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#include <math.h> |
#include <math.h> |
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#include <gsl/gsl_cdf.h> |
#include <gsl/gsl_cdf.h> |
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#include <gsl/gsl_math.h> |
#include <gsl/gsl_math.h> |
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#include <gsl/gsl_randist.h> |
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#include <gsl/gsl_sf_gamma.h> |
#include <gsl/gsl_sf_gamma.h> |
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|
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#include <stdio.h> |
#include <stdio.h> |
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double |
double |
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gsl_cdf_gamma_Pinv (double p, double a, double b) |
gsl_cdf_gamma_Pinv (double p, double a, double b) |
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{ |
{ |
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double x, xc; |
double x; |
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|
|
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if (p == 1.0) |
if (p == 1.0) |
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{ |
{ |
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return 0.0; |
return 0.0; |
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} |
} |
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|
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if (p < 0.05) |
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{ |
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double x0 = exp((lgamma(b) + log(p))/b); |
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x = x0; |
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} |
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else if (p > 0.95) |
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{ |
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double x0 = -log(1-p) + lgamma(b); |
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x = x0; |
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} |
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else |
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{ |
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double xg = gsl_cdf_ugaussian_Pinv (p); |
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double x0 = (xg < -sqrt(b)) ? b : sqrt (b) * xg + b; |
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x = x0; |
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} |
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|
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/* Use Lagrange's interpolation for E(x)/phi(x0) to work backwards |
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to an improved value of x (Abramowitz & Stegun, 3.6.6) |
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|
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where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf. |
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*/ |
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|
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{ |
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double lambda, dp, phi; |
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|
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start: |
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dp = p - gsl_cdf_gamma_P (x, 1.0, b) ; |
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phi = gsl_ran_gamma_pdf (x, 1.0, b); |
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|
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if (dp == 0.0) |
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goto end; |
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|
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lambda = dp / GSL_MAX(2*fabs(dp/x), phi); |
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|
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{ |
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double step0 = lambda; |
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double step1 = -((b-1)/x - 1)*lambda*lambda/4.0; |
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|
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double step = step0; |
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if (fabs(step1) < fabs(step0)) |
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step += step1; |
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|
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if (x + step > 0) |
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x += step; |
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else |
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{ |
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x /= 2.0; |
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} |
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|
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if (fabs(step0) > 1e-10*x) |
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goto start; |
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} |
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|
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} |
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|
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end: |
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return a * x; |
return a * x; |
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} |
} |
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