123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190 |
- /* cdf/gammainv.c
- *
- * Copyright (C) 2003, 2007 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_cdf.h"
- #include "gsl_math.h"
- #include "gsl_randist.h"
- #include "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:
- if (fabs(dP) > GSL_SQRT_DBL_EPSILON * P)
- {
- GSL_ERROR_VAL("inverse failed to converge", GSL_EFAILED, GSL_NAN);
- }
-
- 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;
- }
|