zscale.py

from __future__ import division # confidence high

import math
import numpy

MAX_REJECT = 0.5
MIN_NPIXELS = 5
GOOD_PIXEL = 0
BAD_PIXEL = 1
KREJ = 2.5
MAX_ITERATIONS = 5

def zscale (image, nsamples=600, contrast=0.25, bpmask=None, zmask=None):
    """Implement IRAF zscale algorithm

    Parameters
    ----------
    image : arr
        2-d numpy array

    nsamples : int (Default: 1000)
        Number of points in array to sample for determining scaling factors

    contrast : float (Default: 0.25)
        Scaling factor for determining min and max. Larger values increase the
        difference between min and max values used for display.

    bpmask : None
        Not used at this time

    zmask : None
        Not used at this time

    Returns
    -------
    (z1, z2)
    """

    # Sample the image
    samples = zsc_sample (image, nsamples, bpmask, zmask)
    npix = len(samples)
    samples.sort()
    zmin = samples[0]
    zmax = samples[-1]
    # For a zero-indexed array
    center_pixel = (npix - 1) // 2
    if npix%2 == 1:
        median = samples[center_pixel]
    else:
        median = 0.5 * (samples[center_pixel] + samples[center_pixel + 1])

    #
    # Fit a line to the sorted array of samples
    minpix = max(MIN_NPIXELS, int(npix * MAX_REJECT))
    ngrow = max (1, int (npix * 0.01))
    ngoodpix, zstart, zslope = zsc_fit_line (samples, npix, KREJ, ngrow,
                                             MAX_ITERATIONS)

    if ngoodpix < minpix:
        z1 = zmin
        z2 = zmax
    else:
        if contrast > 0: zslope = zslope / contrast
        z1 = max (zmin, median - (center_pixel - 1) * zslope)
        z2 = min (zmax, median + (npix - center_pixel) * zslope)
    return z1, z2

def zsc_sample (image, maxpix, bpmask=None, zmask=None):

    # Figure out which pixels to use for the zscale algorithm
    # Returns the 1-d array samples
    # Don't worry about the bad pixel mask or zmask for the moment
    # Sample in a square grid, and return the first maxpix in the sample
    nc = image.shape[0]
    nl = image.shape[1]
    stride = max (1.0, math.sqrt((nc - 1) * (nl - 1) / float(maxpix)))
    stride = int (stride)
    samples = image[::stride,::stride].flatten()

    return samples[:maxpix]

def zsc_fit_line (samples, npix, krej, ngrow, maxiter):

    #
    # First re-map indices from -1.0 to 1.0
    xscale = 2.0 / (npix - 1)
    xnorm = numpy.arange(npix)
    xnorm = xnorm * xscale - 1.0

    ngoodpix = npix
    minpix = max (MIN_NPIXELS, int (npix*MAX_REJECT))
    last_ngoodpix = npix + 1

    # This is the mask used in k-sigma clipping.  0 is good, 1 is bad
    badpix = numpy.zeros(npix, dtype="int32")

    #
    #  Iterate

    for niter in range(maxiter):

        if (ngoodpix >= last_ngoodpix) or (ngoodpix < minpix):
            break

        # Accumulate sums to calculate straight line fit
        goodpixels = numpy.where(badpix == GOOD_PIXEL)
        sumx = xnorm[goodpixels].sum()
        sumxx = (xnorm[goodpixels]*xnorm[goodpixels]).sum()
        sumxy = (xnorm[goodpixels]*samples[goodpixels]).sum()
        sumy = samples[goodpixels].sum()
        sum = len(goodpixels[0])

        delta = sum * sumxx - sumx * sumx
        # Slope and intercept
        intercept = (sumxx * sumy - sumx * sumxy) / delta
        slope = (sum * sumxy - sumx * sumy) / delta

        # Subtract fitted line from the data array
        fitted = xnorm*slope + intercept
        flat = samples - fitted

        # Compute the k-sigma rejection threshold
        ngoodpix, mean, sigma = zsc_compute_sigma (flat, badpix, npix)

        threshold = sigma * krej

        # Detect and reject pixels further than k*sigma from the fitted line
        lcut = -threshold
        hcut = threshold
        below = numpy.where(flat < lcut)
        above = numpy.where(flat > hcut)

        badpix[below] = BAD_PIXEL
        badpix[above] = BAD_PIXEL

        # Convolve with a kernel of length ngrow
        kernel = numpy.ones(ngrow,dtype="int32")
        badpix = numpy.convolve(badpix, kernel, mode='same')

        ngoodpix = len(numpy.where(badpix == GOOD_PIXEL)[0])

        niter += 1

    # Transform the line coefficients back to the X range [0:npix-1]
    zstart = intercept - slope
    zslope = slope * xscale

    return ngoodpix, zstart, zslope

def zsc_compute_sigma (flat, badpix, npix):

    # Compute the rms deviation from the mean of a flattened array.
    # Ignore rejected pixels

    # Accumulate sum and sum of squares
    goodpixels = numpy.where(badpix == GOOD_PIXEL)
    sumz = flat[goodpixels].sum()
    sumsq = (flat[goodpixels]*flat[goodpixels]).sum()
    ngoodpix = len(goodpixels[0])
    if ngoodpix == 0:
        mean = None
        sigma = None
    elif ngoodpix == 1:
        mean = sumz
        sigma = None
    else:
        mean = sumz / ngoodpix
        temp = sumsq / (ngoodpix - 1) - sumz*sumz / (ngoodpix * (ngoodpix - 1))
        if temp < 0:
            sigma = 0.0
        else:
            sigma = math.sqrt (temp)

    return ngoodpix, mean, sigma