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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_bspline.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_statistics.h>
int
main (void)
{
const size_t n = 500; /* number of data points to fit */
const size_t k = 4; /* spline order */
const double a = 0.0; /* data interval [a,b] */
const double b = 15.0;
const double sigma = 0.2; /* noise */
gsl_bspline_workspace *work1 = gsl_bspline_alloc(k, 40); /* 40 breakpoints */
gsl_bspline_workspace *work2 = gsl_bspline_alloc(k, 10); /* 10 breakpoints */
const size_t p1 = gsl_bspline_ncontrol(work1); /* number of control points */
const size_t p2 = gsl_bspline_ncontrol(work2); /* number of control points */
const size_t dof1 = n - p1; /* degrees of freedom */
const size_t dof2 = n - p2; /* degrees of freedom */
gsl_vector *c1 = gsl_vector_alloc(p1);
gsl_vector *c2 = gsl_vector_alloc(p2);
gsl_vector *x = gsl_vector_alloc(n);
gsl_vector *y = gsl_vector_alloc(n);
gsl_vector *w = gsl_vector_alloc(n);
size_t i;
gsl_rng *r;
double chisq1, chisq2;
gsl_rng_env_setup();
r = gsl_rng_alloc(gsl_rng_default);
/* this is the data to be fitted */
for (i = 0; i < n; ++i)
{
double xi = (b - a) / (n - 1.0) * i + a;
double yi = cos(xi) * exp(-0.1 * xi);
double dyi = gsl_ran_gaussian(r, sigma);
yi += dyi;
gsl_vector_set(x, i, xi);
gsl_vector_set(y, i, yi);
gsl_vector_set(w, i, 1.0 / (sigma * sigma));
printf("%f %f\n", xi, yi);
}
/* use uniform breakpoints on [a, b] */
gsl_bspline_init_uniform(a, b, work1);
gsl_bspline_init_uniform(a, b, work2);
/* solve least squares problem */
gsl_bspline_wlssolve(x, y, w, c1, &chisq1, work1);
gsl_bspline_wlssolve(x, y, w, c2, &chisq2, work2);
fprintf(stderr, "40 breakpoints: chisq/dof = %e\n", chisq1 / dof1);
fprintf(stderr, "10 breakpoints: chisq/dof = %e\n", chisq2 / dof2);
printf("\n\n");
/* output the spline curves */
{
double xi;
for (xi = a; xi <= b; xi += 0.1)
{
double result1, result2;
gsl_bspline_calc(xi, c1, &result1, work1);
gsl_bspline_calc(xi, c2, &result2, work2);
printf("%f %f %f\n", xi, result1, result2);
}
}
gsl_rng_free(r);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_vector_free(w);
gsl_vector_free(c1);
gsl_vector_free(c2);
gsl_bspline_free(work1);
gsl_bspline_free(work2);
return 0;
}
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