/* $Id: stdtr.c,v 1.1 2003/04/15 03:20:17 cher Exp $ */

/* This file is taken from Cephes math library */

/*
  Cephes Math Library Release 2.8:  June, 2000
  Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*/

#include "cephes.h"
#include "mconf.h"
#include <math.h>

/*							stdtr.c
 *
 *	Student's t distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * double t, stdtr();
 * short k;
 *
 * y = stdtr( k, t );
 *
 *
 * DESCRIPTION:
 *
 * Computes the integral from minus infinity to t of the Student
 * t distribution with integer k > 0 degrees of freedom:
 *
 *                                      t
 *                                      -
 *                                     | |
 *              -                      |         2   -(k+1)/2
 *             | ( (k+1)/2 )           |  (     x   )
 *       ----------------------        |  ( 1 + --- )        dx
 *                     -               |  (      k  )
 *       sqrt( k pi ) | ( k/2 )        |
 *                                   | |
 *                                    -
 *                                   -inf.
 * 
 * Relation to incomplete beta integral:
 *
 *        1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
 * where
 *        z = k/(k + t**2).
 *
 * For t < -2, this is the method of computation.  For higher t,
 * a direct method is derived from integration by parts.
 * Since the function is symmetric about t=0, the area under the
 * right tail of the density is found by calling the function
 * with -t instead of t.
 * 
 * ACCURACY:
 *
 * Tested at random 1 <= k <= 25.  The "domain" refers to t.
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE     -100,-2      50000       5.9e-15     1.4e-15
 *    IEEE     -2,100      500000       2.7e-15     4.9e-17
 */

/*							stdtri.c
 *
 *	Functional inverse of Student's t distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * double p, t, stdtri();
 * int k;
 *
 * t = stdtri( k, p );
 *
 *
 * DESCRIPTION:
 *
 * Given probability p, finds the argument t such that stdtr(k,t)
 * is equal to p.
 * 
 * ACCURACY:
 *
 * Tested at random 1 <= k <= 100.  The "domain" refers to p:
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE    .001,.999     25000       5.7e-15     8.0e-16
 *    IEEE    10^-6,.001    25000       2.0e-12     2.9e-14
 */

extern double PI, MACHEP, MAXNUM;

double
cephes_stdtr(int k, double t)
{
  double x, rk, z, f, tz, p, xsqk;
  int j;

  if( k <= 0 ) {
    cephes_mtherr( "stdtr", DOMAIN );
    return(0.0);
  }

  if( t == 0 )
    return( 0.5 );

  if( t < -2.0 ) {
    rk = k;
    z = rk / (rk + t * t);
    p = 0.5 * cephes_incbet( 0.5*rk, 0.5, z );
    return( p );
  }

  /*	compute integral from -t to + t */
  if( t < 0 )
    x = -t;
  else
    x = t;

  rk = k;	/* degrees of freedom */
  z = 1.0 + ( x * x )/rk;
  
  /* test if k is odd or even */
  if( (k & 1) != 0) {
    /*	computation for odd k	*/
    xsqk = x/sqrt(rk);
    p = atan( xsqk );
    if( k > 1 ) {
      f = 1.0;
      tz = 1.0;
      j = 3;
      while(  (j<=(k-2)) && ( (tz/f) > MACHEP )  ) {
        tz *= (j-1)/( z * j );
        f += tz;
        j += 2;
      }
      p += f * xsqk/z;
    }
    p *= 2.0/PI;
  } else {
    /*	computation for even k	*/
    f = 1.0;
    tz = 1.0;
    j = 2;

    while(  ( j <= (k-2) ) && ( (tz/f) > MACHEP )  ) {
      tz *= (j - 1)/( z * j );
      f += tz;
      j += 2;
    }
    p = f * x/sqrt(z*rk);
  }

  /*	common exit	*/
  if( t < 0 )
    p = -p;	/* note destruction of relative accuracy */

  p = 0.5 + 0.5 * p;
  return(p);
}

double
cephes_stdtri(int k, double p)
{
  double t, rk, z;
  int rflg;

  if( k <= 0 || p <= 0.0 || p >= 1.0 ) {
    cephes_mtherr( "stdtri", DOMAIN );
    return(0.0);
  }

  rk = k;
  if( p > 0.25 && p < 0.75 ) {
    if( p == 0.5 )
      return( 0.0 );
    z = 1.0 - 2.0 * p;
    z = cephes_incbi( 0.5, 0.5*rk, fabs(z) );
    t = sqrt( rk*z/(1.0-z) );
    if( p < 0.5 )
      t = -t;
    return( t );
  }
  rflg = -1;
  if( p >= 0.5) {
    p = 1.0 - p;
    rflg = 1;
  }
  z = cephes_incbi( 0.5*rk, 0.5, 2.0*p );

  if( MAXNUM * z < rk )
    return(rflg* MAXNUM);
  t = sqrt( rk/z - rk );
  return( rflg * t );
}

/*
 * Local variables:
 *  compile-command: "make -C .."
 * End:
 */