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/*!
* \file
* \brief Implementation of modified Bessel functions of noninteager order
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* -------------------------------------------------------------------------
*
* This is slightly modified routine from the Cephes library:
* http://www.netlib.org/cephes/
*/
#include <itpp/base/bessel/bessel_internal.h>
#include <itpp/base/itassert.h>
/*
* Modified 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.
*/
/* Mdified 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("iv(): argument domain error");
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("iv(): overflow range error");
return( MAXNUM );
}
else
return( 0.0 );
}
ax = fabs(x);
t = v * log( 0.5 * ax ) - x;
t = sign * exp(t) / gam( v + 1.0 );
ax = v + 0.5;
return( t * hyperg( ax, 2.0 * ax, 2.0 * x ) );
}
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