//chstwo ---- calculates chi-square for two distributions
// After Numerical Recipes in C
void Test::chstwo(double bins1[], int n1, double bins2[], int n2, int nbins,
int knstrn, float *df, float *chsq, double *prob) {
int j;
float temp;
*df = nbins - knstrn;
*chsq = 0.0;
float ratio1;
float ratio2;
if (n1 > 0) {
ratio1 = (float) (((float) sqrt(n2)) / ((float) sqrt(n1)));
}
else {
ratio1 = 0.0;
}
if (n2 > 0) {
ratio2 = (float) (((float) sqrt(n1)) / ((float) sqrt(n2)));
}
else {
ratio2 = 0.0;
}
for (j = 0; j < nbins; j++) {
if (bins1[j] == 0.0 && bins2[j] == 0.0) {
--(*df); //No data means one less degree of freedom
}
else {
temp = ratio1 * bins1[j] * n1 - ratio2 * bins2[j] * n2;
*chsq += temp * temp / (bins1[j] * n1 + bins2[j] * n2);
}
}
*prob = gammq(0.5 * (*df), 0.5 * (*chsq));
}
float erffc(float x)
{
float gammp(float a, float x);
float gammq(float a, float x);
return x < 0.0 ? 1.0+gammp(0.5,x*x) : gammq(0.5,x*x);
}
void fit(float x[], float y[], int ndata, float sig[], int mwt, float *a,
float *b, float *siga, float *sigb, float *chi2, float *q)
{
float gammq(float a, float x);
int i;
float wt,t,sxoss,sx=0.0,sy=0.0,st2=0.0,ss,sigdat;
*b=0.0;
if (mwt) {
ss=0.0;
for (i=1;i<=ndata;i++) {
wt=1.0/SQR(sig[i]);
ss += wt;
sx += x[i]*wt;
sy += y[i]*wt;
}
} else {
for (i=1;i<=ndata;i++) {
sx += x[i];
sy += y[i];
}
ss=ndata;
}
sxoss=sx/ss;
if (mwt) {
for (i=1;i<=ndata;i++) {
t=(x[i]-sxoss)/sig[i];
st2 += t*t;
*b += t*y[i]/sig[i];
}
} else {
for (i=1;i<=ndata;i++) {
t=x[i]-sxoss;
st2 += t*t;
*b += t*y[i];
}
}
*b /= st2;
*a=(sy-sx*(*b))/ss;
*siga=sqrt((1.0+sx*sx/(ss*st2))/ss);
*sigb=sqrt(1.0/st2);
*chi2=0.0;
if (mwt == 0) {
for (i=1;i<=ndata;i++)
*chi2 += SQR(y[i]-(*a)-(*b)*x[i]);
*q=1.0;
sigdat=sqrt((*chi2)/(ndata-2));
*siga *= sigdat;
*sigb *= sigdat;
} else {
for (i=1;i<=ndata;i++)
*chi2 += SQR((y[i]-(*a)-(*b)*x[i])/sig[i]);
*q=gammq(0.5*(ndata-2),0.5*(*chi2));
}
}
void fit(real *x, real *y,int ndata,real *sig,int mwt,
real *a, real *b,real *siga,real *sigb,real *chi2,real *q)
{
int i;
real wt,t,sxoss,sx=0.0,sy=0.0,st2=0.0,ss,sigdat;
*b=0.0;
if (mwt) {
ss=0.0;
for (i=0;i<ndata;i++) {
wt=1.0/sqr(sig[i]);
ss += wt;
sx += x[i]*wt;
sy += y[i]*wt;
}
} else {
for (i=0;i<ndata;i++) {
sx += x[i];
sy += y[i];
}
ss=ndata;
}
sxoss=sx/ss;
if (mwt) {
for (i=0;i<ndata;i++) {
t=(x[i]-sxoss)/sig[i];
st2 += t*t;
*b += t*y[i]/sig[i];
}
} else {
for (i=0;i<ndata;i++) {
t=x[i]-sxoss;
st2 += t*t;
*b += t*y[i];
}
}
*b /= st2;
*a=(sy-sx*(*b))/ss;
*siga=sqrt((1.0+sx*sx/(ss*st2))/ss);
*sigb=sqrt(1.0/st2);
*chi2=0.0;
if (mwt == 0) {
for (i=0;i<ndata;i++)
*chi2 += sqr(y[i]-(*a)-(*b)*x[i]);
*q=1.0;
sigdat=sqrt((*chi2)/(ndata-2));
*siga *= sigdat;
*sigb *= sigdat;
} else {
for (i=0;i<ndata;i++)
*chi2 += sqr((y[i]-(*a)-(*b)*x[i])/sig[i]);
*q=gammq(0.5*(ndata-2),0.5*(*chi2));
}
}
void AssocChi::Calc(int ** nn, int ni, int nj)
{
int nnj, nni, j, i, minij;
double expected, temp;
Vector sumi(ni), sumj(nj);
sumi.Zero();
sumj.Zero();
sum = 0.0;
nni = ni;
nnj = nj;
// Get the row totals
for (i = 0; i < ni; i++)
{
for ( j = 0; j < nj; j++)
{
sumi[i] += nn[i][j];
sum += nn[i][j];
}
if ( sumi[i] < FPMIN) --nni; // eliminate zero rows by reducing number
}
// Get the column totals
for (j = 0; j < nj; j++)
{
for ( i = 0; i < ni; i++ )
sumj[j] += nn[i][j];
if ( sumj[j] < FPMIN) --nnj; // eliminated any zero columns
}
df = nni * nnj - nni - nnj + 1; // corrected degrees of freedom
chisq = 0.0;
for (i = 0; i < ni; i++)
{
for (j = 0; j < nj; j++)
{
expected = sumj[j] * sumi[i] / sum;
temp = nn[i][j] - expected;
chisq += temp * temp / (expected + TINY);
}
}
prob = df ? gammq ( 0.5 * df, 0.5 * chisq ) : 1.0;
lop = prob > 1e-100 ? -log10(prob) : 99.999;
minij = nni < nnj ? nni - 1 : nnj - 1;
cramrv = minij ? sqrt ( chisq / ( sum * minij ) ) : 0.0;
ccc = sum ? sqrt ( chisq / ( chisq + sum) ) : 0.0;
isValid = 1;
}
//Returns the complementary error function erfc(x).
double erffc(double x)
{
double retval;
if ( x < 0.0 ) {
retval = gammp(0.5,x*x);
return 1+ retval;
} else {
gammq(0.5,x*x, & retval);
return retval;
}
}
/**
* Convert a chi^2 value with a given number of degrees of freedom to a p-value.
*
* @author Matt Steigert
* @param x2val The chi^2 distributed statistic
* @param df Degrees of freedom
* @return Value of chi2(x2val, df)
*
* @throw InvalidChiSquareException() If df < 1 or x2val < 0.0
*/
double Statistics::chi2prob(double x2val, double df)
{
if(df < 1){
throw InvalidChiSquareException();
cerr << "Chi Square Value = " << x2val;
}
if(x2val < 0.0){
throw InvalidChiSquareException();
cerr << "Degrees of Freedom = " << df;
}
double pval;
pval = gammq(df/2.0, x2val/2.0);
return pval;
}
void chsone(double bins[], double ebins[], int nbins, int knstrn, double *df,
double *chsq, double *prob)
{
double gammq(double a, double x);
int j;
double temp;
*df=nbins-knstrn;
*chsq=0.0;
for (j=1;j<=nbins;j++) {
if (ebins[j] <= 0.0) my_error("Bad expected number in chsone");
temp=bins[j]-ebins[j];
*chsq += temp*temp/ebins[j];
}
*prob=gammq(0.5*(*df),0.5*(*chsq));
}
void dchstwo(double bins1[], double bins2[], int nbins, int knstrn,
double *df, double *chsq, double *prob)
{
int j;
double temp;
*df=nbins-knstrn;
*chsq=0.0;
for (j=0;j<nbins;j++)
if (bins1[j] == 0.0 && bins2[j] == 0.0)
--(*df);
else {
temp = bins1[j]-bins2[j];
*chsq += temp*temp/(bins1[j]+bins2[j]);
}
*prob=gammq(0.5*(*df),0.5*(*chsq));
}
void chsone(float bins[], float ebins[], int nbins, int knstrn, float *df,
float *chsq, float *prob)
{
float gammq(float a, float x);
void nrerror(char error_text[]);
int j;
float temp;
*df=nbins-knstrn;
*chsq=0.0;
for (j=1;j<=nbins;j++) {
if (ebins[j] <= 0.0) nrerror("Bad expected number in chsone");
temp=bins[j]-ebins[j];
*chsq += temp*temp/ebins[j];
}
*prob=gammq(0.5*(*df),0.5*(*chsq));
}
void chstwo(float bins1[], float bins2[], int nbins, int knstrn, float *df,
float *chsq, float *prob)
{
float gammq(float a, float x);
int j;
float temp;
*df=nbins-knstrn;
*chsq=0.0;
for (j=1;j<=nbins;j++)
if (bins1[j] == 0.0 && bins2[j] == 0.0)
--(*df);
else {
temp=bins1[j]-bins2[j];
*chsq += temp*temp/(bins1[j]+bins2[j]);
}
*prob=gammq(0.5*(*df),0.5*(*chsq));
}
void NR::chstwo(Vec_I_DP &bins1, Vec_I_DP &bins2, const int knstrn, DP &df,
DP &chsq, DP &prob)
{
int j;
DP temp;
int nbins=bins1.size();
df=nbins-knstrn;
chsq=0.0;
for (j=0;j<nbins;j++)
if (bins1[j] == 0.0 && bins2[j] == 0.0)
--df;
else {
temp=bins1[j]-bins2[j];
chsq += temp*temp/(bins1[j]+bins2[j]);
}
prob=gammq(0.5*df,0.5*chsq);
}
void chstwo(double bins1[], double bins2[], int nbins, int knstrn, double *df,
double *chsq, double *prob)
{
double gammq(double a, double x);
int j;
double temp;
*df=nbins-knstrn;
*chsq=0.0;
for (j=1;j<=nbins;j++)
if (bins1[j] == 0.0 && bins2[j] == 0.0)
--(*df);
else {
temp=bins1[j]-bins2[j];
*chsq += temp*temp/(bins1[j]+bins2[j]);
//printf("%lf %lf\n",bins1[j],bins2[j]);
}
*prob=gammq(0.5*(*df),0.5*(*chsq));
}
int chisquare ( double * array1, double * array2,
int arrlength, double *df, double *chsq, double *prob) {
/* normalize distributions */
int gammq(double a, double x, double * retval);
int j;
double total1, total2;
double temp;
double prefactor1, prefactor2;
total1 = 0;
total2 = 0;
for (j=0; j < arrlength; j++) {
total1 += array1[j];
total2 += array2[j];
printf ( " ** %2d %8.3le %8.3le \n",
j, array1[j], array2[j]);
}
prefactor1 = sqrt (total2/total1);
prefactor2 = 1.0/prefactor1;
*df = arrlength;
*chsq = 0.0;
for (j=0; j < arrlength;j++) {
if (array1[j] == 0.0 && array2[j] == 0.0) {
--(*df);
} else {
temp =prefactor1* array1[j] - prefactor2*array2[j];
*chsq += temp*temp/(array1[j]+array2[j]);
}
}
if ( gammq(0.5*(*df),0.5*(*chsq), prob) ) return 1;
printf ( "AAA %8.0lf %8.1le %8.1le \n", *df, *chsq, *prob);
return 0;
}
void cntab1(int **nn, int ni, int nj, float *chisq, float *df, float *prob,
float *cramrv, float *ccc)
{
float gammq(float a, float x);
int nnj,nni,j,i,minij;
float sum=0.0,expctd,*sumi,*sumj,temp;
sumi=vector(1,ni);
sumj=vector(1,nj);
nni=ni;
nnj=nj;
for (i=1;i<=ni;i++) {
sumi[i]=0.0;
for (j=1;j<=nj;j++) {
sumi[i] += nn[i][j];
sum += nn[i][j];
}
if (sumi[i] == 0.0) --nni;
}
for (j=1;j<=nj;j++) {
sumj[j]=0.0;
for (i=1;i<=ni;i++) sumj[j] += nn[i][j];
if (sumj[j] == 0.0) --nnj;
}
*df=nni*nnj-nni-nnj+1;
*chisq=0.0;
for (i=1;i<=ni;i++) {
for (j=1;j<=nj;j++) {
expctd=sumj[j]*sumi[i]/sum;
temp=nn[i][j]-expctd;
*chisq += temp*temp/(expctd+TINY);
}
}
*prob=gammq(0.5*(*df),0.5*(*chisq));
minij = nni < nnj ? nni-1 : nnj-1;
*cramrv=sqrt(*chisq/(sum*minij));
*ccc=sqrt(*chisq/(*chisq+sum));
free_vector(sumj,1,nj);
free_vector(sumi,1,ni);
}
int chisquare ( int * population_1, int * population_2, int no_bins, int kstr, double *df, double *chsq, double *prob) {
/* normalize distributions */
int gammq(double a, double x, double * retval);
int j;
double total_1, total_2;
double temp;
double p_prefactor, n_prefactor;
total_1 = 0;
total_2 = 0;
for (j=0; j < no_bins;j++) {
total_1 += population_1[j];
total_2 += population_2[j];
}
p_prefactor = sqrt (total_2/total_1);
n_prefactor = 1.0/p_prefactor;
*df = no_bins - kstr;
*chsq = 0.0;
for (j=0; j < no_bins;j++) {
if (population_1[j] == 0.0 && population_2[j] == 0.0) {
--(*df);
} else {
temp = p_prefactor* population_1[j] - n_prefactor*population_2[j];
*chsq += temp*temp/(population_1[j]+population_2[j]);
}
}
if ( gammq(0.5*(*df),0.5*(*chsq), prob) ) return 1;
//printf ( " %8.1le %8.1le %8.1le \n", *df, *chsq, *prob);
return 0;
}
double chival2prob(int dgf, double val){
return gammq((double)dgf/(double)2,val/(double)2);
}
void fitexy(float x[], float y[], int ndat, float sigx[], float sigy[],
float *a, float *b, float *siga, float *sigb, float *chi2, float *q)
{
void avevar(float data[], unsigned long n, float *ave, float *var);
float brent(float ax, float bx, float cx,
float (*f)(float), float tol, float *xmin);
float chixy(float bang);
void fit(float x[], float y[], int ndata, float sig[], int mwt,
float *a, float *b, float *siga, float *sigb, float *chi2, float *q);
float gammq(float a, float x);
void mnbrak(float *ax, float *bx, float *cx, float *fa, float *fb,
float *fc, float (*func)(float));
float zbrent(float (*func)(float), float x1, float x2, float tol);
int j;
float swap,amx,amn,varx,vary,ang[7],ch[7],scale,bmn,bmx,d1,d2,r2,
dum1,dum2,dum3,dum4,dum5;
xx=vector(1,ndat);
yy=vector(1,ndat);
sx=vector(1,ndat);
sy=vector(1,ndat);
ww=vector(1,ndat);
avevar(x,ndat,&dum1,&varx);
avevar(y,ndat,&dum1,&vary);
scale=sqrt(varx/vary);
nn=ndat;
for (j=1;j<=ndat;j++) {
xx[j]=x[j];
yy[j]=y[j]*scale;
sx[j]=sigx[j];
sy[j]=sigy[j]*scale;
ww[j]=sqrt(SQR(sx[j])+SQR(sy[j]));
}
fit(xx,yy,nn,ww,1,&dum1,b,&dum2,&dum3,&dum4,&dum5);
offs=ang[1]=0.0;
ang[2]=atan(*b);
ang[4]=0.0;
ang[5]=ang[2];
ang[6]=POTN;
for (j=4;j<=6;j++) ch[j]=chixy(ang[j]);
mnbrak(&ang[1],&ang[2],&ang[3],&ch[1],&ch[2],&ch[3],chixy);
*chi2=brent(ang[1],ang[2],ang[3],chixy,ACC,b);
*chi2=chixy(*b);
*a=aa;
*q=gammq(0.5*(nn-2),*chi2*0.5);
for (r2=0.0,j=1;j<=nn;j++) r2 += ww[j];
r2=1.0/r2;
bmx=BIG;
bmn=BIG;
offs=(*chi2)+1.0;
for (j=1;j<=6;j++) {
if (ch[j] > offs) {
d1=fabs(ang[j]-(*b));
while (d1 >= PI) d1 -= PI;
d2=PI-d1;
if (ang[j] < *b) {
swap=d1;
d1=d2;
d2=swap;
}
if (d1 < bmx) bmx=d1;
if (d2 < bmn) bmn=d2;
}
}
if (bmx < BIG) {
bmx=zbrent(chixy,*b,*b+bmx,ACC)-(*b);
amx=aa-(*a);
bmn=zbrent(chixy,*b,*b-bmn,ACC)-(*b);
amn=aa-(*a);
*sigb=sqrt(0.5*(bmx*bmx+bmn*bmn))/(scale*SQR(cos(*b)));
*siga=sqrt(0.5*(amx*amx+amn*amn)+r2)/scale;
} else (*sigb)=(*siga)=BIG;
*a /= scale;
*b=tan(*b)/scale;
free_vector(ww,1,ndat);
free_vector(sy,1,ndat);
free_vector(sx,1,ndat);
free_vector(yy,1,ndat);
free_vector(xx,1,ndat);
}
DP NR::erffc(const DP x)
{
return x < 0.0 ? 1.0+gammp(0.5,x*x) : gammq(0.5,x*x);
}
REAL_TYPE erff(REAL_TYPE x)
{
return x<0.0?1.0+gammp(0.5,x*x):gammq(0.5,x*x);
}
Scalar erfc(Scalar x)
{
// Scalar gammp(),gammq();
return x < 0.0 ? 1.0+gammp(0.5,x*x) : gammq(0.5,x*x);
}
double erffc(double x)
{
return x < 0.0 ? 1.0 + gammp(0.5, x*x) : gammq(0.5, x*x);
}
// The chi-squared distribution
//
double chidist(double x, double v)
{ return gammq (0.5 * v, 0.5 * x); }
