/* @(#)lfit.c	17.1.1.1 (ES0-DMD) 01/25/02 17:26:59 */
/*===========================================================================
  Copyright (C) 1995 European Southern Observatory (ESO)
 
  This program is free software; you can redistribute it and/or 
  modify it under the terms of the GNU General Public License as 
  published by the Free Software Foundation; either version 2 of 
  the License, or (at your option) any later version.
 
  This program 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 General Public License for more details.
 
  You should have received a copy of the GNU General Public 
  License along with this program; if not, write to the Free 
  Software Foundation, Inc., 675 Massachusetss Ave, Cambridge, 
  MA 02139, USA.
 
  Corresponding concerning ESO-MIDAS should be addressed as follows:
	Internet e-mail: midas@eso.org
	Postal address: European Southern Observatory
			Data Management Division 
			Karl-Schwarzschild-Strasse 2
			D 85748 Garching bei Muenchen 
			GERMANY
===========================================================================*/

/* @(#)lfit.c	17.1.1.1  (ESO)  01/25/02  17:26:59 */

static double sqrarg;
#define SQR(a) (sqrarg=(a),sqrarg*sqrarg)

void lfit(x,y,sig,ndata,a,ma,lista,mfit,covar,chisq,funcs)
int ndata,ma,lista[],mfit;
double sig[],a[],**covar,*chisq;
float x[],y[];
void (*funcs)();	/* ANSI: void (*funcs)(double,double *,int); */
{
	int k,kk,j,ihit,i;
	double ym,wt,sum,sig2i,**beta,*afunc;
	void gaussj(),covsrt(),nrerror(),free_dmatrix(),free_dvector();
	double **dmatrix(),*dvector();

	beta=dmatrix(1,ma,1,1);
	afunc=dvector(1,ma);
	kk=mfit+1;
	for (j=1;j<=ma;j++) {
		ihit=0;
		for (k=1;k<=mfit;k++)
			if (lista[k] == j) ihit++;
		if (ihit == 0)
			lista[kk++]=j;
		else if (ihit > 1) nrerror("Bad LISTA permutation in LFIT-1");
	}
	if (kk != (ma+1)) nrerror("Bad LISTA permutation in LFIT-2");
	for (j=1;j<=mfit;j++) {
		for (k=1;k<=mfit;k++) covar[j][k]=0.0;
		beta[j][1]=0.0;
	}
	for (i=1;i<=ndata;i++) {
		(*funcs)(x[i],afunc,ma);
		ym=(double)y[i];
		if (mfit < ma)
			for (j=(mfit+1);j<=ma;j++)
				ym -= a[lista[j]]*afunc[lista[j]];
		sig2i=1.0/SQR(sig[i]);
		for (j=1;j<=mfit;j++) {
			wt=afunc[lista[j]]*sig2i;
			for (k=1;k<=j;k++)
				covar[j][k] += wt*afunc[lista[k]];
			beta[j][1] += ym*wt;
		}
	}
	if (mfit > 1)
		for (j=2;j<=mfit;j++)
			for (k=1;k<=j-1;k++)
				covar[k][j]=covar[j][k];
	gaussj(covar,mfit,beta,1);
	for (j=1;j<=mfit;j++) a[lista[j]]=beta[j][1];
	*chisq=0.0;
	for (i=1;i<=ndata;i++) {
		(*funcs)(x[i],afunc,ma);
		for (sum=0.0,j=1;j<=ma;j++) sum += a[j]*afunc[j];
		*chisq += SQR((y[i]-sum)/sig[i]);
	}
	covsrt(covar,ma,lista,mfit);
	free_dvector(afunc,1,ma);
	free_dmatrix(beta,1,ma,1,1);
}

#undef SQR