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/*** File polfit.c
*** July 26, 2012
*** By Jessica Mink, after Bevington, page 141
*--- Polynomial least squares fitting program, almost identical to the
* one in Bevington, "Data Reduction and Error Analysis for the
* Physical Sciences," page 141. The argument list was changed and
* the weighting removed.
* y = a(1) + a(2)*(x-x0) + a(3)*(x-x0)**2 + a(3)*(x-x0)**3 + . . .
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "wcscat.h"
static double determ();
void
polfit (x, y, x0, npts, nterms, a, stdev)
double *x; /* Array of independent variable points */
double *y; /* Array of dependent variable points */
double x0; /* Offset to independent variable */
int npts; /* Number of data points to fit */
int nterms; /* Number of parameters to fit */
double *a; /* Vector containing current fit values */
double *stdev; /* Standard deviation of fit (returned) */
{
double sigma2sum;
double xterm,yterm,xi,yi;
double *sumx, *sumy;
double *array;
int i,j,k,l,n,nmax;
double delta;
/* accumulate weighted sums */
nmax = 2 * nterms - 1;
sumx = (double *) calloc (nmax, sizeof(double));
sumy = (double *) calloc (nterms, sizeof(double));
for (n = 0; n < nmax; n++)
sumx[n] = 0.0;
for (j = 0; j < nterms; j++)
sumy[j] = 0.0;
for (i = 0; i < npts; i++) {
xi = x[i] - x0;
yi = y[i];
xterm = 1.0;
for (n = 0; n < nmax; n++) {
sumx[n] = sumx[n] + xterm;
xterm = xterm * xi;
}
yterm = yi;
for (n = 0; n < nterms; n++) {
sumy[n] = sumy[n] + yterm;
yterm = yterm * xi;
}
}
/* Construct matrices and calculate coeffients */
array = (double *) calloc (nterms*nterms, sizeof(double));
for (j = 0; j < nterms; j++) {
for (k = 0; k < nterms; k++) {
n = j + k;
array[j+k*nterms] = sumx[n];
}
}
delta = determ (array, nterms);
if (delta == 0.0) {
*stdev = 0.;
for (j = 0; j < nterms; j++)
a[j] = 0. ;
free (array);
free (sumx);
free (sumy);
return;
}
for (l = 0; l < nterms; l++) {
for (j = 0; j < nterms; j++) {
for (k = 0; k < nterms; k++) {
n = j + k;
array[j+k*nterms] = sumx[n];
}
array[j+l*nterms] = sumy[j];
}
a[l] = determ (array, nterms) / delta;
}
/* Calculate sigma */
sigma2sum = 0.0;
for (i = 0; i < npts; i++) {
yi = polcomp (x[i], x0, nterms, a);
sigma2sum = sigma2sum + ((y[i] - yi) * (y[i] - yi));
}
*stdev = sqrt (sigma2sum / (double) (npts - 1));
free (array);
free (sumx);
free (sumy);
return;
}
/*--- Calculate the determinant of a square matrix
* This subprogram destroys the input matrix array
* From Bevington, page 294.
*/
static double
determ (array, norder)
double *array; /* Input matrix array */
int norder; /* Order of determinant (degree of matrix) */
{
double save, det;
int i,j,k,k1, zero;
det = 1.0;
for (k = 0; k < norder; k++) {
/* Interchange columns if diagonal element is zero */
if (array[k+k*norder] == 0) {
zero = 1;
for (j = k; j < norder; j++) {
if (array[k+j*norder] != 0.0)
zero = 0;
}
if (zero)
return (0.0);
for (i = k; i < norder; i++) {
save = array[i+j*norder];
array[i+j*norder] = array[i+k*norder];
array[i+k*norder] = save ;
}
det = -det;
}
/* Subtract row k from lower rows to get diagonal matrix */
det = det * array[k+k*norder];
if (k < norder - 1) {
k1 = k + 1;
for (i = k1; i < norder; i++) {
for (j = k1; j < norder; j++) {
array[i+j*norder] = array[i+j*norder] -
(array[i+k*norder] * array[k+j*norder] /
array[k+k*norder]);
}
}
}
}
return (det);
}
/* POLCOMP -- Polynomial evaluation
* Y = A(1) + A(2)*X + A(3)*X**2 + A(3)*X**3 + . . . */
double
polcomp (xi, x0, norder, a)
double xi; /* Independent variable */
double x0; /* Offset to independent variable */
int norder; /* Number of coefficients */
double *a; /* Vector containing coeffiecients */
{
double xterm, x, y;
int iterm;
/* Accumulate polynomial value */
x = xi - x0;
y = 0.0;
xterm = 1.0;
for (iterm = 0; iterm < norder; iterm++) {
y = y + a[iterm] * xterm;
xterm = xterm * x;
}
return (y);
}
/* Sep 10 1987 Program written
*
* Mar 17 1993 Add x offset
*
* Feb 23 1998 Translate to C
*
* Jul 25 2001 Add polcomp to return computed values
*
* Apr 3 2003 Drop unused variable freedom in polfit()
*
* Jul 26 2012 Fix xterm computation in polcomp() from + to *
* (found by Raymond Carlberg of U.Toronto)
*/
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