int
main(void)
{
const size_t N = 500; /* length of time series */
const size_t K = 51; /* window size */
const double alpha[3] = { 0.5, 3.0, 10.0 }; /* alpha values */
gsl_vector *x = gsl_vector_alloc(N); /* input vector */
gsl_vector *y1 = gsl_vector_alloc(N); /* filtered output vector for alpha1 */
gsl_vector *y2 = gsl_vector_alloc(N); /* filtered output vector for alpha2 */
gsl_vector *y3 = gsl_vector_alloc(N); /* filtered output vector for alpha3 */
gsl_vector *k1 = gsl_vector_alloc(K); /* Gaussian kernel for alpha1 */
gsl_vector *k2 = gsl_vector_alloc(K); /* Gaussian kernel for alpha2 */
gsl_vector *k3 = gsl_vector_alloc(K); /* Gaussian kernel for alpha3 */
gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
gsl_filter_gaussian_workspace *gauss_p = gsl_filter_gaussian_alloc(K);
size_t i;
double sum = 0.0;
/* generate input signal */
for (i = 0; i < N; ++i)
{
double ui = gsl_ran_gaussian(r, 1.0);
sum += ui;
gsl_vector_set(x, i, sum);
}
/* compute kernels without normalization */
gsl_filter_gaussian_kernel(alpha[0], 0, 0, k1);
gsl_filter_gaussian_kernel(alpha[1], 0, 0, k2);
gsl_filter_gaussian_kernel(alpha[2], 0, 0, k3);
/* apply filters */
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha[0], 0, x, y1, gauss_p);
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha[1], 0, x, y2, gauss_p);
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha[2], 0, x, y3, gauss_p);
/* print kernels */
for (i = 0; i < K; ++i)
{
double k1i = gsl_vector_get(k1, i);
double k2i = gsl_vector_get(k2, i);
double k3i = gsl_vector_get(k3, i);
printf("%e %e %e\n", k1i, k2i, k3i);
}
printf("\n\n");
/* print filter results */
for (i = 0; i < N; ++i)
{
double xi = gsl_vector_get(x, i);
double y1i = gsl_vector_get(y1, i);
double y2i = gsl_vector_get(y2, i);
double y3i = gsl_vector_get(y3, i);
printf("%.12e %.12e %.12e %.12e\n", xi, y1i, y2i, y3i);
}
gsl_vector_free(x);
gsl_vector_free(y1);
gsl_vector_free(y2);
gsl_vector_free(y3);
gsl_vector_free(k1);
gsl_vector_free(k2);
gsl_vector_free(k3);
gsl_rng_free(r);
gsl_filter_gaussian_free(gauss_p);
return 0;
}
int
main(void)
{
const size_t N = 1000; /* length of time series */
const size_t K = 61; /* window size */
const double alpha = 3.0; /* Gaussian kernel has +/- 3 standard deviations */
gsl_vector *x = gsl_vector_alloc(N); /* input vector */
gsl_vector *y = gsl_vector_alloc(N); /* filtered output vector */
gsl_vector *dy = gsl_vector_alloc(N); /* first derivative filtered vector */
gsl_vector *d2y = gsl_vector_alloc(N); /* second derivative filtered vector */
gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
gsl_filter_gaussian_workspace *gauss_p = gsl_filter_gaussian_alloc(K);
size_t i;
/* generate input signal */
for (i = 0; i < N; ++i)
{
double xi = (i > N / 2) ? 0.5 : 0.0;
double ei = gsl_ran_gaussian(r, 0.1);
gsl_vector_set(x, i, xi + ei);
}
/* apply filters */
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha, 0, x, y, gauss_p);
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha, 1, x, dy, gauss_p);
gsl_filter_gaussian(GSL_FILTER_END_PADVALUE, alpha, 2, x, d2y, gauss_p);
/* print results */
for (i = 0; i < N; ++i)
{
double xi = gsl_vector_get(x, i);
double yi = gsl_vector_get(y, i);
double dyi = gsl_vector_get(dy, i);
double d2yi = gsl_vector_get(d2y, i);
double dxi;
/* compute finite difference of x vector */
if (i == 0)
dxi = gsl_vector_get(x, i + 1) - xi;
else if (i == N - 1)
dxi = gsl_vector_get(x, i) - gsl_vector_get(x, i - 1);
else
dxi = 0.5 * (gsl_vector_get(x, i + 1) - gsl_vector_get(x, i - 1));
printf("%.12e %.12e %.12e %.12e %.12e\n",
xi,
yi,
dxi,
dyi,
d2yi);
}
gsl_vector_free(x);
gsl_vector_free(y);
gsl_vector_free(dy);
gsl_vector_free(d2y);
gsl_rng_free(r);
gsl_filter_gaussian_free(gauss_p);
return 0;
}
