iv.cpp

通信系统中的数字信号处理仿真程序

//
// iv.cpp
//
// $Id: iv.cpp,v 1.2 2005/07/21 20:12:04 ediap Exp $
//

#include <cmath>

#include <itpp/base/itassert.h>
#include <itpp/base/scalfunc.h>

#include <itpp/base/bessel/bessel_internal.h>

using namespace itpp;

// This is slightly modified routine from the Cephes library, see http://www.netlib.org/cephes/
//  
// According to licence agreement this software can be used freely.
//

/* 
 *	odified Bessel function of noninteger order
 *
 * double v, x, y, iv();
 *
 * y = iv( v, x );
 *
 * DESCRIPTION:
 *
 * Returns modified Bessel function of order v of the
 * argument.  If x is negative, v must be integer valued.
 *
 * The function is defined as Iv(x) = Jv( ix ).  It is
 * here computed in terms of the confluent hypergeometric
 * function, according to the formula
 *
 *              v  -x
 * Iv(x) = (x/2)  e   hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
 *
 * If v is a negative integer, then v is replaced by -v.
 *
 *
 * ACCURACY:
 *
 * Tested at random points (v, x), with v between 0 and
 * 30, x between 0 and 28.
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0,30         10000      1.7e-14     2.7e-15
 *
 * Accuracy is diminished if v is near a negative integer.
 *
 * See also hyperg.c.
 */

/*	Modified Bessel function of noninteger order		*/
/* If x < 0, then v must be an integer. */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
*/


#define MAXNUM 1.79769313486231570815E308    /* 2**1024*(1-MACHEP) */

double iv(double v, double x)
{
  int sign;
  double t, ax;

  /* If v is a negative integer, invoke symmetry */
  t = floor(v);
  if( v < 0.0 )
    {
      if( t == v )
	{
	  v = -v;	/* symmetry */
	  t = -t;
	}
    }
  /* If x is negative, require v to be an integer */
  sign = 1;
  if( x < 0.0 )
    {
      if( t != v )
	{
	  it_warning("besseli:: argument domain error");
	  //mtherr( "iv", DOMAIN );
	  return( 0.0 );
	}
      if( v != 2.0 * floor(v/2.0) )
	sign = -1;
    }

  /* Avoid logarithm singularity */
  if( x == 0.0 )
    {
      if( v == 0.0 )
	return( 1.0 );
      if( v < 0.0 )
	{
	  it_warning("besseli:: overflow");
	  //mtherr( "iv", OVERFLOW );
	  return( MAXNUM );
	}
      else
	return( 0.0 );
    }

  ax = fabs(x);
  t = v * log( 0.5 * ax )  -  x;
  t = sign * exp(t) / itpp::gamma( v + 1.0 );
  ax = v + 0.5;
  return( t * hyperg( ax,  2.0 * ax,  2.0 * x ) );
}