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/* multifit/multiwlinear.c
*
* Copyright (C) 2015 Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_multifit.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include "linear_common.c"
int
gsl_multifit_wlinear (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
gsl_vector * c,
gsl_matrix * cov,
double *chisq, gsl_multifit_linear_workspace * work)
{
size_t rank;
int status = gsl_multifit_wlinear_tsvd(X, w, y, GSL_DBL_EPSILON, c, cov, chisq, &rank, work);
return status;
}
int
gsl_multifit_wlinear_tsvd (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
const double tol,
gsl_vector * c,
gsl_matrix * cov,
double * chisq,
size_t * rank,
gsl_multifit_linear_workspace * work)
{
const size_t n = X->size1;
const size_t p = X->size2;
if (y->size != n)
{
GSL_ERROR("number of observations in y does not match matrix",
GSL_EBADLEN);
}
else if (w->size != n)
{
GSL_ERROR("number of weights in w does not match matrix",
GSL_EBADLEN);
}
else if (p != c->size)
{
GSL_ERROR ("number of parameters c does not match matrix",
GSL_EBADLEN);
}
else if (tol <= 0)
{
GSL_ERROR ("tolerance must be positive", GSL_EINVAL);
}
else
{
int status;
double rnorm, snorm;
gsl_matrix_view A = gsl_matrix_submatrix(work->A, 0, 0, n, p);
gsl_vector_view b = gsl_vector_subvector(work->t, 0, n);
/* compute A = sqrt(W) X, b = sqrt(W) y */
status = gsl_multifit_linear_applyW(X, w, y, &A.matrix, &b.vector);
if (status)
return status;
/* compute SVD of A */
status = gsl_multifit_linear_bsvd(&A.matrix, work);
if (status)
return status;
status = multifit_linear_solve(X, &b.vector, tol, 0.0, rank,
c, &rnorm, &snorm, work);
if (status)
return status;
*chisq = rnorm * rnorm;
/* variance-covariance matrix cov = s2 * (Q S^-1) (Q S^-1)^T */
{
const size_t p = X->size2;
size_t i, j;
gsl_matrix_view QSI = gsl_matrix_submatrix(work->QSI, 0, 0, p, p);
gsl_vector_view D = gsl_vector_subvector(work->D, 0, p);
for (i = 0; i < p; i++)
{
gsl_vector_view row_i = gsl_matrix_row (&QSI.matrix, i);
double d_i = gsl_vector_get (&D.vector, i);
for (j = i; j < p; j++)
{
gsl_vector_view row_j = gsl_matrix_row (&QSI.matrix, j);
double d_j = gsl_vector_get (&D.vector, j);
double s;
gsl_blas_ddot (&row_i.vector, &row_j.vector, &s);
gsl_matrix_set (cov, i, j, s / (d_i * d_j));
gsl_matrix_set (cov, j, i, s / (d_i * d_j));
}
}
}
}
return GSL_SUCCESS;
}
int
gsl_multifit_wlinear_svd (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
double tol,
size_t * rank,
gsl_vector * c,
gsl_matrix * cov,
double *chisq, gsl_multifit_linear_workspace * work)
{
int status = gsl_multifit_wlinear_tsvd(X, w, y, tol, c, cov, chisq, rank, work);
return status;
}
int
gsl_multifit_wlinear_usvd (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
double tol,
size_t * rank,
gsl_vector * c,
gsl_matrix * cov,
double *chisq, gsl_multifit_linear_workspace * work)
{
/* FIXME: this call does actually perform balancing, but this function is deprecated anyway */
int status = gsl_multifit_wlinear_tsvd(X, w, y, tol, c, cov, chisq, rank, work);
return status;
}
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