double sncp_model::calculate_normalising_constant(double alpha,double z,double bound){
long double norm =1 ;
if(bound>0){
norm = gsl_cdf_gamma_P(bound,alpha,1.0/(double)z);
}
return norm;
}
void Model::set_custom_prob(double alpha, double scale) {
custom_prob.resize(0);
bool stop = false;
double w = 0.0;
while ((!stop)&(custom_prob.size()<400)) {
w = gsl_cdf_gamma_P(custom_prob.size(), alpha, scale);
custom_prob.push_back(w);
stop = w > 0.99999;
}
for (int i=1; i!=custom_prob.size(); ++i) custom_prob[i-1] = custom_prob[i]-custom_prob[i-1];
custom_prob.pop_back();
}
double
gsl_cdf_poisson_Q (const unsigned int k, const double mu)
{
double Q;
double a;
if (mu <= 0.0)
{
CDF_ERROR ("mu <= 0", GSL_EDOM);
}
a = (double) k + 1.0;
Q = gsl_cdf_gamma_P (mu, a, 1.0);
return Q;
}
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.
BJG: These approximations aren't really valid, the relevant
criterion is P*gamma(a+1) < 1. Need to rework these routines and
use a single bisection style solver for all the inverse
functions.
*/
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 < -0.5*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) < 0.5 * fabs (step0))
step += step1;
if (x + step > 0)
x += step;
else
{
x /= 2.0;
}
if (fabs (step0) > 1e-10 * x || fabs(step0 * phi) > 1e-10 * P)
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 rgamma_inv(void) {
double x = rand_gamma(rng,100,1.0);
return gsl_cdf_gamma_P(x,100,1.0);
}
double
gsl_cdf_chisq_P (const double x, const double nu)
{
return gsl_cdf_gamma_P (x, nu / 2, 2.0);
}
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;
}