int main(void)
{
long idum=(-911);
int i;
float chisq,*x,*y,*sig,*a,*w,**cvm,**u,**v;
x=vector(1,NPT);
y=vector(1,NPT);
sig=vector(1,NPT);
a=vector(1,NPOL);
w=vector(1,NPOL);
cvm=matrix(1,NPOL,1,NPOL);
u=matrix(1,NPT,1,NPOL);
v=matrix(1,NPOL,1,NPOL);
for (i=1;i<=NPT;i++) {
x[i]=0.02*i;
y[i]=1.0+x[i]*(2.0+x[i]*(3.0+x[i]*(4.0+x[i]*5.0)));
y[i] *= (1.0+SPREAD*gasdev(&idum));
sig[i]=y[i]*SPREAD;
}
svdfit(x,y,sig,NPT,a,NPOL,u,v,w,&chisq,fpoly);
svdvar(v,NPOL,w,cvm);
printf("\npolynomial fit:\n\n");
for (i=1;i<=NPOL;i++)
printf("%12.6f %s %10.6f\n",a[i]," +-",sqrt(cvm[i][i]));
printf("\nChi-squared %12.6f\n",chisq);
svdfit(x,y,sig,NPT,a,NPOL,u,v,w,&chisq,fleg);
svdvar(v,NPOL,w,cvm);
printf("\nLegendre polynomial fit:\n\n");
for (i=1;i<=NPOL;i++)
printf("%12.6f %s %10.6f\n",a[i]," +-",sqrt(cvm[i][i]));
printf("\nChi-squared %12.6f\n",chisq);
free_matrix(v,1,NPOL,1,NPOL);
free_matrix(u,1,NPT,1,NPOL);
free_matrix(cvm,1,NPOL,1,NPOL);
free_vector(w,1,NPOL);
free_vector(a,1,NPOL);
free_vector(sig,1,NPT);
free_vector(y,1,NPT);
free_vector(x,1,NPT);
return 0;
}
/******************************************************************************
General linear least squares fit routine
from section 15.4 of Numerical Recipes.
yfit(x) = function which fills f[i],i=0..o-1 with the o
fitting functions evaluated at x.
fom = if nonzero figure-of-merit is returned here.
a = fitting parameters
av = if (av) error variances for the fitting parameters returned here.
x = n abscissas
y = n ordinates
ys = if (ys) = n error standard deviations for y values
tol = smallest fraction of maximum singular value (eigenvalues, roughly)
which a small singular value can equal -- smaller values are
set to zero, assumed to indicate redundancy. NR suggests
of order 10^-6
n = number of abscissas.
o = number of fitting parameters.
*/
static fit_rc fit_lsq(void (*yfit)(), double *fom, double *a, double *av,
const double *x, const double *y, const double *ys,
double tol, int n, int o) {
double wmax,wmin,xsq,sum ;
int i,j ;
const char *me = "fit_lsq" ;
if (check_memory(o,n) != OK) return(memfail(__LINE__,me)) ;
for(i=0;i<n;i++) {
yfit(x[i]) ;
for(j=0;j<o;j++) u[i][j] = f[j] * (ys ? 1.0/ys[i] : 1.0) ;
} ;
memcpy(b,y,n*sizeof(double)) ;
if (ys) for(i=0;i<n;i++) b[i] /= ys[i] ;
if (svdcmp(u,n,o) != OK)
return(punt(__LINE__,me,"singular value decomposition failed.")) ;
wmax = 0.0 ;
for(wmax=0.0,j=0;j<o;j++) if (w[j] > wmax) wmax = w[j] ;
wmin = tol * wmax ;
for(j=0;j<o;j++) if (w[j] < wmin) w[j] = 0.0 ;
if (svbksb(a,n,o) != OK)
return(punt(__LINE__,me,"back substitution failed.")) ;
if (av) {
if (svdvar(o) != OK)
return(punt(__LINE__,me,"variance calculation failed.")) ;
for(i=0;i<o;i++) av[i] = cvm[i][i] ;
} ;
if (fom) {
xsq = 0.0 ;
for(i=0;i<o;i++) {
yfit(x[i]) ;
sum = 0.0 ;
for(j=0;j<o;j++) sum += a[j] * f[j] ;
sum = (y[i] - sum)/(ys ? ys[i]*ys[i] : 1.0) ;
xsq += sum*sum ;
} ;
*fom = xsq ;
} ;
return(OK) ;
}
