From c30d5119b226ae94a8cff56f2c09410d0ab3481d Mon Sep 17 00:00:00 2001 From: Dhruva Date: Sat, 10 Feb 2024 12:16:20 -0500 Subject: [PATCH 1/9] added functions --- .../preprocessor/inf_functions/bessel.c | 147 + .../inf_functions/gsl-latest.tar.gz | Bin 0 -> 7509209 bytes .../preprocessor/inf_functions/header.h | 7 + .../preprocessor/inf_functions/series.c | 7453 +++++++++++++++++ .../preprocessor/inf_functions/series.pyx | 54 + .../preprocessor/inf_functions/setup.py | 33 + 6 files changed, 7694 insertions(+) create mode 100644 matdeeplearn/preprocessor/inf_functions/bessel.c create mode 100644 matdeeplearn/preprocessor/inf_functions/gsl-latest.tar.gz create mode 100644 matdeeplearn/preprocessor/inf_functions/header.h create mode 100644 matdeeplearn/preprocessor/inf_functions/series.c create mode 100644 matdeeplearn/preprocessor/inf_functions/series.pyx create mode 100644 matdeeplearn/preprocessor/inf_functions/setup.py diff --git a/matdeeplearn/preprocessor/inf_functions/bessel.c b/matdeeplearn/preprocessor/inf_functions/bessel.c new file mode 100644 index 00000000..81c3f6a4 --- /dev/null +++ b/matdeeplearn/preprocessor/inf_functions/bessel.c @@ -0,0 +1,147 @@ +#include +#include +#include +#include +#include + + +/* Codes are based on https://github.com/scafacos/scafacos */ + +/* Compute the incomplete Bessel-K function of order nu according to the paper + Richard M. Slevinsky and Hassan Safouhi. 2010. + A recursive algorithm for the G transformation and accurate computation of incomplete Bessel functions. + Appl. Numer. Math. 60, 12 (December 2010), 1411-1417. + http://dx.doi.org/10.1016/j.apnum.2010.04.005 +*/ + +#define FLOAT_PREC 1.0e-14 + + +int is_equal(double x, double y) { + return (fabs(x-y) < FLOAT_PREC); +} + +int is_zero(double x) { + return (fabs(x) < FLOAT_PREC); +} + +/*************************************************/ +/* wrappers for Bessel K and inc. */ +/*************************************************/ + +double upper_bessel_k(double nu, double x, double y, double eps) { + if (is_zero(x)) { + return pow(y, -nu) * (gsl_sf_gamma(nu) - gsl_sf_gamma_inc(nu, y)); + } + + int n = 2, n_max = 127; + double err = 1.0, val_new, val_old; + double N[4], D[4]; + + if (-21 <= nu && nu <= 21) { + if (x > 111) return 0.0; + if (x < y) if (x * y > 58.0 * 58.0) return 0.0; + } else { + const double bound = 1e-50; + + if (nu >= -1) { + if (x > gsl_sf_lambert_W0(1 / bound)) return 0.0; + } else { + double fak = 1.0; + for (int t = 1; t < -nu; t++) + fak *= t; + + if (fak * exp(1 - x) * pow(x, -1) < bound) return 0.0; + } + } + + if (is_zero(y)) + return pow(x, nu) * gsl_sf_gamma_inc(-nu, x); + + if (is_zero(nu)) { + if (pow(x, 2) + pow(y, 2) < pow(0.75, 2)) { + int k = 0; + double fak = 1.0; + double z = 0.0; + while (exp(-x) * pow(y, k + 1) / (x * (k + 1) * fak) > eps) { + z += pow(-1, k) * pow(x * y, k) * gsl_sf_gamma_inc(-k, x) / fak; + k += 1; + fak *= k; + } + return z; + } + } + + N[0] = 0.0; + N[1] = 1.0; + N[2] = 0.5 * (x + nu + 3.0 - y) * N[1]; + N[3] = (x + nu + 5.0 - y) * N[2] + (2.0 * y - nu - 2.0) * N[1]; + N[3] = N[3] / 3.0; + + D[0] = exp(x + y); + D[1] = (x + nu + 1.0 - y) * D[0]; + D[2] = 0.5 * (x + nu + 3.0 - y) * D[1] + 0.5 * (2.0 * y - nu - 1.0) * D[0]; + D[3] = (x + nu + 5.0 - y) * D[2] + (2.0 * y - nu - 2.0) * D[1] - y * D[0]; + D[3] = D[3] / 3.0; + + val_old = N[2] / D[2]; + val_new = N[3] / D[3]; + + err = fabs(val_new - val_old); + + while (err > eps) { + + if (fabs(val_new) < eps) + break; + + if (n >= n_max) { + break; + } + n++; + + val_old = val_new; + + N[0] = N[1]; + N[1] = N[2]; + N[2] = N[3]; + + D[0] = D[1]; + D[1] = D[2]; + D[2] = D[3]; + + N[3] = (x + nu + 1 + 2 * n - y) * N[2] + (2 * y - nu - n) * N[1] - y * N[0]; + N[3] = N[3] / (n + 1); + + D[3] = (x + nu + 1 + 2 * n - y) * D[2] + (2 * y - nu - n) * D[1] - y * D[0]; + D[3] = D[3] / (n + 1); + + val_new = N[3] / D[3]; + + if (isnan(val_new)) { + val_new = val_old; + break; + } + + if (is_zero(val_new)) { + val_new = val_old; + break; + } + + if (isinf(val_new)) { + val_new = val_old; + break; + } + + err = fabs(val_new - val_old); + } + + return val_new; +} + +/*************************************************/ +/* wrappers for Bessel K and low. */ +/*************************************************/ + +double lower_bessel_k(double nu, double x, double y, double eps) { + return upper_bessel_k(-nu, y, x, eps); +} diff --git a/matdeeplearn/preprocessor/inf_functions/gsl-latest.tar.gz b/matdeeplearn/preprocessor/inf_functions/gsl-latest.tar.gz new file mode 100644 index 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