[Bug-gsl] [bug #45924] Bug in the inverse beta function gsl_cdf_beta_Pinv, and suggested fix

[Patrick Alken]

URL:
  <http://savannah.gnu.org/bugs/?45924>

                 Summary: Bug in the inverse beta function gsl_cdf_beta_Pinv,
and suggested fix
                 Project: GNU Scientific Library
            Submitted by: psa
            Submitted on: Fri 11 Sep 2015 10:06:25 AM GMT
                Category: Runtime error
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

    _______________________________________________________

Details:

from jorg =at= google =dot= com

For low or high values of P, the inverse beta function fails to converge.
Here are some inputs and results (the boost inverse-beta function is
included for context.)

a: 8000, b:2000, p: 0.995,   boost: 0.810189,  gsl:nan
a: 8000, b:2000, p: 0.005,   boost: 0.789585,  gsl:nan
a: 8000, b:2000, p: 0.99995, boost: 0.815275,  gsl:nan
a: 8000, b:2000, p: 5e-05,   boost: 0.78416,   gsl:nan
a: 630,  b:9370, p: 0.995,   boost: 0.0694215, gsl:nan
a: 630,  b:9370, p: 0.99995, boost: 0.0728637, gsl:nan
a: 5000, b:5000, p: 0.995,   boost: 0.512877,  gsl:nan
a: 5000, b:5000, p: 0.005,   boost: 0.487123,  gsl:nan
a: 5000, b:5000, p: 0.99995, boost: 0.519446,  gsl:nan
a: 5000, b:5000, p: 5e-05,   boost: 0.480554,  gsl:nan

As I looked into this bug, what appears to be going on is that the call to
bisect does an early return, thinking that the initial guess is good
enough.  But the early guess is too far away for the rest of the routine to
converge.

If I change these two lines:

  /* Do bisection to get closer */
  x = bisect (x, P, a, b, 0.01, 0.01);

To this:

  /* Do bisection to get closer */
  if (P < 0.1) {
    x = bisect (x, P, a, b, P/10, P/10);
  } else {
    x = bisect (x, P, a, b, 0.01, 0.01);
  }

Then the problem goes away.

Boilerplate follows:
Version number of GSL: 1.16, however the latest sources downloaded from git
appear to have the same problem.
Hardware and OS: HP Z620, Ubuntu Trusty
Compiler used: either gcc or clang, optimized or not.
Short program which exercises the bug:

(Code is in C++11)

#include <iostream>
#include "third_party/gsl/gsl_1_16/cdf/gsl_cdf.h"

int main(int argc, char *argv[]) {
  std::cout << "Hello World\n";
  struct Test {
    double a;
    double b;
    double p;
    double x;
  } test_cases[] = {
                 {8000, 2000, 0.995,   0.810189},
                 {8000, 2000, 0.005,   0.789585},
                 {8000, 2000, 0.99995, 0.815275},
                 {8000, 2000, 0.00005, 0.78416},
                 { 630, 9370, 0.995,   0.0694215},
                 { 630, 9370, 0.99995, 0.0728637},
                 {5000, 5000, 0.995,   0.512877},
                 {5000, 5000, 0.005,   0.487123},
                 {5000, 5000, 0.99995, 0.519446},
                 {5000, 5000, 0.00005, 0.480554},
               };
  // beta function
  for (auto t : test_cases) {
    std::cout << "a=" << t.a << " b=" << t.b << " x=" << t.x << " gsl=" <<
gsl_cdf_beta_P(t.x, t.a, t.b) << "\n";
  }
  // inverse beta function
  for (auto t : test_cases) {
    std::cout << "a=" << t.a << " b=" << t.b << " p=" << t.p << " gsl=" <<
gsl_cdf_beta_Pinv(t.p, t.a, t.b) << "\n";
  }
}





    _______________________________________________________

Reply to this item at:

  <http://savannah.gnu.org/bugs/?45924>

_______________________________________________
  Message sent via/by Savannah
  http://savannah.gnu.org/