diff options
Diffstat (limited to 'gsl-1.9/cdf/gammainv.c')
| -rw-r--r-- | gsl-1.9/cdf/gammainv.c | 185 |
1 files changed, 185 insertions, 0 deletions
diff --git a/gsl-1.9/cdf/gammainv.c b/gsl-1.9/cdf/gammainv.c new file mode 100644 index 0000000..47a77dd --- /dev/null +++ b/gsl-1.9/cdf/gammainv.c @@ -0,0 +1,185 @@ +/* cdf/gammainv.c + * + * Copyright (C) 2003 Brian Gough + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA. + */ + +#include <config.h> +#include <math.h> +#include <gsl/gsl_cdf.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_randist.h> +#include <gsl/gsl_sf_gamma.h> + +#include <stdio.h> + +double +gsl_cdf_gamma_Pinv (const double P, const double a, const double b) +{ + double x; + + if (P == 1.0) + { + return GSL_POSINF; + } + else if (P == 0.0) + { + return 0.0; + } + + /* Consider, small, large and intermediate cases separately. The + boundaries at 0.05 and 0.95 have not been optimised, but seem ok + for an initial approximation. */ + + if (P < 0.05) + { + double x0 = exp ((gsl_sf_lngamma (a) + log (P)) / a); + x = x0; + } + else if (P > 0.95) + { + double x0 = -log1p (-P) + gsl_sf_lngamma (a); + x = x0; + } + else + { + double xg = gsl_cdf_ugaussian_Pinv (P); + double x0 = (xg < -sqrt (a)) ? a : sqrt (a) * xg + a; + x = x0; + } + + /* Use Lagrange's interpolation for E(x)/phi(x0) to work backwards + to an improved value of x (Abramowitz & Stegun, 3.6.6) + + where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. + */ + + { + double lambda, dP, phi; + unsigned int n = 0; + + start: + dP = P - gsl_cdf_gamma_P (x, a, 1.0); + phi = gsl_ran_gamma_pdf (x, a, 1.0); + + if (dP == 0.0 || n++ > 32) + goto end; + + lambda = dP / GSL_MAX (2 * fabs (dP / x), phi); + + { + double step0 = lambda; + double step1 = -((a - 1) / x - 1) * lambda * lambda / 4.0; + + double step = step0; + if (fabs (step1) < fabs (step0)) + step += step1; + + if (x + step > 0) + x += step; + else + { + x /= 2.0; + } + + if (fabs (step0) > 1e-10 * x) + goto start; + } + + } + +end: + return b * x; +} + +double +gsl_cdf_gamma_Qinv (const double Q, const double a, const double b) +{ + double x; + + if (Q == 1.0) + { + return 0.0; + } + else if (Q == 0.0) + { + return GSL_POSINF; + } + + /* Consider, small, large and intermediate cases separately. The + boundaries at 0.05 and 0.95 have not been optimised, but seem ok + for an initial approximation. */ + + if (Q < 0.05) + { + double x0 = -log (Q) + gsl_sf_lngamma (a); + x = x0; + } + else if (Q > 0.95) + { + double x0 = exp ((gsl_sf_lngamma (a) + log1p (-Q)) / a); + x = x0; + } + else + { + double xg = gsl_cdf_ugaussian_Qinv (Q); + double x0 = (xg < -sqrt (a)) ? a : sqrt (a) * xg + a; + x = x0; + } + + /* Use Lagrange's interpolation for E(x)/phi(x0) to work backwards + to an improved value of x (Abramowitz & Stegun, 3.6.6) + + where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. + */ + + { + double lambda, dQ, phi; + unsigned int n = 0; + + start: + dQ = Q - gsl_cdf_gamma_Q (x, a, 1.0); + phi = gsl_ran_gamma_pdf (x, a, 1.0); + + if (dQ == 0.0 || n++ > 32) + goto end; + + lambda = -dQ / GSL_MAX (2 * fabs (dQ / x), phi); + + { + double step0 = lambda; + double step1 = -((a - 1) / x - 1) * lambda * lambda / 4.0; + + double step = step0; + if (fabs (step1) < fabs (step0)) + step += step1; + + if (x + step > 0) + x += step; + else + { + x /= 2.0; + } + + if (fabs (step0) > 1e-10 * x) + goto start; + } + + } + +end: + return b * x; +} |