/* Analytical solution for change point for given CDF and change point
k0 as well as hyperparameters alpha and beta */
double probChangePoint(const int *CDF, int k0, int n,
double alpha, double beta) {
int succIn1=CDF[k0], failIn1 = k0-CDF[k0];
int succIn2=CDF[n-1]-CDF[k0], failIn2 = n-k0-succIn2;
int status;
double p1,p2;
gsl_sf_result result;
/* fprintf(OUT, "Successes until k0 = %i: %i\n", k0, succIn1); */
/* fprintf(OUT, "Failures: %i\n", failIn1); */
/* fprintf(OUT, "\nSuccesses after k0 = %i: %i\n", k0, succIn2); */
/* fprintf(OUT, "Failures: %i\n", failIn2); */
status = gsl_sf_beta_e (succIn1+alpha+1, failIn1+beta+1, &result);
if(status != GSL_SUCCESS) {
fprintf(ERR, "Evaluation of beta function B(%f,%f) failed.\n",
succIn1+alpha+1, failIn1+beta+1);
exit(1);
}
p1=result.val;
status = gsl_sf_beta_e (succIn2+alpha+1, failIn2+beta+1, &result);
if(status != GSL_SUCCESS) {
fprintf(ERR, "Evaluation of beta function B(%f,%f) failed.\n",
succIn2+alpha+1, failIn2+beta+1);
exit(1);
}
p2=result.val;
return p1*p2;
}
/// Beta functions.
double
beta(double x, double y)
{
gsl_sf_result result;
int stat = gsl_sf_beta_e(x, y, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in beta:");
msg << " x=" << x << " y=" << y;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
double gsl_sf_beta(const double x, const double y)
{
EVAL_RESULT(gsl_sf_beta_e(x, y, &result));
}
int
gsl_sf_beta_inc_e(
const double a,
const double b,
const double x,
gsl_sf_result * result
)
{
if(x < 0.0 || x > 1.0) {
DOMAIN_ERROR(result);
} else if (isnegint(a) || isnegint(b)) {
DOMAIN_ERROR(result);
} else if (isnegint(a+b)) {
DOMAIN_ERROR(result);
} else if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(x == 1.0) {
result->val = 1.0;
result->err = 0.0;
return GSL_SUCCESS;
} else if (a <= 0 || b <= 0) {
gsl_sf_result f, beta;
int stat;
const int stat_f = gsl_sf_hyperg_2F1_e(a, 1-b, a+1, x, &f);
const int stat_beta = gsl_sf_beta_e(a, b, &beta);
double prefactor = (pow(x, a) / a);
result->val = prefactor * f.val / beta.val;
result->err = fabs(prefactor) * f.err/ fabs(beta.val) + fabs(result->val/beta.val) * beta.err;
stat = GSL_ERROR_SELECT_2(stat_f, stat_beta);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
} else {
gsl_sf_result ln_beta;
gsl_sf_result ln_x;
gsl_sf_result ln_1mx;
gsl_sf_result prefactor;
const int stat_ln_beta = gsl_sf_lnbeta_e(a, b, &ln_beta);
const int stat_ln_1mx = gsl_sf_log_1plusx_e(-x, &ln_1mx);
const int stat_ln_x = gsl_sf_log_e(x, &ln_x);
const int stat_ln = GSL_ERROR_SELECT_3(stat_ln_beta, stat_ln_1mx, stat_ln_x);
const double ln_pre_val = -ln_beta.val + a * ln_x.val + b * ln_1mx.val;
const double ln_pre_err = ln_beta.err + fabs(a*ln_x.err) + fabs(b*ln_1mx.err);
const int stat_exp = gsl_sf_exp_err_e(ln_pre_val, ln_pre_err, &prefactor);
if(stat_ln != GSL_SUCCESS) {
result->val = 0.0;
result->err = 0.0;
GSL_ERROR ("error", GSL_ESANITY);
}
if(x < (a + 1.0)/(a+b+2.0)) {
/* Apply continued fraction directly. */
gsl_sf_result cf;
const int stat_cf = beta_cont_frac(a, b, x, &cf);
int stat;
result->val = prefactor.val * cf.val / a;
result->err = (fabs(prefactor.err * cf.val) + fabs(prefactor.val * cf.err))/a;
stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
}
else {
/* Apply continued fraction after hypergeometric transformation. */
gsl_sf_result cf;
const int stat_cf = beta_cont_frac(b, a, 1.0-x, &cf);
int stat;
const double term = prefactor.val * cf.val / b;
result->val = 1.0 - term;
result->err = fabs(prefactor.err * cf.val)/b;
result->err += fabs(prefactor.val * cf.err)/b;
result->err += 2.0 * GSL_DBL_EPSILON * (1.0 + fabs(term));
stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf);
if(stat == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
}
return stat;
}
}
}
