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C/C++ Users Group Library 1996 July
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v_13_11
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phillip2
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fitt.c
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1993-08-20
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/* (C) Copr. 1986-92 Numerical Recipes Software */
/********************************************
*
* This file contains code from the
* Numerical Recipies in C text by
* Press, Flannery, Teukolsky, Vetterling
* I needed the routines to fit data to
* a straight line y=mx+b.
*
*
* This files contains the files:
* nrutil.h
* fit.c
* gammq.c
* gcf.c
* gser.c
* gammln.c
* nrutil.c
*
* 21 August 1993
*
********************************************/
#include <math.h>
/* file nrutil.h */
#ifndef _NR_UTILS_H_
#define _NR_UTILS_H_
static float sqrarg;
#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
static double dsqrarg;
#define DSQR(a) ((dsqrarg=(a)) == 0.0 ? 0.0 : dsqrarg*dsqrarg)
static double dmaxarg1,dmaxarg2;
#define DMAX(a,b) (dmaxarg1=(a),dmaxarg2=(b),(dmaxarg1) > (dmaxarg2) ?\
(dmaxarg1) : (dmaxarg2))
static double dminarg1,dminarg2;
#define DMIN(a,b) (dminarg1=(a),dminarg2=(b),(dminarg1) < (dminarg2) ?\
(dminarg1) : (dminarg2))
static float maxarg1,maxarg2;
#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
(maxarg1) : (maxarg2))
static float minarg1,minarg2;
#define FMIN(a,b) (minarg1=(a),minarg2=(b),(minarg1) < (minarg2) ?\
(minarg1) : (minarg2))
static long lmaxarg1,lmaxarg2;
#define LMAX(a,b) (lmaxarg1=(a),lmaxarg2=(b),(lmaxarg1) > (lmaxarg2) ?\
(lmaxarg1) : (lmaxarg2))
static long lminarg1,lminarg2;
#define LMIN(a,b) (lminarg1=(a),lminarg2=(b),(lminarg1) < (lminarg2) ?\
(lminarg1) : (lminarg2))
static int imaxarg1,imaxarg2;
#define IMAX(a,b) (imaxarg1=(a),imaxarg2=(b),(imaxarg1) > (imaxarg2) ?\
(imaxarg1) : (imaxarg2))
static int iminarg1,iminarg2;
#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
(iminarg1) : (iminarg2))
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
#if defined(__STDC__) || defined(ANSI) || defined(NRANSI) /* ANSI */
void nrerror(char error_text[]);
float *vector(long nl, long nh);
int *ivector(long nl, long nh);
unsigned char *cvector(long nl, long nh);
unsigned long *lvector(long nl, long nh);
double *dvector(long nl, long nh);
float **matrix(long nrl, long nrh, long ncl, long nch);
double **dmatrix(long nrl, long nrh, long ncl, long nch);
int **imatrix(long nrl, long nrh, long ncl, long nch);
float **submatrix(float **a, long oldrl, long oldrh, long oldcl, long oldch,
long newrl, long newcl);
float **convert_matrix(float *a, long nrl, long nrh, long ncl, long nch);
float ***f3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh);
void free_vector(float *v, long nl, long nh);
void free_ivector(int *v, long nl, long nh);
void free_cvector(unsigned char *v, long nl, long nh);
void free_lvector(unsigned long *v, long nl, long nh);
void free_dvector(double *v, long nl, long nh);
void free_matrix(float **m, long nrl, long nrh, long ncl, long nch);
void free_dmatrix(double **m, long nrl, long nrh, long ncl, long nch);
void free_imatrix(int **m, long nrl, long nrh, long ncl, long nch);
void free_submatrix(float **b, long nrl, long nrh, long ncl, long nch);
void free_convert_matrix(float **b, long nrl, long nrh, long ncl, long nch);
void free_f3tensor(float ***t, long nrl, long nrh, long ncl, long nch,
long ndl, long ndh);
#else /* ANSI */
/* traditional - K&R */
void nrerror();
float *vector();
float **matrix();
float **submatrix();
float **convert_matrix();
float ***f3tensor();
double *dvector();
double **dmatrix();
int *ivector();
int **imatrix();
unsigned char *cvector();
unsigned long *lvector();
void free_vector();
void free_dvector();
void free_ivector();
void free_cvector();
void free_lvector();
void free_matrix();
void free_submatrix();
void free_convert_matrix();
void free_dmatrix();
void free_imatrix();
void free_f3tensor();
#endif /* ANSI */
#endif /* _NR_UTILS_H_ */
/* file fit.c */
#undef DDEBUG
#define NRANSI
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;
int iii;
#ifdef DDEBUG
printf("\nDEBUG> ndata=%d mwt=%d", ndata, mwt);
for(iii=1; iii<=ndata; iii++)
printf("\nDEBUG> x=%f y=%f sig=%f",x[iii],y[iii],sig[iii]);
printf("\nDEBUG> start of fit");
#endif DDEBUG
/*
change 8-21-93
The sig array is all 1's so I will remove
all uses of it in mult and division.
*/
*b=0.0;
if (mwt) {
ss=0.0;
for (i=1;i<=ndata;i++) {
wt=1.0;
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);
st2 += t*t;
*b += t*y[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]));
*q=gammq(0.5*(ndata-2),0.5*(*chi2));
}
}
#undef NRANSI
/* file gammq.c */
/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */
float gammq(float a, float x)
{
void gcf(float *gammcf, float a, float x, float *gln);
void gser(float *gamser, float a, float x, float *gln);
void nrerror(char error_text[]);
float gamser,gammcf,gln;
if (x < 0.0 || a <= 0.0) nrerror("Invalid arguments in routine gammq");
if (x < (a+1.0)) {
gser(&gamser,a,x,&gln);
return 1.0-gamser;
} else {
gcf(&gammcf,a,x,&gln);
return gammcf;
}
}
/* file gcf.c */
/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */
#define ITMAX 100
#define EPS 3.0e-7
#define FPMIN 1.0e-30
void gcf(float *gammcf, float a, float x, float *gln)
{
float gammln(float xx);
void nrerror(char error_text[]);
int i;
float 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<=ITMAX;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;
}
if (i > ITMAX) nrerror("a too large, ITMAX too small in gcf");
*gammcf=exp(-x+a*log(x)-(*gln))*h;
}
#undef ITMAX
#undef EPS
#undef FPMIN
/* file gser.c */
/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */
#define ITMAX 100
#define EPS 3.0e-7
void gser(float *gamser, float a, float x, float *gln)
{
float gammln(float xx);
void nrerror(char error_text[]);
int n;
float sum,del,ap;
*gln=gammln(a);
if (x <= 0.0) {
if (x < 0.0) nrerror("x less than 0 in routine gser");
*gamser=0.0;
return;
} else {
ap=a;
del=sum=1.0/a;
for (n=1;n<=ITMAX;n++) {
++ap;
del *= x/ap;
sum += del;
if (fabs(del) < fabs(sum)*EPS) {
*gamser=sum*exp(-x+a*log(x)-(*gln));
return;
}
}
nrerror("a too large, ITMAX too small in routine gser");
return;
}
}
#undef ITMAX
#undef EPS
/* file gammln.c */
/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */
float gammln(float xx)
{
double x,y,tmp,ser;
static double cof[6]={76.18009172947146,-86.50532032941677,
24.01409824083