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#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_multifit.h>
#include <gsl/gsl_multilarge.h>
#include <gsl/gsl_blas.h>
/* function to be fitted */
double
func(const double t)
{
double x = sin(10.0 * t);
return exp(x*x*x);
}
/* construct a row of the least squares matrix */
int
build_row(const double t, gsl_vector *row)
{
const size_t p = row->size;
double Xj = 1.0;
size_t j;
for (j = 0; j < p; ++j)
{
gsl_vector_set(row, j, Xj);
Xj *= t;
}
return 0;
}
int
solve_system(const int print_data, const gsl_multilarge_linear_type * T,
const double lambda, const size_t n, const size_t p,
gsl_vector * c)
{
const size_t nblock = 5; /* number of blocks to accumulate */
const size_t nrows = n / nblock; /* number of rows per block */
gsl_multilarge_linear_workspace * w =
gsl_multilarge_linear_alloc(T, p);
gsl_matrix *X = gsl_matrix_alloc(nrows, p);
gsl_vector *y = gsl_vector_alloc(nrows);
gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
const size_t nlcurve = 200;
gsl_vector *reg_param = gsl_vector_alloc(nlcurve);
gsl_vector *rho = gsl_vector_alloc(nlcurve);
gsl_vector *eta = gsl_vector_alloc(nlcurve);
size_t rowidx = 0;
double rnorm, snorm, rcond;
double t = 0.0;
double dt = 1.0 / (n - 1.0);
while (rowidx < n)
{
size_t nleft = n - rowidx; /* number of rows left to accumulate */
size_t nr = GSL_MIN(nrows, nleft); /* number of rows in this block */
gsl_matrix_view Xv = gsl_matrix_submatrix(X, 0, 0, nr, p);
gsl_vector_view yv = gsl_vector_subvector(y, 0, nr);
size_t i;
/* build (X,y) block with 'nr' rows */
for (i = 0; i < nr; ++i)
{
gsl_vector_view row = gsl_matrix_row(&Xv.matrix, i);
double fi = func(t);
double ei = gsl_ran_gaussian (r, 0.1 * fi); /* noise */
double yi = fi + ei;
/* construct this row of LS matrix */
build_row(t, &row.vector);
/* set right hand side value with added noise */
gsl_vector_set(&yv.vector, i, yi);
if (print_data && (i % 100 == 0))
printf("%f %f\n", t, yi);
t += dt;
}
/* accumulate (X,y) block into LS system */
gsl_multilarge_linear_accumulate(&Xv.matrix, &yv.vector, w);
rowidx += nr;
}
if (print_data)
printf("\n\n");
/* compute L-curve */
gsl_multilarge_linear_lcurve(reg_param, rho, eta, w);
/* solve large LS system and store solution in c */
gsl_multilarge_linear_solve(lambda, c, &rnorm, &snorm, w);
/* compute reciprocal condition number */
gsl_multilarge_linear_rcond(&rcond, w);
fprintf(stderr, "=== Method %s ===\n", gsl_multilarge_linear_name(w));
fprintf(stderr, "condition number = %e\n", 1.0 / rcond);
fprintf(stderr, "residual norm = %e\n", rnorm);
fprintf(stderr, "solution norm = %e\n", snorm);
/* output L-curve */
{
size_t i;
for (i = 0; i < nlcurve; ++i)
{
printf("%.12e %.12e %.12e\n",
gsl_vector_get(reg_param, i),
gsl_vector_get(rho, i),
gsl_vector_get(eta, i));
}
printf("\n\n");
}
gsl_matrix_free(X);
gsl_vector_free(y);
gsl_multilarge_linear_free(w);
gsl_rng_free(r);
gsl_vector_free(reg_param);
gsl_vector_free(rho);
gsl_vector_free(eta);
return 0;
}
int
main(int argc, char *argv[])
{
const size_t n = 50000; /* number of observations */
const size_t p = 16; /* polynomial order + 1 */
double lambda = 0.0; /* regularization parameter */
gsl_vector *c_tsqr = gsl_vector_alloc(p);
gsl_vector *c_normal = gsl_vector_alloc(p);
if (argc > 1)
lambda = atof(argv[1]);
/* solve system with TSQR method */
solve_system(1, gsl_multilarge_linear_tsqr, lambda, n, p, c_tsqr);
/* solve system with Normal equations method */
solve_system(0, gsl_multilarge_linear_normal, lambda, n, p, c_normal);
/* output solutions */
{
gsl_vector *v = gsl_vector_alloc(p);
double t;
for (t = 0.0; t <= 1.0; t += 0.01)
{
double f_exact = func(t);
double f_tsqr, f_normal;
build_row(t, v);
gsl_blas_ddot(v, c_tsqr, &f_tsqr);
gsl_blas_ddot(v, c_normal, &f_normal);
printf("%f %e %e %e\n", t, f_exact, f_tsqr, f_normal);
}
gsl_vector_free(v);
}
gsl_vector_free(c_tsqr);
gsl_vector_free(c_normal);
return 0;
}
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