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chisquare.cpp
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chisquare.cpp
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#include <cmath>
#include <iostream>
#include <limits>
#include <cstdio>
#include "chisquare.h"
using namespace chisq;
/*
taken from numerical recipis 2007 third edition
modified by thorfinn@binf.ku.dk 30 aug 2013
ppl on the internet complain that numerecial recp can't be used in academic gnu software, will need to check that and use a different impl.
*/
const double Gauleg18::y[18] = {0.0021695375159141994,
0.011413521097787704,0.027972308950302116,0.051727015600492421,
0.082502225484340941, 0.12007019910960293,0.16415283300752470,
0.21442376986779355, 0.27051082840644336, 0.33199876341447887,
0.39843234186401943, 0.46931971407375483, 0.54413605556657973,
0.62232745288031077, 0.70331500465597174, 0.78649910768313447,
0.87126389619061517, 0.95698180152629142};
const double Gauleg18::w[18] = {0.0055657196642445571,
0.012915947284065419,0.020181515297735382,0.027298621498568734,
0.034213810770299537,0.040875750923643261,0.047235083490265582,
0.053244713977759692,0.058860144245324798,0.064039797355015485,
0.068745323835736408,0.072941885005653087,0.076598410645870640,
0.079687828912071670,0.082187266704339706,0.084078218979661945,
0.085346685739338721,0.085983275670394821};
double chisq::gammln(const double xx) {
int j;
double x,tmp,y,ser;
static const double cof[14]={57.1562356658629235,-59.5979603554754912,
14.1360979747417471,-0.491913816097620199,.339946499848118887e-4,
.465236289270485756e-4,-.983744753048795646e-4,.158088703224912494e-3,
-.210264441724104883e-3,.217439618115212643e-3,-.164318106536763890e-3,
.844182239838527433e-4,-.261908384015814087e-4,.368991826595316234e-5};
if (xx <= 0) throw("bad arg in gammln");
y=x=xx;
tmp = x+5.24218750000000000;
tmp = (x+0.5)*log(tmp)-tmp;
ser = 0.999999999999997092;
for (j=0;j<14;j++)
ser += cof[j]/++y;
return tmp+log(2.5066282746310005*ser/x);
}
double Gamma::gammp(const double a, const double x) {
if (x < 0.0 || a <= 0.0)
throw("bad args in gammp");
if (x == 0.0) return 0.0;
else if ((int)a >= ASWITCH) return gammpapprox(a,x,1);
else if (x < a+1.0) return gser(a,x);
else return 1.0-gcf(a,x);
}
double Gamma::gammq(const double a, const double x) {
if (x < 0.0 || a <= 0.0) throw("bad args in gammq");
if (x == 0.0) return 1.0;
else if ((int)a >= ASWITCH)
return gammpapprox(a,x,0);
else if (x < a+1.0) return 1.0-gser(a,x);
else return gcf(a,x);
}
double Gamma::gser(const double a, const double x) {
double sum,del,ap;
gln=gammln(a);
ap=a;
del=sum=1.0/a;
for (;;) {
++ap;
del *= x/ap;
sum += del;
if (fabs(del) < fabs(sum)*EPS) {
return sum*exp(-x+a*log(x)-gln);
}
}
}
double Gamma::gcf(const double a, const double x) {
int i;
double an,b,c,d,del,h;
gln=gammln(a);
b=x+1.0-a;
c=1.0/FPMIN;
d=1.0/b;
h=d;
for (i=1;;i++) {
an = -i*(i-a);
b += 2.0;
d=an*d+b;
if (fabs(d) < FPMIN)
d=FPMIN;
c=b+an/c;
if (fabs(c) < FPMIN)
c=FPMIN;
d=1.0/d;
del=d*c;
h *= del;
if (fabs(del-1.0) <= EPS)
break;
}
return exp(-x+a*log(x)-gln)*h;
}
double Gamma::gammpapprox(double a, double x, int psig) {
int j;
double xu,t,sum,ans;
double a1 = a-1.0, lna1 = log(a1), sqrta1 = sqrt(a1);
gln = gammln(a);
if (x > a1) xu = std::max(a1 + 11.5*sqrta1, x + 6.0*sqrta1);
else xu = std::max(0.,std::min(a1 - 7.5*sqrta1, x - 5.0*sqrta1));
sum = 0;
for (j=0;j<ngau;j++) {
t = x + (xu-x)*y[j];
sum += w[j]*exp(-(t-a1)+a1*(log(t)-lna1));
}
ans = sum*(xu-x)*exp(a1*(lna1-1.)-gln);
return (psig?(ans>0.0? 1.0-ans:-ans):(ans>=0.0? ans:1.0+ans));
}
double Gamma::invgammp(double p, double a) {
int j;
double x,err,t,u,pp,lna1,afac,a1=a-1;
const double EPS=1.e-8;
gln=gammln(a);
if (a <= 0.) throw("a must be pos in invgammap");
if (p >= 1.) return std::max(100.,a + 100.*sqrt(a));
if (p <= 0.) return 0.0;
if (a > 1.) {
lna1=log(a1);
afac = exp(a1*(lna1-1.)-gln);
pp = (p < 0.5)? p : 1. - p;
t = sqrt(-2.*log(pp));
x = (2.30753+t*0.27061)/(1.+t*(0.99229+t*0.04481)) - t;
if (p < 0.5) x = -x;
x = std::max(1.e-3,a*pow(1.-1./(9.*a)-x/(3.*sqrt(a)),3));
} else {
t = 1.0 - a*(0.253+a*0.12);
if (p < t) x = pow(p/t,1./a);
else x = 1.-log(1.-(p-t)/(1.-t));
}
for (j=0;j<12;j++) {
if (x <= 0.0) return 0.0;
err = gammp(a,x) - p;
if (a > 1.) t = afac*exp(-(x-a1)+a1*(log(x)-lna1));
else t = exp(-x+a1*log(x)-gln);
u = err/t;
x -= (t = u/(1.-0.5*std::min(1.,u*((a-1.)/x - 1))));
if (x <= 0.) x = 0.5*(x + t);
if (fabs(t) < EPS*x ) break;
}
return x;
}
const double Gamma::EPS = std::numeric_limits<double>::epsilon();
const double Gamma::FPMIN = std::numeric_limits<double>::min()/EPS;
/*
//in .h now
struct Chisqdist : Gamma {
double nu,fac;
Chisqdist(double nnu) : nu(nnu) {
fac = 0.693147180559945309*(0.5*nu)+gammln(0.5*nu);
}
double p(double x2) {
if (x2 <= 0.) throw("bad x2 in Chisqdist");
return exp(-0.5*(x2-(nu-2.)*log(x2))-fac);
}
double cdf(double x2) {
if (x2 < 0.) throw("bad x2 in Chisqdist");
return gammp(0.5*nu,0.5*x2);
}
double invcdf(double p) {
if (p < 0. || p >= 1.) throw("bad p in Chisqdist");
return 2.*invgammp(p,0.5*nu);
}
};
*/
#ifdef __WITH_MAIN__
int main(int argc, char **argv){
fprintf(stderr,"Thorfinn chisquare function\n------------------\n");
double df;
std::cout << "Type degrees of freedom"<<std::endl;
std::cin >> df;
int type =0;
std::cout << "Type 1-3.\n\t1: density (R::dchisq)\n\t2: cdf (R::pchisq)\n\t3: invcdf (R::qchisq)"<<std::endl;
std::cin>>type;
if(type==0) return 0;
Chisqdist tmp(df);
while(1){
double val;
std::cout << "Type point for evaluation"<<std::endl;
std::cin >>val;
if(type==1)
fprintf(stderr,"Chisquare.p(%f,%f)=%e\n",val,df,tmp.p(val));
if(type==2)
fprintf(stderr,"Chisquare.cdf(%f,%f)=%e\n",val,df,tmp.cdf(val));
if(type==3)
fprintf(stderr,"Chisquare.invcdf(%f,%f)=%e\n",val,df,tmp.invcdf(val));
}
return 0;
}
#endif