| /* 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; |
| } |