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dws_numerical.cpp
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dws_numerical.cpp
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/*************************************************************************/
// FILE NAME: dws_numerical.cpp
// VERSION: $Revision: 1.3 $
// FUNCTION: Dylan Schwilk's numerical function library
// REMARKS:
//-----------------------------------------------------------------------*/
// Copyright © 2003 - 2005
/*-----------------------------------------------------------------------*/
// AUTHOR/S: Dylan W. Schwilk */
//-----------------------------------------------------------------------*/
// CREATION DATE: 2002-08-30
//--------+------+------------------------------------+------------------*/
// REVISION LOG:
//
// $Log: dws_numerical.cpp $
// Revision 1.3 2005/01/26 17:01:27 schwilkd
// Added GNU comment header.
//
// Revision 1.2 2005/01/26 16:58:12 schwilkd
// I made some minor changes to remove dependency on dws_math template
// library. Now dws_math and dws_numerical are independent.
//
// Revision 1.1 2005/01/26 16:56:18 schwilkd
// Initial revision
//
/**************************************************************************/
///////////////////////////////////////////////////////////////////////////
// GNU
// This library is free software; you can redistribute it and/or modify it
// under the terms of the GNU Library General Public License as published
// by the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version. This library 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 Library General Public License for more details.
// You should have received a copy of the GNU Library General Public
// License along with this library; if not, write to the Free Software
// Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
///////////////////////////////////////////////////////////////////////////
#include "dws_numerical.h"
#include <cmath>
#include <cassert>
#include <iostream>
#include <stdexcept>
namespace DWS{
// Static constants
static int MAXIT(100);
void SetMAXIT(int it)
{
MAXIT=it;
}
// local static functions
REAL_TYPE square(REAL_TYPE a);
REAL_TYPE betacf(REAL_TYPE a, REAL_TYPE b, REAL_TYPE x);
void gser(REAL_TYPE *gamser, REAL_TYPE a, REAL_TYPE x, REAL_TYPE *gln); // Num Rec. p. 218.
void gcf(REAL_TYPE *gammcf, REAL_TYPE a, REAL_TYPE x, REAL_TYPE *gln); // Numerical recipes p. 219
/******************************************************************************
* Public Functions
******************************************************************************/
// Function: gammln(x)
//
REAL_TYPE gammln(REAL_TYPE xx)
{
double x,y,tmp,ser;
static double cof[6] =
{
76.18009172947146,-86.50532032941677,24.01409824083091,
-1.231739572450155, 0.1208650973866179e-2,-0.5395239384953e-5
};
int j;
y=x=xx;
tmp=x+5.5;
tmp -= (x+0.5)*std::log(tmp);
ser=1.000000000190015;
for(j=0;j<=5;j++) ser+=cof[j]/++y;
return -tmp+std::log(2.5066282746310005*ser/x);
}
REAL_TYPE gammp(REAL_TYPE a, REAL_TYPE x)
{
REAL_TYPE gamser, gammcf, gln;
assert(!(x<0.0||a<=0.0)); // Invalid arguments
if(x<(a+1.0))
{
gser(&gamser,a,x,&gln);
return gamser;
}
else
{
gcf(&gammcf,a,x,&gln);
return 1.0-gammcf;
}
}
REAL_TYPE gammq(REAL_TYPE a, REAL_TYPE x)
{
REAL_TYPE gamser, gammcf, gln;
assert(!(x<0.0||a<=0.0)); // Invalid arguments
if(x<(a+1.0))
{
gser(&gamser,a,x,&gln);
return 1.0-gamser;
}
else
{
gcf(&gammcf,a,x,&gln);
return gammcf;
}
}
/* Incomplete beta function
* ------------------------
* Numerical Recipes pg 227
*/
REAL_TYPE betai(REAL_TYPE a, REAL_TYPE b, REAL_TYPE x)
{
REAL_TYPE bt;
if(x<0.00||x>1.00) throw(std::invalid_argument(std::string("betai():x must be between 0.0 and 1.0")));
if(x==0.0 || x==1.0) bt=0.0;
else bt=std::exp(gammln(a+b)-gammln(a)-gammln(b)+a*std::log(x)+b*std::log(1.0-x));
if(x< (a+1.0)/(a+b+2.0))
{
return (bt*betacf(a,b,x)/a);
}
else
{
return(1.0-bt*betacf(b,a,1.0-x)/b);
}
}
REAL_TYPE erff(REAL_TYPE x)
{
return x<0.0?1.0+gammp(0.5,x*x):gammq(0.5,x*x);
}
////////////////////////////////////////////////////////////////////////////
// Classes
////////////////////////////////////////////////////////////////////////////
void QuadraticT::Solve(REAL_TYPE& first, REAL_TYPE& second ) const
{
REAL_TYPE root = std::sqrt(_b*_b-4*_a*_c)/2*_a;
first = -_b+ root;
second = -_b-root;
}
REAL_TYPE QuadraticT::DSolve() const
{
return(_b/(-2.0*_a));
}
////////////////////////////////////////////////////////////////////////////
// Static functions
////////////////////////////////////////////////////////////////////////////
inline REAL_TYPE square(REAL_TYPE a)
{
return a*a;
}
// Num Rec. p. 218. Returns incomplete gamma fctn P(a,x)
// evaluated by its series representation gamser
void gser(REAL_TYPE *gamser, REAL_TYPE a, REAL_TYPE x, REAL_TYPE *gln)
{
REAL_TYPE sum,del,ap;
assert(x>=0.0);
*gln=gammln(a);
if(x<=0.0)
{
*gamser=0.0;
return;
}
else
{
ap=a;
del=sum=1.0/a;
for(int n=1;n<=MAXIT;n++)
{
++ap;
del *= x/ap;
if(std::abs(del) < std::abs(sum)*EPS)
{
*gamser=sum*std::exp(-x+a*std::log(x)-(*gln));
return;
}
}
throw(std::range_error("a too large, MAXIT too small in routine gser"));
}
}
/* Function: gcf
* -------------
* Numerical recipes p. 219
* Returns Incomplete gamma fctn Q(a,x) evaluated by it's continued
* fraction representation as gammcf
*/
void gcf(REAL_TYPE *gammcf, REAL_TYPE a, REAL_TYPE x, REAL_TYPE *gln)
{
int i;
REAL_TYPE an,b,c,d,del,h;
*gln=gammln(a);
b=x+1.0-a;
c=1.0/REAL_MIN;
d=1.0/b;
h=d;
for(i=1;i<=MAXIT;i++)
{
an=-i*(i-a);
b+=2.0;
d=an*d+b;
if(std::abs(d)<REAL_MIN) d =REAL_MIN;
c=b+an/c;
if(std::abs(c) < REAL_MIN) c=REAL_MIN;
d=1.0/d;
del=d*c;
h*=del;
if(std::abs(del-1.0) < EPS) break;
}
if(i>MAXIT) throw(std::range_error("a too large, MAXIT too small in routine gcf"));
*gammcf=std::exp(-x+a*std::log(x)-(*gln))*h;
}
/* Function: betacf
----------------
* Used by betai. evaluates continued fractin for incomplete
* beta function by modified Lentz's method.
*/
REAL_TYPE betacf(REAL_TYPE a, REAL_TYPE b, REAL_TYPE x)
{
int m,m2;
REAL_TYPE h, aa,c,d, del,qab, qam, qap;
qab=a+b;
qap=a+1.0;
qam=a-1.0;
c=1.0;
d = 1.0-qab*x/qap;
if(std::abs(d) < REAL_MIN) d=REAL_MIN;
d=1.0/d;
h=d;
for(m=1;m<=MAXIT;m++)
{
m2=2*m;
aa=m*(b-m)*x/((qam+m2)*(a+m2));
d=1.0+aa*d;
if( std::abs(d) < REAL_MIN) d=REAL_MIN;
c=1.0+aa/c;
if(std::abs(c) < REAL_MIN) c=REAL_MIN;
d=1.0/d;
h*=d*c;
aa= -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
d=1.0+aa*d;
if( std::abs(d) < REAL_MIN) d=REAL_MIN;
c=1.0+aa/c;
if(std::abs(c) < REAL_MIN) c=REAL_MIN;
d=1.0/d;
del=d*c;
h *= del;
if(std::abs(del-1.0) < EPS) break;
}
if(m>MAXIT) throw(std::range_error("MAXIT too small in function betacf()"));
return h;
}
/* function: factrl(int n)
* ------------------------
* Numerical Recipes Pg 214
*/
REAL_TYPE factrl(int n)
{
static int ntop=4;
static REAL_TYPE a[33]={1.0,1.0,2.0,6.0,24.0};
int j;
if(n<0) throw std::logic_error("negative factorial in routine factrl");
if(n>32) return std::exp(gammln(n+1.0));
while(ntop<n)
{
j=ntop++;
a[ntop]=a[j]*ntop;
}
return a[n];
}
/* function bico(int n, int k)
* ----------------------------
* Binomial coefficient
*/
REAL_TYPE bico(int n, int k)
{
return std::floor(0.5+std::exp(factln(n)-factln(k)-factln(n-k)));
}
// function: factln
// ----------------
REAL_TYPE factln(int n)
{
static REAL_TYPE a[101];
if (n<0) throw std::logic_error("Negative factorial in function factln, dwsmath");
if(n<=1) return 0.0;
if (n<= 100) return a[n]?a[n]:(a[n]=gammln(n+1.0));
else return gammln(n+1.0); // out of range table
}
// function: normal_probability
// ----------------------------
REAL_TYPE normal_probability(REAL_TYPE distance, REAL_TYPE sd)
{
static const double SQRT2PI(2.5066282746310005024147107274575);
double twoSDSqr = square(2.0*sd);
return (std::pow(E, - square(distance) / twoSDSqr) / SQRT2PI ); //
}
}; // namespace DWS