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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 double a = 0.0; /* data interval [a,b] */
const double b = 2.0 * M_PI;
const size_t spline_order = 6; /* spline order */
const size_t ncontrol = 15; /* number of control points */
const double sigma = 0.2; /* noise */
gsl_bspline_workspace *w = gsl_bspline_alloc_ncontrol(spline_order, ncontrol);
gsl_bspline_workspace *wper = gsl_bspline_alloc_ncontrol(spline_order, ncontrol);
gsl_vector *c = gsl_vector_alloc(ncontrol); /* non-periodic coefficients */
gsl_vector *cper = gsl_vector_alloc(ncontrol); /* periodic coefficients */
gsl_vector *x = gsl_vector_alloc(n);
gsl_vector *y = gsl_vector_alloc(n);
gsl_vector *wts = gsl_vector_alloc(n);
size_t i;
gsl_rng *r;
double chisq;
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 = sin(xi) - cos(2.0 * 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(wts, i, 1.0 / (sigma * sigma));
printf("%f %f\n", xi, yi);
}
printf("\n\n");
/* use uniform non-periodic knots on [a, b] */
gsl_bspline_init_uniform(a, b, w);
/* solve least squares problem for non-periodic spline */
gsl_bspline_wlssolve(x, y, wts, c, &chisq, w);
/* use periodic knots on [a, b] */
gsl_bspline_init_periodic(a, b, wper);
/* solve least squares problem for periodic spline */
gsl_bspline_pwlssolve(x, y, wts, cper, &chisq, wper);
/* output the spline curves */
{
double xi;
for (xi = a; xi <= b; xi += 0.01)
{
double result, result_per;
gsl_bspline_calc(xi, c, &result, w);
gsl_bspline_calc(xi, cper, &result_per, wper);
printf("%f %f %f\n", xi, result, result_per);
}
}
fprintf(stderr, "=== Non-periodic spline endpoint derivatives ===\n");
for (i = 0; i < spline_order; ++i)
{
double result0, result1;
gsl_bspline_calc_deriv(a, c, i, &result0, w);
gsl_bspline_calc_deriv(b, c, i, &result1, w);
fprintf(stderr, "deriv %zu: [%14.6e, %14.6e]\n", i, result0, result1);
}
fprintf(stderr, "=== Periodic spline endpoint derivatives ===\n");
for (i = 0; i < spline_order; ++i)
{
double result0, result1;
gsl_bspline_calc_deriv(a, cper, i, &result0, wper);
gsl_bspline_calc_deriv(b, cper, i, &result1, wper);
fprintf(stderr, "deriv %zu: [%14.6e, %14.6e]\n", i, result0, result1);
}
gsl_vector_free(c);
gsl_vector_free(cper);
gsl_bspline_free(w);
gsl_bspline_free(wper);
gsl_rng_free(r);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_vector_free(wts);
return 0;
}
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