RIBxRC648JeLlVwYv7VXRGBj+3pFzDOfUxLClPLW186N5smzLY0qvEqUAZpfjadMMBN2PTnSQDMIGu7VSsrDgPPR4nIkjU/3IsYwW9uSYIY1cqjyYLphU27YsxxhjLGTmRQty9I9GCLINV5e6d1q3cKk7qQd61PfuA27c/0es6y73bo3FVAj17gMbXqK3beAXugj3Uc12PA0Ul1o9lDJphoC8YR7uP+mdHdRMudeT+bNMEtvZLeHG/io2dMrREETS3bOL0uhjOnBlDrXPiauMDlcZjtJpd5FDQUOFCuXt6r2aP5uB6t4wdrBwldPIz4pOjorXNTcXcdG30lLVQb2GKk8k2aokymlAvIPCfTMYYY9Ocuwroa6RtVp4022BGfEDnViruadXKrbuS0sCrF2fe89owaEUZJvX5zoXSOUDfHmDPq8D800ffnhYNAE2v0zVZWRqt0rIQimnoCcQG0sYFgVK5S5XhCwi+mIBX2xT8vUXB/tDg5xYWafjizDhOqo7DlsKaQ1wzEIjGEdUMOBQJM0ocqPLYp+Xe7FTx1SNjBwN7CdC1jdK7JgPVA4S6qHjage0+dI2C3lydEMcj2ymwPnAiwDSp0nshxsQYY4zlk+oCfG1UDCzdgLtrO51HrdyXbPNQDZruHZkH3L4W6geei9XtJFGkfuO9e4A9G6i6+tDir1oM2PsW1V8pn5vTVPJktfFOfxQdvghCsdHTxpOr2etaFLzVqSBu0Gq2XTJxSk0cZ86IYW7RxEXQTMNEIKYjGItDFkQUORQsqLajzDV9Ko1ng78CjB0MRAkomz85VrcBqggej9BJ+cCAO9RDgbhVfUDTGpczUUE9QFkBSbEApZpb0SaFMcYYm+xcFRTgVi+i6uWpCPVSBXBXpfXBpKuCKpZXHZp+P3LTBDq30b+5njgXJVq57tlDdWjK5gIw6bWDXbT4UTo7ZzVqopqBnmAU7f1h9Ibi0BPVxg9MG++PCljfpuClVgWtQ1az53p0fHFGDCfXxFPqnR2J6whENOimAadK7bwqXTYUTfG+2VbjgJuxg4ViL/QIhhNlWjWuXDj8/mAXoEVptTnfkj3CDwy4Iz7qG37g5ABjjDE2HdmLge5OoLcJmJFiwN2xlc6Xuai6bS8GerootTzdgNvXmti7neZqfaZEmYLu3kbKEhi6D76ozvK+6qZpwhuJo8cfQ6s3gmAsDkUUqdq4PDjxoRvAh70yXmpRsKlbhm4OrmafXB3HF2fGMM9jTLhtX0u080oWQKv02FBVZEOZywabfHCmjE+EA27GWGGoLtrHbejDC5H17ytMsA0k2qWZtMdqqKgvMU7+k8kYY+wgIAg08dz1KVB5yMRVvf3ticJmNda07xptPM4yWiGuPCT1PuWmSRXTTZ2y2PJFUihtPIeSq9kdvgh6AzHEdQMum4Jqtx3CkNXl1pCIl1sVvNKmoDc6GBAfUqzhC3W0N9sxweWNYZgIxnSEYhoEASi2JwqguWxw2aRhq+dsJL56ZIwVhs0DhLqBcN/gynHUT0VaRis0kjcCpbWb5uBFQ6iPq5Mzxhg7uDgraIW2fy+lco/FNIH2LYAWAWwzcjceRylVQO/4BJh9QmrP8bfR6rY7h3u388gwaDW7OxBFuy+KYDQOWRRRZBveOzukAW92KFjfqmCbdzDcK1IMLK+N4/S6OGa7x9+bneyZHYjq0E2qaJ6sMl7ikCEdpAXQMsEBN2OsMBTHyH3cwS4g5s+8KIoVXBVA+8f0b+UhiYJp7fmdGWeMMcYKTRQBmwvo+JSKgY21Nc3bTIF5UW1uxyOIgKc2MZ45E7cJM016rK5Z23e7AMJxHb3BGNq9YfSF4tANA05FHraarZvAll4Jr7Qp2NipIJYogCbCxJJyDafXxXFspQZlgjg5Fqcq4zGdqozXFNtQ6bGjzKkOS1FnqUs74A4Gg/j5z3+Ol19+GZ2dnTCM4bMje/bssWxwjLFpTpCAYOfgPm5/BwAxp5U7J2Qvpln6vW9SkO0soz1pHHCzKUbXdaxdu3bM8/X69esLNDLG2JThqqYV4r1vAXNOGuzTnWToQNuWREGyPJwn7UWUhdbyARVnk8ZpIdq/F+jdDXgKUITVAsm+2d2BKLr8UYRiGlRp5N7sfQERr7Yp2NCuoGdIyvhMl47TauNYXhtHmW38vtkD+7I1HYooosSpoLrIgVKXAhdXGc9a2l/Bb3/729iwYQO++c1vora2lnP2GWOZS/bjNnQ6WfftpfsKzV1Ne8mbXgdqDqeCac7yQo+KsbR8//vfx9q1a3HOOedg8eLFfL5mjKVPkoGSWUDHFvr/WScMts2MBYHWzRSQl9Tnb0xFMwYLko2V6h7qBfZupK1h6iS4rkiRaZrwRzX0BmJo90XgC2sADLhtyrBK431RAa+3K3i1XcEe/+CWN7ds4uSaOE6tjWFB0fgF0HTdoH3ZcQ2SIMBjVzCn3IUytwq3KkPkKuOWSTvgfv755/Hcc8/hxBNPzMV4GGMHE5uHZqrDfYChUUuuXPbITEdxPV1EdH1GEwISz/CyqeWxxx7Dn/70J5x99tmFHgpjbCpT7EDRTAquRQWo/zxNSre8D3j356Ty9rhklSbnWz+g4PvAAmrxCK3Ih7oTbbkmv3BcR18ohg5fBH2BGGKGAbssodylDPTNDmnA250KXmtX8HGvBAMUEMuCiaMrNJxaG8cxFeOnjA8WP4tDgAC3TcaCSg9KXSqKeV92zqR9BVlaWoqysjTL8TPG2GgUB6Vvh3oBPQrosfyetMcjCLRHrHc3IE2SMTGWBlVVMX/+/EIPgzE2HahO2j+9/z0g4gX6mmj7V/n8whQVdVdRAbX2LcCs4xNdRgAYBtDyHq1+l80t7Ba1CcQ0A/3hGLr9UXQHYgjFdSgiBcFlCn1N4wawqVPG6x0KNnXJA/uyAaoyvqwmjpOqNRSpY6eMm4aJUFxHMKrBhAmnTcGccjfKXCpKnAoUafJ+jaaLtAPuW2+9FT/96U/x4IMPwunkPY2MsWyJVCwt0j8Je4VLQMVCwBy/kidjk9H111+P3/zmN7jrrrs4nZwxlj2bGzArge7tFHzbPIUbiyDSynrrh0Cgg7LSXBXU7aTtI6B4xvj7uwtENwz0hzX0BqPo8kURiGoAALdNRrXHBkEQoBvA5h4Jr7cr2NilIKQN/v2e4dRxSk0cp9TEUescJ8g2TYRjOoIxDboJOFUJM0udqPCoKHFw8bN8Szvg/vWvf43du3ejuroac+bMgaIM/2H+4IMPLBscY+wgYHNThdN4qMDtwMYxiWfIGRvLG2+8gVdeeQXPP/88DjvssBHn66eeeqpAI2OMTVn24slzrrZ5aGI80k/1YIBEZXXPpNq3bRgmfJF4ImU8Cl8kDsM04VJklLtVSKII3QQ+6ZPwZoeCjZ0yvPHB645ym4ETqynInucZe1/20CDbME04FBl1JQ6Uu20odSqwydzetFDSDrjPP//8HAyDMXbQsrkppTweoWJljDFLlJSU4IILLij0MBhjLHcUJ908oGw0LTYpsuUMw0QgpqEvOBhka4k2W2VOFbJEQfa2fglvJYLsvthgkF2kGDi+SsPJNXEsKtExVv2yZLp46MAg26WixKnCrnCQPRmkHXDfcsstuRgHY+xgJTuo0qmk8EoyYxZ64IEHCj0ExhjLH0G0NNjWDRPvdgCdYaDKAXy+GpDGqdydDLL7Q3F0+iLwhamXtU2RBlp56QawtV/Cxk4Fbx8QZLtkE0ur4jipOo4jSnWMtbXaSAbZUQ0GKF08uZJd4lA4yJ6EMi67+/7772Pbtm0QBAGLFi3CkiVLrBwXY+xgIQhUmVxSJ34sYyxtXV1d2L59OwRBwMKFC1FZWVnoITHG2KT2QpOJ1e+YaAsN3lfrBG45DjhzzmDQPWqQbRiwSSLcNgWqIiJuAB/3yni7U8Y7XTJ88eFB9nGVcZxQreHIsrErjOu6gVBMRziuARDgUGXMLHWi3E2FzzhdfHJLO+Du7OzE17/+dbz66qsoKSmBaZrwer049dRT8dhjj/GJnDGWvsmyH4yxaSQYDOJ73/seHnroIRgGFf6TJAmXXHIJ/vu///vgKXyqRakbAmOMpeCFJhPfecXEgSXJ2kPAd14xcfdyEyfUaPCG4ujyR+ENxxHXDdhkEa5EhfGwBmzqkfF2p4L3u2WE9MEg3aMYOK5Sw/FVGo4YJ8iO6wZCUR1hTYMIEU6bhDnl7kQLL4ULn00haQfc3/ve9+Dz+bB161Yceig1m//0009x6aWX4pprrsGjjz5q+SAZY4wxlp7rrrsOGzZswF/+8heceOKJAKiQ2jXXXIPrr78e9957b4FHmCc71wF/ugRwlgOVh1C7v7IG+lc5SCYdGGMp0Q1a2R6t/reZ+O9PNppYc1QfDJNWsj2Jley+qIBXO2S82yXjo14ZmjkYZJeqBo6r0nBCVRyHlYydLh6N6wjFdEQ1HbIowm2XMbPUgxKXiiK7zC28pqi0A+4XXngBL7300kCwDQCLFi3C3XffjTPOOMPSwTHGGGMsM08++ST+3//7f1i+fPnAfWeffTYcDge+9rWvHTQBt975Gd7VFqLTV4IqXzc+L74BSTABCEBRLfXqLZtH/YRL50zKVkKMsfx4twPD0shHEtATFdASceCoCgN7gyJe2i9jU5eMnT4JJgaD7BqHgaVVcRxfpWFB0eiFz5KVxUNxHVpildxjVzDX40KRQ0GRXYYkcpA91aUdcBuGMaK1CAAoijKQssYYY4yxwgqFQqiuHln5v6qqCqHQuFeU08YLn7ThljePQkd8cJGgVvLjFsfjOFNbD/ha6db0Bn1SlCjoLl9AAXjFQsBViTH78DDGpg3TNNHs0wFMHOD+udmGe7dL6IwMf+yCIh2fr4zjuEoN9a7RW3gN7sfWYcCEQ5ZR6bah3G1DsUOBS5UgjlOcjU09aQfcp512Gr7//e/j0UcfRV1dHQCgpaUFP/jBD3D66adbPkDGGGOMpe/444/HLbfcgoceegh2O1XuDYfDWL16NY4//vgCjy73XvikDd95+IOR+zB1D74T+DbuPekbONO1A+jdA/TsolvUD/TspluSvZgC72QAXjYXkG15fS95p0WAJ1bS/391LSAXvs0SY7mgGQb8EQ2+cBzdgSh6vABQMuHzNvfS4qMqmjiiTMOxFRqOrdRQZhuZjG6aJmKagVBcR1QzIAqAU5Uxq8yJksR+bAdXFp/W0g6477rrLpx33nmYM2cO6uvrIQgC9u3bh8MPPxwPP/xwLsbIGGOMsTT95je/wZlnnomZM2fiyCOPhCAI2Lx5M+x2O1588cWMj/vaa6/hV7/6Fd5//320tbXh6aefxvnnnz/wedM0sXr1avzud79DX18fjjvuONx999047LDDLHhXqdENE6v/8umY+zAFAKs/dGDFV46CVLckOXAg2Al07wJ6dgLdO4G+JiDiBfZvohsACBJQOptWwSsSK+Hual4FZ2yKCMU0+CIafKE4uoNRhKI6NNOAKoo4slxGuc1AT1QAMPrvtAATp9fFcWyFhiPLNdhHiZV1w0AkTivZemKvt8umYE45rWJ7eD/2QSXtgLu+vh4ffPAB1q1bh88++wymaWLRokX4whe+kIvxMcYYYywDixcvxs6dO/Hwww8PnK+//vWv4xvf+AYcDkfGxw0GgzjyyCNx2WWX4ctf/vKIz//yl7/E7bffjrVr12LhwoX42c9+hhUrVmD79u3weDzZvKWUvdvYizbv2JXJTQBtQdqveXxt4k5BoMDZXQ3MoSJz0GJAXyPQvYMC8J6dQLiPVsV79wA7ExMXNg8F3mXzgPLEzVaU0/eYU+aQLYKd24CaIwHeR8qmqLhuIBDR4IvG0ROIwR+OI6zpEAUBdllCiVNBV1TC2z0yNvfI8MXHCrZpCu+Hh4dxQrU2/DOJVexwnAqeCYnWXbXFNpS5bSiyKXByqvhBK+M+3CtWrMCKFSusHAtjjDHGLORwOHDFFVdYesyzzjoLZ5111qifM00Td955J3784x/jwgsvBAA8+OCDqK6uxiOPPIIrr7zS0rGMpdOfWhuwzvAED5BVqmxeeQh9bJpAqGdwBbx7JwXkUT/Q+iHdklwVQOncRFG2BqBkNuAoyej95FXzu8D7Dwx+vOEXgKMM+IeVQP3nCzYsxlJlGCaCMR3+aBz9wTh6QzGEYxp004QqinCoEkRZwSf9Cjb3yNjcK6MjPHxCySkb0A0BUWMwQK6wmfjWIREcX0XBtq4bCMUNhGMaDNNMtAVTMKvMiWKnCo9N5tZdDECKAfdvf/tb/Mu//Avsdjt++9vfjvvYa665xpKBMcYYYyw9zz77LM466ywoioJnn3123Mf+4z/+o+Wv39jYiPb29mFdS2w2G5YtW4a33norbwF3lSe1PcdV6S70CwIF0q4KYFZiH7weB/r3JvaB76Z//W1AsJtu+98dfL6jlALvkll0K64HimYAUsbrH9Zqfhd44/aR94d76f6TruOgm006pmkiFNdpFTtCq9ihqIaYYUBMrDS7bCp2BhR83Cvj414Zu30ijCGr2LJg4pBiHUvKNRxdrmGOx4AJ4NM+CX0xAaWqiUOLNcR1Hb0BnY4tCHCqMmaWOlHiUngVm40ppb/wd9xxB77xjW/AbrfjjjvuGPNxgiBwwM0YY4wVyPnnn4/29nZUVVUN21d9IEEQoOu65a/f3t4OACOqo1dXV2Pv3r1jPi8ajSIajQ587PP5shrH5xvKUFtsR7s3Muo+bsBEtQM4stwEkGWxIkmhdPLy+YP3xUK08p1MPe/bS0F4uI9ubZsHHytIgKeGAu/iGfRvUR3dl88+4YYBvL92/Md88CAw4xhOL2cFZZomwnEdwagOXziOnmAMwVgcMY22QthlGXZFQUdYwZZeCVv6ZHzmlRA3hgfCM506jirXcFS5jsNKNDjkka+z0BNLpIkb6AmasMsySt0qylwqimwK3LwXm6UgpYC7sbFx1P9njDHG2OQxtD1nIVt1CgcUEDNNc8R9Q61ZswarV6+27PUlUcAt5y7Cdx7+AAJwQNBNH10ww4f3mjR4HDLKnCrcdgVumwybFSmgqhOoPoxuSfEI4N1Hhdj69wHeZqC/GYiHAF8L3fYfcBxHKeCuoeDbUzO4x9xTbX0w3rWNVrLHE+qhx1XnrwAeY4aRCLBjGvxhDb2hGIJRDZHEXmmbLEKRZLRFFWztl/FJn4zP+qVh6eAAUGYzcHiphqPKdBxRpqHcPnI6LqYZCMdoH7YBc6DYWX2piiIHBdhcUZylK+0cpv/4j//ADTfcAKdz+B/6cDiMX/3qV/jpT39q2eAYY4wxlpmHHnoIF110EWy24S2sYrEYHnvsMVxyySWWv2ZNTQ0AWumura0duL+zs3PUnuBJN910E6677rqBj30+H+rr67May5mLa3HvPx+N1X/5dFgBteQ+zOMqgEhcQF8ghg5fBCIE2BVpIAB32WS4bTLsVl1cK3ZqK1axcPC+5J5wXwvgTQTdvv2Arx2IegdXxLu2jTye6gE8VYCrGnBX0c2V+NdZkf4qdLjf2scxliHdMBCM6QhGNfijGvoCMYTiGqKaCQGgSTFRQkfcjk/7FXzaL2G7V0LsgAC7SDFwWCkF10eU6qhzjuyLHdMMROM6wpoOI7HH22mTUVtsR5FDhtuuwKlwmjjLjmCa5ujZVmOQJAltbW2oqqoadn9PTw+qqqpykqJmFZ/Ph+LiYni9XhQVZVk9VNeAjx6j/VzOMmsGyBhjbOrp2QXMPRWoWZz1oaw8T+XjfC0IwrC2YKZpoq6uDj/4wQ9w4403AqAAv6qqCr/4xS9S3sNt5dehqTuIO599G0rfLhw2sxSHl+mQRrl21g0D0biBSFwf2PtpkyW4bBLKXCrcdhkulVa38nLxHQsC/nZKRfe3A4EOINAO+DuA6AQp94IEuCoHV8Pd1YOr5K7q0feMd2wF1t868bhO+wmvcDNLRTVKDw/FNHjDcXhDcYTjOuKGCQEm7LKEsCljT0DBZ14Z2/pl7PaLMMzhv4fFioFDS3QcXqZhcamOehf1vB4qptHveCROK9hKoohamVNFkZOyXFyqDIkD7Okp3A8YceCIiwDZNuHDx5POeSrtFe6x0sI++ugjlJVx4MkYY4xNBmOdr/fv34/i4uKMjxsIBLBr166BjxsbG7F582aUlZVh1qxZuPbaa3HbbbdhwYIFWLBgAW677TY4nU5cfPHFGb9mNjbu6cEzOyIAZuLPPSbmFen4XLGOQxK3UhutO0iiCKeNVrcASmONajr8EerVCwiwyQIcioxSpwqPQ4ZTleBSc7SHU3UNthg7UDwMBDqpb7i/g/4NdA7eZ2gUnAfagfYDnisItBJeVAd4aunf4nqgpJ6qkY+XVu4sByoPtfRtsoOLZlBv6lBMRzCioS8UQyimI5JYYZYEEYokoitux56AjO1eCZ95R1YRB4BKOwXYh5VoOKxUx4wDVrBN00xMohmJFHFAEQU4VAmzPM4hAbYEiesSsBxKOeAuLS2FIAgQBAELFy4cdhLXdR2BQAD/+q//mpNBTjqxIHBbHf3/OWMXkWOMMcbybcmSJQPn69NPPx2yPHiq13UdjY2NOPPMMzM+/nvvvYdTTz114ONkKvill16KtWvX4sYbb0Q4HMZVV12Fvr4+HHfccfj73/+etx7cB6ousuGEmSq2tAXh1xVs66cVsqQqu4FDinUsKNaxsEhHg0eHTQJEkaobO1R6bLLPbiRuYG9PEIZpQhZF2BQJHruMEocCp02CM7EKntMVMsUBlM6m24EMg4LmQMfgzd+RWCVvB7TI4P34cPhzVdf4r3v0pVwwjaVMNwyE47QnOhTT0B+Owx/REI3riBtUI1wRJQQNGXtDduzyy9jplbDLN3L/tQATs90GPlei49ASDYtKdFQesAfbMExavdYMxDVjYA829cO2w+OQ4eIVbFYAKQfcd955J0zTxOWXX47Vq1cPmx1XVRVz5szB8ccfn/FAXnvtNfzqV7/C+++/j7a2tmEpagCd6FavXo3f/e53Ayfwu+++G4cdVoC0JmNIGl7PLkrV4hMQY4yxSSB57ty8eTO++MUvwu12D3wueb7+8pe/nPHxly9fjvF2owmCgFWrVmHVqlUZv4aVTvtcNeaapWjb9CZ6iw/FZ14JnyX2fDYHRXRG6PZ6hwIAkAS6sF9QpGN+4jbLZUASBdgUCTZFAkCP1XUDEc1ATyCKdl8YgACbRI8rsiu0Cq7QSrg910F4kigOti47MPXbNIFIP+BrpVR1XwvgbQV8zUColxYURiNIQNWhQMRLrc9KZlF1dmaZUNzEoofp9+rTfxbgVKZWQKgZBsIxStcOxTT4ksG1piOqUwFHRRQRNWXsDznQGJSx2ydhp09CX2zkNbRTpjZdC4sowF5YrMN5QNQS1w1EE3uw4wPbQER4bDJKSxPbQGwy78FmBZdywH3ppZcCABoaGnDCCSdAUaz9QxsMBnHkkUfisssuG/VC4Je//CVuv/12rF27FgsXLsTPfvYzrFixAtu3b8/vrPmnzwLP3zj48dt3Ax89CvzDSu5NyRhjrOBuueUWAMCcOXNw0UUXwW5PrSf1dCcIwAyXgRkuA6fXxQEAQQ3Y5aXge6dPwg6fBG9MxB6/hD1+CS+20HNV0cQct455RQbmenTM8+iodxtQJBEuSYTLNrgKHtcoFb3dF8H+flrFU2URNllCkV2Gx67AqVIxNocqQs7nhL0gUOVzR+nIYDweosJt/fuA3t3A7vWDnzN1oOMTugGAKFPQXTaP2qFVLKD94QIvPkx3pmkiptOqdTiuIxzT4YtoCEQ1xOI6YoYJgLI/IrqE1ogDTUEZe/wSdvsldEVG/oyIgok5iUmuhcV0m+Ecvv/aMExEYgYimo5YYvU6mWFS6bGh2KnAneiDbZfFcbsiMJZvKQXcPp9vYDP4kiVLEA6HEQ6HR31spsVNzjrrLJx11lmjfs40Tdx555348Y9/jAsvvBAA8OCDD6K6uhqPPPJIykVYsvbps8CfLsGBDUYQ7gXeuJ2K5pTPoxORKI888ZhG4mYO+X/9gPvN4ccXRAACzViLMiAqNKssqZRSNnBzAqobELlVAWOMscGJcjY2lwwcWa7jyHLKXDNNoCsiYKeP0lp3+STs9kkI6QJ2+GTsGFKrTBZM1LsMNHh0NHgMzHFTOrpbEaAqIpJLAclU9JhmoN0Xxf7+CACqhqwoEtw2GUV2GQ5VgkOWYFcl2CQx/ytyipMC54oFgHbiYMB99q9oRby3MXHbDcQCgz3Gd61LPN+VCL7nUyX28vkTp6izSS2mUYAbjRsIxTUEozr84TgicQMxXYduUtVwSRDRqyloDdvQHJLQ6KfbaCvXAFDn1LGgiCaw5hfRBJZtyOXr0ImrqGZAMwdXrx2KhLpSx0BxM6cqcR9sNumlFHCXlpYOVDotKSkZddYoWZwlF1XKGxsb0d7ejjPOOGPgPpvNhmXLluGtt97KT8Bt6MALP8KIYHuoPa/QrWAEOrnZigB7MeAsBRzlVEXdWZ7o31lFATpjjLFpp6ysDDt27EBFRcVA7ZWx9PZO0HN5mtFhIhTVoMoi5DEu0AUBqHKYqHJoOLFaAwAYJtAeFrHbJ2K3nwLwPX4JQU1AY0BCY0AC2gaPUWEzMMejY7bbwCw3/TvDKcCjSMOC8LhOK4V9gSg6fWGYAERBgE2iVTu3TYLbpsCuiLAnUtnzFojLduCfHhv8uLgeqD8uOXgqzNazm269uyjwjgeB9o/ollQ0IxHEL6R/i2bwKvgYdGPw+vLddhMnz0BetiAYhom4YSAcp8A6oukIR2nVOqLpiGsG4olVa0kQETEktEcUtIYdaA7J2BuQsC8gjthzDdC+6zqngbkeA/MSgfXcIh2uIdFH8nfBHzEQ03RohgFAgJrYmlHjsqPIocBlk+FQKODm1Ws21aQUcK9fv36gAvkrr+Q/oGxvpxKbB/bwrK6uxt69e8d8XjQaRTQaHfjY55ugjcZ49r5FM7wTqVhIQa+uATAG7zdBZ3JBoJPNmDcBQPIGOoZp0kq4oQN6jI6txwAtTJVK4yEgTjPmiAXo5h9nrDZPokVIHVBUS1VKi2cA7trRW4UwxhibEu64446BbVZ33HEHX5gmuG0yylw2dJkmQuH4QHAjiwJUmQJZRRZG/XqJAlDnNFDnNHByDQXhyZXwPYmVvMaAiCa/hM6IiO4o3d7rHjyGJJiodRqodxmY5TJQ79Ix00XHdNuGFLUzDMQ1WhFvj2rQDNoXLgmAKolQZEpf9yT6gyeDcFWmW14IQmICvxqYfQLdZ2hAfzPQvQPo2Ql076SibL5Eb/E9r9LjFAdQllgFL19A/9qybNM6DbzQZOKWdwY/XvkSUOs0cctxwJlzsv8dTga1UY2qdcc0CrADUQ3BqIa4RkF3MtgVTQEhU0RXVEFHVEZLSEJzkAJrX3z0nzNVpNoHczw6Gtw65nro/+2jrFwPDa5NAKooQlUkVHhsVHxQTWR85KvuAWM5llJ0tWzZslH/P98OPBGO1fIkac2aNVi9erU1Lx7oSO1xC74IzDnRmtdMh2EAMT/15oz4qLBJqBcI9wChPiDYRTPSUf/grWfX8GMIIuCuoeC7aAZQPJNmtYtqKYWdMcbYpDY0jXzlypWFG8gkU+G2oaLGg3nF5Yl9pxpCMR3+xN7TYCyOaNiAAGFgz7WaCGRHWw0fuhK+tEobuD+oAU1+CXsDIvYF6N+9QQkhTcD+oIT9QQkbhxxHhIkqh4mZLh11TgMznLTHvM5poNxuDrQ40nUDcd1EXDfQ7Y+i3ZtYEYcARRIgSxJUSaAKzDYZNmVw/DZZhCLmeGVclIGyBrrhi3RfxEuBdzIA79lNiwQdW+iW5K6iIDzZAq1kDqAcPHUHXmgy8Z1XzBH5k+0h4DuvmLj31NSCbs0wBrYuxHT6Nxo3EIhpCMcoyI7rBjRjcOuiCRF9cQVdUQkdERltYQktIRH7g5TBMRoBJqodJmYnsjdmu3XMcRuocRrD+tsnJ4+8URqPbibqGUgiVDmx79qhJAJrOf/1DBjLo7SXM1944QW43W6cdNJJAIC7774bv//977Fo0SLcfffdKC0ttXyQNTU1AGilu7a2duD+zs7OEaveQ910000D7UoAWuGur6/PbBDusV9nGEdJZsfPlihSGrm9GBivvWo8RH06/e2JCqVttBrua6ETob81sTq+afA5ggC4qgcD8aIZg/07be4xX4pNAloEeGIl/f9X11KaIGPsoPDBBx9AURQcfvjhAIA///nPeOCBB7Bo0SKsWrUKqnrwTaQmV4KLHYOFX4e2LorEdQRjOnzhOFVbDscTq36AnOgPrMoCVEmENEog7pKBw0p1HFaqA6DCbKYJ9EQFNAcpCN8XFLE/KKI5EYi3hwW0j9Jj2C5ROm6t00CNw0Ctg4KaGoeBSpsJURhcudR0qg7tj2owDBMGTAgQIIsCZFGEIgmwq8mWZbRSPjChIAqJfy0OduzFwMxj6AZQll7/Pprs79lJ//paB/uH73sr8USBrjHKGoDSudT6rGT2tLze0A0Tq98ZGWwDicRIAKvfNXHaTBMmTMQ0mnSJ6dT2ilaqNYRiVK1bM3RougndpGeLADRTQF9cQU9MRXdURmdERFtYQmtIRHdEgInRA+uhk0EDmRlu+v/R9luHYwZicVq1NiBAFDCwPaLSo8JtV+BQpESALXLfa3ZQSTvg/uEPf4hf/OIXAIAtW7bguuuuw/XXX4/169fjuuuuwwMPPGD5IBsaGlBTU4N169ZhyZIlAIBYLIYNGzYMjGU0NpsNNpvNmkHMPoFOAL42jLmP21kOVB5qzevliuIESufQbSjTBMJ9gHc/3Xwtg/8fD1LvzkA70PL+8Oepbgq83VWAqzJxq6B94/ZSSq/nlEbGGMu7K6+8Ev/2b/+Gww8/HHv27MFFF12ECy+8EE888QRCoRDuvPPOQg9xUpBEEW6bOCy1G8BA2m0kcQtENfgjGmKagWAsPpB+K0GAkgjCZYmC26HZd4IAVNhNVNh1LCkfrHNjmkB/TMD+oJhYVRTRGqIVxq6wgIguDFRLP5Aimqi0G6hxmKhyGKiyJ24Our9YNSHAhGZQMK7pJryhGHr8MRigcZuJKs+yKECSRKiiQJXTFQk2ZfC9KKIISaLgXZHo8RltVRClwVXwBSsSX+QA0LOHCrH17KZ/w32DqehNbww+31lBwXcy+664nq7Lpmh7MtM0sbHNRFtonMcAaAsCazf7cIiHfuZ0gwJ0EyZECNAhwBeX0BuX0RezoTsqoSsioTMioCMson+MwmVJTom2OwxkWbgMzExsoVAPDKx1E3HNQCg62OdaSOy3VmQJJS4VxXYFDttgAUCuGM5YBgF3Y2MjFi1aBAB48sknce655+K2227DBx98gLPPPjvjgQQCAezaNZji3NjYiM2bN6OsrAyzZs3Ctddei9tuuw0LFizAggULcNttt8HpdOLiiy/O+DXTIkrAmb9IVCkXMGrQffSlU7cftyAkiquVAbVHDN6f7NnpbRk8AXpbaHU83Js4WSZSxkYjKoCjGFA9FJzbXFTJVLYlbnY6WQoSfY0FaWSAPqyq+xi35OOSc8JD98VLMqXEJ28DVd2dXN2dMTZt7dixA0cddRQA4IknnsCyZcvwyCOP4M0338TXv/51DrgnMNpqeLIlUiROK8oRTUcoqif6DRuIROIDBaYAJFaXE4GrJEIaEqwKAlBqM1Fq03F42fCCs3ED6AiLaA2JaAuJaAuLaA+JaA+L6IwIiBsCWkMSWscI1mTBTAT5BirtBspsJsptBirsJsps9HGRbECAibhhQjdMROIGglEN2sAKORLjFCAJAiRRgCSKkERKC7YrIlRJgiIng3YKypOPkYTEvwMfjxKoq2665hh63RHupyJsfY1AXxPQt5e2xIW66TZ04n9oBp6njgLwolraHmcvzsuEv26YMEz6GuoGrS4n/18zzIGiZIaBYXuo45qBtzpVABOv3G/tl9EfE+GNU+XvnqiI7gitUHvH2FM9lEs2KUsimS2RyJyocyQmZ4amgutUJC0aNxEI69AMWl1PFjKTJQkem4yikmR7OyrqZ1c4JZyxsaQdcKuqilCI/sK/9NJLuOSSSwBQZdRsipK99957OPXUUwc+TqaCX3rppVi7di1uvPFGhMNhXHXVVejr68Nxxx2Hv//97/ntwb3oH4GvPUR9uP1DSpI6yynYno59uIf27KxZPPxzWgTwd9DXItg1/BbuA2JBwIgDwW66TVoCFZKzJ6q7O8oSq/Tlg9XdXZVTdhadMWYNU9NhRGL/n70/j5Lkuq878c+LNbfK2rt67wYaOwEuIAgQgCgugChKI1Oew7E9OrZMjTUjy7JIj2EdU/Iiyj/LImWP+ZMsenhMSTMU7d9IsqUztDQaUhJIkZIlkhAIbiBAYmsAvVVXd21ZucXy3vv98SIyI7OyqrL26u64faIzMjIy82VWZkbcd+/3flFBgA4iVDtENlvISy9RKL4G7/B+j7AXWmtUYod+/PHH+YEf+AEATpw4wdWrB/k3+eBCCIHv2PiO3UPEASKpOinPQaw6qngjiAljnVHFzbS9UZetpAa7Vxl3LTheVhwvq/4hIBVcDYx6ebllMZeQ8Lm2WV8IBLFe26qewkIz6mlD+j3FmKcZ8zVjnmbUM0Rs1NWMOIpSQs6V0kipqccxyy2dqK2pAJGKEcZObAmBlRBvQ9pN6rZjG5u7WbdwElJuCfP+WsLHqtyJqNyJdVJgCYGIGrj189i187i181gr57FXzmNFza4Dj14HnnaKqMoMsjyDKh9ClQ6hyoeIS9PowgQqSUtXSYCe0tp8Z0i7tBryrBUdEh0r4xZIybRRnJP7psRbm+tK6yQRQHfeG6EtIi1oKItGbHN1QE/qQfiv50rr3l6wNYeSyZXU5XC4qJhJlkrf6YtMXkekNMstU2stSTIMkoA+z7aoVHxGfJuC2yXWvmPlbbhy5NgkNk24v+u7vovHHnuMhx9+mCeeeILf/u3fBsxM+vHjx7c8kLe97W1ovXbLLSEEP/dzP8fP/dzPbfk5dgR3vRtufht8OKkFf/Pfh1MPX7vK9nbgFIy9a/zU4NtlaGaq20sQ1A0BD5NLGUAcQhyY/dJ+5CpOFOtkujWddl2V5m73Jrt3pmeTg5tSgDKXKgIZJQnvgUl0j5oQNk3SO9qEzQU1Y6EfCGHI98hMZhY9WUqTB7fNic6crM09C4dfd2N+VnPkGAJaa3QUo9ohOghRQWhIdaONWmmg2gEqitFRDEqhpSa6soicn0UWv4n72rci7IPjlrnvvvv4+Z//eR599FG+8IUv8LGPfQwwDrL18k9ybA1Gybao9J1apQpnkIRYmUtJIwluC2NFO4oySiKINAzNsnBsoxq7lkBYAtuCmaJmpiiB1a1YYwULgeBKooBeDSzm2xbzgWAhMJdLoUBpwWIoWAwBNv7clhxN1dWMJEvF1VQcTdnVlB2zXnI0JUdRtDS+rSmg8G2FA0gNUaTQkU7qzBOTWudfeuTvughFYn031w5hiUMwei+MAVpTiFcoB3OU27OUg8uUgiuUgjkK4SIibmEvvYy99PKq16KETcudoOlP0vQmaXlTtLwJWt4UTW8KuSoo1lBnSwikhlBZtJVILi3aUtCSglZs0ZSCprRoxIJ6JFjpW2K9WdVdc6Ro3AmTvgnTS90K0wnJLju9Yr7WmlgmEwSxZiFQyecrsaKLbthexXcoV00/az8h1GbJE8Jz5NgpbJpwf/SjH+UnfuIn+J3f+R0+9rGPcezYMQA+/elP8653vWvHB3ggUajCP5+Hr/+W+YXLCcxg2J6p7a4c2u+RrA0lk9T2JNm9tWSs8s15szSumIT6OOja2S5/q/cxHD8Jkjue1JYlCe/l6f0l4ueegK9kMhW+8ItGvX/jj1yfbowcOYaAVgodRolSHaGDENkOUPUmst4yRDs0pFon9YlYFsJzsFwHu1xCuA7t519l8Q+/iKobx9fKEy9y9T9+ipl/8jNU3/nOfX6VBr/0S7/E3/ybf5NPfepT/NN/+k+55ZZbAPid3/kdHnrooX0e3Y0DyxL4llHF6cut7PTjjhWBNK2STO24ohXGtCJJJDXN0LQyM1Oo3UC0jkqcWL6dZDEJ6qvJeAqpoRaKhHxbLAWGfC+FguXk+lzbEMSWNK1Km7FIQt629j4UbE3B1vg2+FZ33bM0rgW+rXEso+67wmxzLNNSzRZm3cKExQlACI1gBMFRhIM5oy0bqm7piPFwjtH4CmPxHOPxFcYjczkm57G1pBxeoRxeGTjWJapcFIc4zwyvcJiz6jAvqsM8Gx+lpotbewMy8C1N1TNuAqU1L3bq9LME10wzfOC1LR7MJOGDsX3HiW09ijSLCaHulgJkAvMcQaXgUfYcCp5tkuttC881xDq3gefIsfsQej1Z+TpDrVZjdHSU5eVlqtVt9n2UcZdwlyZ2ZoA5Dia0NmS8fjlJd79oklVrl6B+yZD2QbC9bqJ79Vi3xqwyA84upwOfewL+20fWvv27HstJd47rFlpKVGL57ijVrQC50kA22+ggMoQ6loBGC4Fl2wjX6V3WOBFtfftl5n/3s6tvSCSmY7/8S1sm3Tt6nFoD7XYb27Zx3YNbJrPj78Pcs/DC4zB5y/Yfaw9h1HETVBXKbrunKEmnbiWKeZaAddVigYXo1lHbqa3bwhZmImBQmNUX5xx+7TsF5oPu53/CU7zndMDNVcVKZJTbVL1txIJGDPVkPSXmTSloxayZgr1fsJEcZoGT1hwnxBwnO8tlToo5JkR93ftf1BO8qI5ylqO8Ko5xwT7GJfsY0i1TThT/imNU/xFPM+IYN8CIa0h21dU9Kd9g3vNf/bbPQti9YcKT/M2bGrx+PMhY943ib4vUmm+bBHrXppSE3ZnsAbuTQu9aYndbwuXIcS2htWScr6/9G0Yw2wY2c5zatMINIKXkU5/6FM8++yxCCO68805+8Ad/EPsAWelyHEAoBVeeNR/24phJdL8WZlaFMOMtjsH07b23KWmI+PJ5WD7XTXevXTQW9sWzZulHadKEulQOmXrxNN29OAGFse31IFUKvvKJ9fd56jfg2H3XxvufI8cAqChGt4MOsVZBiGq2kStNVKuFjiQ6jNFKdsiHcB2E5yA8F6tSQjj2ptNztVIs/dGX1rhRgxBc/oUPMfLIIwfGXv6Vr3yl53h977337veQcgwJo44LfGft32qp0h7dpmVUlPTsjqWindjXg05vZo3SETKpS+5WF5vE668u+XzsudUK7kIo+NXnCvzje5o8NBOvun0taA2hglYsaEloS0EgBYGEQAnaEiIlCBWE0lzGShBrExwXK2PhjjXJmAUKUNosGiC5TF+LwPyXrlsC7KTyzBYaR4AtRrGtKqF1C68IuGBpnrTAs6AiGkzJK0zHc0zGlxmPLzMazjESXsaPVzgqFjhqL/AWnk5eJBBDZI3SKhynVTxGq3ycZuk4zcIhlLaQWpkxK00r0NSV7iHRNxc0P3fXVaa/9RvMMcb5m36I1x4yCnTB9Sl4Nr5t2rm5Sd1/2tpty6nxOXLk2DNsmnC/8MILfP/3fz8XLlzg9ttvR2vNc889x4kTJ/iDP/gDzpw5sxvjzHGt49wThgS2Frrbrgd7s2V3a7mzryMl4rWL3WT3WpLuHjW7lvW5bw1+XMc3AW7eiElT98omUd3xexPXhW1Ic1rPDua5su/zIDTn4cv/uyH6WXTS4i2TMO94YGcS5b1yd3HLOWHPsWvQSplgskSh1kHUZ/2OknrqqHvWbVkI10W4DlaxgKg6CGfzpFdrjaq3iGt15LJZ4uU6stYwNdsrjfXuTDw7S/PJr1B+YH9/2+bm5vgbf+Nv8IUvfIGxsTG01iwvL/P2t7+d3/qt32J6enrjB8lx4JGmgBc2MCykQV+RVJ3wL9M2TCOVIef/5Osp2e4ncIaW/+p3CpwuzGOL3qA0QRJuloalJQFoIln3gIIjEG66Hazk7lbCjveLNKZGT6UNc1fYaH0YrWeIuYfLSjOLIfh21KDQnqXYukypPUupNUulfYlitIgbLuOGy1QXu8f12PKoF49RL52kUTlJc+QUqnwY33XwbGPvdpJ09yiMOPHtZwFYfO3/QrVczGuoc+S4TrBpwv3+97+fM2fO8KUvfYmJCWOlnp+f52/9rb/F+9//fv7gD/5gxweZ4xrHWvbm1oLZfj3am7NEnPu627WGcCWxps9mkt2TJPf2kkl/jwOozwFzuzfGbH/TrUBY4FeNIl8YNaUV5SnTK7U8ZazzpYmDGyiXY9+ho9go1GnqdxAimwGy3kQ1Wsb2HcXo2Chq/dZvu1Ba1/q95vNKiaw1DInuI9RyuU5cqxs5bRuIrwyuDd1LvO9972NlZYVvfetb3HnnnQA888wzvPe97+X9738/v/mbv7nPI8yxl7CTmu+11PIvXtJcDdarMhQshjZWcYLXTUmjPCftrroqe9faHiuVJHwngYTa9G0mo06nJDcN80pj0rKJ5902rKvrm9O9+7cP2je1Y/cnh6eBaCn5N5MG2etJWJ0AUSgjS7fStm5D2oKmZVGzLRzVxm9epFA/j7dyDnflHE7tVRwZMtY4y1jjLKQ/CW4RJs7A5BmYvNWUORTHIO6OebxoJYPIkSPH9YBNE+4vfOELPWQbYHJykg9/+MM8/PDDOzq4HNcBcntzL4QwJNWvwtRtg/eJ2oZ4t5e7qe5R01ymqe7pkvYhV8mlENCuwdXvbDyWY/cZa3s6rmxfcxWbJU6eJw4gakFUT9Ld22a/9pJZ1oLlGtv8yGEYOdKtZ68eNa3YclzX6ASUJeFkaVCZIdRNcz1N/Zaq03GgU0Pte9iVEmzS+q2CsEuiEwLdJdaNTtDZuhACe6SEXa1gj1ZwRivY1TIqCKn9yZMb3t05AOrxZz7zGR5//PEO2Qa46667+Pf//t/zzgMS7Jbj4GBuyDC0QLgcHh0uh0QlQV4qSSM3PavN3HOnDVdKvrPtuUhIevpAKSlP3Syd9dXo/lSIbqOT9JJEYcco8ZDUsif79Kv05tK0N7NYrxa6AkwBmX7iSpnMl4WzsPgSzCe9xaMWXH7aLCnK0zB+U/f65afhyL03xnlRjhw3ADZNuH3fZ2VlZdX2er2O5+1yEFSOaw9Xnh3O3nzlWZh5zd6M6aDDLYB72JDUrUAp+L2fXP99L00aZ8FWD+YqNsS+vWwId5ru3kiS3FPlXkXGSl+7sPox/NHeVPfR4ybpvbA7QVE5dgddlbovoKze7A0oi7oqtbBtLNdBuHYn9VsM2ddVa41qtLrqdL9SXauj2+HGD+TYONUK9mgZu5oQ6tHupT1SHjgmrRSNJ59d21YuBM7MDKX73jjU69lNKKUGBqO5rtvpz50jR4pDQ4ZvD7sfGDJrkfrHbzBYVvfYdtNbzDYlTc7L/Auw8CJcfd5cT4+ZKf70fwPLgSOvg5veClO3QnF8f15Hjhw5to1NE+4f+IEf4Md+7Mf49V//de6/39iAv/zlL/PjP/7jvPvd797xAea4xtFa2tn9cmwMyzK18eullN/73u3NnFuOsYuvl9CvlCHf9cumdr12sVvT3pyHYBnmllfXsftVQ8KzCe8jR4xVPZ/t33P01lJn2mg1WqaWuh2i4rQ3dSI5dVRqG+F7mwooG2j3Tqze6Tpy7XZHKUTBW02iRysJya5glQpbqhkVlsXYO9+8bkr5zD/5mQMRmPaOd7yDf/AP/gG/+Zu/ydGjRwG4cOEC//Af/kMeeeSRfR7dHkJJuPAVuPR149a5VgI79xj3z8CREsw2YZB4LIDDZbNfji3CsmH8lFlIvoMv/xl88d+v3lfF5nN74SvmemkKpm7p2tDHb9r9jic5cuTYEWyacP+7f/fveO9738uDDz7YmTmP45h3v/vd/PIv//KODzDHNY7i2M7ul2M4nLjfKNhf+T+htdjdXpo0ZHsvauYtq9uH/fA9vbdF7Uyi+/kk5f0CNOZMT/S5mmnj0/N4NpQTe3o5SXcvTSbLhFHM85OPTUNr3Wv7DiJ0GCKbbWS9hWq2M7XUSRstBJaT1FI7zqZU6sF270Zn29B270rJqNMdu3ev9dvyd++zULzjNJPveYSlP/pSj9LtzMwcqD7cH/3oR/nBH/xBTp8+zYkTJxBC8Oqrr3LPPffwn/7Tf9rv4e0Nnvk9+MwHzGRfiushsHMXYFuCDz4Af+9PdE/lNHQroj94v8iDvHYSSsHXNshSEDZoaSawX70Kr36pu330BEzebGrCJ2421+0tNSDKkSPHLmLLfbhfeOEFnn32WbTW3HXXXdxyy8HvbZn34d4HDGtv/iu/kisOu4GoCb/zd8z6Wz8Ah193sN/nuG1OjJfPG1V8+YK5Xp81s/0bwSmaADc/SXVPF8cH2zXJ7pZryDsiSXdPTi11sqAzteyyt7Zda6DfiivM41mOOQGy3eT5knR3twheBfyKuXSLex4k12P7Dg2pVq0A2Wih6i1UmLV9pyq11W2j5ThYrrNhLbWxe7cH1E1v3e69ikyvY/feSWht+hDpWJpFxpn1RGGXmmhuAbUyT/m7HmH0b//EtpXt3ejD/fjjj/ccrx999NEdedzdxI68D8/8Hvznv81gvZbrM7BzB/CZlzX/4suaS5m5ryNlQ7bfdTon2zuKy9+Cz/3Ljff77g+YCeWrzxs7+vwLg/NTLBtGT8LETTB2EsZOmcUr7fjQc+S4JnHQ+3Arpfi3//bf8qlPfYooinj00Uf52Z/9WQqFbfQLznH9Yy/szTnWRpbYHboGbJROwczST9zcu10paM3DymVDvhtXoDFvZvybV5Mf0BjiFtRbUN+X0Q8HyzaTAsVxKIwn6e7T3V7slUOmHdwm7M5ayj6FOhpo+yaK0Unv105f6kSltor+honfWkriWqPX4r1cR9a6gWRbsnv3Eeqt2r2HhZYKHccd8qxjCQmZhlTDx5Bnx8ZyklT0kTJWsYBV9LA8F8szLchE/Rz23d99IGzkKf7Lf/kvPcfr973vffs9pL2FkkbZXotsw40V2LkJvOu04HtOwhOXTZDaoaKxkefK9i5g2HK6qAnH3tDNutHalGYtvATzL5p68MWzJlx18axZsihPG/U7rSkfPQHVI+aYmyNHjl3H0IT7F3/xF/ln/+yf8cgjj1AsFvnIRz7C1atX+fjHP76b48txPaBjb/5Er9K9l/bmHNc2LKtLSrl79e1amxOS9nKS7p4ku0dNk6ouQ5CRmdXMprtr3U13x0p8k0lP82x/8+yS9IzteW4ljeVPxeZ5ZABRALJtEmnDhkmcjwOzb3PBLGvBLUP1MFSOQPUIunIUVTiEdsdRMR1iLZstVL2JagfoSBqVWkpAoAXdFlpD2r5VEBKvqpnuKtVy5WDbvbXqKtJkyLSOU6eCoV+WbYHjIBzLvDfVAlbRN4vvIVwXy3MQKaFOl75JgGakues/aWCUZ14jOCga0sc//nF+/Md/nFtvvZVCocDv/u7vcvbsWT70oQ/t99D2Dq/8Ra+NfBDywM41YVuCB4/s9yhuAGy17E4IM0FbnuqeQ2ltJqMXz5pk9KVXYOlV8zlPQ9kuPtX7OKWpJC/lSLebyMhhKE3nE1E5cuwghibcn/jEJ/iVX/kVfuInfgIw7Ub+6l/9q/yH//AfdlWJyHGd4MT9Rkm48qyZ0S2O5cE1ewGnAD/0W/s9it2HEOCVzVI9ut+jWRsyMjXqrcVusntzAV2fM33XG1cRwRJEDaNazL8IGH5vg9GlRZVYjKOtCbQ9ifamwZ/CKhYQVRvswbbv3bB7Z9O9O4R6F+zeA+3dUUKopUJonbQUA+E4JqDNsYwaXfKxSwUT3pYh0D2E+jr7HfqVX/kV/uk//af8y39prKqf+MQneN/73ndjEe765eH2ywM7c+wnpu80mQIbld1N37n27SmE6OamnHiguz2ow/KrplRr6VySmXIewpWuS2z2672PZdlmgrsy07ccMhkqbq6M58ixGQxNuF955RV+4Ad+oHP9e7/3e9Fac/HiRY4dO7Yrg8txncGyciUhxw0JLdN+1CEqEOhwBBX4qNYosnEY1b4ZjUR7MVq0sPUKtl7C0is4LGPrRWy5gNAhtl7G1sugXoYYCECvCJQ9ThBOELZHiFpFoqZDVNfIldbW7d7VAene5Z21e69SpWPZsXsne4AG4ay2d9slo0wLzzVtxjwX4TlYbkKknYNj8d5LvPTSS/xP/9P/1Ln+wz/8w/zYj/0Ys7OzHD68xXaD1xoqQ0Zp54GdOfYTe1F251fg0F1mySKoQe1S0rrzkinXql0yk1UqgpVZswx8zNEuua8c6iXlxfFNlUTlyHEjYGjCHYYhxWK3+aIQAs/zCIJgVwaWI0eOHNcKdCxN8FiY9qOOEst3G9VoolqBIZGJ7RswsrVld+3KvoddKYEz3iG0Ckg1ZxWEqIXLqIVZ5OIV5NIystYkXomIGhZxywKaybI27LKLUy0kRHoUe2wMe6y6K3bvjqU76g8dUwg0qT0/q0rblSJWyTfqtO+Z0LbU4u26yfXV9u79gFTd+uAnLrR5yzF9IOpcW60WlUqlc922bXzfp9kcoiTgesGph4zbpXaJNeu4h1UOc+TYTexXVxG/CtNVmL69d7tSRnGvX07aes4mDqw5cz1smLaewTLMP7/6cW0PKocTi3qyVJNWn35l9f45ctwA2FTvgH/+z/85pVK3Si0MQ/7Vv/pXjI6OdrZ95CPrzNLlyJEjxzUIFcWGRIdJMFmqVjfaqEYLFfTXUJtTfGHbhky6DlahgKjYA5O+tdaoZpvoymK3/3QtY/deXs/u7XbWhC1wKhZOWeEVQ9xiC7cscUvSXBYlYoDoq60CulVCB0W05aMtDywPLTwQNlrYJoEdq/Pa0Bibt5JGOVdmXWiFmSrQ3dJ4S4AlELZlSHMxsb47LjgewvXA9RFeEeGXTSmEGybp7iPgF822A0CyU3zmZc0Hv9y9/iOfusKRP/kcH/wrd/Guu/e/+PXXfu3Xekh3HMd84hOfYGpqqrPt/e9//34MbW9g2fCuX0xSyvubXCXIAztzHBScuB8O330wuopYVrc+fJArMaxD/UpCyOd6L5tXTE7K8qtm6YdfNcR79DiMnUiC3E4cXCIet+G//IhZ/2ufyEPmcmwZQ7cFe9vb3rahoiCE4HOf+9yODGw3kLcFy5EjRz+0Up22WR2FOoxQ7dC0zWq00GHcTfmWCgRoIRCWbazMaU9qd3ANtZYKudLokumedO8Gca0O8ZB272pfzfR6dm8VYkVLiHgRK1rEipcQ8QpWXEPEKwhZT5TmawCWa6yKxXEojUNxEipJkF5aV7jNFh/D4jMva/7en+hV71z6zn/sb927ZdK9E8ep06dPD3W8fumll7b0+HuBHTteD+rDnQd25jiIuB7InYpNONvKrGntuZLY1FcumvC2tVCaNO3Lxk/B+GkYv8n8tu/3JOu11lo1x8Y46G3BPv/5z29rUDly5MixH+i1e3dJtWq2jeW72e61e2tDpIQQnTpg4TrYfgnh2gNbP6kw6gkgy6rTQ6d7A/ZIyZDpajfRu6dd1mbt3paH8g+BfwiJUdJ1FHfrpaMIogZCNkC1sAgQOsKyYoQVYwkJtui0GDdB7VZHscY274ew7CS0zMrumJyYiOSkKT1xSmhq2udcxUm6e2hS3OMk2T1qmVCfYKWbMN9IbI1roTSZpOyadPeOjbE0uWMnblKZHsWDpikSkzz/4vef4XvuOrxv9vKXX355X573QOKud8Md/x18/Tfhpc/D9B15YGeOHLsFy+n+BvOG3tuitiHhaWjb8jmjgjeuGjLenO9NUfcqpp/4xM0weQtMnNlbgevcE8bmn+ILv2gC7t74I/lkXY5NY1OW8hw5cuQ4SOhXp3VobN+qHRhC3WijgzCpI07s3ilTsm1DoJ2kRrhUNOS670Q8TfeOF5YHE+paA9UaIsvCtgaq03a13CHX2+njrLXuvM6e8DEp0VojzCxCdxLBsU1f6fIkVimpl3Ydk+Sd9pj2nIPRWzoOTLu31qJZmgtJq5s5Y21szBklIj1pu/x07/2dQtfGmF1Kk7296ofAl2c1l9aZP9HApeU2T5xd4MEzk5t/rTl2HpYNx95oPjuTt+z3aHLkGIzrvauIW0gI9E2926OmaV+2+DIsvmIul1811vXZb5olRXHCfIenbk1I+M2742w698TgILvWgtn+XY/lpDvHppAT7hw5chxIdNTYMO4o1KlKbcLIWkn/6bhDLnvU6U4Panvdllkdu/fVpQGEept274xCbZWLWw760lp3SXQycdB53Vp3HrdjbU/Dx8qFDpnutMTyXZPi7bk73r5r1+D43TTctRCsGPUktS/WLkHtPKxcNqr5wotmycL2YfSYCdeqHusqMyOHV53EKaWZb4Q8eSGCITpuz620t/BCc+TIkeMGg1tKnCd3dLfJKCHhZ017zIUXjSLeWoDzT5gFzITp2ClDwKduM5flQ9tzNCkFX/nE+vs89Rum1W3ulMkxJHLCnSNHjn2BjrpEWoVxV51uGZu3agboKELFEiKJVsrcj8TWnKrTnmvI7AB1Gtayeze6du96E4aIsrAqpUSVLvfUTW/Z7p19L/raYXVs31p1bMpGiTfKtFUqYJcLJsm74GUU6e7lNUOmdwr+iFmmbuvdruKkjvBCxsZ43pBzGcDCS2bpR3EcKodQpUO0vAnmdYWrskw5OAbcuuFwDo1cg/WXOXLkyHEQYLswecYstzxqtkXthIC/AFefNwnprUWzbfEsPP9HZr/CKEzempDwWxMVfBO/x1eeXb8vOhgn1ZVn81a3OYZGTrhz5Mix48jWTadEWocxqh1066aDyASRSWMLRwhDfC2r1/Zc8M36AGtzmu4dX10irvUFki03kLX65u3eqcW7T6neqrW602c6itFRhN1+FRHXUbpAbB0GYZkaaNf0mLZ8F2u8agh1wTd9pVMSnRLqG7S/9JZgOV0L+YkHutuVNKm6KRHPKuNRo2Nft/gOZaAMnARepwW/xr9jlnE0qyc1BHB4tMD9N+1fmOb58+c5fvz4vj1/jhw5cuw43AIcutMsYM4XmvOGeF99zpDwxbOm/OjCk2YBo4KPnjAW9HSpHltbnW4tDTeeYffLkYOccOfIkWOTWI9Mp0FkOox6VVtAJOFZKZEWjoOdKNODrN7QtXvL5XqGUDd6yLXeRrq3XS3jVCtYla3ZvbXWIJM+01l1Oq2bhuQ1O3jqLKXmF7BUvXt/b4z4tr+GOP7GLqF285/lPYFlJ1byo3D8TZ3NsZTMz19l4fJ5otplStECVbmIHy3jhsu44RIfVJ/k70X/KwLVQ7rTT9AH/8pd+9qP++677+ZXfuVX+OEf/uF9G0OOHDly7CqE6LYvO/mg2SZDWEhV8ISEtxZg6RWzvPhZs5/jmyT0iZuT5SaoHDEkvDg23PMPu1+OgwOl4Mp3zGeiehxufqs5F9gDDH1m97M/+7P87M/+LI4z+C6vvvoqP/qjP8of//Ef79jgcuTIsbdQUZwh0kaR7bTISpXptcg09CjTVrGwZpuszvOFEfHiSk8AWU+696bs3uUuod4hu3enjjxTJ64jadTRxOvdUyueWr1LRp3u2Lznv4H11B+senwRLuE+/aswNpIHsOwzIqm4shJwfrHFYlPjOMcZO3YTddui3rfvYSX5mdl5/sMLo8yHXcJ9eLRwIPpw/8Iv/AJ//+//fT71qU/x8Y9/nMnJPLwtR44cNwBsD6ZvNwv/ndnWXDAEfP55uPoCLL5kgjivfNssnfv6pi3Z6Elwy8bptBZKk6bbQY5rB+eeMLX5abnAU79hJtzf9Yumm8UuY2jC/YlPfILf//3f55Of/CT33HNPz20f//jH+amf+ikefvjhHR9gjhw5tg+ttSHKUdypl9ZhhIribs10K+j2m04INZAUEFs9yrRVdDck06ndWy4vJop0o6//9A7ZvUfKW7ZYa6kSEp1Rp5PWYGnoSk9rsJEqdikh1J5rAsg8F5GGkg0ah1Lw3zZIns0DWPYNQay4stLm/GKLpVaIZ1lMlT3s9WrgLZv7jthEdsS/+aYLwA/fU+Tnfujt+6psp/iJn/gJvu/7vo8f/dEf5TWveQ0f//jHefe7d/+EIkeOHDkOHEoTULq/O6mtlCkfSsPY0nR0GSSq+HMbP+Zr/3p+vL6WsFbqfO0S/Oe/DX/9k7tOuocm3E8//TQ/+ZM/yZve9CY++MEP8oEPfIDz58/zd/7O3+HJJ5/kIx/5CP/z//w/7+ZYc+TIMQBaSkOUI2Pt7ti8oxjZDDqEWsfStMXqBJAlEq1lLM+dmmm/iHAcsK11bdZaqW7N9Hbs3r63ukVWRqneqt27895EcdfynYaRpbBMmyzLsVfXTnfIdCaIbCsH2DyA5UCiFUnmam0uLLaotSMKrs10xcfe4G/clvAnl1z+n1c9LjS7EyxKcyDIdoqbbrqJz33uc3z0ox/lPe95D3feeecqh9pTTz21xr1z5MiR4zqFZXVzPW5+q9mmlAnSXDxr0tGXXjWKeLiGyv2lj8FX/y+oJl0tRo5AZSa5PARuce9eT471sW7qfHIe/Jmfhjv+u121lw9NuKvVKp/85Cd5z3vew9/9u3+X3/7t3+bs2bM8+OCDfPOb3+TEiRO7NsgcOW5EdPoqJ+S5p146CBMiHaCCAB2rTGssTHssIRC21VGlhetgFX2zPkSCtQoj4lpjQMJ3sr6yCbt3tbyqftqEkVWwCttM947ijtVbxzFKSoROjO6W1Q0jS+3e5aJpk+Undm/fpHwL19kysV8XeQDLgUIjiJmttbm41KYRRBRdh5mRAmIDsjzXEvy/5z3++IJHIzb7VmzJj00/zUP2Mxw9+t2g9q4ebBi88sor/O7v/i4TExP84A/+4JolYTly5MhxQ8OyTIvI0WO92+tz8PvvN+tH7zUtJldmzSR6sAxXlntt6Sn8qiHglZluS8vKIdOyrDRhgtxy7A02FD20CU995S/gprfs2jA2ffR94IEHuOeee/jsZz9LuVzmH//jf5yT7Rw5NgktlWl5la2TDpOe0602shWgW6bHdNbirUWmXjol0o5tLM1le83WWKueP7V79xHqrDq9Kbv3WoR6G3ZvoMfmrWNpasylRCSvwXK69dOdvtMdQp20y0oV6v0KI8sDWA4Eau2I2aU2l5ZbtCJJ2XeZqRbWd3FoeGbJ5g/OeXxpzkEl373DRcU/mvwi7679//CXlszOf/r78LX/757Vg22EX/3VX+Uf/aN/xKOPPsrTTz/N9PT0fg8pR44cOa4tVA7BDw0oCYtaRhGvXTTdLlYuwcplQ8bDFQhqZpl/fvV9LccQ7w4RPwwjM+aycsi0RMuxcxhWzKhf3tVhbOoM9Dd/8zf5yZ/8SV7/+tfz7LPP8uu//ut83/d9Hz/+4z/Ohz/8YYrF3EKR48ZGJ2QrIdI9hDqIOrXSA1VpNDpRZbv10qnFe/166VXjUJl07+VM/XStG06mo3jDx+nYvRNCvZN2b8havvsUaqXRsIpQu2VDqu2C3yHT69ZPHwRM3wnFifVnWPMAll2BUpqlVsSl5RZztTZBrKgWXKpFd93PbSjhzy4b2/jZevdz9dqJmB84EfKI+Etu/vZ/WH3HPawHWw/vete7eOKJJ/joRz/K3/7bf3vfxpEjR44c1yXcYjfhvB9h05C3dGlcyazPg4pNDfnKxQEPLKA8bazp1SPJZaK8F8Y62TI5NoFhxYzKzK4OY2jC/T/8D/8Df/iHf8gv/MIv8L73vQ+Af/2v/zX//X//3/MjP/IjfPrTn+Y3fuM3ePDBB3dtsDly7Cd0FHdTvKO4UyetgsjYu1sBqh1CHKNiaVRpmdZKA4htqdJZqDBapU5v2e6dpntXs+2yzPp27N7QF0qWUarTsQk76T/tOtiVRJ0uF68tQr0RLAve+CODAztS3PvePIBlByGVYqERcWGpxdV6gFSK0YLHeHn9z9CVtuAz5z3++IJLLTJ/D8/SvPVIxA+cCDlVUaAVJ/7yt4FuG7Au9q4ebD1IKfnGN76R9+LOkSNHjr2GVzJtxiZuWn2bkiazpT7XS8pXksu4BY05s8x+vfe+btnUnY+dMH3Fx07C2CnzfDnWxoaihzBp5ace2tVhDE24L126xFe/+lVuueWWnu0PPvggX//61/nABz7AW9/6VsIw3PFB5sixm1gVOhZl7N1B0JPgraXstMSCjiZtAsY6wWOOIYyODdb6wWMDx7NTdm/Lwh4td2qld9runY61h0ynS/q+dELJTP24PT2GVS4Zm7fvGTKdrl+rhHoYnLgfvuux3pYUYJTte9+btwTbIURScaUecHGxxUIjQgjNaMHDc9eezNAavpXYxr98xUFp832dLii+/3jIo8dCRjIOv8ry83jh0jqj2Jt6sPWQt+fMkSNHjgMIy+5aybm79zatob2c2NMvGcfUykVYvgCNy6ZN2dXvmCWLyiEYOw3jpxOifwYK1T16QdcA1hU9kvPzd3141yfIhybcf/Znf4a1hgJTKBT45V/+Zd7znvfs2MBy5NguVtVJR7LbCqsdmMCxVtvctqa9O5PgbdtdpdUZ3t69alw9du/G6qTvoe3e7kAybezeZaxKadshYFprSGunM0o1SkG297brIDwHZ7xqaqkLSQ11lljvVw31QcGJ+03rryvPmpqi4piZec2V7W2jHclOD+3ldohrWUyUXZx1wgHbEr5wyeX/Pe/xSsY2fs94zPefCLl/KmbQ3Z2oNtygdrkeLEeOHDlyXEcQwpwXFMfgUF+JmQwNAV8+B0vnYDlJUu+o5XNw/onu/qUpY3efPAOTtxgS7hb28tUcLKwlelSPGrJ9kPpwr0W2s/ju7/7ubQ0mR45h0LEpp0FjHWU1QrVDow63AnQYdom0lCBVwhEFCNGtk7ZtrIKfqNSbt3f3Q0Vxl0Rvx+5dLq6qme4Gk5XNmHcAZmKi+z52g8mSpO+0jtp1sBNCbZcKCM/rWr6TxO9dSfm+nmBZeeuvHUS9HXO51ubiskkcH6a116Wm4NPnPT57sZs27ie28e8/EXK6otZ9ztgdUjnY5XqwHDly5Mhxg8D2YPyUWbII6qaP+NIrsHAWFl8yxLx51SwpCRcCqidg6haYvBWmbjM14jdSWnoqepz/S0O67/qrpi3cHpV+3eCSU469hGoHfOdv/AwAt//2h1YRxnWJdFon3QxQQZiQaAVxbHpKJ6WTCKuHSG+nTnoQtNaoVrBKle4Ek9XqqGZ74weyrN6e09n66dEyTrVsemHvAHps32n7rDBCa20Ictb2XS7gVjJ11IlC3WmdNUQ7sRw5dhNaa5aaEbO1NpdrbdpDJI5LDV+56vDp8x5fne9+rw4XjW38HUdDKkMGw9ZHbyX0xnDDpQE13LBX9WA5cuTIkeMGh1+Bw3ebJUXUNCR8/kWYf8EszXmjii+/Ci9+zuznlo36PXWLIeCTt4BX3peXsWewLJi+HVQEpx/e05yVnHDn2HWkRFquNDvbgvNzCEsYRTq1dw8i0qYBlCHSSZ00aeBYWje9gyTQ2L2bXRJd61eqt2H3ziR974Tdu2fcmbRvldq+pSR9/4TrIlwb4SXjqpSwin6mjjpRqW9023eOA4tYKRZ7gtA0I77DWGntYL/lUPD4RZfPnPe40ja/EwLNG6di3nU84t7JmA3ab6+GsDh76q9x2/O/2pnny9xoLvagHixHjhw5cuRYBbcEh+4yS4rWoiHeV583rcrmXzI14bNfz4SzCZOI3iHgt5rrednbjiA/u86xZaQ10iaxe4C1uxUkLbAMkVbtbqBe46vfQbj2aiLtuaYV1A4T6RQ9du9MCNlW7N49IWRVo0x3CPUO2b1TaK3NZEQY9arU6ETYt8B1sFwHp1LCGilhp/2oC5la6tz2neMaQxArrtYDLiy2WGqGCCEYLbhrBqFpDd9Ztvn0eZc/v+wSJyFoI67ikaMR7zoWcri08Xe8H7FU1IOYdiTxR+7Gv+PvcuLl/4zdXuzutIf1YDly5MiRI8dQKI7D8TeZBUxa+tKrcPW5hIQ/Z+rAa+fN8tLnzX5OIakFvyWpBb/ZhL3m55GbRk64c6xCN7U77SHdVU5VO0S30hrpqJvYLSVaaTotsFJrt213iLTISEkqiimcmNkRm3dn3GvYveVyo6NWHzS7d8/4ler28I6TSQwpEVqbsnMnCSfz+1TqgmfqqdOgsus57TvHDYN6EDNXa3Npuc1KO8J3LCbLHvYaE3GtGD4/6/KH5z1ezoSg3VqVfN/xkIdnIvxNfjW00jQiSTOIQcBoweWmqTKTZZ+y/zbE695qQvCufBtOfze84W/mynaOHDly5DjYsOxu67Lbvtdsay93FfCrz8PCixC3Ye4Zs6Twq0kP8ptg/CaTjl6eviZIuNSKp+qvcCVcZvryk9x75M3YeQ13jp2GjmWnd3SqROvIbFPtANUKV6d2S5kkUsOgsLFOjbRtr6tIt779Mot/+MXO9fnf/iPskTJj73wzxTtODzf+1O7dZ/OOE6u3XK4PZ/f23N5U7wy5dqoVrJGdtXt3xq+1mZiIZKYFWZwo6tq0EEtrqUsF3EMlQ6p9N1GpM+FkucUnx3UIpTRLrYjZ5TZzK0l9tucwM1LombDL4uyKxR+e9/j8rEtbmn08S/OWmYjvOxFyS3X9ELRBaEeSehATK0XJczg5WWZ6xGes6PQGsglhQvAcH47dm5PtHDly5MhxbaIwCsfvMwuYc//ahcSC/gIsvGQS0oMaXPqaWVK45aQv+EnTJ3zspOkZ7u5ej/BYS2KtiJXsrmtJpHuvx1rSlhFfWn6e/zz3JZbipLz13P/DTGmGn77/p3n01KO7Ns4UOeG+xtGxGkcmbKxTxxsmZDpVo9tJH2llCJ+W0ojRiXq6m2FjrW+/zPzvfnbVdrnSYP53P8vkex6heMfp1enetT5CXWtsI9179+zeWazVlxo0WoPlOqaW2nWxJ9LE72KP7dvyvbyWOscNhUgq5usBF5fbLNRDlNZUfIfR4uASiEDCf7vs8kcXXL6z3P2uHC9Jvvd4xNuPDB+ClkJKxUpqGXcsJiseM9UCk2UPP3eN5MiRI0eOGwmWlZDnE3DmHWZbHCaJ6C+aYLbFl02rsqiRuL2e7X2M0iRUj8PoUVMPPnLElF4VxpBoYi2RWiUkOSHIajVhDlVMW0WEOrlUEpncV2qFRKOSdZWUWhqYHKMXWpf51JUnV73EueYcj33+MT7yto/sOunOz+oPKDr24khmeknHnXWjSAeodgAJge7Yu5MoH42p7e1pf+W5UDFq9F6opFoplv7oS+vuM/9//wnCd9GtYOMHtESvxXuP7N5ZaKU66rSx2kcmoExjHABJCy3LN6TaqhSxioVuPbWX1FPnid85bnA0w5grKwEXl9rU2hG2JagWXTxn8Hfj1brFH15w+fylbksvR2jefCjme4+F3D0uN+Vq00pTDyWt0FjGq4llfLzsMeI7ed5Bjhw5cuTIkcLxYOpWmLoVmRBiGYfI2jlYehVr6Rz28nmc2gWcds2kozfnM8FsBpHt0SiNUS+OsVIcpVYcpVYcYbkwQt3NukyT4F8hsLGwRe/iCRdbCGxhYSW3W33HbaUVv3bxTwa+HJODJPjFJ36Rt594+67ay3PCvcdYO2gsRgVhhkiHXUt3SqSF6LZysvuItO+a2l3b3peTxNV2b2PxDmevIlca699ZqQ7ZNnbvcl/P6Yzdu1Lcm4mCxDWQrWNHa7PYXeu3XSngViYS63ceUJYjx0ZQSrPcjpirBcwut2lFMUXXZqriDeyfHUj4i0TNfjajZh8qKL73eMgjRyLG/OFD0LTWBJFRs5VWlDyX05NlJgdZxnPkyJEjR47rDFrrjoIsO0py76XsUZgloY4IEqU50jGRkih0V2WulFDlW5FHb0EAXhRQbS4y1lxgvLnIaHOZamuJcquGK0PGVuYYW5lbNTZl2bSK47RLY8nleM915azdmST7+kIdE6iY7zQudm3kg/ZFM9uc5am5p3jT4Tdt521dFznh3iGsWR8dZdTobNDYoNZXmPpoUlu362AVfRM8Zlv7St7WTffehN17LVTffh+VN9yBKHh78jp7rPiZemqNRmjMREaiVNtjI9gjJexSwVjtC15u/c6RY5NIbeOXam3m62GnrVe1OLh/9it1iz/qU7Mtobl/KuZ7j4e8bkJuqqVXFCvqQUQQK3zX4tCIz0zVZ7zs46+hqOfIkSNHjhwHCSlZlpj6ZYkiSi7T6z01zcpYsgMVEaqYUMfGkk1iwR5oyRYd9TdVmK0ehdkozo6w8S3XbCNRmkVyPC0C1eNEwFyyAAgVU2wuUmwuUGwsUGwu4jfn0a0lVFijKQTNqEZzZYVG/QINS9C0BE1h0bAsao7HildgxfFo2C5126YlBE2haWtJoMzEgGZznORK88rO/ZEGIGcLW4TWmtbz54lrTbT2BtdHmx1NGFZ/fbSzcdDYXqEn3bvW23M6XR8u3bvf7l1GxzH1Lz294V29Y4ewirvQSiuT+q3DCBXHndqOVanfI+VOb+qekDI7r9/cdcgQhJ2HTl2HqAcxV1cCLi63qLVjHEtQLQy2jbdi+PPLLn98sbc2e7qgeOexkEeORkxsQs2WUtEIJc0oxrEsRosut1QLjJc9Kn5++MuRI0eOHHuHVA3OqshZhVkOUJo7RLmPLGcJsrlUSN0lyemRUiCwEtu1sV53150hLNlrvY5ARbRVREO2O8p3SnaDZL2tu9fbfbd1trkxYVVCdQQY2cS7GZlFrr2HABwsIjYOT50uTW/iuTeP/Ixjq5CS8MI8stnGGp3Yl/roYaGVQtabGVW6sSqYbPh0783ZvbVStL51dl1buV0t45+Y2fJr67HlhzHIGJOo3iXVnXrqkTJ20e8GlCU11Qfp73VDYuGs6fc4fmq/R5JjByCTtPHLmbTxouswPcA2rjW8ULP444sef5pJGreF5v7pmHce25yarbWmGUoaYQwaKr7DrdMjTFQ8Rgsu1mZk8RzXBZpRkwc+/dcB+PLYz1OyN7Yk5siRIwd0FWVFlhh3l6iHOCskklgZQhpqSZiEfaVBXwqN0r0kWQ1QltNLWwisDclyn7q8avyyQ4pDHbMi272kt4cwDybJbR0RJttivfnuH8NAIChYDr7lUrBcvOTStxx84VJEUJYxIzJiJAqphk1Ggybj7RVGwyYlpSgrTVkrSkpT0Gbi4XtPHOOybQ1sXSYQzJRmuPfQvbvymlLkhHubsCtF7LHNzMjsPHQUd2zecdJ3ul+pHjbdu6f/dCfh2xDrrdi9hWUx9s43D0wpTzH2PW9el/CauvckMC5RrJGmph1hJgJWtdIq5PXU1wziNrhFiIcIzctxoBHEkqv1kEtLLRaaIWhNxXcHpo2vRPCFSy6PX+ztm32kKPmeYxFvPxIxPqSandZl14OYWCtKrsPx8RLTFZ+xkot7AJxEOXLkyJFjb6CyBDi1XycKcrpd9WxXHdU2SlKxTd1y3LFpq46arFEoVB9RXktV7pLhrg3btkSPomzRVZa79cddItyUwWBSrPtI8SCVWUWoTdqrh4UjLHzLxRddkux3Fmed6w4F0UeoLRdXbD2HqhUHiMY8NObRjavo+hV0/Sql5jw/Pb/AY4emQGt05vFF4nn9wP0f2PV+3DnhPuDo2L37ek9v1e7dIdQ96d4Vk+69S/XIxTtOM/meR1j8wy+i6t3gArtaZux7TB9uLSU6HBBSlu1P7To4IyXsStkkf3fqqV1EwcfK66mvTbRr4FeBmiHdzu61bcux81BKU2tHzNUDLi8HNIIIz7YYL3mriK7S8M0Fm8cvenzpikOkzMHOtTQPHor5nqObSxoPY0UjU5c9NeJzqOozUfIouHl5Qo4cOXIcdGQV5KxynNYpq3UIcqQkkU7t1mbdtJbKWK1TotwhybqnPrlLksESVqIqmzrllAgbRdnB6lOZrUSJzhLetHVVIPtJcES7z1LdIdE6S5I3X388LFxh95DelAwX+kiz10eWs6Q4e39HHJzjrHR8VkaPsjJ6tGe7UJLRxlX+4cJ3+GT7Fa5mPOgzpRk+cP8H8j7cNwK6du/VNu+UUA9l93adHot3Zz21f+9RuvdaKN5xGvf4IWZ/+TcBGPu+h3FnJgFNeHEOYdkILwkpGx3Brpb6+lP7Zj3vh7spNGXIA3/5zwD48psOqJUyWIHD90ANCGrg7G4dTY6dQRgr5hsBszXTOztSirLnMlNdHYI21xJ87pLLZy96XGl3f4dOVyTvPBby3YejoftmS2mU7FYscSyLsbQuu+RR9venS0OOHDlyXO8wqrFeRYwl2lile6zX3RrjlOiGKibSkii9TAiyVLpDrDV0rNaq81yGfGYJcm+Yl+ghwlYn4Et0bNfZ21MFud1PejPr4bD1x0ld9W5htXLsdKzWWcW4MIAY+6KfJDsDLef7DZ1MgCi0ERnpToqozG3929J1NWAb0Bv85lhYh+7ivfpOzjUuIVA88rr/hfuPP7zrynaKnHDvMrJ2b7nc6BDqjlK90jCyzwawSoXVhLpaTraN7Fm693rQWoOUve3OwqiT/J21tRfvuglvasyElBU8REKo85CyGwxpq7XqMRAWzH4TyjnhPqjQWrMSmN7Zs8tt6kGEbVlUfRfP7T2QBxK+dMXhcxc9vrFgoxPrVsnRvPVwxCNHQ86MqKHUbKkUzVDRDGNE0i/75GSJ8bJH1c/rsnPkyJGjlxDrjiKc1gt3g7YMQe4mU2skCWFWskOG04TrGNMWKlWKe4lx116dkqXehOu01zGZpGuRWK6thCyvVpCthEgLBEprAp0huzomUOEahDlRmftJtO7evlv1xxZigAqcIcbCHaAgr96/0LFXO0MFmO0GVhHfVWRYrUl2+8nxqkmS5PNB5nPScRcIsJK/vJVss5LPiwBsbGxb4AgbB2PNd7BxLRsLC1fYOJbdcSlYmQkZO/3MVU7ha83U0Qf2NKg3J9zbgNYa3Y6Qs1cNmV7VLquOagxp9x4p96jSXWJtQsoOSvupTjutMEqSv00COEr3hJQJz8EZHV2V/D32rodMTXVeU7knkJkDy1dqL/HQ2G3YB2mGM2qAV4byJGgF6quGgOcq5YFCGCsWmiGzy20W6gGhUpRdh+lKoYfsag3P12w+d9HlTy+7NOPuba+diHnkaMibp2P8IY5xnfCzwNjryr7LTdNlJss+o0UHJw86zDEkpOpaCA/k72CO6xpaZ+zMfe2XjOVZ95DhVEFWmft1A7pMTkVaVxwqSaxjoox1ukN8OoQ4JUsq0XfMMVbrLilORtqjGIsM8c3WGQ8ixun+Ajr1x+2MRbpHOV5lpR6kIHcJ827WH3vC7QnpypLktZTjrP06S5KdbdQfbwZdMqs65HY9Ipx+5tLtOvk8pKQ31YINuiTYSslv+jfu/J3pbHP6CLBr2aZO3bKxRUKAhXkMGysJf+t+ltIJGEOI0/2ykzH9+4vtv8faBhVt7zG2gIPB4q4xaK05+9f/R8KXXkBH6+TRJ1hl9+6rn95vu3c/ekh1JgE8ubW3ndZYFXukiFXwkyXpT+3nyd/7jccXvsmHzv7XzvWf+M7/wYw3yk+ffjePTtyzjyPLoF2D0gQUxkApcEsQt8xljn1FVs2+vNymFsQ4QjBScJjoq49eCASfv+TyuUsu5xvd26YLikeOhrz9SMRMceOTJq017UhSD0ywTRp+NjXiMVb0BrYSOwiQWpH7cg4mHn/lcT70xIc61w/k72COPYfUvZblrHor6bueIcE6Dc3qU49NUnVXEY5UN9VaqoTs9il/qTqsNR3VOFWDs7+WorNFdNS+LBEWfYS4Q5IyVursfbKERWm1qv64qcI1lONh6o+jXaLH4Amnh/SurjN2OiryoHrjfkK9W/XHOjOxMogQy57PQC9BTq8D9NLKrp2+Q3wTQrz6c2CIsGPb2ELgCvNanYQApyqwNYAEZ0PeuiR5dRJ6lhTvt7v2WkFOuLcAIQRqZaVDtq1yYUAIWaJOHxC7dz86Paoz1m8lJUJrM/mZqNSW55l2WpUidqmYt9O6RvD4wjd57Ln/uOrANxcu89hz/5GP3PbDB+NkM2zB0VNG0S6OQ2HUkPCccO8b0trsy7U2i42QIFaUvNUtvQIJT1xx+JNLHl+bt1HJ6YFnaR48FPHI0Yi7x4dr59WOjJIdKUXRsTk86jNV8Rnfh/CztIVKqOMkkEf21B2GOiaUMS0V0pIhLR0iV2Z5beMuTnP3no41x/p4/JXHeezzj60KIDpwv4M3MPrJST/57bRQQhmluI8Y96rHqmOLTtszRcq0YUqJsNQqCdTqEtyuGpxcH0iCV9PgrFVasD4RFpAofdYa+ySPsMG5Yrb/caAiGjJcu85Yr65P7k+y3q36YwFdcit664i9PiKctVEXLDdRnXe//nhtYpz53HUmWbqTLen1rDsgO1GSVYezEyGpzTm1Rnu2jS1sXMvCFS6uMAnmbqIOZ8lwd3018e0EuOVE+EDjmiHcP/dzP8e/+Bf/omfbzMwMs7Oz+zKeo//mX9P8r7+GXS3hzBzZlzFshA6pDpPk7yhGxbJjHRGu2+1RPTmKVSklPaq9blutvJ3WNQepFR9++fcGzjKnBqJffPn3ePv4a/bXVqmkGUx5yly3LBg7Aeef3L8x3aBIk8bn6yGXam0aQYQtLEYKDuPlLuHVGr69bPO5Sy5/3mcZv3M05h1HIx6eiSgNcWQJI0U9iAilwncsJioeh0YKjJVcyt7OHZrSOsR+4hxlCHVLhrRURFuFtGXUPTHvpOXKzqmVho4yIBBcDBa53LhAtPgsJ9Q79iyA5aBjv4/ZUkk+/MSHV5FtOGC/gwcEWcVXZUjFYCLSZ4/OEN8sAU6/O0YBVj3XTQ2x6qi/mi7B7Se/aDp26JTYZK2vvWRnMAEWGVK7igyL3m2bJcFrIZ286yjDsluDPFz98d71Pzb1x4NI8Xr1x6uV492sP85+PuWgSZlV21THTk9y5tv9v9c23R+6JjC/8Z5tdxRiLyHDrnDwLKdzHEjJriOM3uxkgtsckSHNwu4Q4vw358bDNUO4AV7zmtfw+OOPd67b+xiuVbz7NYRfqDCUfLOLWJNUaw2W6Ni/rYKHPT1mSHVi/Rap/Tsn1dcVnqqd5XK4vObtGpgNl3mqdpY3jZ7Zu4H1I1gBfwRKk91t5ekkSE2ZELWDgOu4prwVSRYaIbPLLRabEfEatdmXmoIvzLp8/pLHbKv7d5kuKN5+JOLtR0KOlDY2Ekaxoh7GBLHEtSxGiy6HkoTxyhAJ4yqxbnYJdJc0p4p0oCJDnmVIW4dG2eo72e9tBKM7J0uOsJPwHtNbNN02SC342sor/M7cl1mOTavDz3zrRT529vf46ft/ek9ajFwL2M9j9lNzT3G5eXnN2w/M72CC1LrcX3OZkth+y2la/9tvTe0+RqL26uznX3XIbpoiHSN7SG9PCnCm5tNsW2197iW+6TU6t/UT2W7rJbq3IZJEaWcV6e253GXVrpteHfbYp9esL16j/jh7fTfrj9O06kImjXqo+uO+GuTdrD/OWvK7pHjQtn6CbJAqxhrdTSPP1v5mFF3PdhMybONiSLHbUYztpP68qxw7HcW4u273bcvPjXPsFK4pwu04DocPH97vYew51laq6QSVWZ6DVewj1UW/YwHPSfWNgytRbUf32zUENRg7ZULTUpQmwS9D2AS/sn9jS6EVLLwElgvjp/Z7NDuCWCmWmhFXVwLmVgKaYYxrW1QLbk+NdD2CP7/s8vlLLs8udw8VBVvz0KGItx+JeM0QlvFYKhqZNl7VgsvNU2WqRYeiZyGFJFIBV6N+BVp2Tl5bMuysd1vRpAQ6VbdS8iw6xNlOTpoKltsh0umJ16pxaklThjRlwJIyl00Z0lRBz3pDhlwJawO/P3PNOR77/GN85G0fyUk3+3vMvtK8Mtx+UW0A2c2c/NMNtspaSwcpvP2Km6bX3hwn6dAp8V2P8EJW6U1uTZRerekQuX6rc0p211J7+0nvamKbqf9NCK4gUzea3OcgnE/01x8HKu6Q4I3qj3tIst77+uP+Psi+cHCExWcXvwXA/zjzIBW7sCZh3k2FVPd9tgeFuXVbg6UW/O4nr58kp6pxSnTTz5Yn3I6C7Akbz3LwhNMhyCn5TUmynU6AdlLNrUQ17gZv5chxUHFNEe7nn3+eo0eP4vs+DzzwAL/wC7/AzTffvN/D2hEMT6p97EPj2JVy1/btJ+20clKdA5h2qzu6364hDmD0eO+2wqip5W4uHAzCvfgKlA9BY26/R7ItaK2pB5KFRsCl5TYr7RilFRW/t292pOArVx0+f8nlyasOse5qWK+dkLztSMSDhyIKfUKlStrKxEkrmVDG1IKQhgzRKHzPYqRqgaepO4pFHdOuR4Y0J2m7MlHjUqT1cemJVUqiPcvpnHilJ2TZ19lWUUKSE9KsQhoy6CPQ5raGCmhJc/tO1DKmSt8vPvGLvP3E2294e/l+HrOnS8O1F3yuMUuo4nXIbp/am1xCV8XtWpr7qzrJkNzNE9619kvXrzVIrXpIcJYUD6o/Xq0yZ/fZ/fpjT/T3OR5MmAddz9532PrjQEUdwn1f9WZ8y9302FUfMc4qytlk9HS71nrVJI2GnuToblq0ZZKobTshxg6+ZeMJF9eye36Ts7/Zdo+CbPeoyTly3Ci4Zgj3Aw88wCc/+Uluu+02Ll++zM///M/z0EMP8a1vfYvJycmB9wmCgCAIOtdrtf1V9DZPqkud5O9OXbW3+R/gHDcW7q3exIw3yly4PHC2XgAz3ij3Vm/a66F1EYdgu9367RRCGNV76fz+jCuLlUvglWDqVmheBRWDdc38ZAIQxIqFRsBcLWChERDEioJrM1FysZPWfErDM4s2fzpr6rLrmbrs4+WIhw43ue9QnREvRKKYlZI4TpQkHRHqyPRsVZJmHNOOI7QA1xFUfIeSZxO7Fi1hYSsLJ+oqFY6wKThuV7lIlLNISVqJmtySAYsdxdkQ6H71uSFDWgmR3o6FUwAFy6Nke5Rtn5LlU7K95NKsr8RtPrv49JqPodHMNmd5au4p3nT4TVsey7WOzR6zd/p4fe+he5kpzTDXnMuUEPSiahc5XpjoJcbCwhIMIMm9hPl6n9zWWicuk75kaj2YJK8mxJltiYK8V/XHfg9J7q9DHnz7Qeh/nG1f90z9AmeKh0CQIcuDVeVsLftairKpRzaBZKZG26jJXmInz5LktO44Xc8qybnNOkeOreGaOXv8vu/7vs76Pffcw4MPPsiZM2f4jd/4DR577LGB9/nQhz60KrRlt7FtpTon1Tm2CVtY/PTpd/PYc/9x1W3pYfIDx75nf2eXg5ppBVYaMFlWmjTEW0nYL4WwtQgygjPvgJEjcOnrEDXB32dXwBCQSrHUirlaa3NppUUtDEBoCr7AK0Co21xWkvMrDk9cLvPk3AhLgde5f9kNuGNqjtunZxkvrSC14gWloJ19liQ0TEMsIZamNq7k+BwfqzJa8Cm5FrGQPapyQwYdIt1LnnvV5+0qV66wDUG2DHEuZkhz2fYoWuaylCXVtk/RcjdUop6svTTUGIa1NF+v2Owxe6eP17Zl89P3/zSPfX7w+QHAX5t5M1PeyI49534irT/ut0+v19/YqMj70/84a6Xub9fUG8K1dv/j9La96n+8Efr7a8t1riut6OrJ8FzzEp9L1G2A/+PS56naRb5/6vXcXT6Bb/u4wu5MDKQKc2/2hE1/FoUtbNxMinWOHDn2B9cM4e5HuVzmnnvu4fnnn19zn5/5mZ/pObDXajVOnDixo+OQjTZKLuSkOseBwqMT9/CR236YD730fzMX1zvbZ0qH+cDRR3jUndjH0WEC0w7fY1TufpQmjZ08rBuL+V4jbBpL+6mHjbqttQl3C1b2jXCngV9pQFicSdyOtSJUMUtBwHyzxaV6g6WwTaQktgOurVFCoyLF0orHC/MzvDB/hIVml2i4VsyZySvcMTXHqdEabhIaY4sySmsikiAhHdJWAStxYGzYREgRo+yYiIggimgtpopzuKayOAwEUMyQ4ZLlJYS5u96vPpdtn6Ll4e2iE6FqF4fab1hL842CjY7Zu3G8fvTUo3zkbR/hQ098iLlmtyxkzCnxnkMP8PqR/ctlWK/+eHUI19r1x2nv5L2vP16tDGeTrLtK8t71P94uUsIsO3X73byITu/t5Pp66nK2dZMtLFzhULZt854k71GqLDvC4svLL/B7V59aNZ6abPHbl7/Im249wzsnX7v3b0iOHDl2DNcs4Q6CgGeffZa3vOUta+7j+z6+7+/OACwLu1JAeA721HROqnMcODw6cQ8PxDYPvfQJAP73R/53Hjr6EPbcM/DC5/Z3cDoerG6DIdulSahf3h/CXZ+FQ3fBkeQERwgYOQz17ddxZ1O20/TgSMddEp1sb6VKUyZpuzcszJwMRkrTDGJWgph2KFEKPNuh5NiUkrrBIPL4zvwkz8yPcKllIewWwr6EW32BQyOLHKosUCnUCAl5WYd8u5ESa3MpGcIGGq19kyccSrZHMVGbS+nSIdBeh1hnbdwFy9u1tjJr1zf2rqdpud3UZXCFw4hdYEW2Bz6HQDBTmuHeQ/fu6NivdWx0zN6t4/Wjpx7lgcMP8NBvPQTAjx97lDvLRzet9sV99up2v1rcE8K1fv1xW5kyjN1AT//jhOANbuHUm2qdrVXeSv3xQUBvmFdv0NdghRnSb/Z6hNkTLr7tdFpi+cLFS2qWV6vKdlLP3K1XXm+CQWrFj3/719d9Xf/mld/nkYm785rnHDmuYVwzhPunfuqn+Ct/5a9w8uRJ5ubm+Pmf/3lqtRrvfe9792U8wrKo3HsbwragtM9qYY4cgyDjngP0G2feaEKcyofALUDcBqew9+NKrXTZdPJ+lCZh6dU9G1IPtIKRmV47e3HC1HAnSMly3Kc4xxniHGnZPSmXIYGOCRObpgkK69oMkycm26aq06IkqZtzkxO6ZhyyEkQstFosBm0aMiASEdKKiUREW0Y0w5DlWNKQMVK0wQ8QxzT9MXS1ZCFc/y0RgC+6pLni+FTsAsUOSfY6RLpseRQz6rO7Q2UBao06xg55RvVYOpVOI6y6StSg+sb05Nq3PdyOktetb8yG/KQn11WnyM+d/Z0B75M5ef/A/R+44QPTDtIxeznTJrEhA56ovbhGH+T9rj8erAxnWzl1WkH19T1O7+MJ50DYq7eK9Dscd6zYsjMJln7H4zQ1XuvOTFgaYGenPY8z329X2JRtv0dh9jO1y+a3NWkfhdUhzCmh3k2ie8208cwiWIHGVRN6OsilliNHjlW4Zgj3+fPn+aEf+iGuXr3K9PQ0b37zm/nSl77EqVP7ZwkT+9yDO0eOddFeMonf/ShPQWEc2stQ2QfCLUNwfPDWSSH3q7BLClCK9MStS5YVkYyIoxXicJlo8XliFROpiPbKOdrN8wRXm4TITm9nlVGcU+IsMv+n7UtS4pySOyEEUsWdk/1WXxBYY0CidlMGxMOozSkE4HSVWQAHh6LlUhAevvAoCKMkp+s+DpZysLWDLzyqToHpUonJYomyb+NYWzvxTJOds+m4KWleW1neOAwoTc11bBs/qWkcVN/YrzZtt77xPTP3M+oW+fDLv9dzsjxTmuED938gbwnGwTpmf/bVz3bW/+Psn23rsVb3Px6sHA9Wlbs1yAet/nin0P9d71qyV9c0pypz1gpvd3os24Y4J7+dvu0lynL3/XStXoXZ7VOcHevgB31dM208U9TnIGyYSemFl2D8JnC8je+XI8cNjmuGcP/Wb/3Wfg8hR45rC60lSifexDff+83e7ZYN46fh3JehMrP344oSZX09hdsrgd74BEknraSihDh3yHPGsp1uy9Y9hsm6UUx0QpglMg5QUQNx9WtQ647PljG2amEHi9huEUubrOJYy0QBMyp2S4U0+hK1GzJpPaUCWjKgpdbxXw8BgTBEWbh4wkPFZRrBCLXWKDIuoWURLUuMODY3j8TcOd5mpggF4Q1UapRStCNFqKR5bN9mrOhSKbgUPQvHsjrqctDpg73aqtl7Ep3tx2pGbWVOnrPEOZucmypQ65HlXrXZ3reT6Ucn7uHt46/hqdpZriw+z/SJh7n3jvfc8Mp2ioN0zJ4odF1oNxWmKdpeJnhr7frjQanXN4KtdxjS3F/LPNChQ9ep42BTsr2OOp8S5/Q73CHLGRKdJdDXiq19s7hm2nhqBUvnDLk+83YYOwkv/znMPWM6i7j7MHmfI8c1hGuGcOfIkWMLKK8R3DQykySB70Orq7htarOTA7TSiljFHTU5VjGxbBGrFnHjIpGwkEntcz9pDjs9nBOVGZlYEjW9FKxL+FKl1BE2ApCYOuq2DGlHK8aS3ZyluRLQjJo04ybNqEGjPmuIs45oyiFrm9dBwXJ765qTdlQeHrZy0LGFkA6OdqjYBaqeT9EuYCmXl5ZHeebKON9ZGCOUXYI35ge8ZmqBu6cXOVRqYXhoAZ1YrkMdJ7XfklYUEyY2edcVlIoWvmfhuYJQBCxoAQF96rKF3deTtez4iRW7q+Zl+2S7A2ocs+1mruUTaVtYxuYZa5i4a/9S9XOsi0dOPtJZ//sn3rml/sbXIgYR5LVIc6oyp46SfmdO9vs+yJrtDqhpThc3/b09oCrzfuKaaOOpYlg4C5XDcPphGD1mtt/03eb84fI3oXrcTJTnyJFjIHLCnSPH9Yi0z7W/RsubyiFDeoOVwbbzTUAnCnGse1XlbihYb21zWDtPSx8hfOVxAhkQqQilEoVZS6SSqKiFbLyCaF9K6szNqUi25rZ7QijQwii1YaZHbNrD2SjLRmlu9qnP7bXU5vm/HOq121iZdOwkAKyn9VQ2Sbs3bTurlLUjST2QLDcDGqEklgrHtigkNu5IwotLIzwzP85zC+OEsvvTXfHa3DI5x5mJy0yWl0GYZj6XJaSKk0CgJUQKlALXsig5LoeKFcZ8n7FCgaK9urZx9Qm0lVGhzMl4fhKd46Cj5Jb4v7/r3/Ln3/7P1xzZTktfsqUYsV7fWZJiLaV5MGl2cK3V33lX9BLp/Pu+sxiqjef4fdhhff/aUtYvQ/UI3PI9UBzrbncLcNNbzLnGha/A5Jm9n8DPkeMaQf7NyJHjekTcNgfDteqk3aI5cNbn0IWxgYRZ9pDl7ra27AYJ9avM/fW4qa04S/zs1jx2qYrdXkhOCG0c2yi5oQyJiQmBlla0gkUasd1X37yaSG+3X2zBck3gl7Yo+lXK5WlKTomSW+peBk3KyxcojhztEOnNBBSlKnNqzW5GEfUwZqkZUg8jQhmDBY4tcDyQyuJb85O8tDDDK4vThLJLFMpuwG2TV7l98iqnqk08y9iyXXEYTziYykWBlIIo0kgJBdthtOxzuFJkouwzVvDx7fwQkCPHbiMb+BevozoPSs62ReIoIbVWix57tm+5FDMTZR07dk9ZRm99c06aDxYenbiHj5z5IT708n9lTjY722dKh/nAGx/jUXsMLn7NtKwcOby3g5MxhC04/ZZesp3CduH4m6B20QSp7fX4cuS4RpCfbeXIsZPQGvb4ZKY//EtqRdy6gnSLxO2rRC1j15ZKEqmIQAYEMiBsnCNceJ6wfalz0qc6J4C9hLkbBKYHq8zCwhEudlLX3NZpTXPUUZUbMjA1zq1FmvECzctfSuzaxrYdyGBb74MjrJ6ezINU5bRPc9bGXbQztc21i3Dk9TA2oP9v4yq61UK5VWJh3p+6CpKT6EySbrJoUsWp+7+UmiDWtANFO1DEElzbZswpUy64CO3y0tI4X58f5en5CoHsquBjnuRN023ePBNy56jEs0rYnO45edZa046kUcmVouJYjFZcpkcKjJZcKp6DlYc95sixaaR1zenEo/m+y57fy+53P1vXTE9JhpP5/SwlQWBpnXjR9laryz01zc6WQv5yHHw8ao/xwBs+wENPfhDItPG0bHNeUZow7TzD5t5at+uzxkI+vo6l3S3AzGvgxc+ZLihbDNfMkeN6Rk64c+TYKagYrjxnDoxDzvKmLVCiJLQrVT96yHPmMlKSQGfqmHVMpGSnDVKnjrmxgCxPIc79iTn5SwRgkaolwsbSIY5sYyGTWlu3E2altaatYloqVZPXDwLLJmoPpTa31r6p6BSNqixsylJS9EcoWR5luzCQQKfr7iZqBLOtZ9oqNOsqRsYtZNxA1i8glUQn/wQCojZat3FaV7DdQicp2+nr05qePHuJ4hTHmmagWWnG1JuKUGp84TBSdim7HpGy+cq8w+NzLl+56tCW3dcw4SsePBTx8EzMHaMSw5XtZElei9K0IkkzjFFaU3Bspis+UyM+o0WXspfXTubIkaK37VQ3LT/9nR1s0e7WNaelFIO++/3p2W6fupxtN+UKOyfNOQyCOtgO9uHXdTZ12niCmcSfug2Wz5uQsslb9mZcMjQhp4fv2TiJfOImmJ2E5lVTspYjR44e5IQ7R44tYhVZbs4j/RJxe55YNoj9aocox1oRqTipMY6JVEygzWX2BC9NzU5P/ESniisxZndapvSqzI6wsa3MbXYLqqcJitM9KnLPZesqjfqrNFuv9li2mzIk1PHaL3wIuMLuUZBLaT2zsChhUZq6g5I/Stkt99i2i06xexK6dA4ufd3Ujq2BrKoUJqnj/TWOqeKUfSe76nzGpqkVJbeMP3KMQmkK3/bxbR/HcnAtFwcLN7JwZIhTmcmoT+b9z6IZxiy1IubrAQv1iFYcY4sCk55NsWxTjwVPXnH54hWHr807hKpLiKd8xUMzEQ8dirmtQ7L7XrdUNEMTfKaBoudwdKzIRNljtOhS8vKf9hw5shCYVPzz7YXV331sirZp9VW01g4D6287ld6WI8eWoTWsXIKjr6c0cfPqriIphIDDr4XFV6C1NNjevdNYuWzcXuOnN97XK8P0XfDyn5qw1nySN0eOHuRnZTluSPQqx70qctx3m9SSUEnCjrIcEyXKckqQlVbIxhVUZQbp+qirzyG8MtrxE9KsM2Q5TcvutkfKqsvpbVZywIpUnLFlhzRls9ufOdunOatCx22as4+jh1Gb14AAiol63LVo96rK/dbt1LLtrRWc0q6BsODEW3psZ2lSeSADpErC02SLOG4g24sd26ZBVnEyir2D3ZmEcIVNxS6sUpyMHXN1jWNq03Ray0YJvuldpi5tECZvMwqDu7qlWSOIWW5HXF0JWGyEtCKJbVmUPZtqscBiaPGFKw5fmnN5etFGZtqeHSlKHjwU8+ChiFuqauC5ShgrWmFMO5YIIah4DqcnK4yXPapFF9/J1bIcOdbC0dI0b6ucwhm/OfPdNyQ6t2jn2De0FkwY2szdG5PUyjTM3AWvfhkKVXMs3S3EIcjIqNtrHQ/7MXkGZr8BrUXj9MuRI0cHOeHOcU0hawccTJANCe6EgCmVEGVJlBDmMCF0WRu26tQw64wa2q3B61WWu+tpWyMbgWX5WOM3Y48cxfIn4Orz4FbB8VFa006s2IYoNzsEutUXBNZPoCMtt/WeeZbXUY/LbrmrJtsFyvUrlCyXkj+aSds2lwXL3fRJaKrOtzv9mmWP2hy3FpCFCnrlVUNuNWihjcVdWDjCwbZsbGHjehUqboWCW6HglilYXkKc7Z76xn7b5pZDgeK2KQVY7+SiNAlJsrnWmkYgWWpFXKm3WW5GtCOJY1mUfZtq0eVi0+bPLjl8+YrDd5Z7f25PVyQPTBuSfaqymmRrrQliRTOICZPU8orvcHyixFjJo1pwcO2cJOTIMQyKts9xtwr+2H4PJUcOA6VM0NjptwxPUGdeA/MvQuMKVGZ2b2wrl4y6PXZq+PsUqjB9J5z7Uk64c+ToQ064c+wJsq2j0mTWnutJIrbMEOkwUZL7VeVeC7bukHDVZxsGYyPs779sCWMtNDbs3vAvC7EuWQtV3CXDcdBtNRXWjVX7Yp2mimhGDZqtBZpzdZpa0lLhtnK0RRKws14QmCHMBUpaUdKC0smHKRXHcddrg3Puy0Z1HnBwVKlNO6P091u2s3WOOhlnGgo0qA1NMYzxJ+/GO/IGY9NO7Nqddds17WlsFyeOEK0IHN+0MNttxG0T+LIOlDdCM1AszNe5Ug+ptSKCWOHaFmXPYaTg8uKKzadfdfnyFYfzjV676e2jcYdkHymt/kToTj22majwHYvRktupxx7xXew89CxHjhw5rn00LptJ3kN3DH8ffwSOvM4ElBUnYTc6TcQBKAmH797840/dAnNP753tPUeOawQ54c6xLjZLlHvt14Y0hzomzrSOUtlgmsSSnVqEszXLVkKA+1OxUwu21WPNFkOrsUorWiqkmbSUanWU52B1orbMKs4BcadtyxqorX+zJ5ye3szFRFUeZMvOXvqW27GYb4jWMtgelLp1VKlNO1Zx7yUK1bpKbHX/DiIhz/12bUdYFJL2U0XLpWB7FCzX2DITy3bHom31Ks6dv416HmbeAJN3bfw6XAfcEkQNYA8IN9rM0Pchkor5esjcSpsLl1qMzYU0xGUsr0LZdyj5Fk8vuTxxzuGJKw6LYfdzaAvN3eOSNx+KeGA6ZsJfTbKz9dgKKLkOM6M+kxWfaiEPPcuRI0eO6w4ygqABJx8y9c+bwdStcPW5rgq901iZ3by6naI0AZO3mjZme0G448CEyYFJS3eK5v10/N1/7hw5NoGccF+n6A/06qiSqA75zdqy097AUaIsb6Qop72WRYcoQ6f5kWCV/Tolx45wMzXMXTK9WWitCXXcQ4bT9f5E7d5AsIBWYgneKqwetTkhylJRrhymWJmh7Ja79u3FC5SCGqWRI5SSli/bhez7u/X/HWVrHlWeRKy8at4rdBIQ5GAL21i2LZuSXaJQOUKxsUSxfBLX6hLlftLs7kRAkDZxZUOfXAgBpXGYX9j6cw4LlSj1vulb3o4kV1YCLtfavLLQZLkZEisouz4zpRGIFV+sVfjLqw5fne9NFi/amjdOxdw/HXHvZExlgMEgiCTNSBLEEitTjz1WdhktuvjOkO9zUAct98YBkCNHjhzXI5Q0v6NKmZIiaw+C8FJSO3lm8/d1fKNyP/cZU2u9UYL4ZiBD837MvGbr78PUbXDlWQgbm59M2AyUNCFyh+6Awjg05kz9+PJ5U+/ur55Az5Fjv5AT7gMErXVHBe4P88raeuMOeTY1yqY9lKlRDpUk0jGxUr2BXqus16kNONWU+xVl0RPqtVNEuR9SK+pxu0OYG33keVAoWKo+b6g2b4CC5Q7sydyvOPcHhBUst1dxlJH5kT/5ZiiO9z6JVYbL3zSzrgOgeghz9u/bdRSktu20otz8HWycTFp5Kam5LlouRQnezH24M3cbu7bdtWx7ltexbduWbQ5W9TqMnNzdABYAGZgTg80cgIsTIJ/dvTGliFu0cJldEVycu8qFpRa1dgQaKgWHmZEC842Qp84t8R9fOs5zSwJF9zMw6SveNB3zwHTE3eMSt++tTK3i8y3J+56cBuCfvLbOO07aTJZcRooOzmZ7lzauGMKtopxw58iRI8dmsXzOKKTCAmEbghk2YOwkuIOP2TsCuYVAsn6MnYLRE1C7CONbUKLXQn3OdAYZO7n1x6gcgtFTsPCiaRe2G9DanL+MnYBTD3cmy4lDOP+XcP5JmBrJ09JzHBjkhHsHsFaQV5Y899uuIyV7WkRF2oR5Ge1Yd3qDppbrbmuj3npZoKdGOUuWO4FeCWnerPV6WKRq82pbdjcIrNUh073qc3tH1GZDhsuWT9H2Kfepz+XMejHTz3knJgwACJvgVVBeBSkjYh13Ldw6QsYt4tY8UpjPStZUbCGwLQs3k7Jdsj0KlmfIs+Xh2U5PwraXSdxOVeiev6m0YOoeGB+iV6c/YmbL42B3TzDA9PO0/c0Rbq/Mtorf14FUmnoQU2tFLC/MstJWPB3WsZ2AkYLL4arPS1eafPGleb5xfpkr9SC5p3mvb6pI7p+OedN0xJmR1aFncWIVbydW8W/VSvxfZ8c6t//CNyr8ny/ABx8QvOv0Jk4KtDYnWQDH3gizX4eotft/vxw5cuS4XrByCSwPbn2bIWuWa4j37Dfg0jdg9Ch4lV167lkYO741y3YK2zGEffmcyR9xCtsfl4zNcXrm7q1PBIAhudO3wfzzZnLB3kEFPkXtoikBO/2WLtkGM6l/+G5YeCkJlst7gufoQrUDvvM//n8AuP2Jd2NV9670ICfcW4TSii+vnGVBtojrxYFq8mDbtYHoI8DZ4C4Xy9TsZral4V+7CanVahv2GsnZ/ftJtq82l2w/Ic1eb+upjsLc24aqbPt4wtm1+ta1W4d1bfoANOfNTHPjYkc5dixj3/YKYxQKYxTdEQp+laKVhIJZNp7IWrhtY+lOWtRsfdCxmakfltR6FXOg3gvCFrcTgr+JEwOvbCoVlOppI7ZVhLGi1o5YbkZcqQc0gphIKsaiOlSPMVYp8a2LNb5x/hLfulgjiLufa8cS3HF4hPumJY+Kv6QydbznsXtSxZXCERYl3+Z0tcJXlzw++m2n71cAZpvw9/5E87G3Mxzp1srM6vsjcPq7jAqxcBaClZxw58iRI8cwaFwFFcPN7zAhX1mc/i5DEC88ZcjagFyPbSEOzXPPbCGQrB9jJ2H8JnNMmDi9/bE15qB6eLi+2xth9ARUjxrSWz22/cfLorkAKDj9sLGO96MwCkffkATLTexOsFyOAwmtNTqK0WGECqKeddVqEy2tdPeV8Z6OLf8UbhFKK2ajFRo6pOwWOmryVoO8dgpaa9oqWteK3eiraU73C/T2Pnw2Vk/w1+pezd31/uCwHVOb14BxCcg1XQixlijdrUU3dc/GJWBj4Vh2J227aHlJj2cPD4EnyrinHsGduLknddu1XVxsiISxqe1mC48UccsEh/hDzsw7nqlzal7d3XGBUdHHT2/O4uWWjB1fBmBtnlBqrWmEklo7YrERstCIaIUxCk3RsSn7Lq82Xf70Cnzp7AQvLX+j5/6jRZd7jo3yuuOj3HmkSsG18ZuzTJ9XtJREakEzUrSjGKl1N1W84lMtuowUHASC935hcEd041SBf/GE5ntOsnECef2yKVs483aTbgswegxmv7np9yZHjhw5bji0lyGowU1vXU22wSi7J99sFO8Lf2kmOXcy/GvlkiGj21G3U1i2qbVeesUo0+42VG4lzXnKqYd2pibcduDQnfD8H+/YhDlgziOaC3DTW2Di5rX3m7oN5l+A2oWdtdzn2DesSabDCNUKkI0Wqh1AFKNiCVGMVubMS6MRlo1WXRGl8eRXGHnHowh7DzIbyAn3tjFi+Yy6Ox8KESlJaxVpNiS5IbMW7dX1zmqbHty0xVRKjIsdu7a3LpHeTbW5H7KfOPesZ9TnBKLjFjCp2Y6wKNouBeFRsD1Klotvu12rdiZ528skcK+aQGktwYgPM69bW1UeOQqXvr47b0Q/4rYhqZv5TFamoXZ+98aUQkWra9w3Qpo2GreHVnAjqVhpG6v41XrAShARRMrY9X0bz/f5+qLLU0ngWS2ygO77dXqyxGuPj/Ha46OcnCj1OEu01qxoHze0qYdLKLdM0XM4NlZivOxSLbiU+lLFv3hJc6m59ng1cKkBT1yGB49s8OLCJszc0yXbYCZy1NeGem9y5MiR44ZF1IT6FUOoZ16z9n6WDcfvM6Tx5T83rqztkNkU22m3tRZGT5iJ7IWz26uXTu3XO6Fupxg7aRTm1gKUp3bmMWsXYOqMsdOvB8eDo6+Hb386Kfsr7czz59gVaKUyBNpc6ijuKNOy2Ua1A3QYo6WESGbIswbLRjg2wrURjoNd8BGOg7C75+ytb7/M4h9+sXP9wvv+V5zDh5n5Jz9D9Z3v3PXXmBPuXUSqNm8UBNZf+9yUIeE21WZHWKtU5dSGPSgIrJTUPhctb19U+Wx/537rdpwkpKdqYBoc5gi7oz7bWFSdYq/6bDk99c5OH4neicRw2ssmZXQ9C3dp0hxk9wJRGyqHNzebXBjdm/FpNp9Y6vjG9t5eWvthMyr2UiNivhkaFVuDb1v4rsNc6PLVeYenrjo8X7N7rN0lW/PG0Rp33HyaO246yWixt3YtloqVIGalFRMpRdl1OVoocrTsUh6foFpwcO213++51nAvdcP9tDZLf8/00gS4/vYVjhw5cuS4XqE1LF8wRO3YvRs7rSwLDr/WqKlzz8DEme2rtCuzRm3dCXU7hWUZe/riy2ZCwd0CsVQS2jUzybCTpUleGabvgFf/YmcId7tmcmCOvH64BPWxUzB9O1z+1mA3Q449QUqmjSod9ZBq2QxQrTaq2UbHEh1LiLPKNAjL6pJp18EqribTG6H17ZeZ/93PrtoeX77MhX/wv8Iv/9Kuk+6ccG8Rf3D2/+Uv6mdpqxhZf2mN+uaQwUbS4SBI1eaNbdn9idqetX9/2n77tkQRZfpw99u3SdpW2cLq1DC7wqZiFyhZRoFOa587BDqpfc7WQe/1RAFgAkFGj6+/T3HMzGbvVnhI/3g2e2DzKiYsRqvdSypXsTkx2EqLkNKEsVJnEMaGBNdaIVfrIfUgIog1toCC62DZPt9c8vjavMPXFmxWot7XdaoieeNkzL1TMa8p1yjEdWZP3o/0XLTWNEPJSjumEcY4lmCk4HLr4QpHRotMVTyqr5zCqs9CeeO/56Ehz1823C8ODLEujPVuL4yBVzU2yZxw58iRI8dqtBZN+dSR1w3f7sp24OQD0F404WTbsSZHLXOM3U67rbVQPQaTt8Dct40AsFmnYe2CKU2a2EKLso0webMJomvXtlcPrxXUZ+HYfaY2fBgIAUdeC4tnzfExbxO249BSosMYFUZdVTqtmW62DZluh0a9jqVRp5Wm0yXJTsi042yZTG84RqVY+qMvrXGjBiG4/AsfYuSRR3bVXp4T7i3i3z71SywGi0Pt6wp7XVU5S5jLtt8h2UZt3v+WBlkC3d+6KiXV0NtkzMnYt+0++3Y5k7ztZcLCPKtr53aEvWf29C1Dhqbeqzix/n6FMUM0wyYUd5lwozefrNpJKg93j7DFbVOLvRXCXRhFyoh6K2KlHbPYDFhqxp1abN+xsW2H2ZbL1xZcvjbv8HK990ez5GhePxHzhkmzTBW6E2FuOyCwfK4ENiv1BlJpip7NZNnntSdGmar4TJQ9Cm7mMcvTJqhmCNw/A0dKJiBt0PSbAA6XzX7rIqybUoH+FmC2k9dx58iRI8daUMpYpk9912qH0EbwR+DEm+G5PzRq92bvD4YsLp0zZHsn1e0UlmVCwmoXTfDZZvJighVDOhQCJjwAAG6PSURBVI7ftzu269KEsbpffnp7hLtxBUpTG1vJ+1GeMu/51edywr0JaK0NQQ4zinQUGXIdhKhGC9kK0GFo9osSdZoMF7BTi7eN8D2scrK+U/X8641fKVSzjay3aL90AbnSWO/FEs/O0nzyK5QfuH/XxpQT7i2gGTU7ZPu+0gkmi+M9lu2ilRDphGS7+6g2D4LSOmPbHlwDnUVa/+wk6rOT6fuc9q72VpFmp2PfTuuhrzuEiX1ro4OIWzCkfGV2Z8NX+qFio1APG5iWIk0qTwPXdgNx0LWHDwGtNbVWzEIzZGUuQlxYZs5bIErSvwuuTYMC31j0+PqCw9OLNqHqTtAINLdUFa+fjLl3Mua2qiQ7YaqVph1LWqHEay7RLB3HchzunCoyUy0wWfYYLbprT/r4IzBkMr9tCT74gEkjT0siuuM0+OD9YuPAtLBhbHGDav8qM6C+OtR4cuTIkeOGQn3W5F7M3Lm1+4+dMIT07J8lGSmbPE6uzEJlyjzGbpGN8hQcf5NJ5varw1nDlYLaJTOu3ZgISHHoTph/0WTebOUcSEbQXoFb3rE10j55Bq582zzOdtqdXSfQUqGjXhLdqZduB8hmG90KzLY4htTqLSA9axGuY8izbWMVClBJyPQuCmVaa1QrMGS/3jSXjRay3uqsq3oL2WiiGu1NP3585coujLqLg8UErxHITL3rXcUZ3jh51/7YmROoAbXPWUI9MEDMsnDoKtAV26dgm77PRctfVf/sZtRnz3J2PVX8mkDcMiFgwxzYqkeNrWlXx5MEi21W4c4mlW821GwzY6scXtdK1wxj5ush8/WAi0ttFpoBzVAyEkpuUwKpbZ5tVPj6vM3XFxwWw97P4ISveP1EzOsnY143IRn1evXkMFK0oph2LNFA0bEZr3gcLnh4N93KyJljeM6Qn2uvZJhzYkfaCO86LfjY2+GDX9ZczgSoHS4bsj1USzAZQnmNnqKlCXMSmNdx58iRI0cXMjST46ce3prDKsXM3aad2OWnjWI7bHlY1DS/y6ffsrsT7mDqlVdm4fI3jcV8o/O0lQvm3OTo6zdvQ98MRg6boLhXv2wI82bPH2sXYfwkTN66tecfPW6Onc353sDR6ww9qnQ2gCyKjCrdClCNNioIO/XSxuKt6CQkWZaxdDuGQNt+EeHYRq3ehc+I1trUcveQ5iaynqx3CHUT2WgldvQhIQRWqYBwHWSmHdhacKYHtJjbQeSEe5N4/JXH+dATH+pc/+T8k/ze8jO859ADvH5kZ2YI1yLQvQnc5suhAQuRtK2yOkr0iF3oqNAFy8O3+hXnrp3b26/652sdYQumh5wxL4xuiqBtCVHbKNVbOako73JSedReVVvejiSLzZCFRsiFpRYL9ZCVIEZrTcl1sC2LpWabJy5KPnbuTl5t+T339yzN3eOS103EvG4y5lRZ9by1UirTsis0+QGeZVHyHY6NF5OWXS5F14b5eZiYgmHJNphJDdc37cqG7Cv+rtOC7zlp0sjnWqZm+/6ZIVqBgTkgCmvtE7a0jjtcyQl3jhw5cqSoXTK115PbrE+2HdMyS4Vw9QVDujdyL2oFy+dN+NrkHoR2penqjStJXfaJtfcN6yAlHH/j9iYihsXM3SZJvX4ZRjZqx5FBa6lrmd9quzLbhUN3wEt/YtxgB71ccQB0LE2ddBR3yXR62Qo6Kd5EsqtKSyMuCA0IYYhzWi+9yxZvFcVdJTohz10FOiXQbVS92bGiDwur6GOVi9iVorksJ5eVklmvFLHLJaySj7AstFLMfvQ/r20rFwJnZobSfW/cgVe+NnLCvQk8/srjPPb5x1YFoS3FTX794p/wo0ffPpB0b4dApwncI07RBIhZLiXbH6g6Zy+vawJ9UGxBWg4/Y50q4XFraymiwyBuwejJrQWyFHc5qVwrQrfCYq3NQiNkdrnN3EpAPYiQUuO7Nr5j0Qxinrtc59lLNV6eb2QmM30EmjNVxesmYl47EXPnqMSzs09hws5akSRSClsIip7D0fEC4yWPSsGh4jlYWYK7ZRt+2aSlppMcQ8K2xMatvwYhahhVvT8wrfPAmTru8u7O0ubIkSPHNYGwCWgTlLYT5wxeySjVMoKFl00f6PXIysolQ/COvXH3rOT9KFThxP3r15wHdUPIj90L49toJbYZ+BVDml943OTFDEOe48BMHpx8yLQY2w7GTphSsKC2OgdlH6GlTILG+uzdUWwU6ZZJ8dZhZPaNTeK3ubNGC9FN8d5lVVpL2SHJvepzau3u2rx1EG3qsYXnZshysUOo7XKpu61SxC4lr20zj21ZjL3zzQNTytPJl5l/8jO73o87J9xDQirJh5/48Lqp4//l8peYcMrJPr0E2rYsXOyBCnSXQHcV6BuKQG8GYd2Ej/iV9WdvdxtKGmI7bAhHYdSoomFjFwn3FhLKU3SSyndOgY+kohHE1NshwdUGz6omc+IisdR4jkXBtWgFkheu1Pn27AovzNWJ++xCMyM+dxyp8oD3MvcVL+GNdi3VWmvakaIVSYJYYiEouDYTFY+JskfVd6ls0LJr6zb8xEkQ1jd3v60ibJjPmj+y9j6VQ2YCIUeOHDlyGCvyoTu3T9ay8EfgpreC/KwpE5u4abVFWsWmBZllmbrq7YSFbQXjpw3Jn/0mXH3eTMIWRo29vnbRTNAeu9fss5dq7+QtsPCSaWG2Uc9wrWDpVZi6HY6+bvvPXRw3kwtzz+wJ4V5FpCPZVaWD0AR6dULH1AB7Nx1VOl2sQgHSVO8dmsAx4WKBqXvusXGvJtWqFWzuwR0bu0eJ7pLnfnJtebsrohXvOM3kex5h8Q+/iKp36/qcmZm8D/dBw1NzT3G5eXndfWrSNNJ9w8hNqyzcOYHeITSuwtStZuZ28RVzIN0Pe1DUMkRtPQKUhWUbQnT1Odgt95ZWw4+nH14lSSoPtmxJjqSiHsQ0gpilZshiKyYIJcQNSrFFMFmkFSlenKvzndkVnr9SJ4x78wXGii53HBnhjsNV7jw8wmTF2MirV+cZvfoiyx2CHZu23o5FxXc5NVFipOAyUnB608Q3HHQbnNLmLXVCmCC8xtXN3W+rCJvmxGO9z3ppMq/jzpEjRw4wVmSvbNpC7fQ5QnEMbn4rvPA5EwbmFAyh88qmTri1YASBo28w5HevIQSceJMhtVeeg6vfhquzYLlGlT/yOlO7vdfnTrZj6sVrFzZuE1a7YM6ZTj6wc47GyTOGcG+jRWvH2h3HHTW6o0i3g44qvZpIm1ZYRoXLKNL2zid4a63R7bBXde5XolNy3WwboWVYWCIhySXscgGrx8adkmuzTfjrBM/uA4p3nMY7fYRL//Y/AXDsV36JkXc8uuvKdoqccA+JK83h0utGxQi3ewNmU1NeIWFzRoscHSgJLQXHb4dxH17+c7h8zliF9vpL3WiBPQKyAK0hVUVnClrPwG4I3CqG2AVV6hmPVJonX13kykrA9IjPfSfHB9cMq6JZGm0oDkfWwljRCBOC3YpYacW0oxiptQnjs20uBUWeW3R5unaYZ54+TyB7CXbFd7htusLthyrcMTPCzIjf8wPdqofUw5jFZYfDyxGBiil6DlOjRaoFh4rvUHQztikFwWYmYZsBVKch0MAm1WFrDNoSNjnpuyUE2jzfep81XQE9CvU6lHLCvZewIsEBKHLJkSMHmMnnxhwcv9+Qtt1AeQpuf5chhgsvmbCy2gVDxm/6bpPvst8Tn+Upsxy6w1jgCyNG5R3U6WKvUD0Kh14DF76SBIEOcOW1kpa7J9+8s0FzI0dN/Xjjak8vb611tzY6JdCZemnVCowa3TbJ3R1rdxwnZFWYy10k0p1wsazqnCRyr07pbiVK+fCwyoWeWui0NrpDoBOV2ir6B4pErwWtNShtJjukQiuFlsrUuSco3fuGPSPbkBPuoTFdGq4usn1plOfmcvV6EOIY/uJPzWnp3a+LGZ/Qm+PJYRM4DNoF24b264xd6qUlo+7t5W9A04GRSWjNDX+ftgUXx2GOzad0boRYQzwJUQDuLAB/MbvEx5+5wHzQJWmTBZcfu/MoDx0eW/0Ys5Nm1rk4YGzaKNhBrAilpBlK2pEikgqNxsZG2y4XIosXA5vn24KXAkGos38URcm2uLlS4EylyC2VIjMF1/SaV8ClgMULLYJIEsQKpcGxBb5rU7WqOMEpit4UnnRQbVjCLNtCowATVVic3fx968DlUdjt77uKoT0BIXB2g3FenTGWwXL+G7SX8MMqN92kc9KdI0c/mvPmuAKGCINxYpWnd2+ivHHVOJBmXrM7j5+iUDXL9B2GJDaumNe1lV7du4nSxMEa04k3gV+GC0/B/Eswdtyo7+1l87dzPDh237bdAaYmOkSFoVGcwxDdKKFf/Cqq2O4md7dDkBIVJ+QsE+KlobdG2rZ21Nqto3hAoFjG0p3Z1qndHhKi4HWDxPps3IZUF4zNu1zYk97YW4XWGqQ07cykSgi07K5LlZlg6Kr1wrJMHbttmckQ28IqdsN3xR5PPOWEe0jce+heZkozzDXn1qzjnhRjvLZ4M/bBn/zZc1yeFXznme5M0tNfd/ALmtvvlMwcHtLOEq7A1BkYSSTi0hQUbbj4VXBa4AzRnmunEIYwUoHSJk6xvQosOuAEuzDWADwHRspgWfy3C4t86KuvrNprvh3xoa++ws++2eG7jvW1ABsdgXgOfNOrPYoVrVgSRpKVQBLGkkhqNBrHspC2xTnp8EJg8XzL4uW2INa9H/6Kpbndb3PzaJmTU8c5UvIMwU4QKWmSxGNFrBSubVEs2EyWiowWXcq+Q8mzseMSnHsJPLmzs/NRDJXi5v6OKUQRlpUZk9jFWdKwDSXP/H02staNjkA7BH/93XLsHGQMQWShNtOuJEeO6x1aG8VXWHD4HpPonU40X/m2UYXHTu58AKqS0F6Cm9+2d7XTQhw8UnuQYbvG1j5yBM49YWz5YGqrj77eWL8rg9t3GSt3mCHSUXI9QIUhqtFENRvoZgsdhYZ0x0apRkmT2zI7D/YyolAxqd22jbAdbN9HONa2w8a0VF37drY39Kq07ubWw8X666A7tdHdOunNhovtBbTqkuRe9Vl2t2tjv+/+BZKEddsykx+WhXAd7LKL8Fws3zOXrtNT847jIJxMm7OEfI8/dBuoCCp7kM6fQU64h4Rt2fz0/T/NY59/bM19/peRH6TgHdxZov3C7EXBN766+osftOEbX7W59z7J4aMbnKyqEHwLxg6Bn3ksbxJqFQhWhuuHvSNQ4GjzZfU38YPmlY3VNw3q2kmEgTlAFV2k0nzsG+fW3f1j3zjHd5+e7NjLo1jSsn10FFCrN2kEMVGsiJRCAK5t0RQ2ryib51sWzzctzrVFz08iwKijub2kuLWkuL2kOOpriq05apN3ExSLRErSiIw6HiuFY1kUXYtjYwXGSh5l36bim5ZgPVACfBcITTuunYBW4AoolTb3d0whSmZMVgS7eWCLAiiNQ2mIz0ypZH7VXQXkv0V7hTyq7tpAFAnUXpSA3OhQCpZfBX8UTr15dWhZ6TSc/0u4fBZK06ZLxk5h5TJ4x6B8Zvhyrxz7A3sCjr8D7R41pLg4jRYF9FyEvnDWEOYwRDWbqGYL1W6hgxAtY2Pnjs2lOXsUxjBhOwnBcgzBcstQTK6n5xUlAYsvoyvGzr7q7HNAwxatFLoVdPpBq6S1lVq13kRvNlzMto1du1xKLrNLqfdyiHAxlSy7fWDSSq8mzD3rGrTqvL8CTBCcZRnynC6Ohyh5WJ6N5XlYnodwEweB7RiF2k3Is23ammFba06KJNXyqzfGyRIILPa+DCwn3JvAo6ce5SNv+wgf+vKHmMtYiSfFGD9a+kHut+8hzn/fe6A1fOvplIz0fzlMkvu3nraZnI7Xd5e16+CNg12FqK82xZ+G5Xn27NsjIxAFoLB6LBvBHYVGbee/eVEMdgUixdfnalxphuvufqUZ8oUXr3J6xGexGdEIY2i0mVqKCLw2lm1zNXZ4JbR5sWXxUkswH/USOAeYchW3FDVnSorbioppr7dMIA4lzUhweUXQbDeNgu0IDlc8RkseZc+m3EewtYRY9r+vFlhlCJZgp7htHACeWTb7dwTQHigXghDYxVq9MITR8SHH6AE+BJFpW5Zj1yFjkFIks/I5DiqiUHH2XJXgcj4RNQykhD//gjmoPvzWiKFLHZU0oaaF4zB1CzznAQNKYdTdsDwOr74KrOwM6VYxtHyYvhmaS9t/vBxbgwYt40SxjI0dOE5rnyXEsVGnoxAdhOYzIxVaXYCUsCES0qQRlrFuC9s26riVWLqtPkt3llSth+g4LMVQ9yGWiFajd2k2EO3kMt3WbiI28RuvhUAXy+hiCV2sJOvp9WS9VEYXyuD5G5dXxMDy0E+/aWgwNc9KmYA3pUzbseS6VrpzjOuMVCS2bUsgLGFeg50qzA6Wb/p+p3ZuYQuElVy3LLAT8t0vsETsbthVVMB3bG66W+LuIQvOCfcm8eipR7l34j7+t3/52zTdGqWoypHaGWpY/NF+D+6ahCBowx9/eiO2PJNcPrvG7TvY9mNDuEAFWG3ZHg7HdnAsKU4CTeBpnnXjoZLQv/r5c7Sj3p+AOnf2XD+cLA8PMYLFZFmNKcyv51VCTCny1o4bPt3PwU7ABarA2W08xl5YCLt/2+Gwk+9RjuFwhFu+e7/HkGM9KGWs/05xfzOjrhXIDGnxvWHfMw0rczAxA4duB3e9A5ELlVugWoG5Z0EtmLrrLUPByhWYOALTh01nkBw7Byk7ynJKmrU0JJpYdm3dQYSOgmR/2Qmu0kohEpEFIbAsG2F3CRq+g7D8bs3tdhC2oVFD1GvQWEE0auZ6Y8UIHo0aYmUBmg3EJsLFNEChCCVDmCmW0aXS6uvFstmvj0QL1ooaGqjJbgtZ4qyVQuvMdakyyeRpG2MMabbSemeRqNAOlmsjXKejLKd/I2EJY8lPCXVCpg86pFL7UgaWH3a2gBFvhGO1W/d7GDlyDERZbzBTusn9cuTIkeN6ge2Am6fbbYgsV3BccIY5W2wtQKUCx+4EvzLcE/nHwLPg8tMQz0NxckvjpbkAlRE4eruZIcixPpTMJG4n9mwp0XEEsURFETowddEEoSHaShrrQxJa1YEmUTltLNs2hMy1EUUvIXA7QKLjCBICTaPWXa/XuteTdRGt7/Drh/Z8U45VKkMxuSyVzbZiCUqV7npCKNOvx9pnUWkbsKSv9jYDAg2BViCN6ty5rrSpeyatezaTGkJYGfU5sXD7NsItYLkOuA5Wqj4nYXAdIm0nboJrgDxvCaHeFzdyTri3AMezeO+/eoAX/p/P4HvglIc8sNyAWJgXPPnljT9m9z0QMzG5xmxTYw6qx+Dw3Ws/wKWvQ/2yqQfbbaxcMm02Jm7e/H3DJpz7oglN22ZwmtKKKNaE7RWiMOTS6BuoxYIzkWLk2QusxAMKkVJo+N1y2HOwmPBdzvght7o1To8UOOZrsh3ElNJEUhNIhUxmq90kRbziO/ieTdGx8bK1Nc2rUD4ER1+3rdcKQP0KXPhLKM/sTMp7fdb0dJ+8ZeuPsXwOLn3ThL/sBoKaCWQ79eDwis3V50wIzRqhMzl2FnEEweJVHHeLRCFHjgOIrHt2YV4wfWiDriJx25RbHXrN8GQ7RTX5/bz8tCHtm1W6w7oZ8PTtm3/u6wWpbTtOVed0Pe4S6DBEBQGEoSHbiZWbNPE57ROdCNEdtdm2jX3b9RC+uW6CxbY5ZiX7SPMaZLpRQ7Rbm3po7XpQrkKlCuURqIxm1quGRLfnwHOhPLbNF7IGwibEybiFbdLXbR8se20CndQ+62xCjtZd67UtDJm2LUTBM0Fh6dJHmo36nLm+091xcmwKOeHeAoQQuL6d/uYMN/N7g2L6kKZQ0LTbMHguUFMosPbBXEuwFIzNgLvOj0V1Eurn9uYTbWsz07neeNa8bwn8IsjNJZUrrQilJowUQSxphjGt0LTlEsEy0vaZLwosG5a15M6JMk/M1dYehgUnR4qcHilyulrg9EiRqudQqL9KZfkcQcFHKkOuw1ijUQgh8Byb0YLDiO/gOza+a+E7FmvP84bm4LaV96ofpTJ4ngkp24n6ZEtt/e+YolAwnwena8vaUQRtQ+b9TUhyxQrYan9+3VVs0ohvIGgNtq2vid6kOXIMg9mLIpO9Ak9+2aFQ0Nx19xoBp1qZydXJM1uffKweAbQh3c2rptXnML+pKjLtpKbvhJHrZJJRa1PnHMuEMMerCLXOKtBh1KtAd+qgSZzKyfEpQ6CNsukifLt73dqB3zCtoNXsUZx7FegMqW42OpXaQz207RjC3E+gV12vgj9ErspKCZZeNe/3dhVorbuEWUp0e8W87cUJtLbR7bqZGJJXEU4B3EKPAr0mgU5Jcyal20rW97YXbo7t4sY6M8qx5xAC7rpb8tSTNtlaEQPzQ3vX3XLt37o4AKewcXsPvwq2Z9LMrV20k6ko8SSWtnZ/y4LimElwXQNSG5IbxpIwVj3kOkqUZcsSWJbFnHS42C7yghrnxflLXGoErFeRVLQtvufEJG89Ot5JKE+fsxXFtGIH2hENHeBYNp5jMVlxKPkOvmNRcG2czdiMBDuXyO4WzN84DrdPuLUyf4vttmdziibERcWmj+hOQ8Um6XczcAuAMK9xL2e0g5pZnIJRqPLZ9Bw5rjnMXhTJ8boX7TY89eQaXUWa84YgT5zZng21etQogVeehZVZ445az9mjlXE+VY/BxOmtP+9uI+5atzvqc2rlTrenra6CAB1FZntC4IwCLftIoUhqbVMiZicEurCzBBoMIQ3aGfW51keoe1Vqodc7C+l7aCG6JLlSTS77ryeXA+qit4XCGNiXQbYHngsMVKHTunSVOAKAbg20BUJD1EAUyoiJk4iRKayCj/A8c0isX0Ysn0WMzoDrdsi0yAn0dY+ccG8TUrK7aXrXASanNa99g+Q7z9gEmW4JfgFuv1MyOa2J1noPW21jEZOusR+tiZJp09RoQWEXCXcYgPJNQnWw3njWgahAqMCDWClDrKUijBWtUNKONJFSSGVqcmzLwhIWV2KX86HFK4HglcDifCCItKCbkG3e3BHX5mS5wMlKgeNlD6UhkJqqZ3PzSBEhIApj6rEiiM3zWAJ8x2bEKTNaGmGy7ON7RTxHYGWIk5YQDfuyVQzSAe1v/b3qfeNAlE2P1e1yuTj9O7rbG5tyQHmm9/WOF4ZqiATowubGqDzznrdDQ373Cs0GjN5k1KbFS4Z073i/+YMHuQ+1YDk2B601UaiRUiDjnT1nv56wpa4iUQOkgNFbAH9rHR+yKEzDtA9XvgPLlw2RHzTBGqxAWDM132O3gLINOdptZBO3MwncSJXYuCU6TvtEGxs3UprQqo76nA2twtiH08Rt2zY1z5aNcDzTDjVNdl7nc6v7LtEMbG/VgzCA5oqxcjdXehXoZj2jRq8ghv2hE46Z7y2WDEkuj0BpBEYSG3e5mrk+YgLGhp2k2YE/r5aqG+gmJTouwOJVtCf7gsQA0jRtECJRm31TA225Lpab1DmnhFloRHseMXY7YuZOKIysHoA8ArM2un4Z3MNdA0J+HNkzJH/6Pe8skhPuLcKyBL6rCSLLdBfKsS7GxjX3PxSzvCQIA9MFYXTM2MiD9d6/lgJ/fLh+mtYUrJzb3UnClgS/BIHFZmZatIYglgSxIqqDtaioL9cJFUipkImlyQawLeZil4uRxauh4NVQcCFMyXUvikJz2g05OlLl2MgoJ0sFRl27x94aq8SOHkuuLpp6IscSeK7NtO9S8R2Knk3RtfGsMsRV0/da2Wwye6QXcQxxAULHOAN2AnoEWvPbJ9yhBOFD6LL2bM8w47FAFpKJmG2OqR8yBlmE2IPmJsaoXTOmODZdwvYCKjbvpXsIiqdg6RysXAQR7myP3QMK31VYO6Um5dhxxKHiN/63OWCXshZuGAzqKjKWLHPJslMoAqfWuX2CbpeIrXYM2W3YmNdxUOEny1R3kwOMJstOQwEryXJ5Fx5/KFjJkn6Gb0+WncIwn0kPOLGDz5ljcxgH4JYf2IMJugxywr1FuL7NTacDlBZQOsg/qNc4FpbglvtgcojarIUWPPdNmBjbPTvrwjwcOQ4nB49Ha00QKepBRCOUNNqShUbAQiukHUraQuFWLG4aXaDiRQR2mUuByysth7N1m7N1i/MNi3gQubY1N1ckN48ozoxIzlQkR7w2hWCeuePfS+SPI5U21vBQ0o4UsdJ4tkXBt5gqehyq+IyWXKoFl0rBwRmUHPqdp6FxGUa2+bluLINTgtec3DlJ6coyvPg1mNxmQFVtydgXb92BE/CzI3B1FsZ2OKynuQwIuPuksa1vBs8XoHYRqlssfdgsGvNGhbrrjBmrPmnC2176AoyVrvsWPdZiDdfLCXeOHDly5MiRYzVywr0NuK42auoO5DflGIC4DUUHxibM5UaYmDYkUTR3L6nUi2F8HIoO7UjSCGIagaQexCw2Q+brAc1Q0ookkTSzZ75t4zuC2BIsRjEXFuGPLp/m5brDxfZgIlVxNDeNSM5UpSHXVcXhoupJDddKo1p16lica9sEYQtbCIqezehogdtGfMbLHqNFl2rRpeAOSXomDkHz5e1/rptNGD8OpR20Wler4Gtw1fZqBa2W+bwM87naCBNTsPjNnf8daDdg7BRUtjDxMXEI6i/s3W9TfRkOP9A71sOn4cpfgqhvvg79WoO7t9a0HJuD41m896cO8cLnv44/PoWTtwUbiE11FRltmBTmI6+Hyg51B9G6Y/fNhoB1LNthCx220HjoOEKFkUncjuOk37BMeg0nqdtp2jYkTZCtjG272ze4d9seTZyl4WKplbtZTy5XumndjTo0a9DYZLiYZUO50q2HLiU10eVKktA9kmyvGrvhHtZYrLJ066SPt5RoJXvceSK116ep6L6P5XsIz8fyPJNY7NgI1wXbwXKSXtGbTTKOWnDhKybMtrCFXvDtJUDB4ddDeUgxQEkTELh8AUZm2L5tL8ewiJt1ggCcnQjz3QRywp3j4CJsgluGwpAn64VRKI6bfpw7RLi1Nq2w2rEkCELkSsSFy5LZ2YusBDFBZOqgQeNYFgXXQgCtUDJba3N+scX5xSbnF1s0w2xBVZeYTPqKm0YkNyXK9c0jkulCb2q71powqbkOY0WsFRaCatxAlKa45fgUkxWPasGQ67Jnbz01uTgGmzi4rwkZDX/wGRZ+xdQFx23wtqHeag3+gPqqLY1pBFO0tv2k0x7EAVQObWNMewQZGkfJ6NHe7V4ZSlOmjd6w3+EcOXYBQghcT2DbGnsL5+M3CobuKjItEfVF01Zx7NDg371OnXO2XrZb92xSuGOIQlQQoaPQhIX1hFN12yV1eXPS0zhJdjbtqSyEZyPstO9z0vt5r00nWkPYHhwotqqHdA2xiZpzLYSpgU4DxNIwsUFJ3YXSngcVmDC43r93h1in7cbQyd/NSYLCbITrm7rogrkUjo1wHEOik0uREundek1uGQ7dDBe/ZrqgbCYANW4CARx+LYxtZuLJgplbIVoEWTfBvzn2BDoJ5t/rziL5YSfHwUXYgPFTpnfhMBACxk7D0vlNP5VUulNjHUTmsh7E1NuxIblSIcIVHCl52Rc4hQjXtkxd9ErAxaU2F5ZanF9qcWVlcFG6LQSHRwucmChyS2GFu+W3OTJziFGvl9xqpZNxmOeV2iSTe47Ad2ymKgUqBZeSZ1NurOCfuB3rpqmBz7kl+CMmKVbGJpF9O/B22GngjZjU87i1dcKtpDkh26mx+dVkTO2dS2TXyQnKVg/CfsWQ4L1o09VaMsFGlZnVt40eh8WXdvf5c+TIsSMYpqvIHbc0kJdnwSmh2wU4dw4lJYQBOopRYTg4ZTtNfO6ZSaabtG2l/Z4t0xLJ3wfVeS1E4dqp3D2EuoaIN5cJoovl3pTuDqEe6b1eqmzP1bUFaI05Xq4i0iYcLrNnR4U2rcdsRKGEVSggCgUs1zWJ3BkibSXXsQ9IudHIERi5bNLxh20vF7eguQTTt8Losc0/p1+B6gmTyp9O3Oe4bpET7hwHF7K9+b6a5ak1iYbWmlAmxDpRpttRzEogaQWxSQqXCqVBoLGFhWtbCCGoK58rjYizwSGeW1rm4vIsl2tBkiS+GqNFl2NjRY6NFzkxXuTEeInDowXcpGa6UD/H9IUGdSuiFdJRrxUaC4GXtOCaHvE65Lro2RQduzecKQBK45t7jzaCP2LansVNsLdI+OLQTJTstNJqO0aBr13a+mPESQsQr7wzY/KTSYCotXOEWwbm/duqMuxVkjG1d6+8IkVQg+kHBteZlyYBK5nkOCAnVjly3HDQppWRNFZr3Wk1pTKkWKFiyXgkufu4z3OXJgll9zvt2xFnRi4wMjtHK25D9TjMv9h5+NXW7Eyf50R1FoMyQ/YLMs4Q55Xedld9ba9EuLlkXO0VuspzT2urkf9/e/ce3Vh53o/+u/eWtHWX5bs9HttzzzDDZJgh4ZZArgSaFFKSlpPwo80vQENpUgJtcyDtKZeuhGRlldAmi4T+SDjJak8zzW0tmuYXfpOGQFKYQIYhISEDDAwwF8/FM7YlW5ctab/nj0eS77Yue0v2+PtZy8u2LEuvtmW9evb7vM8zY4U6Uv9J7RqVU7tLrcpKgfS0CupTA+niqnTAL4G0WUzr9nrl71xM7S6tSDf65EDddANoWyst7qzxxU/I59NAakR6z7dtqH31PdojvcCtCecXKGhJYcBNS5OyAehVBxy2P46cJwArOYqMHoFVsJHJyR7rtCV9raf2s9YgFbu9HgO6biCZ8+Fo2oPDEwYOTUgBs6OpUhGzUvA5Ur4/06NLYF0Mrle1BNAXDyDinx58lFLCR7MW0rkCkNah0kCukIThC8PvNdAVCyBsGgj4PAh4dfhnBtfzHSOnAypfCDBDMgHUusKaT0tLKjdSm4PtwOmDtf9+Li29qp0am+GVrQyJI5isUFonKyUnPWodoy8sBevyaXcD7vnSyUuCrXL/1jjTyonqpWwoW8nqoi1fl1aSywGUlYZKJYvBtA6lPBI/FWxpg2PbM/oIz9jorGlo1XWc2zqEJ06eAwDY2vYK2mIWNM0GLAWtZZ1kryw1ti17oBcLpCeS0NITVd208njnSOOeI5AORwFvo9pDzDFOW02uQJdWpUv74dVkarem67K3YuqKdCAwO5D2esor08sykK5GIA7E+4GTL8r38wXA5WB7PdCxsb6TyWZYCrieeokB9xmOATfNzUrJm2k7Lx+aXvt+0qJUTuGsf5GJ/fn/oSHoXSCYzBUDDn/LrB9l8wVkLBvpnBQnS1sFTFh5jExYSGbz6BwCjPRRJHwd5QQdjy6r1R5dQ0b5cNIycDRl4EhKguojKQMn0hrUPCk9fkNhwJ9GV2sMnR1d6G3xY1VLAK0h36x9IHnbxngmj0x+avE0DaZHR8BroDPqR0d3P3o9XfAbCoGWVviKK+lVyWckqHX6RVrTgFAnMPF87beRS0uA5dSK71T+KOraY55LAfG1zq64hruA0y87d3u5tGR3eGqseqbrsro8UseJiUoslE4OTNnHfYwBNy0JS6JverHA1/QVZgmCVb6Yem3bsvqYL8DOFdN6S5crGyiocgAOWwEFC6qQhWZ45f9O80CzswDSgLJlf7M/BM2jy3yuaxJ0zUEBQDqLlpEXYVoJtJgJ2LE+IDsBhLqBQE/j+gYrBWRSstJcLCqmlVaeJ6Z/RmocWhW9dZWul/tCq2LArIqrzyo8/XL4/JWvYrpwbOSkSWkVupTenYfKy3NJA2R8mjZZZMwwoHn90CMmdNMPzecDvJ7iinQpkJbv5wqkFWb09c5V0tx7mQsNAjkdGH0VSKelz3up642y5f1DNikr29F1xe6wdR6TQA+Aw1Jo1tugziIrWKEw9SRj4zDgptnSI/JhRqR4hC8EjJ+QILyeQlUVKBUpy40nYGl+jI0bSI8mkLYKGEtbSGTyyORsWPmC7G8upnTrmgafocP06MiHexBIH0dShTCUlhXqoylDPk/oSBXmnzTDHoW+UAF9Ibv80R8qoMNnIZAewonVl8MKSHBhK4VMTgL/TK6AbKEAKA26DgS8BoI+D3qLQXnE70HY9CDs98D0FAO93GrZ3+qpMfDLFfcMu7KK3ConWmplpYD2jc6NZypfGIAmb0prOduezwLRKrcqLMYfdfb1O5+ufjvFTKE24OR+Z8Yzn4XSyUu4j5uWAF2XfulZiV3rp1QxNduestoswbAqrSAXV6DtfAHISRVmCahltbEcLJe+nnrzmhQI03RNguNioTBoXilobJQCZqkvAk8cCMShzIiciAUkQChkZa5InZKsJW8A8HilJ/I8NbuMV1+Eb8+PsSM1Lhf8DrCDIVjnvROFN24D8nWerFQKyGWhFYNlLVX6nJz7MrvyP5iCFBezg7LybAcliFbBiHwORaGKl0lxsQrnkOq2ZldFlSqsF7MUMLXYXImGcsq+rE77oAXD0E0TmlcC6alVusuFxopz5LTgeao8iv8QZ3ggXY1AP4CIZNKdOiknvu3iE8Awgcg6IDAIZBb4J6qKH/B2S8XyMANu1xV0mN7cwhmkLmDATbOlRoCes4G+NwOGT86avvC/ZZ+Jb6Dmm83lJ1/uH309j50dNmxbUrzTORtpK490roB8QSEwfhQnQhtx1Doh28M0DV5Dh8/Q4fPoCPi9yNkKpyayOJnM4kQyixOJLE4kMziZUEhkt807Dh0KnQGFVcECVoVsrApKYL0qZCPmVbNOYiuloDIpjNs+HMn4MDExARsKmqbBX9xr3dMSQFvIh2jAg7ApPa6D3kVSwsMd9QVEubTs/6m2R3MlypW37ep7misFqELdGRHzMsOTRcqqPQFk52VlO+DCvnfDI5XZnfp71LsibEbcrcGyWDp5Cfdx0xLg9elYszoBOz5ZSVgpNa0glMqX9rVOti6Syto27KwUA7OtAlQuN5mya9tQhWKwXaw6raCKG5aKSoW/fDq0QHGv85RiYfJ9DVVz7QIwfhzo6gU6B2W+nkaHdMQIAIWgvKEfe01qbATic1wfyLxwEImf/HjW5XpqAv5HH0Z0sAv+N26fczjKsmAnk7CTCdiJhHxOJsqXFRKT38OyqnqoWjAIPRKFHolAj8bk88zvo1HoobAc1yVCFYrPl1xOMhZKXxfyk8+Q8v5nDzTDAz3ghx4OQw+GoAf8xTZYXsA0ofl80ExTrt/wMuwrSTdg9QNDv5KTVdF1QKhV/m/cWORIasCLLwP+pHP1ZWhu6Qx05OA1G/s6wYCbpisUz+K1DMg+15L2DVIgZY43zbatkLcVcsXgOV9Q5c+lPdQ/PaLjwRf9AOR3//xxAy0+4Or+CZzTmoUBHR5DUr89uoagV0co3oOg14Ph8SyGxy2cTGZxclwC7JPJrOyFXkDcV0BPUKE3aE/76AnamKv9Xnl1vVg8LZe3IcngClErATvYilg0hvURE1G/FyHTQNj0IGR6ysXQquKPycmMWttJ5dOS+u0GMyqrJPlM9SlO+bT8TtDhlmAlvoi08chNVB9wZ4vFUAIO7bUumVo4rd6Au2BJZkm9bULMCKA5fBJgqkxCtnzMl05ewn3ctATkRxPIvXoE9rG8tKGyclC5fDlQLqV2l1O8JUcXQDGA1qTol25MFgfTfLqkcJcvq2FrUPEepn+u5FcKQOoYEO8FujdXsP3EDwTWAS3FrSaJISCnFQNveX1Qto1T//XkgreS3PWvUMPHoJJJFBLFILr4WUk/sYpppgk9GoVR/NCjURiRCIyYBNBTL9O8S6t5ulIKmBlEFz+g7PJead0jFbp1jwcIeqGHWmCEQ3JiwPTJCrVf0r1105RgegmdMFjRAjEgdnFj7svfC4wNAsMvAJG1jbnPlaqUWdRgDLhpuvQI7GAbrEAncplcOQDN2a3wFkKwjx1FxtcKK28jky8WIcvbyNsKBduWjCg1PXnp2VE/vvLi7H3Go5aOBw7E8H+tyaIjoHAireNERsOJtIYTqbMwbCWh8JsFh9sS8KIjYqIr6kdnxJSvIya2jD2GiBorp39PVbBtZHNSsTyXLyBvq/KKhNfQ4DEMREwPojEvgqYB02MgNJ6Ed3ALvIM9dR/iskBLMUiroTqlKqYxOd3nusTfIpNNJlF9wJ1NSmA1x/57RxgeacFx7DkgVE3fS0hKZaTb+a0R3qAEyJmx4h7zOpS2btR7O76wnDTLO3ASYC7WBNC+fvHb5j5uWgIKI6NIvTgELa5BM4oVs4uVszWvZ0ogrc+7t3nJUDaQPC4nu7q2TKaQV8LfAtV5NmwthsLRF2G/9jsU0nnYGRvZY6dRSC5cTEylUkj+x3/MfwWPZ3oAPeWzEZUV6VJArZs11qhwmSrtn7csKThmWeXAutzaTMNkUTGvF3ooKCvSkTCMYFACZ9OcDKJLq9Nclaa5aBrQ+QYpnuZkxxNaMhhwn6EKtkLBVrCVfC6UPttTvi/I13lbWlJZeRu+sUM43nIOTjx3Un5WkJ8XbIXOsTi6Rp9FIuSBBg2GXvqQVWm/xwt5D6MB0DCWk+D5Xw6WgpuZE418/62D879Z8Bk62sI+dERMtIdNdIQlqJbvfZP7oWfest0FnDyKlJ6Xkwa2jXwx3U/S0zX4DAPx4v7qgM8D0yOVwU2vPnvF2tKdD279LbK6kB6pPuC2UsVAxqWAW9eB2ABw+Knqfzc7AbRvcreaabgLsPdV/3u5DBCtoV/mYjRNUuiTx+q/rVxKAtR6J1xfqJgJkK5/tXwuBWvx1e0S7uOmJUDzGPB1OZzd0mhKSU2VUBvQvbX8OqGUgkqnURgbQyGZLK86lz5P/doeH5fAsUa+DRtgrl1bXoU2olHosRiMaFRWa5dwUKlse/aKdC4Hlc9NSzaTFG+fBNPRKIxIWNK8AwFJ8fab04PqJbYCT8tQpBeIDwCnXwNaB5s9GnIYA+4GUEoVuzEoKVyhJrszKCVBcelyu3jdmZ8LpespCabl9yCBZMGGbUs6dL4YQNvFlWZVDLrt8m1IivTUViAaNOi6Bp+dRbBgYNzsgVfXEfBo8OgaDEODR9fhC29E3H4FPi9w2g7gZEbH6ayG01kdp7IaTmV1nMpoGC5+llZalVkfLWBtpIBOv41V+ghao0F41l6MqN8z7+QtKeB2sad2QU4aFGzYSiGWDmCNlUfeZ8PvNdBm+hA2PTC9k0G16TFgVFI0oWBJT2+nV+c0TVL3x45U/7vZRDFV14VAqiRcXD2upjiZksq5ru3fLgm2Vd/7WhXTRJ3uW14SiNdXaK4k50DBNKBYbb4dGH6x/tuaqdq98MFWcB83UfVsKwd7PI3CRAqF8TTs0dMopDKwVQSF1K+K+6IlvRv5Kl5/NA16KDQlbTsMO59DZt+vFv3V6HvfC/9Gl4pi1mGuYFpZllTzVqr4XkKD5iv1i/bCiBX3gUci0l/a55vsM11amfbwrTI1gK4DnWdJsbZ8tvYuJbQk8VWkRrZSOHAiiVTOhjXlxKYqBs9AMcC2S1+jHFSXr1fc42NDou/JIByTl824X618W9LASoMGXdOgabJyqxc/a7oGj6ZB9+rQIZWzS9eZK4BVCrDHR3HS14cj+QjGTiQxlsphLJOTz2n5SIxvxFiusuBLg0LQUJgoLH79K/qzuLhb3iwEkicw1n4uEgFvuX91tpi+ni1+lI6p15B2W6bXQHvERDzoQ8j0IFwwEXtlP3yRILz+UH1n3EuryfWm+M4l1C5/mGoDkVwKiG2vbe93pUIdxb23ycpPNuSK6dBBl1eRAi2AGZP09UoD7lKqttMF00rMiBQRq7V6eolS8vicEGoDTlRXnKgiVkpWzyvdNhBs4z5uoiKVz6MwkYY9npkMpCfSKIynYE9Mv0zlqjuJpwUC86dxly4rBpgz9wor28axv/1bFEZH5719Ix6HuX59LQ+7LosG0wCgG+UUb83jhRFvkVXpcBi63z8ZQE/9mvulaSmJrZaP5BDQ0t/s0ZCDll3Aff/99+MLX/gChoaGsGXLFtx3331461vf2tAxFGyFJ185hacOmQhqOWzqyEOfUmAFKG/xmfwGpYC3VItFK7ZM1MuBM6b9fP7guFJWARjLaUhakt6dsDSMWTrGchrGrMmPUUvHqKXBsksB5UIrYhJIeDSFVlOh1bTRaiq0mTba/PK51VRo98vn/aMG/p9nFq+4GDFspLJ55PI2cqkcDqa8SKhxKAA+jw7TMODz6miLmIgHvAj5PQh6PQj4DAR9BgIzK4LbQWC4FcinAK3OPtW5lKzYurGnJtQugVo2WXmQZUspN9f2b5eYYSnKNna48iApm5QgzHQ5qNINSVM++kzlq+lWaWwuZQWUCqfl07VXGS0UV46dGqMZlf5CtVSbX4g1PlkMrRLcx01nOFWwYafSKIynJZieSBeD5tSsy1S2ygrdXg/0cACG34ARi0Pv6JsWQJcC6nqLi2m6jpY//EOc+l//a97rtHzwg47vcZ9zz/SsNO/iyrRHVqeNeAv0UKi4Mh2AbvoknX3qyjSDaVpudEPqMoy+7l7BU2qKZRVw79q1C5/85Cdx//3346KLLsIDDzyAyy+/HM8//zz6+xtzJuhHvxnCXf/xPIbGMgBk/2LbIRvXb8rggk4H0klnUAqwbGAir2E8p2G8+HkipyFZ/DqZk8+J4telj8wC/abn4/doiAR8iPm9iAW9iAUmP1oCXsR9ChtOP4qop4B8BZWez4oX0GbaOJWV0wpzPELEfTb6A2nklY6AkUMsEsHmNf3wxzoR8BrloNrvWaTN1lS6AUR7pbBWvXJpIFThXtVq+UISMI4eqjzgtsbd3b89VUs/cOpA5de3xoHOLe7u3y4Jd07uz6jkxJSVkrG5lRVgRqV4Wq6OgDuXkttwKpvCH5tsoVZt8buF5FJAdP7We3OK9Ul1ZKJlQikFO5UpB8qFieIK9HhKLisH1WnYqeoqdMPQYYQC0EMBGKEAjHBQvg4XLwsHy1/rPi+QGpb/5VXnOvu/PEPgnHPQdsMNGPn3f4c9NjY53HgcLR/8IALnnFPV7ZWrec+1Og2U3xZM3TNdTvMu7pnmyjStKC398v51/IQUiKUzwrIKuO+9915cd911uP766wEA9913Hx555BF85StfwT333OP6/f/oN0P4s395Zlaa96mshs//OoD/e1u6HHTbCsgWgHRBAt9MXr5OFzSkS1/nNaTyGtIFCahTUz4m8nLZRK66vdAzeTSFiFch6lOI+RRiXoWoz0bUq9Dik4+YT6ErfxT+eA8mVr+tgtschG94bzngVrZCrlilvFRkLV8ASk21/nC1wlcPRIHy3vESOZKfPhc4b7ANPkOHN3MKmtEDrBuQatT1CHdK65S6Kff2/QISiAy/VPn1s0kg0uVOL8iZQu3Sq7WS/USl/RPhdvfHBcgKa2kf92JVx0uV80Mujk03ZBW3nqDSSkpWgVNvqM3olL3uDt1mae9LtdsGAi3F/TAOr7YTVUEpBZW1JtO4y6nc6Smp3ZMr0uV9YJXQtGIA7Z8VNBuhAPRwUILrUACav4qK1bmUbDtq3+hqsF0SOOcc+N7wBgz95V8CANr+/M/h37x51sq29DGf3RZLqnkXZMbXtMlq3j6fVPEOhyWgDgQmV6SnBtPcM00rmeGVVe4X/0+xXgr/H84Ey+avaFkW9u7di9tuu23a5ZdeeimeeOIJ1++/YCvc9R/Pz9MlU3ZWf+HXAQQ9CpatwbKdXUXToRDyKoQ8QMSrEPJIIB3xKoS9CmGPQsRXDK69ChGvjahPIWhUsKCnbATHUxiOzc4SUEoKsVl56bGdKyiM5OPIpxUm7CQKuhc6AI+uwWNItfKQ34egz4OAV4fXo+PcQQMbu218fq+O4+nJ2+4JabjjzRouG5xypjqXAmIb6w+2gWJ/0QqDxfnkiz2R3UyDDbbLC2zBkvEuJpeSPT6NEGyTNOxsAvAs0oLL7crpM/lbJIjLJhYPuPNpwBNwb/92SbgdOLm/9t+30kDvaudW4Q2PnGQYfQ2AQ3+XfEbajVXb9q0U/Du92k60iMSPfoThf/oicseOwc7+AihUdyJWD/qhh/wwQjMD6ACMUHDy+6DpfEsxVQBSp4GOTZV3BXCAEQhg1Ze+VE7vLoyMTAumS32mtVKfaZ9XVqM7OmBEi8F0KYiemurNat5Ei4sPyv/7xEkg4mA7WmqaZRNwDw8Po1AooKtr+oTT1dWFY8fmbsWTzWaRzWbL3ycSiZrv/6mDp4tp5PPRYAMYz09/o6xDwW8ApqEQ8MjXQY9CwFDy2QMEiz8LehSCHiBU/DrsKQXZ8nuVZlNXShVbhSGbQNL240ghjtRoGrmCLWeui/vKPboGn0daZYVMA9FwL3oKHfAZGoxwDD6PIavTHh1eXZsz7fuqDcC7+22c/f/J9//vu4C3rtJmVwkvWM5VuA7Epd2WNV57wJ2bkCDSzWrgwbZiD+fE4iuwdh7QjMYFtYYXaFkNHN23eM/rbAIIuFw5fSpdlxMPh59e/LrZcckIcHv/sBmde+dEJexCsbK4w3/bcKezlcqtccBXw7E0o3JixEox4KaGssfHkX3l9WmXaaZ3Mo17ZgAdnnJZKCA9u5tlYljeeLeuQe0vLrNNK0JW2jNd3DetaRqgII/b54Pu8ULzeWG0xqXgWig0fVW69NlXwQljIlqcxwS6twAH/gsIcZX7TLDs/oIzU7AmWz3Mds899+Cuu+5y5H5PJCvbn/Un6zO4sCsHvwH4DQWf7m4h6bkopWDbsjJd6rudL/fhLvXelEEZuoZoNgEr2AUzFEGb34OI34uA14Dfa8BfbJ/l9+rwe43J/tSBNwDHfwvEKi8kFjF1vPo/F7hCudVQS02PexbDK+2Vhl+qPUDNpYBwt6zoucXjk7Ty479dPODOjkuhqkYF3IAcw1K7r4VSgXMpoGd7Y5/wofbKxmZNAK1r3W9JZUZrz6rIJt3525rRyfYHTvxtrAmgo7/6LBTDAwQ72I+bGi50wQXouvk6WL99CuYbNsMIBqB5l8Hbn0xC5rGOjYBR+etJOdV7aiBdCqwxowiZt1iELNoKPRyBEQnLarTfD830S7/pYruspdxfm+iM07oOiL0grWPjA80eDdVpGcw4or29HYZhzFrNPnHixKxV75Lbb78dt956a/n7RCKB1atrS8XtjFQWcK2PFtAVqGLPVxXsUgBdDJ7zBQVb2SjYQEFNtsrSoMHQNBgGYOiS5h0sB9DF1WhDg9djSFut0THo694Ib18VxRkiPcDQr5x7Ew9MthpyMu030g2c+G0dY0o3Jp2n0uNpJYFo3+Ip1E4KtgFmSP4+81WlLlVOd7sd2EzBNslAWGhsgJzMWWyF3glmZLJwWrUBd/lvW2PBtfn4Y3JSp5AFPA6cOCrkJnu0VyvcUV/KPVENvKtWIbTjbKhjv4Mn1oDaF04oWHJyq3uLZA5NoQqF6cF08WsoezLVuxhIl/dNRyLQwxHoAf9kQD015bsRhS6JqHJeP9B3LvDC/5YMwkZlD5Irlk3A7fP5sHPnTuzevRt/8Ad/UL589+7duPLKK+f8HdM0YZrONI5/85pW9MT8ODaWmWcft0K7qXBWvPK9YaWV6FLAXFBAYVYQrZXvT9cAQ9Pg0TXohg7Tq8P0eGB6dfg9svrsMbRpn726BNfznpm2C4DXAMJVrqqF2ouBRcq5AKHUasjJgCPYBug1rjiWUnwbEUQG26ZUuF4gmM5nZDW8kfwxINAGpE7OH9TmGlg5fdbY4kBmZP6x5Yt7493evw3IBBlsBRJHqs/UcOtvW6qebqXqD7hLbctqPZb+WLHkhYMn6ojOIEopCaBHj0EFO6AyfqjDhyXVG5BUb49RTvXW/Sb0tjZpDRYKFlejzfLKNPdNEy1jsdVA11bg8C+BtrAzHWDsfPHDlvcEPNnWEMsm4AaAW2+9Fddeey3OPfdcXHDBBfjnf/5nvP7667jxxhtdv29D13DH75+FP/uXZ4ol0qaS7/7nhjTsgo1cKZBWgG3bKNgKtgIKpUrJZcWVaB3QNR2GoU0Los2pQXRxpdpTXJ32GBo8TvyTWBOyz7mCFl/TBOISXKVPOxcg59JAxOEWCMH24jhHZLW7GtmktGdyak/5QgLxxQuAFRq8f7tE04B4PzD22vzXmRgG4msaUzl9Kk2TCWnsMDDfXadPy9+xEQE3UGyl9nJ1v+Pm39ZTPNmQnLvWRVWscXm9qLZgWok/JhN8PuNOX/uF1FM8kcgBSimgUOw5nSvI53wBKje9paiWS0ALhKC1rYMRb5dgOhwur0pPDaiZ6k10BtM0oOeN8h4nOVR7mzBrAkgMyQlvzZAtXpohc3rLAOfGBlhWAffVV1+NU6dO4e6778bQ0BC2bt2KH/7whxgYaMzehsu29uAr/2PHlD7cIu6z8Uf949gYyiKZkaJhuq7Bo2kwfR74PDp8Hg2mYZRXno0pVb0nK3xLCnhDWUkpyLJQOu5cNE32lIwdcWYcpX7KTq8mGx4JBF/fM39ANp/MqLRhcTrFdy66DsT6gcNPzX8dKymrlY0OuAFpVaV5iydoZhyP1Olif9gdzVm1LBUZs+3ZZ2oLOTlx0vcmCTwbIdwlk1cuU/ne/1K6mFt/20i3Mz2wcxPy+Grd0lBOuU81NuBOnQZSpwBoktbudvE8OrMpW57DuleyZ4qve8q2ywG0yhfKgTXsycw3zTAAjwHd44EeMGEEpYWY7vdB83mhW6ehmf3QN70LWvcGpnoTrXRmWFLLX/xRce6sYv61C0DiqHQ76N4qtWwM32RHnCN7gZO/AyK91ccBVJVlFXADwE033YSbbrqpafd/2dYevPusbjz18km8vHc34j4b5/SFYXpCMLQQPLqsVHt0Wb2eq2L3kmJlZN9oLULt8kbDiT6B+SzgNZ0rmDZVtFvy8SttuwVI8F/INTZ9O9IpAeN8L6il1jBuFnCbd2w9QPfZwNFnZAW3dDa0YEkgs+at1WcQOCXUISu448eAaO/0n40dkfYaHZsaN55gm2SMZEYBb4XHJJsE2ta597d1KsDMpWVirpXhdb5NWSVSp4Hec+Tr4ZeA8ZPy/8Y9ca67//778YUvfAFDQ0PYsmUL7rvvPrz1rW9t9rCqpvIWkE5ApVOyh1rzQlk5KCsDZRfbY5lhaD4/NK8BzeOBEYlKpfOACd3nhWZ6i5990L2e2YXbkscAFQXWvk1eD4iIAFk46jwLOPZreU9TyXvZ9Ii0FYuuAlbtlN+buSiy9m2StTa0TzLPFivcSzVbdgH3UmDoGi5Y24oLkkoqIwebEAA5wbbr26Mc6pBU3Wyy/nRda1wKptWaqrqQUGcxABqrvHBWKdW+EenkJbF+oGOzvKC2rp++Wjt+XM4+9ryxceOZSteB1W+WftYnngfiayV7YPQQ0LZe9hg1ixkGBi4ADvxYAqvS8zmblHH3niOBXqPohkxsh/ZU/jsFa/bJAieZUVmNq+ak00yquB0mWOf/ergTOOlgm7LFWONyIqNjk9x352bgxH55g+Hx1348aFG7du3CJz/5Sdx///246KKL8MADD+Dyyy/H888/j/7+/mYPbxppkzV9ZVrlivsc8ynASkMLtUCL9kILt8Jo6YAe8EP3KejIQs+egpY7Bd1nQmvtlZTwalanJ04Cdg5Y8zYG20Q0na5L0JxPA8MHigsNLXNfN5eROjK+INB/oaxsz5dR5vEB/efL+6hDe2R7IINuVzDgXsly4/IPWWvA7Q3Iquaplx0IuCeA9g3VtxqqhMcnAdCRvZUH3JkxINLlzgmA+ei6pD6nTgFjhybbQFjjQHYCWP/Oxp4AmMnjAwYulFXOkVcBf0ROSvS9qbEB7Vza1kmA/erPZZzeoOxXWrWj8UXmAHnuQK8s+yNvyfFzc6uAf0oP7ECNAWYuBXgC9f9PlFaVG1U4bfykvLaU/vdD7UD/efI/lknwzYWL7r33Xlx33XW4/vrrAQD33XcfHnnkEXzlK1/BPffc0/gB2QqFxMRkUJ2fUuRU16B5PNA8BjSfB0Y0DCPkh24noXvi0AbOhd63DVowNHchMrsgz6njz8vrY3ZYXq8X25Jk5+WEaiEHrLlEWoAREc3kjwLr3iXtNY8+U+xsskoW/uyCvJZMDEtHkvaNQO/2yt4z6jrQsw2AAl55TOZ4N96Lr3A8os1S+sco/ZOogqTpRh0uGraQ7LgUFfPVsW8j1gec+F39Y7Etd4PJaK8E3JWmv+dSc6ffuM0My9nGFx+RwNsfA8aOypnN9iXwRswXkvTxfFYKeKx7R+0topzWvU1O3Bz+5eSJpJ5tTdpX3imTYyax+Amt0v7tagsXVsMbAMwYkBqufdtGNim/W2/A7Y/J9pF81v3tEQVLAvv2DdOfB4ZXCsUc3ceA2yWWZWHv3r247bbbpl1+6aWX4oknnph1/Ww2i2w2W/4+kUg4OyDDgBEyAU3BCAegh/zQgwHophe66ZX90z75rPm80JSSrQ9mHzBw0eKrzqXMlli/BN4nnpdCR4mjxaKYrdOzluwCMHFC5uFoD9CzXbKFiIjm4/EBq98k89ahX8iCl6ZJ0K175HWm9xzZq11t/YeOzcDpg7I6zr7fjmPA3SyJo/LG098ib4Z1j/SLLlUBboRcCmhZXV9AEmyXN83VFIiayS4A0N1dTQ53yfHOjC2+kpjPyMmPUJNWk2N9EmAf/JmkSLcOAn07l07rhkAcWHsJMPo60PGGZo9mkq5LYZHsOHDqRVmNb1ZxLK9fqqefeL6CgDspe7PcLuoW6ZZAoFbWBNC5pf7noRkFPKXCaS4H3BMnJZiZq05FtKd4Em6OYntUt+HhYRQKBXR1dU27vKurC8eOza6Yf8899+Cuu+5ybTy+vh543rQeevcmaau1EGUDp1+R58jgW6qrT6Hr8ma1pR8YPyHFCodfAkZemXEfSk4yrz5fgnlWCSaiSrWukfcWE8MSPxjFAo6+cO3zqscnWYH7fyjvo1hEzVEMuJvBLkga6aqdsvICyOSbSwMn90uvPdfHID2+664KHmwFzBYgO1b7P3mu1JrMxbZNXr+sPgz9evGAOzMmZwmbufLVtVWCheRxoP+CxrdQWky4s7np7fPxmMDghVIor9kZAbFVwPHn5M27tkBAZ+cbU3Au0IKZDQ0rZtvFAMGBbAaPTyrLjx0G4OKqvm1LCv3ARXOnx4WLWQjZhDvFGgkAZrWsUkrN2cbq9ttvx6233lr+PpFIYPXq1c6NQ9dhBHzAYsE2AIy8Jv+T699Z+7ykabK1JNIlBSfHj8vcr2z5rBsSlC+113YiWh78MecXFWKrga6zJPvLt6E5GYJnKAbczZA6JcFcbMqbCU2TJ/npl+VNYq1tdyqVm5D7qDeNVTekR/Php2UVuRbWhLypcbv9VrQXGHp28RWtbLK4klfBGzO3GB4JFLLJpRnYLmVmpHnF5aYq7d+0xuevhp1Ly0mCRrR6M6PSd7OQr35/llU82+3UOMNdUvjFTenT8vrWMk9xLl9IskmGX2TA7YL29nYYhjFrNfvEiROzVr0BwDRNmOYSWOVNDsncOPgW504C+0KS4klEtJRpmmzPG3lNFn34/tMxzKNrNKWkVH/HG2avCEd6ZFIen51u57hSZXGz2ubUc4h0o1wgqhZWSloNuX0mLdItQUd2gb2BhTwAvXktrqbyBYvFt2hZ8scksMyMzX+dxJAEhE73n59zPNHJHtjVyiblJKHfoTZa/hjg9onz1Gl5nV3oRF6sT4pVqRpX/mlePp8PO3fuxO7du6ddvnv3blx44YVNGtUiUqfl+TDwFkknJyJaaQItsg88Myavh+QIBtyNlk3Km9a5ChJomrSs0fTa3hRXw0pJcRcngtxw9+T+6GopG4BqzApfaUUrPTL/dbJj8lgqrWZOtJCWAalvMJf0qKxu957TmGwKb1Bee2p5bcmlpmfk1MuMyn6z/DzHpl7WeHFVcXDh64U7ZTuLNeHOOFa4W2+9FQ8++CC+/vWv43e/+x1uueUWvP7667jxxhubPbTZrAmZG1a/GWhn8TIiWsHaN0qNp0YsAK4QDLgbbWJYGtjPt6IV6ZUex8nj7o1B2fLZqVU1r1/e2KZrCLiz443tdx0flJW17PjsnylbVjji/e4Xc6KVIdwpQXUuPf1yZUtBpa4tjcum0DQpHmbN8dxfSCEvJwScrGlQWm23XDqxmEnIPvHFTuT5W2Rfei0nC2lRV199Ne677z7cfffd2L59Ox5//HH88Ic/xMDAEquAW7CkMm/PNkmnJCJayTw+qSWUt7jK7RAG3I2Uz8qb3oVaf+g60LVZvp5vZaxe1gRghpxNYy21M6s2rTw9Ir/rVKrqYuJrpP1K8qj8PUqUkj0r4S55kSFyQrBNVrlHX58eXI4fl2C8++zGjida3P5RqOL/tNS2LOhgwO0xZUvLzBMRTrEmgJbBxTN4NE1OwrmdUbSC3XTTTXj11VeRzWaxd+9eXHzxxc0e0nS2La/97RuAvjc3t3YHEdFSER+U2kfjJ5o9kjMCA+5GKreo6V34etE+eaInXUrlyCaBQNv8hZxqEekp9h2uYqVIKVlZaGS/P10HVp0rbZhGXiu2JINUTDYj0u6qEftpaWXQDWDt26TVRuKopJHnLQm+e89pfNuNcJfsz8pW8X+aTcoqvNNZH5EedwLu0op8pRXVQ8UsBLfS22lpG31dnov9FzKziYioxPBKFl4uXd1JepoTA+5GsW150nZsXvwMuq4DHZtktbgUEDrJStfff3umUtutatLKraQEHLVWN6+VxyettuL9wMirEggZHgm2l0KxNDqzeP1ScX7gQiAzCpw+IMURF8p0cYvHlCJt6dHKf6dgTWawOKlUGdzpgmXVrsiH2qWaeTXHhM4MyWPSlmvwIlaqJyKaKb5GFgonXNzmukIw4G6UzKikULZUWHgo0iNvAJzeW2gXZA+zGz2mY30AVOUnCdKjk4+z0cwwMPhWIBiX/bSDF8/fPoioXrohq9zr3inPs97t1bfmckq0F/J/ai9+3XxGgnQ3Xi8CcQl2nF7lzozJa1Glq5W6IScL56rrQGeu9Kg8vwcuXDzrjIhoJSrt5bbStXciIgAMuBsnm5BVokp7TfuC8iYwM+rwOJLO9tOdKlJFtXKlZA91fI3z46hUqB1Y+3Zg3TtYlZbcp2lAx0Zg85XNfYMf7pLtEwu1xyvJJgEzJivATvPHZBzVFnFbiFLypqDa4xvpkr9PJSchaPlLj0if9r43y95tIiKaW+saed/Avdx1YcDdKLW8CYz1Tb6BdIqVlD2LlQb+1fAGKj9JYI1L4N/sPtPRXqBtXXPHQCuLx9fc+zfDcvKvkhNjmSTQ0ufOarxuyP+fky25cmmpfl5tWz9/i5zkzLE92BlvYlie+wMXSh0FJ7dWERGdaTwm0L1V5mo3trmuEAy4GyGXBjz+6tMyq1kxrlQ+U0z9dklsVfEkwSL/lOnRYv/uFvfGQkRza+mXvdkL7Z9WSrZbuFljIdTu7ASeHZOih9W+rpgR+R0nV9tp6clnpSL9moulW4XOt0BERItqXVtc5eZe7lpxtmmEbELezAXi1f2eNyCpHLX0t55LIQdoHnfSyUsiPYufJFBKAv/WNVxdIGqGcCfgCy+8upwekUC02tXiagTisnqet5y5veyEtGGrNpDStOJqu0ttymhpCHfJNqKuLZx7iIgq5fUDPduKq9zcy10LBtyNkE3KilIt/T1jfVLkzIkneDYpb6DdDLi9AWnzlTo9/3WsCUlpb3R1ciIS/hZpm5UZmfvnypbU266t7hY1DMSLgb8DK8t2XoKoStuBzRRsA8A93GesWB+w/l1SR4GIiKrTulZOTCe5yl0LBtxus21AQVaUalFKu3aiZY1b/XRn6tgsPbnn6yOeGZFxVLviT0TO0DQpWDhfhfDxE/Ka1bXZ3XF4TLkfJ/ZxZ5PyulPriry/BTB87Md9pjIj0t6GiIiq5zGB7m1APi0Zs1QVBtxuKxUHq7Wtjtcvb4ydqFbuVj/dmcIdQP/5slduZqud9Kikj7auZUofUTOFu+Zuy1XIyf9tzxvdKa44U6TbmSA3k5AtLd5Abb8faFk8zZ6IiGilal0DxFbPv6BG82LA7bZsQlZczEjttxFbBUAHCnWkleezsnrjZjr5VO0bgZ5zgOTRyTNhE8OyL7T/AqB9U2PGQURzC7ZJ0D12aHrQnRySyuRtDWqVF4gDml5/8bSCVV9BSMMrHRwYcBMREc1meIHuswE751ztlRWCAbfb8mnZv12PSDcQjNe3yp1NSjGzoAv9dOeiacCqHUDrOmDkNSBxVI7F2kvkclaHJWouXS8WkNoKjB2RNPJcWgLfnjc2rn1ZIC4r6fW05MqlZGW73gJvkS45OUlERESztQwUV7mHmj2SZYVRj5sKllQFrzWdvMRj1p9Wnk1KsQPDW99YquH1y2p2aQVr3TtZHZZoKfFHgbVvA9a/Q7oHnHpZVrZbBhs3Bl9Y0rlnbj+pRnpUXmcDdZ5QDLQ4s9pORER0JjI8ssqtbDnZTRVhwO2m8qpynQE3IJW/dU9tex1LfbEjTSgYE2qTN/MbLwPa1jX+/oloYbohJ8Le8HuSfdK7vbEZKJoGRFbVN3FbE1IXot5x+1vqX20nIiI6k7UMAJ2bgbHDUhyaFsWA202ZhBQpcyI1M9wtAfPEcPW/m00CZqj+lfZaRXtZHZZoqQt3AuvfWXtHhXqE2qSbg1LV/24uU6x23l3/OMyInCTlPm4iIqK56TrQdy4Q6QUSh5s9mmWBAbdbSqvK0V5nbk/XgY5NssdSVXk2KXUKiPU3bv82EVE1AnHZg52fp03ZQjIjUgDOiROKmiYnSa0axkFERLRSmBFg9Ztl3syMNXs0Sx4Dbrfk0vIG0smq4LHVsvpSTU/uQh6AYjo3ES1d/pi0T6xlH7c1LsUZdcOZsQRbATBFjoiIaEHxAaB7O5A8zt7ci2DA7ZbsmLxxC8Sdu00zLAWNUqcr/53UsOwhb0T/bSKiWuiGvEZVG3DnLUDzSnVxp/hbpIWiE73BiYiIzmS9b5T+3KOvV5+BC0hGcDYhnVImTsrW2Ylh2S52BmHA7ZbshKRxO118KD4oFQIrfTOYSQAdGxvX4oeIqBax4klBO1/572RG5MRmyMF954EWqZzOfdxEREQL85jSkSjYDgwfqDw+KVjSWuzUSzLfevyAYUqMo3uknXDyWG21XZYgT7MHcEay88XKuy4UH4p0y8fEqck3qPPJJmVVvGXA+XEQETkpukqC59Tpygu3ZZJA/xaZoJ1ieOX+T7/i7JYgIiKiM1G4A9h0GXD4aeDkfskUm6uuim1Li+P0KKBB5tpV5wKxvul1pmwbGH4BOPxL4PTLsoC5zBcOGXC7odQOLNTh/G3rBtDxBmD0/0jqhrbACvrEMNC+gcXSiGjp85hA2wbg9f+uLOAu5CSDKOJAdfKZwl3Ayd85f7tERERnokALsPbtMn8e+SUw/JJsz9INiVUKOfkIxICebUBLvxSWNryzb0vXpe1YuAs49AtZOQ93SGy1TDHgdkMmIUXKvAF3bj/WJ2eP0qPzB9N2XgLy1rXujIGIyGnxfmDoGcBKAb7gwtfNjEqNjLCD+7dLgq2AZsjrqM5pkoiIaFGGR4LpcCcw8pqkl+ez8uExZa93tBfwhSq7vWArsP5dQKANOLQH8ASW7Uo330m4oWBJUOwWMyIrQYefkpRxY44nX+qUpHO4OQ4iIieFOop9PY9WEHCPSSqaG5NvoFX2cWfH5aw9ERERVaa0/dUJhhdYdQ6QPg0MvygLmgtl9y5Ry2/ES10uJSvbbqSTT7VqhxRDG3l1dpGhvCWr3+0b5YwSEdFyoGmyDSafWbjaaS4tK9DRXnfG4QvKa7iVdOf2iYiIqDKGF+g/TxYSk0PNHk1NGHA7LZOQNMeAy/umvX5g8K1SEO30q5NvTtOjEoR3bJQ3rkREy0l0lawqp0fn/rlSwNgReX2LrXZvHLFVEtgTERFRcwXiwOrzZB94NtHs0VSNAbfTrAkJgp1uBzYXMwKsuVj2MI68Jh/WODD4FmD9u+XnRETLiRmW2hPpkbl/nhoG/BFg1U53X2cDrYDmqa5NGREREbmjdS3Qsx1IDEngvYww4HaSXZCUyEpb2jgh2AqsvUSq/oXagI3vAfp2zl31j4hoOWgZkNfSvDX98oIFpMeA3nPc774QbJXgPzvu7v0QERHR4jRN5v/WtZLptoww4HZSNimrym7v354p0gVsvBzY9HtSZp+IaDmL9ADhbmD0telp3WNHgPgA0LHZ/TH4QrJfzGLATUREtCR4/UDvdgm+l9H8zIDbSZkxeZO4WHVdNwRbKy+zT0S0lBkeYOBC2ac9fhw4/Yp8NnxAn0uVyecSXQXkuY+biIhoyYitBjo2AYljUtdlGWBbMCcVLKDFxSI+REQrRbRH6lMkjwIn9stqd/dW9yqTzyXYBsCQ7UK60bj7JSIiorlpGtDzRqldlT5dnKuXNgbcTrEa1A6MiGil0HUg1icrzalTgBlt7P0HWwEzJGlr/lhj75uIiIjmFmwFus8GXvs54I83plh1HZb26JaTiZOS4rAMzrIQES0rmib7qRuVSl7iCwHBdqnPQUREREtH52bZyjt+rNkjWRQDbicUcpJy2LFR3hgSEdGZIdbHfdxERERLjS8oVcut1OyuJksMA24nTJyUSuEx7t8mIjqjBFsB6HJSlYiIiJaO1rVA2zqp97KEMeCum5I+rR1vYO9rIqIzTbAN8IWXVfsRIiKiFcHwSAE13QCyiWaPZl4MuOuVHpEVkPhgs0dCRERO84WAUJucWCUiIqKlJbYK6NyypNuEMeCuV3ZcesWa4WaPhIiI3BDrA3KpZo+CiIiI5tK9VRZAJ042eyRzYsBdr1AH0Lqu2aMgIiK3RPuk7aM10eyREBER0Uz+mBRQyySkmPUSw4C7HpoGxAekXQ0REZ2ZQu2yyr1Ez5wTERGteO0bgZbVQGLpFVBjwF0rTQMCLfLHZSswIqIzl6bJa71dAOx8s0dDREREM3l8sspdKmi9hDDgrpVuAGvfJivcRER0Zov1ScXy1Olmj4SIiIjm0tIPdG8DEkeWVGr5sgm4BwcHoWnatI/bbrutuYPyhZp7/0RE1BgeU9o/ZkabPRIiIiKai6YBq3YCbeuBkdeWTNVyT7MHUI27774bN9xwQ/n7cJiVwYmIqEFa+qUndzYJmJFmj4aIiIhm8vqB/guAzBiQPApEVzV7RMsr4I5EIuju7m72MIiIaCUKtUnQPfwSA24iIqKlKtQG9J8PvLRbAm9/rKnDWTYp5QDw+c9/Hm1tbdi+fTs+85nPwLKsZg+JiIhWkrb1kqK2hPaGERER0QytayW9PHm86UXUls0K980334wdO3YgHo/jqaeewu23346DBw/iwQcfnPd3stksstls+ftEItGIoRIR0ZkqugoIdQDjx4DIKkBfVuetiYiIVgZNA3q3AwULGPoVkE0A3mBThtLUdwp33nnnrEJoMz9++ctfAgBuueUWXHLJJdi2bRuuv/56fPWrX8XXvvY1nDp1at7bv+eeexCLxcofq1evbtRDIyKiM5HHB/S+EfAEgNMvA2OHpF0YERERLS2GFxi4ENjwbil+mjjSlGFoSjWvfNvw8DCGh4cXvM7g4CD8fv+sy48cOYK+vj7s2bMH55133py/O9cK9+rVqzE2NoZoNFrf4ImIaOWyJoCxw8DJF4CJk7JXrGtL3TebSCQQi8VW/DzF40BERI5KnQYO7ZH08rPeLyfQ61DNPNXUlPL29na0t7fX9Lv79u0DAPT09Mx7HdM0YZpmTbdPREQ0L18I6NgEtG2QgJtF1IiIiJauYCuw/t1AerTuYLtay2IP95NPPok9e/bg7W9/O2KxGJ5++mnccsstuOKKK9Df39/s4RER0Uql60Ckq9mjICIiosUYXiDc0fC7XRYBt2ma2LVrF+666y5ks1kMDAzghhtuwKc+9almD42IiIiIiIhoTssi4N6xYwf27NnT7GEQERERERERVYz9TIiIiIiIiIhcwICbiIiIiIiIyAUMuImIiIiIiIhcwICbiIiIiIiIyAUMuImIiIiIiIhcwICbiIiIiIiIyAUMuImIiIiIiIhcwICbiIiIiIiIyAUMuImIiIiIiIhcwICbiIiIHDU4OAhN06Z93Hbbbc0eFhERUcN5mj0AIiIiOvPcfffduOGGG8rfh8PhJo6GiIioORhwExERkeMikQi6u7ubPQwiIqKmYko5EREROe7zn/882trasH37dnzmM5+BZVnzXjebzSKRSEz7ICIiOhOsqBVupRQAcCInIqIlqTQ/lear5ermm2/Gjh07EI/H8dRTT+H222/HwYMH8eCDD855/XvuuQd33XXXrMs5XxMR0VJUzXytqeU+q1fh8OHDWL16dbOHQUREtKBDhw6hr6+v2cOY5s4775wzKJ7q6aefxrnnnjvr8u9+97v44Ac/iOHhYbS1tc36eTabRTabLX9/5MgRnHXWWfUPmoiIyEWVzNcrKuC2bRtHjx5FJBKBpml13VYikcDq1atx6NAhRKNRh0Z45uNxqx6PWfV4zGrD41Y9p4+ZUgrJZBK9vb3Q9aW162t4eBjDw8MLXmdwcBB+v3/W5UeOHEFfXx/27NmD8847b9H7cnK+BvjcrgWPWW143KrHY1Y9HrPaOHncqpmvV1RKua7rjq8YRKNRPtFrwONWPR6z6vGY1YbHrXpOHrNYLObI7Titvb0d7e3tNf3uvn37AAA9PT0VXd+N+Rrgc7sWPGa14XGrHo9Z9XjMauPUcat0vl5RATcRERG568knn8SePXvw9re/HbFYDE8//TRuueUWXHHFFejv72/28IiIiBqKATcRERE5xjRN7Nq1C3fddRey2SwGBgZwww034FOf+lSzh0ZERNRwDLhrZJom7rjjDpim2eyhLCs8btXjMasej1lteNyqx2M2244dO7Bnz55mD2Ma/p2qx2NWGx636vGYVY/HrDbNOm4rqmgaERERERERUaMsrRKoRERERERERGcIBtxERERERERELmDATUREREREROSCFRtw33PPPXjTm96ESCSCzs5OvP/978cLL7ww7TpKKdx5553o7e1FIBDA2972Nvz2t78t//z06dP4xCc+gU2bNiEYDKK/vx9/8Rd/gbGxsWm3Mzg4CE3Tpn3cdtttDXmcTmvkcQOA//zP/8R5552HQCCA9vZ2XHXVVa4/Rqc16pj99Kc/nfU8K308/fTTDXu8Tmnkc+3FF1/ElVdeifb2dkSjUVx00UV49NFHG/I4ndTIY/bMM8/g3e9+N1paWtDW1oY//dM/xfj4eEMep9OcOG4A8LGPfQzr1q1DIBBAR0cHrrzySuzfv3/adUZGRnDttdciFoshFovh2muvxejoqNsPcdnjnF09zte14ZxdPc7XteGcXb1lO1+rFeo973mPeuihh9RvfvMb9eyzz6r3vve9qr+/X42Pj5ev87nPfU5FIhH13e9+Vz333HPq6quvVj09PSqRSCillHruuefUVVddpR5++GF14MAB9V//9V9qw4YN6gMf+MC0+xoYGFB33323GhoaKn8kk8mGPl6nNPK4fec731HxeFx95StfUS+88ILav3+/+va3v93Qx+uERh2zbDY77Tk2NDSkrr/+ejU4OKhs2274465XI59r69evV7/3e7+nfvWrX6kXX3xR3XTTTSoYDKqhoaGGPuZ6NeqYHTlyRMXjcXXjjTeq/fv3q6eeekpdeOGFs47rcuHEcVNKqQceeEA99thj6uDBg2rv3r3q93//99Xq1atVPp8vX+eyyy5TW7duVU888YR64okn1NatW9X73ve+hj7e5YhzdvU4X9eGc3b1OF/XhnN29ZbrfL1iA+6ZTpw4oQCoxx57TCmllG3bqru7W33uc58rXyeTyahYLKa++tWvzns7//7v/658Pp/K5XLlywYGBtQXv/hF18beTG4dt1wup1atWqUefPBBdx9AE7j5XJvKsizV2dmp7r77bmcfQJO4ddxOnjypAKjHH3+8fJ1EIqEAqB//+McuPZrGcOuYPfDAA6qzs1MVCoXydfbt26cAqJdeesmlR9M4Th23X/3qVwqAOnDggFJKqeeff14BUHv27Clf58knn1QA1P79+116NGcmztnV43xdG87Z1eN8XRvO2dVbLvP1ik0pn6mUetHa2goAOHjwII4dO4ZLL720fB3TNHHJJZfgiSeeWPB2otEoPJ7pLc4///nPo62tDdu3b8dnPvMZWJblwqNoPLeO2zPPPIMjR45A13Wcc8456OnpweWXXz4rJWQ5cvu5VvLwww9jeHgYH/nIR5wbfBO5ddza2tqwefNmfPOb38TExATy+TweeOABdHV1YefOnS4+Ive5dcyy2Sx8Ph90fXIKCQQCAICf//znjj+ORnPiuE1MTOChhx7CmjVrsHr1agDAk08+iVgshvPOO698vfPPPx+xWGzB40+zcc6uHufr2nDOrh7n69pwzq7ecpmvGXBDcv1vvfVWvOUtb8HWrVsBAMeOHQMAdHV1TbtuV1dX+WcznTp1Cn//93+Pj33sY9Muv/nmm/Gtb30Ljz76KD7+8Y/jvvvuw0033eTCI2ksN4/bK6+8AgC488478bd/+7f4wQ9+gHg8jksuuQSnT5924+E0hNvPtam+9rWv4T3veU/5xWM5c/O4aZqG3bt3Y9++fYhEIvD7/fjiF7+IH/3oR2hpaXHnATWAm8fsHe94B44dO4YvfOELsCwLIyMj+PSnPw0AGBoacuPhNEy9x+3+++9HOBxGOBzGj370I+zevRs+n698O52dnbPus7Ozc97jT7Nxzq4e5+vacM6uHufr2nDOrt5ymq8ZcAP4+Mc/jl//+tf4t3/7t1k/0zRt2vdKqVmXAUAikcB73/tenHXWWbjjjjum/eyWW27BJZdcgm3btuH666/HV7/6VXzta1/DqVOnnH0gDebmcbNtGwDwN3/zN/jABz6AnTt34qGHHoKmafj2t7/t8CNpHLefayWHDx/GI488guuuu86ZgTeZm8dNKYWbbroJnZ2d+NnPfoannnoKV155Jd73vvct64nIzWO2ZcsWfOMb38A//MM/IBgMoru7G2vXrkVXVxcMw3D+wTRQvcftmmuuwb59+/DYY49hw4YN+KM/+iNkMpl5b2O+26H5cc6uHufr2nDOrh7n69pwzq7ecpqvV3zA/YlPfAIPP/wwHn30UfT19ZUv7+7uBoBZZzFOnDgx66xJMpnEZZddhnA4jO9///vwer0L3uf5558PADhw4IATD6Ep3D5uPT09AICzzjqrfJlpmli7di1ef/11xx9PIzTyufbQQw+hra0NV1xxhcOPovHcPm4/+clP8IMf/ADf+ta3cNFFF2HHjh24//77EQgE8I1vfMPFR+aeRjzXPvzhD+PYsWM4cuQITp06hTvvvBMnT57EmjVrXHpU7nPiuMViMWzYsAEXX3wxvvOd72D//v34/ve/X76d48ePz7rfkydPzrodmhvn7Opxvq4N5+zqcb6uDefs6i23+XrFBtxKKXz84x/H9773PfzkJz+Z9YRbs2YNuru7sXv37vJllmXhsccew4UXXli+LJFI4NJLL4XP58PDDz8Mv9+/6H3v27cPwOQktZw06rjt3LkTpmlOK/Wfy+Xw6quvYmBgwKVH545GP9eUUnjooYfwx3/8x4u+kVzKGnXcUqkUAEzb21T6vrRys1w043Wtq6sL4XAYu3btgt/vx7vf/W7nH5jLnDpu8912NpsFAFxwwQUYGxvDU089Vf75L37xC4yNjS16Oysd5+zqcb6uDefs6nG+rg3n7Oot2/m66jJrZ4g/+7M/U7FYTP30pz+d1pIhlUqVr/O5z31OxWIx9b3vfU8999xz6kMf+tC0svKJREKdd9556uyzz1YHDhyYdjulsvJPPPGEuvfee9W+ffvUK6+8onbt2qV6e3vVFVdc0ZTHXa9GHTellLr55pvVqlWr1COPPKL279+vrrvuOtXZ2alOnz7d8Mddj0YeM6WU+vGPf6wAqOeff76hj9NpjTpuJ0+eVG1tbeqqq65Szz77rHrhhRfUX/3VXymv16ueffbZpjz2WjXyufalL31J7d27V73wwgvqy1/+sgoEAuof//EfG/6YneDEcXv55ZfVZz/7WfXLX/5Svfbaa+qJJ55QV155pWptbVXHjx8v385ll12mtm3bpp588kn15JNPqrPPPpttwSrAObt6nK9rwzm7epyva8M5u3rLdb5esQE3gDk/HnroofJ1bNtWd9xxh+ru7lamaaqLL75YPffcc+WfP/roo/PezsGDB5VSSu3du1edd955KhaLKb/frzZt2qTuuOMONTEx0eBH7IxGHTelpEXGX/7lX6rOzk4ViUTUu971LvWb3/ymgY/WGY08Zkop9aEPfUhdeOGFDXp07mnkcXv66afVpZdeqlpbW1UkElHnn3+++uEPf9jAR+uMRh6za6+9VrW2tiqfz6e2bdumvvnNbzbwkTrLieN25MgRdfnll6vOzk7l9XpVX1+f+vCHPzyrfcipU6fUNddcoyKRiIpEIuqaa65RIyMjDXqkyxfn7Opxvq4N5+zqcb6uDefs6i3X+VorDp6IiIiIiIiIHLRi93ATERERERERuYkBNxEREREREZELGHATERERERERuYABNxEREREREZELGHATERERERERuYABNxEREREREZELGHATERERERERuYABNxEREREREZELGHAT0YLuvPNObN++vdnDICIiogVwviZamjSllGr2IIioOTRNW/Dnf/Inf4Ivf/nLyGazaGtra9CoiIiIaCrO10TLFwNuohXs2LFj5a937dqFv/u7v8MLL7xQviwQCCAWizVjaERERFTE+Zpo+WJKOdEK1t3dXf6IxWLQNG3WZTNT1D7ykY/g/e9/Pz772c+iq6sLLS0tuOuuu5DP5/HXf/3XaG1tRV9fH77+9a9Pu68jR47g6quvRjweR1tbG6688kq8+uqrjX3AREREyxDna6LliwE3EVXtJz/5CY4ePYrHH38c9957L+688068733vQzwexy9+8QvceOONuPHGG3Ho0CEAQCqVwtvf/naEw2E8/vjj+PnPf45wOIzLLrsMlmU1+dEQERGdmThfEzUfA24iqlprayv+6Z/+CZs2bcJHP/pRbNq0CalUCp/+9KexYcMG3H777fD5fPjv//5vAMC3vvUt6LqOBx98EGeffTY2b96Mhx56CK+//jp++tOfNvfBEBERnaE4XxM1n6fZAyCi5WfLli3Q9cnzdV1dXdi6dWv5e8Mw0NbWhhMnTgAA9u7diwMHDiASiUy7nUwmg5dffrkxgyYiIlphOF8TNR8DbiKqmtfrnfa9pmlzXmbbNgDAtm3s3LkT//qv/zrrtjo6OtwbKBER0QrG+Zqo+RhwE5HrduzYgV27dqGzsxPRaLTZwyEiIqI5cL4mch73cBOR66655hq0t7fjyiuvxM9+9jMcPHgQjz32GG6++WYcPny42cMjIiIicL4mcgMDbiJyXTAYxOOPP47+/n5cddVV2Lx5Mz760Y8inU7zDDoREdESwfmayHmaUko1exBEREREREREZxqucBMRERERERG5gAE3ERERERERkQsYcBMRERERERG5gAE3ERERERERkQsYcBMRERERERG5gAE3ERERERERkQsYcBMRERERERG5gAE3ERERERERkQsYcBMRERERERG5gAE3ERERERERkQsYcBMRERERERG5gAE3ERERERERkQv+f8ZqD6VV4nMSAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "visualize_fit(t, x, y, xe, ye, x_model, y_model, xe_model, ye_model, mm.name, t_test)" + ] + }, + { + "cell_type": "markdown", + "id": "12bb0136", + "metadata": {}, + "source": [ + "## 2.5. Speed Test" + ] + }, + { + "cell_type": "markdown", + "id": "43fd87c5", + "metadata": {}, + "source": [ + "Speed test for the most commonly used Linear model. As the `use_scipy=False` option for the Linear model uses the [matrix multiplication solution](https://en.wikipedia.org/wiki/Weighted_least_squares#Solution), it is extremely fast at fewer epochs: " + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "de576a47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitting 10 epochs...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:01<00:00, 6350.75it/s]\n", + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:00<00:00, 25802.05it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitting 31 epochs...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:01<00:00, 6184.77it/s]\n", + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:00<00:00, 23908.79it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitting 100 epochs...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:01<00:00, 6347.19it/s]\n", + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:00<00:00, 14309.49it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitting 316 epochs...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:01<00:00, 5023.37it/s]\n", + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:03<00:00, 3288.47it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitting 1000 epochs...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Fitting motion model Linear: 100%|██████████| 10000/10000 [00:02<00:00, 4314.91it/s]\n", + "Fitting motion model Linear: 100%|██████████| 10000/10000 [01:19<00:00, 125.47it/s]\n" + ] + } + ], + "source": [ + "import time\n", + "N = 10000\n", + "dims = np.logspace(1, 3, 5, dtype=int)\n", + "rng = np.random.default_rng(42)\n", + "\n", + "scipy_times = []\n", + "analytic_times = []\n", + "\n", + "for dim in dims:\n", + " print(f'Fitting {dim} epochs...')\n", + " t = np.linspace(2025.0, 2030.0, dim)\n", + " x = rng.random((N, dim))\n", + " y = rng.random((N, dim))\n", + " xe = rng.uniform(0, 0.2, size=(N, dim))\n", + " ye = rng.uniform(0, 0.2, size=(N, dim))\n", + " tab = StarTable({\n", + " 'x': x,\n", + " 'y': y,\n", + " 'xe': xe,\n", + " 'ye': ye\n", + " })\n", + " tab.meta['list_times'] = t\n", + " \n", + " start = time.time()\n", + " tab.fit_motion_model(use_scipy=True)\n", + " end = time.time()\n", + " scipy_times.append(end - start)\n", + " \n", + " start = time.time()\n", + " tab.fit_motion_model(use_scipy=False)\n", + " end = time.time()\n", + " analytic_times.append(end - start)\n", + "\n", + "scipy_times = np.array(scipy_times)\n", + "analytic_times = np.array(analytic_times)\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "3d2a8457", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "280" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Collect memory garbage data\n", + "import gc\n", + "gc.collect()" + ] + }, + { + "cell_type": "markdown", + "id": "06442faf", + "metadata": {}, + "source": [ + "Let's visualize the performance:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "03d53769", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(dims, N / scipy_times, marker='o', label='Scipy Curve Fit')\n", + "ax.plot(dims, N / analytic_times, marker='o', color='C3', label='Motion Model Analytic')\n", + "ax.set_xscale('log')\n", + "ax.set_xlabel('Number of Epochs')\n", + "ax.set_ylabel('Stars Fit per Second')\n", + "ax.set_title(f'Motion Model Fitting Performance of {N} Stars')\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ea672ab4", + "metadata": {}, + "source": [ + "It can be seen that for epochs < 200, the analytic solution is faster than scipy, and vice versa for > 300 epochs." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "main", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/flystar/motion_model.py b/flystar/motion_model.py index 7a28690..b8cde55 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -35,7 +35,7 @@ def __init__(self, *args, **kwargs): def model_fit(self, dt): return np.full_like(dt, np.nan) - def model(self, t, fit_params, fixed_params=None, fit_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params=None): if fit_param_errs is None: return np.full_like(t, np.nan), np.full_like(t, np.nan) return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) @@ -114,6 +114,8 @@ def fit( params, params_err, chi2_x, chi2_y Parameters, uncertainties, and chi squares. The corresponding parameter names are in self.fit_param_names. """ + assert np.ndim(t) == np.ndim(x) == np.ndim(y) == np.ndim(xe) == np.ndim(ye) == 1, "Input arrays must be 1D! Motion model can only fit individual stars" + assert len(t) == len(x) == len(y) == len(xe) == len(ye), "Input arrays must have the same length!" fit_result = self.run_fit( t, x, y, xe, ye, fixed_params_dict=fixed_params_dict, @@ -186,7 +188,7 @@ def calc_chi2(self, t, x, y, xe, ye, fit_params, fixed_params_dict=None, reduced """ Get the chi^2 value for the input motion model parameters and data. """ - x_pred, y_pred = self.model(t, fit_params, fixed_params_dict) + x_pred, y_pred = self.model(t, fit_params, fixed_params_dict=fixed_params_dict) chi2x = np.sum((x - x_pred)**2 / xe**2) chi2y = np.sum((y - y_pred)**2 / ye**2) if reduced: @@ -213,7 +215,7 @@ def __init__(self, **kwargs): def model_fit(self, dt): return np.full_like(dt, np.nan) - def model(self, t, fit_params, fixed_params_dict, fixed_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params_dict=None): """Predicted positions (and uncertainties, if fit_param_errs is provided) at time t of Empty model. Parameters @@ -222,10 +224,10 @@ def model(self, t, fit_params, fixed_params_dict, fixed_param_errs=None): Time array, shape (N_times,) fit_params : array-like Fit parameters, shape (N_params,) or (N_stars, N_params) - fixed_params_dict : dict - Dictionary of fixed parameters, not applicable for Empty model - fixed_param_errs : array-like, optional - Uncertainties for fixed parameters, not applicable for Empty model, by default None + fit_param_errs : array-like, optional + Uncertainties for fit parameters, not applicable for Empty model, by default None + fixed_params_dict : dict, optional + Not applicable for Empty model, by default None Returns ------- @@ -234,7 +236,7 @@ def model(self, t, fit_params, fixed_params_dict, fixed_param_errs=None): """ t = np.atleast_1d(t) - if fixed_param_errs is None: + if fit_param_errs is None: return np.full_like(t, np.nan), np.full_like(t, np.nan) return np.full_like(t, np.nan), np.full_like(t, np.nan), np.full_like(t, np.inf), np.full_like(t, np.inf) @@ -285,6 +287,7 @@ def run_fit( params, param_errors (, chi2_x, chi2_y) Fitted parameters, their uncertainties, and optionally chi-squared values """ + self.fixed_params_dict = fixed_params_dict if verbose: warnings.warn(f"Empty data cannot be fit. Setting parameters to {fill_value} and uncertainties to np.inf.", OptimizeWarning, stacklevel=2) params = np.full(self.n_params, fill_value) @@ -332,7 +335,7 @@ def model_fit(self, dt, x0): x0 = np.asarray(x0) return np.broadcast_to(x0[:, np.newaxis], (x0.shape[0], dt.shape[0])) if x0.ndim > 0 else np.full_like(dt, x0) - def model(self, t, fit_params, fixed_params_dict=None, fit_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params_dict=None): """Predicted positions (and uncertainties, if fit_param_errs is provided) at time t of Fixed model. Parameters @@ -341,16 +344,18 @@ def model(self, t, fit_params, fixed_params_dict=None, fit_param_errs=None): Time array, shape (N_times,) fit_params : array-like x0, y0 in shape (N_params,) or (N_stars, N_params) - fixed_params_dict : dict, optional - Not applicable for Fixed, by default None fit_param_errs : array-like, optional Uncertainties for x0, y0 in shape (N_params,) or (N_stars, N_params), by default None + fixed_params_dict : dict, optional + Not applicable for Fixed, by default None + Returns ------- x, y (, xe, ye) Predicted position (and uncertainties) of Fixed model, shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + self.fixed_params_dict = fixed_params_dict t = np.atleast_1d(t) fit_params = np.atleast_2d(fit_params) # (N_stars, N_params) @@ -484,7 +489,7 @@ def model_fit(self, dt, x0, v): """ return x0 + v * dt - def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params_dict=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Linear model. Parameters @@ -493,16 +498,18 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): Time(s) at which to evaluate the model fit_params : array-like x0, vx, y0, vy in shape (N_params,) or (N_stars, N_params) - fixed_params_dict : dict - t0, shape (1,) or (N_stars,) fit_param_errs : array-like, optional Uncertainties of fit parameters in shape (N_params,) or (N_stars, N_params), by default None + fixed_params_dict : dict + t0, shape (1,) or (N_stars,) Returns ------- x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + if fixed_params_dict is None: + fixed_params_dict = self.fixed_params_dict assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Linear model." t = np.atleast_1d(t) @@ -540,7 +547,7 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): def run_fit( self, t, x, y, xe, ye, - fixed_params_dict, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, @@ -549,7 +556,13 @@ def run_fit( return_chi2=False, verbose=True ): - t0 = fixed_params_dict.get('t0', np.average(t, weights=1./np.hypot(xe, ye))) + if fixed_params_dict is None: + fixed_params_dict = {} + if 't0' not in fixed_params_dict: + # Default t0 to weighted average time + fixed_params_dict['t0'] = np.average(t, weights=1./np.hypot(xe, ye)) + self.fixed_params_dict = fixed_params_dict + t0 = np.atleast_1d(fixed_params_dict['t0']) t = np.atleast_1d(t) x = np.atleast_1d(x) y = np.atleast_1d(y) @@ -592,7 +605,7 @@ def run_fit( return params, param_errors, chi2_x, chi2_y else: return params, param_errors - + # Linear algebraic solution # Use https://en.wikipedia.org/wiki/Weighted_least_squares#Solution_scheme X_mat_t = np.vander(dt, 2) @@ -685,7 +698,7 @@ def model_fit(self, t, x0, v0, a): """ return x0 + v0*t + 0.5*a*t**2 - def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params_dict=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Acceleration model. Parameters @@ -693,17 +706,19 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): t : float or array-like Time(s) at which to evaluate the model fit_params : array-like - x0, vx0, ax, y0, vy0, ay in shape (N_params,) or (N_stars, N_params) - fixed_params_dict : dict - t0, shape (1,) or (N_stars,) + x0, vx, ax, y0, vy, ay in shape (N_params,) or (N_stars, N_params) fit_param_errs : array-like, optional Fit parameter uncertainties with shape (N_stars, N_params) or (N_params,), by default None + fixed_params_dict : dict + t0, shape (1,) or (N_stars,) Returns ------- x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ + if fixed_params_dict is None: + fixed_params_dict = self.fixed_params_dict assert 't0' in fixed_params_dict, "Fixed parameter t0 is required for Acceleration model." t = np.atleast_1d(t) @@ -743,7 +758,7 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): def run_fit( self, t, x, y, xe, ye, - fixed_params_dict, + fixed_params_dict=None, weighting='var', use_scipy=True, absolute_sigma=True, @@ -752,7 +767,13 @@ def run_fit( return_chi2=False, verbose=True ): - t0 = fixed_params_dict.get('t0', np.average(t, weights=1./np.hypot(xe, ye))) + if fixed_params_dict is None: + fixed_params_dict = {} + if 't0' not in fixed_params_dict: + # Default t0 to weighted average time + fixed_params_dict['t0'] = np.average(t, weights=1./np.hypot(xe, ye)) + self.fixed_params_dict = fixed_params_dict + t0 = np.atleast_1d(fixed_params_dict['t0']) t = np.atleast_1d(t) x = np.atleast_1d(x) y = np.atleast_1d(y) @@ -895,7 +916,7 @@ def _model_fit(self, dt, x0, vx, y0, vy, pi): x_res, y_res = self.model_fit(dt, x0, vx, y0, vy, pi) return np.hstack([x_res, y_res]) # Shape (N_stars, 2*N_times) - def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): + def model(self, t, fit_params, fit_param_errs=None, fixed_params_dict=None): """Model positions (and uncertainties, if fit_param_errs is provided) at time t of Parallax model. Parameters @@ -904,21 +925,22 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): Times at which to evaluate the model fit_params : array-like x0, vx, y0, vy, pi in shape (N_params,) or (N_stars, N_params) + fit_param_errs : array-like, optional + Uncertainties in fit parameters, by default None fixed_params : dict - t0, shape (N_stars,) or (1,). - ra, shape (N_stars,) or (1,). - dec, shape (N_stars,) or (1,). - pa, optional, shape (N_stars,) or (1,), by default 0. - obsLocation, optional, string, by default 'earth' - fit_param_errs : array-like, optional - Uncertainties in fit parameters, by default None Returns ------- x, y (, xe, ye) Predicted positions (and uncertainties, if fit_param_errs is provided) with shape (N_stars, N_times), or (N_times,) if N_stars=1, or (N_stars,) if N_times=1 """ - + if fixed_params_dict is None: + fixed_params_dict = self.fixed_params_dict assert all([_ in fixed_params_dict for _ in ['t0', 'ra', 'dec']]), "Fixed parameters t0, ra, and dec are required for Parallax model." t = np.atleast_1d(t) @@ -934,7 +956,10 @@ def model(self, t, fit_params, fixed_params_dict, fit_param_errs=None): obsLocation = fixed_params_dict.get('obsLocation', 'earth') # TODO: vectorize parallax.parallax_in_direction to handle multiple obsLocation? - assert type(obsLocation) == str, "obsLocation must be a single string for all stars at this time." + + assert (type(obsLocation) == str) or (np.unique(obsLocation).size == 1), "obsLocation must be a single string for all stars at this time." + if type(obsLocation) != str: + obsLocation = np.unique(obsLocation)[0] dt = t[np.newaxis, :] - t0[:, np.newaxis] # Shape (N_stars, N_times) t_mjd = Time(t, format='decimalyear', scale='utc').mjd # Shape (N_times,) @@ -975,14 +1000,21 @@ def run_fit( if not use_scipy: if verbose: warnings.warn("Parallax model has no non-scipy fitter option. Running with scipy.", UserWarning) - - assert all([k in fixed_params_dict for k in ['t0', 'ra', 'dec']]), "Parallax model requires 't0', 'ra', and 'dec' in fixed_params." + + assert all([k in fixed_params_dict for k in ['ra', 'dec']]), "Parallax model requires 'ra' and 'dec' in fixed_params." t = np.atleast_1d(t) + + if 't0' not in fixed_params_dict: + # Default t0 to weighted average time + fixed_params_dict['t0'] = np.average(t, weights=1./np.hypot(xe, ye)) + if 'obsLocation' not in fixed_params_dict: + fixed_params_dict['obsLocation'] = 'earth' + self.fixed_params_dict = fixed_params_dict t0 = np.atleast_1d(fixed_params_dict['t0']) ra = np.atleast_1d(fixed_params_dict['ra']) dec = np.atleast_1d(fixed_params_dict['dec']) pa = np.atleast_1d(fixed_params_dict.get('pa', 0.0)) - obsLocation = fixed_params_dict.get('obsLocation', 'earth') + obsLocation = fixed_params_dict['obsLocation'] n_fit = len(t) degree_of_freedom = n_fit - self.n_params diff --git a/flystar/startables.py b/flystar/startables.py index 2bb062c..b25f8c5 100644 --- a/flystar/startables.py +++ b/flystar/startables.py @@ -538,7 +538,7 @@ def detections(self): def fit_motion_model( self, - motion_models=[Empty, Fixed, Linear], + motion_models=None, fixed_params_dict=None, weighting='var', use_scipy=False, @@ -556,7 +556,7 @@ def fit_motion_model( Parameters ---------- motion_models : list of MotionModel or str, optional - Motion models to use. + Motion models to use, by default Empty, Fixed and Linear. Empty and Fixed models are always added automatically for stars with n_fit = 0 or 1. The behavior is as follows: 1. If 'motion_model_input' column is NOT in table: @@ -619,8 +619,12 @@ def fit_motion_model( if fixed_params_dict is not None: if not isinstance(fixed_params_dict, dict): raise ValueError("fit_motion_model: fixed_params_dict must be a dictionary!") - + # Convert motion_models to MotionModel objects if they are strings: + if motion_models is None: + # Setting the default to None to avoid mutable default argument issue + # See https://stackoverflow.com/questions/15189245/assigning-class-variable-as-default-value-to-class-method-argument + motion_models = [Empty, Fixed, Linear] all_mm_map = motion_model.motion_model_map() if all(isinstance(mm, str) for mm in motion_models): mm_names = motion_models @@ -653,7 +657,8 @@ def fit_motion_model( if 'motion_model_input' not in self.colnames: # If motion_model_input column is not provided, assert that motion model n_params are unique and sorted # Otherwise the fitter does not know which motion model to use based on n_obs - assert len(mm_n_params) == len(set(mm_n_params)), "fit_motion_model: Provided motion model n_params are not unique! Cannot decide which motion model to use based on n_obs. Please provide unique motion_models or a 'motion_model_input' column." + assert len(mm_n_params) == len(set(mm_n_params)), \ + f"fit_motion_model: Provided motion model n_params are not unique! Motion Models are: {[_.name for _ in motion_models]} Cannot decide which motion model to use based on n_obs. Please provide unique motion_models or a 'motion_model_input' column." ########################### @@ -684,7 +689,6 @@ def fit_motion_model( if fixed_params_dict is None: weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None fixed_params_dict = {'t0': np.average(t_data, axis=1, weights=weights)} - elif 't0' not in fixed_params_dict: weights = 1/np.hypot(xe_data, ye_data) if xe_data is not None else None fixed_params_dict['t0'] = np.average(t_data, axis=1, weights=weights) @@ -692,8 +696,7 @@ def fit_motion_model( if np.ndim(fixed_params_dict['t0']) == 0: fixed_params_dict['t0'] = np.full(N_stars, fixed_params_dict['t0']) - t0 = fixed_params_dict['t0'] - + t0 = fixed_params_dict['t0'] # Prepare fixed_params_dict for each star # This avoids checking types and slicing inside the fitting loop @@ -734,24 +737,35 @@ def fit_motion_model( ########################### ####### Determine MM ###### ########################### + n_fit = np.array(self['n_fit']) if 'motion_model_input' in self.colnames: # Determine which motion model to use based on motion_model_input column # If n_fit < required n_params for the input motion model, use the most complicated motion model with n_fit >= n_params required_params = np.array([all_mm_map[mm_name].n_params for mm_name in self['motion_model_input']]) + reassign_mm = n_fit < required_params + mm_digitized = np.digitize( - x=np.minimum(np.array(self['n_fit']), required_params), + x=n_fit[reassign_mm], bins=mm_n_params ) - 1 # Convert to 0-based index + # Assign motion models to stars + self['motion_model_used'] = self['motion_model_input'] + self['motion_model_used'][reassign_mm] = np.array([motion_models[d].name for d in mm_digitized], dtype='U20') + else: mm_digitized = np.digitize( - x=np.array(self['n_fit']), + x=n_fit, bins=mm_n_params ) - 1 # Convert to 0-based index - # Assign motion models to stars - self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized], dtype='U20') + # Assign motion models to stars + self['motion_model_used'] = np.array([motion_models[d].name for d in mm_digitized], dtype='U20') + # Add default obsLocation if not provided in fixed_params_dict + mm_used = np.unique(self['motion_model_used'].name) + if 'Parallax' in mm_used and 'obsLocation' not in fixed_params_dict: + fixed_params_dict['obsLocation'] = 'earth' ############################ ####### Prepare Table ###### @@ -786,6 +800,7 @@ def fit_motion_model( for param in mm.fixed_param_names: if param not in fixed_param_names: fixed_param_names.append(param) + # Remove t0 from fixed_param_names as it will be saved during fitting if 't0' in fixed_param_names: fixed_param_names.remove('t0') @@ -943,7 +958,7 @@ def infer_positions(self, times, fill_value=np.nan): # Predict positions x, y, xe, ye = motion_model_instance.model( - times, fit_params, fixed_params, fit_param_errs + times, fit_params, fit_param_errs, fixed_params ) x_pred[unique_index] = x y_pred[unique_index] = y diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index ad082cb..c5ae094 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -410,10 +410,10 @@ def test_MosaicToRef_acc(): ref_list = Table.read(ref_file) # Convert velocities to arcsec/yr - ref_list['vx0'] *= 1e-3 - ref_list['vy0'] *= 1e-3 - ref_list['vx0_err'] *= 1e-3 - ref_list['vy0_err'] *= 1e-3 + ref_list['vx'] *= 1e-3 + ref_list['vy'] *= 1e-3 + ref_list['vx_err'] *= 1e-3 + ref_list['vy_err'] *= 1e-3 # Convert accelerations to arcsec/yr**2 ref_list['ax'] *= 1e-3 @@ -423,7 +423,7 @@ def test_MosaicToRef_acc(): # Switch our list to a "increasing to the West" list. ref_list['x0'] *= -1.0 - ref_list['vx0'] *= -1.0 + ref_list['vx'] *= -1.0 ref_list['ax'] *= -1.0 lists = [starlists.StarList.read(lf) for lf in list_files] From 5a049fe02cd2db035d708b17325b879d599c8b2a Mon Sep 17 00:00:00 2001 From: Wei Lingfeng Date: Fri, 16 Jan 2026 00:17:36 +0900 Subject: [PATCH 29/29] Fix bootstrap index size error --- flystar/motion_model.py | 5 ++--- flystar/tests/test_align.py | 2 +- 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/flystar/motion_model.py b/flystar/motion_model.py index b8cde55..b69f8f2 100644 --- a/flystar/motion_model.py +++ b/flystar/motion_model.py @@ -138,8 +138,6 @@ def fit( n_obs = len(t) if bootstrap > 0 and n_obs > (self.n_params): - # Use m out of n bootstrap to ensure enough unique points - m = np.max([self.n_params, int(len(t) * 0.8)]) rng = np.random.default_rng(seed) edx = np.arange(n_obs, dtype=int) # Precompute All Bootstrap Draws at Once @@ -148,8 +146,9 @@ def fit( rng.choice(edx, size=self.n_params, replace=False) for _ in range(bootstrap) ]) + # Draw with replacement for the rest bdx_extra = np.stack([ - rng.choice(edx, size=self.n_params, replace=True) + rng.choice(edx, size=n_obs - self.n_params, replace=True) for _ in range(bootstrap) ]) bdx_all = np.hstack((bdx_unique, bdx_extra)) diff --git a/flystar/tests/test_align.py b/flystar/tests/test_align.py index c5ae094..3937ea6 100644 --- a/flystar/tests/test_align.py +++ b/flystar/tests/test_align.py @@ -572,7 +572,7 @@ def test_bootstrap(): list1 = starlists.StarList.from_table(list1) list2 = starlists.StarList.from_table(list2) - + # Set parameters for alignment transModel = transforms.PolyTransform trans_args = {'order':2}