/* (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,
      24.01409824083091,-1.231739572450155,
      0.1208650973866179e-2,-0.5395239384953e-5};
   int j;

   y=x=xx;
   tmp=x+5.5;
   tmp -= (x+0.5)*log(tmp);
   ser=1.000000000190015;
   for (j=0;j<=5;j++) ser += cof[j]/++y;
   return -tmp+log(2.5066282746310005*ser/x);
}




/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */


   /* file nrutil.c */


/* CAUTION: This is the ANSI C (only) version of the Numerical Recipes
   utility file nrutil.c.  Do not confuse this file with the same-named
   file nrutil.c that is supplied in the same subdirectory or archive
   as the header file nrutil.h.  *That* file contains both ANSI and
   traditional K&R versions, along with #ifdef macros to select the
   correct version.  *This* file contains only ANSI C.               */

#include <stdio.h>
#include <stddef.h>
#include <stdlib.h>
#define NR_END 1
#define FREE_ARG char*

void nrerror(char error_text[])
/* Numerical Recipes standard error handler */
{
   fprintf(stderr,"Numerical Recipes run-time error...\n");
   fprintf(stderr,"%s\n",error_text);
   fprintf(stderr,"...now exiting to system...\n");
   exit(1);
}

float *vector(long nl, long nh)
/* allocate a float vector with subscript range v[nl..nh] */
{
   float *v;

   v=(float *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(float)));
   if (!v) nrerror("allocation failure in vector()");
   return v-nl+NR_END;
}

int *ivector(long nl, long nh)
/* allocate an int vector with subscript range v[nl..nh] */
{
   int *v;

   v=(int *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(int)));
   if (!v) nrerror("allocation failure in ivector()");
   return v-nl+NR_END;
}

unsigned char *cvector(long nl, long nh)
/* allocate an unsigned char vector with subscript range v[nl..nh] */
{
   unsigned char *v;

   v=(unsigned char *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(unsigned char)));
   if (!v) nrerror("allocation failure in cvector()");
   return v-nl+NR_END;
}

unsigned long *lvector(long nl, long nh)
/* allocate an unsigned long vector with subscript range v[nl..nh] */
{
   unsigned long *v;

   v=(unsigned long *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(long)));
   if (!v) nrerror("allocation failure in lvector()");
   return v-nl+NR_END;
}

double *dvector(long nl, long nh)
/* allocate a double vector with subscript range v[nl..nh] */
{
   double *v;

   v=(double *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(double)));
   if (!v) nrerror("allocation failure in dvector()");
   return v-nl+NR_END;
}

float **matrix(long nrl, long nrh, long ncl, long nch)
/* allocate a float matrix with subscript range m[nrl..nrh][ncl..nch] */
{
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
   float **m;

   /* allocate pointers to rows */
   m=(float **) malloc((size_t)((nrow+NR_END)*sizeof(float*)));
   if (!m) nrerror("allocation failure 1 in matrix()");
   m += NR_END;
   m -= nrl;

   /* allocate rows and set pointers to them */
   m[nrl]=(float *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float)));
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   m[nrl] += NR_END;
   m[nrl] -= ncl;

   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;

   /* return pointer to array of pointers to rows */
   return m;
}

double **dmatrix(long nrl, long nrh, long ncl, long nch)
/* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
{
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
   double **m;

   /* allocate pointers to rows */
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   if (!m) nrerror("allocation failure 1 in matrix()");
   m += NR_END;
   m -= nrl;

   /* allocate rows and set pointers to them */
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   m[nrl] += NR_END;
   m[nrl] -= ncl;

   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;

   /* return pointer to array of pointers to rows */
   return m;
}

int **imatrix(long nrl, long nrh, long ncl, long nch)
/* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
{
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
   int **m;

   /* allocate pointers to rows */
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
   if (!m) nrerror("allocation failure 1 in matrix()");
   m += NR_END;
   m -= nrl;


   /* allocate rows and set pointers to them */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   m[nrl] += NR_END;
   m[nrl] -= ncl;

   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;

   /* return pointer to array of pointers to rows */
   return m;
}

float **submatrix(float **a, long oldrl, long oldrh, long oldcl, long oldch,
   long newrl, long newcl)
/* point a submatrix [newrl..][newcl..] to a[oldrl..oldrh][oldcl..oldch] */
{
   long i,j,nrow=oldrh-oldrl+1,ncol=oldcl-newcl;
   float **m;

   /* allocate array of pointers to rows */
   m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
   if (!m) nrerror("allocation failure in submatrix()");
   m += NR_END;
   m -= newrl;

   /* set pointers to rows */
   for(i=oldrl,j=newrl;i<=oldrh;i++,j++) m[j]=a[i]+ncol;

   /* return pointer to array of pointers to rows */
   return m;
}

float **convert_matrix(float *a, long nrl, long nrh, long ncl, long nch)
/* allocate a float matrix m[nrl..nrh][ncl..nch] that points to the matrix
declared in the standard C manner as a[nrow][ncol], where nrow=nrh-nrl+1
and ncol=nch-ncl+1. The routine should be called with the address
&a[0][0] as the first argument. */
{
   long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1;
   float **m;

   /* allocate pointers to rows */
   m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
   if (!m) nrerror("allocation failure in convert_matrix()");
   m += NR_END;
   m -= nrl;

   /* set pointers to rows */
   m[nrl]=a-ncl;
   for(i=1,j=nrl+1;i<nrow;i++,j++) m[j]=m[j-1]+ncol;
   /* return pointer to array of pointers to rows */
   return m;
}

float ***f3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
/* allocate a float 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
{
   long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1,ndep=ndh-ndl+1;
   float ***t;

   /* allocate pointers to pointers to rows */
   t=(float ***) malloc((size_t)((nrow+NR_END)*sizeof(float**)));
   if (!t) nrerror("allocation failure 1 in f3tensor()");
   t += NR_END;
   t -= nrl;

   /* allocate pointers to rows and set pointers to them */
   t[nrl]=(float **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float*)));
   if (!t[nrl]) nrerror("allocation failure 2 in f3tensor()");
   t[nrl] += NR_END;
   t[nrl] -= ncl;

   /* allocate rows and set pointers to them */
   t[nrl][ncl]=(float *) malloc((size_t)((nrow*ncol*ndep+NR_END)*sizeof(float)));
   if (!t[nrl][ncl]) nrerror("allocation failure 3 in f3tensor()");
   t[nrl][ncl] += NR_END;
   t[nrl][ncl] -= ndl;

   for(j=ncl+1;j<=nch;j++) t[nrl][j]=t[nrl][j-1]+ndep;
   for(i=nrl+1;i<=nrh;i++) {
      t[i]=t[i-1]+ncol;
      t[i][ncl]=t[i-1][ncl]+ncol*ndep;
      for(j=ncl+1;j<=nch;j++) t[i][j]=t[i][j-1]+ndep;
   }

   /* return pointer to array of pointers to rows */
   return t;
}

void free_vector(float *v, long nl, long nh)
/* free a float vector allocated with vector() */
{
   free((FREE_ARG) (v+nl-NR_END));
}

void free_ivector(int *v, long nl, long nh)
/* free an int vector allocated with ivector() */
{
   free((FREE_ARG) (v+nl-NR_END));
}

void free_cvector(unsigned char *v, long nl, long nh)
/* free an unsigned char vector allocated with cvector() */
{
   free((FREE_ARG) (v+nl-NR_END));
}

void free_lvector(unsigned long *v, long nl, long nh)
/* free an unsigned long vector allocated with lvector() */
{
   free((FREE_ARG) (v+nl-NR_END));
}

void free_dvector(double *v, long nl, long nh)
/* free a double vector allocated with dvector() */
{
   free((FREE_ARG) (v+nl-NR_END));
}

void free_matrix(float **m, long nrl, long nrh, long ncl, long nch)
/* free a float matrix allocated by matrix() */
{
   free((FREE_ARG) (m[nrl]+ncl-NR_END));
   free((FREE_ARG) (m+nrl-NR_END));
}

void free_dmatrix(double **m, long nrl, long nrh, long ncl, long nch)
/* free a double matrix allocated by dmatrix() */
{
   free((FREE_ARG) (m[nrl]+ncl-NR_END));
   free((FREE_ARG) (m+nrl-NR_END));
}

void free_imatrix(int **m, long nrl, long nrh, long ncl, long nch)
/* free an int matrix allocated by imatrix() */
{
   free((FREE_ARG) (m[nrl]+ncl-NR_END));
   free((FREE_ARG) (m+nrl-NR_END));
}

void free_submatrix(float **b, long nrl, long nrh, long ncl, long nch)
/* free a submatrix allocated by submatrix() */
{
   free((FREE_ARG) (b+nrl-NR_END));
}

void free_convert_matrix(float **b, long nrl, long nrh, long ncl, long nch)
/* free a matrix allocated by convert_matrix() */
{
   free((FREE_ARG) (b+nrl-NR_END));
}

void free_f3tensor(float ***t, long nrl, long nrh, long ncl, long nch,
   long ndl, long ndh)
/* free a float f3tensor allocated by f3tensor() */
{
   free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
   free((FREE_ARG) (t[nrl]+ncl-NR_END));
   free((FREE_ARG) (t+nrl-NR_END));
}
/* (C) Copr. 1986-92 Numerical Recipes Software $|9`0S[)03. */