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/* linalg/lq.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Gerard Jungman, Brian Gough
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* Copyright (C) 2004 Joerg Wensch, modifications for LQ.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <stdlib.h>
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#include <string.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_vector.h>
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#include <gsl/gsl_matrix.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_linalg.h>
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#include "apply_givens.c"
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/* Note: The standard in numerical linear algebra is to solve A x = b
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* resp. ||A x - b||_2 -> min by QR-decompositions where x, b are
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* column vectors.
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*
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* When the matrix A has a large number of rows it is much more
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* efficient to work with the transposed matrix A^T and to solve the
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* system x^T A = b^T resp. ||x^T A - b^T||_2 -> min. This is caused
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* by the row-oriented format in which GSL stores matrices. Therefore
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* the QR-decomposition of A has to be replaced by a LQ decomposition
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* of A^T
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*
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* The purpose of this package is to provide the algorithms to compute
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* the LQ-decomposition and to solve the linear equations resp. least
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* squares problems. The dimensions N, M of the matrix are switched
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* because here A will probably be a transposed matrix. We write x^T,
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* b^T,... for vectors the comments to emphasize that they are row
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* vectors.
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*
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* It may even be useful to transpose your matrix explicitly (assumed
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* that there are no memory restrictions) because this takes O(M x N)
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* computing time where the decompostion takes O(M x N^2) computing
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* time. */
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/* Factorise a general N x M matrix A into
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*
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* A = L Q
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*
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* where Q is orthogonal (M x M) and L is lower triangular (N x M).
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*
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* Q is stored as a packed set of Householder transformations in the
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* strict upper triangular part of the input matrix.
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*
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* R is stored in the diagonal and lower triangle of the input matrix.
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*
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* The full matrix for Q can be obtained as the product
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*
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* Q = Q_k .. Q_2 Q_1
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*
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* where k = MIN(M,N) and
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*
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* Q_i = (I - tau_i * v_i * v_i')
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*
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* and where v_i is a Householder vector
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*
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* v_i = [1, m(i+1,i), m(i+2,i), ... , m(M,i)]
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*
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* This storage scheme is the same as in LAPACK. */
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int
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gsl_linalg_LQ_decomp (gsl_matrix * A, gsl_vector * tau)
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{
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const size_t N = A->size1;
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const size_t M = A->size2;
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if (tau->size != GSL_MIN (M, N))
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{
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GSL_ERROR ("size of tau must be MIN(M,N)", GSL_EBADLEN);
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}
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else
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{
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size_t i;
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for (i = 0; i < GSL_MIN (M, N); i++)
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{
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/* Compute the Householder transformation to reduce the j-th
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column of the matrix to a multiple of the j-th unit vector */
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gsl_vector_view c_full = gsl_matrix_row (A, i);
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gsl_vector_view c = gsl_vector_subvector (&(c_full.vector), i, M-i);
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double tau_i = gsl_linalg_householder_transform (&(c.vector));
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gsl_vector_set (tau, i, tau_i);
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/* Apply the transformation to the remaining columns and
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update the norms */
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if (i + 1 < N)
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{
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gsl_matrix_view m = gsl_matrix_submatrix (A, i + 1, i, N - (i + 1), M - i );
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gsl_linalg_householder_mh (tau_i, &(c.vector), &(m.matrix));
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}
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}
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return GSL_SUCCESS;
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}
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}
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/* Solves the system x^T A = b^T using the LQ factorisation,
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* x^T L = b^T Q^T
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*
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* to obtain x. Based on SLATEC code.
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*/
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int
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gsl_linalg_LQ_solve_T (const gsl_matrix * LQ, const gsl_vector * tau, const gsl_vector * b, gsl_vector * x)
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{
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if (LQ->size1 != LQ->size2)
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{
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GSL_ERROR ("LQ matrix must be square", GSL_ENOTSQR);
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}
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else if (LQ->size2 != b->size)
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{
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GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
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}
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else if (LQ->size1 != x->size)
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{
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GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
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}
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else
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{
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/* Copy x <- b */
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gsl_vector_memcpy (x, b);
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/* Solve for x */
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gsl_linalg_LQ_svx_T (LQ, tau, x);
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return GSL_SUCCESS;
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}
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}
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/* Solves the system x^T A = b^T in place using the LQ factorisation,
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*
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* x^T L = b^T Q^T
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*
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* to obtain x. Based on SLATEC code.
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*/
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int
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gsl_linalg_LQ_svx_T (const gsl_matrix * LQ, const gsl_vector * tau, gsl_vector * x)
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{
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if (LQ->size1 != LQ->size2)
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{
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GSL_ERROR ("LQ matrix must be square", GSL_ENOTSQR);
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}
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else if (LQ->size1 != x->size)
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{
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GSL_ERROR ("matrix size must match x/rhs size", GSL_EBADLEN);
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}
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else
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{
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/* compute rhs = Q^T b */
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gsl_linalg_LQ_vecQT (LQ, tau, x);
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/* Solve R x = rhs, storing x in-place */
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gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, LQ, x);
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return GSL_SUCCESS;
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}
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}
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/* Find the least squares solution to the overdetermined system
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*
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* x^T A = b^T
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*
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* for M >= N using the LQ factorization A = L Q.
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*/
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int
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gsl_linalg_LQ_lssolve_T (const gsl_matrix * LQ, const gsl_vector * tau, const gsl_vector * b, gsl_vector * x, gsl_vector * residual)
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{
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const size_t N = LQ->size1;
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const size_t M = LQ->size2;
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if (M < N)
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{
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GSL_ERROR ("LQ matrix must have M>=N", GSL_EBADLEN);
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}
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else if (M != b->size)
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{
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GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
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}
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else if (N != x->size)
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{
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GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
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}
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else if (M != residual->size)
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{
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GSL_ERROR ("matrix size must match residual size", GSL_EBADLEN);
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}
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else
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{
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gsl_matrix_const_view L = gsl_matrix_const_submatrix (LQ, 0, 0, N, N);
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gsl_vector_view c = gsl_vector_subvector(residual, 0, N);
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gsl_vector_memcpy(residual, b);
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/* compute rhs = b^T Q^T */
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gsl_linalg_LQ_vecQT (LQ, tau, residual);
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/* Solve x^T L = rhs */
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gsl_vector_memcpy(x, &(c.vector));
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gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, &(L.matrix), x);
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/* Compute residual = b^T - x^T A = (b^T Q^T - x^T L) Q */
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gsl_vector_set_zero(&(c.vector));
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gsl_linalg_LQ_vecQ(LQ, tau, residual);
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return GSL_SUCCESS;
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}
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}
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int
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gsl_linalg_LQ_Lsolve_T (const gsl_matrix * LQ, const gsl_vector * b, gsl_vector * x)
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{
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if (LQ->size1 != LQ->size2)
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{
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GSL_ERROR ("LQ matrix must be square", GSL_ENOTSQR);
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}
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else if (LQ->size1 != b->size)
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{
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GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
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}
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else if (LQ->size1 != x->size)
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{
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GSL_ERROR ("matrix size must match x size", GSL_EBADLEN);
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}
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else
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{
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/* Copy x <- b */
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gsl_vector_memcpy (x, b);
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/* Solve R x = b, storing x in-place */
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gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, LQ, x);
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return GSL_SUCCESS;
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}
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}
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int
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gsl_linalg_LQ_Lsvx_T (const gsl_matrix * LQ, gsl_vector * x)
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{
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if (LQ->size1 != LQ->size2)
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Packit |
67cb25 |
{
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GSL_ERROR ("LQ matrix must be square", GSL_ENOTSQR);
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}
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else if (LQ->size2 != x->size)
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67cb25 |
{
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GSL_ERROR ("matrix size must match rhs size", GSL_EBADLEN);
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67cb25 |
}
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else
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Packit |
67cb25 |
{
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Packit |
67cb25 |
/* Solve x^T L = b^T, storing x in-place */
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Packit |
67cb25 |
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gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, LQ, x);
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67cb25 |
return GSL_SUCCESS;
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67cb25 |
}
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Packit |
67cb25 |
}
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67cb25 |
int
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67cb25 |
gsl_linalg_L_solve_T (const gsl_matrix * L, const gsl_vector * b, gsl_vector * x)
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Packit |
67cb25 |
{
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Packit |
67cb25 |
if (L->size1 != L->size2)
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Packit |
67cb25 |
{
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Packit |
67cb25 |
GSL_ERROR ("R matrix must be square", GSL_ENOTSQR);
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Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (L->size2 != b->size)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (L->size1 != x->size)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
/* Copy x <- b */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_memcpy (x, b);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Solve R x = b, storing x inplace in b */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, L, x);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_linalg_LQ_vecQT (const gsl_matrix * LQ, const gsl_vector * tau, gsl_vector * v)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const size_t N = LQ->size1;
|
|
Packit |
67cb25 |
const size_t M = LQ->size2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (tau->size != GSL_MIN (M, N))
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("size of tau must be MIN(M,N)", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (v->size != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("vector size must be M", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* compute v Q^T */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < GSL_MIN (M, N); i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_vector_const_view c = gsl_matrix_const_row (LQ, i);
|
|
Packit |
67cb25 |
gsl_vector_const_view h = gsl_vector_const_subvector (&(c.vector),
|
|
Packit |
67cb25 |
i, M - i);
|
|
Packit |
67cb25 |
gsl_vector_view w = gsl_vector_subvector (v, i, M - i);
|
|
Packit |
67cb25 |
double ti = gsl_vector_get (tau, i);
|
|
Packit |
67cb25 |
gsl_linalg_householder_hv (ti, &(h.vector), &(w.vector));
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_linalg_LQ_vecQ (const gsl_matrix * LQ, const gsl_vector * tau, gsl_vector * v)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const size_t N = LQ->size1;
|
|
Packit |
67cb25 |
const size_t M = LQ->size2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (tau->size != GSL_MIN (M, N))
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("size of tau must be MIN(M,N)", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (v->size != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("vector size must be M", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* compute v Q^T */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = GSL_MIN (M, N); i-- > 0;)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_vector_const_view c = gsl_matrix_const_row (LQ, i);
|
|
Packit |
67cb25 |
gsl_vector_const_view h = gsl_vector_const_subvector (&(c.vector),
|
|
Packit |
67cb25 |
i, M - i);
|
|
Packit |
67cb25 |
gsl_vector_view w = gsl_vector_subvector (v, i, M - i);
|
|
Packit |
67cb25 |
double ti = gsl_vector_get (tau, i);
|
|
Packit |
67cb25 |
gsl_linalg_householder_hv (ti, &(h.vector), &(w.vector));
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Form the orthogonal matrix Q from the packed LQ matrix */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_linalg_LQ_unpack (const gsl_matrix * LQ, const gsl_vector * tau, gsl_matrix * Q, gsl_matrix * L)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const size_t N = LQ->size1;
|
|
Packit |
67cb25 |
const size_t M = LQ->size2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (Q->size1 != M || Q->size2 != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("Q matrix must be M x M", GSL_ENOTSQR);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (L->size1 != N || L->size2 != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("R matrix must be N x M", GSL_ENOTSQR);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (tau->size != GSL_MIN (M, N))
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("size of tau must be MIN(M,N)", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i, j, l_border;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Initialize Q to the identity */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_matrix_set_identity (Q);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = GSL_MIN (M, N); i-- > 0;)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_vector_const_view c = gsl_matrix_const_row (LQ, i);
|
|
Packit |
67cb25 |
gsl_vector_const_view h = gsl_vector_const_subvector (&c.vector,
|
|
Packit |
67cb25 |
i, M - i);
|
|
Packit |
67cb25 |
gsl_matrix_view m = gsl_matrix_submatrix (Q, i, i, M - i, M - i);
|
|
Packit |
67cb25 |
double ti = gsl_vector_get (tau, i);
|
|
Packit |
67cb25 |
gsl_linalg_householder_mh (ti, &h.vector, &m.matrix);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Form the lower triangular matrix L from a packed LQ matrix */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < N; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
l_border=GSL_MIN(i,M-1);
|
|
Packit |
67cb25 |
for (j = 0; j <= l_border ; j++)
|
|
Packit |
67cb25 |
gsl_matrix_set (L, i, j, gsl_matrix_get (LQ, i, j));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = l_border+1; j < M; j++)
|
|
Packit |
67cb25 |
gsl_matrix_set (L, i, j, 0.0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Update a LQ factorisation for A= L Q , A' = A + v u^T,
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
* L' Q' = LQ + v u^T
|
|
Packit |
67cb25 |
* = (L + v u^T Q^T) Q
|
|
Packit |
67cb25 |
* = (L + v w^T) Q
|
|
Packit |
67cb25 |
*
|
|
Packit |
67cb25 |
* where w = Q u.
|
|
Packit |
67cb25 |
*
|
|
Packit |
67cb25 |
* Algorithm from Golub and Van Loan, "Matrix Computations", Section
|
|
Packit |
67cb25 |
* 12.5 (Updating Matrix Factorizations, Rank-One Changes)
|
|
Packit |
67cb25 |
*/
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_linalg_LQ_update (gsl_matrix * Q, gsl_matrix * L,
|
|
Packit |
67cb25 |
const gsl_vector * v, gsl_vector * w)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const size_t N = L->size1;
|
|
Packit |
67cb25 |
const size_t M = L->size2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (Q->size1 != M || Q->size2 != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("Q matrix must be N x N if L is M x N", GSL_ENOTSQR);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (w->size != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("w must be length N if L is M x N", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (v->size != N)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR ("v must be length M if L is M x N", GSL_EBADLEN);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t j, k;
|
|
Packit |
67cb25 |
double w0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Apply Given's rotations to reduce w to (|w|, 0, 0, ... , 0)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
J_1^T .... J_(n-1)^T w = +/- |w| e_1
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
simultaneously applied to L, H = J_1^T ... J^T_(n-1) L
|
|
Packit |
67cb25 |
so that H is upper Hessenberg. (12.5.2) */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = M - 1; k > 0; k--) /* loop from k = M-1 to 1 */
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double c, s;
|
|
Packit |
67cb25 |
double wk = gsl_vector_get (w, k);
|
|
Packit |
67cb25 |
double wkm1 = gsl_vector_get (w, k - 1);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_linalg_givens (wkm1, wk, &c, &s);
|
|
Packit |
67cb25 |
gsl_linalg_givens_gv (w, k - 1, k, c, s);
|
|
Packit |
67cb25 |
apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
w0 = gsl_vector_get (w, 0);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Add in v w^T (Equation 12.5.3) */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < N; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double lj0 = gsl_matrix_get (L, j, 0);
|
|
Packit |
67cb25 |
double vj = gsl_vector_get (v, j);
|
|
Packit |
67cb25 |
gsl_matrix_set (L, j, 0, lj0 + w0 * vj);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Apply Givens transformations L' = G_(n-1)^T ... G_1^T H
|
|
Packit |
67cb25 |
Equation 12.5.4 */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = 1; k < GSL_MIN(M,N+1); k++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double c, s;
|
|
Packit |
67cb25 |
double diag = gsl_matrix_get (L, k - 1, k - 1);
|
|
Packit |
67cb25 |
double offdiag = gsl_matrix_get (L, k - 1 , k);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_linalg_givens (diag, offdiag, &c, &s);
|
|
Packit |
67cb25 |
apply_givens_lq (M, N, Q, L, k - 1, k, c, s);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_matrix_set (L, k - 1, k, 0.0); /* exact zero of G^T */
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_linalg_LQ_LQsolve (gsl_matrix * Q, gsl_matrix * L, const gsl_vector * b, gsl_vector * x)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const size_t N = L->size1;
|
|
Packit |
67cb25 |
const size_t M = L->size2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (M != N)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
return GSL_ENOTSQR;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else if (Q->size1 != M || b->size != M || x->size != M)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
return GSL_EBADLEN;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
/* compute sol = b^T Q^T */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_blas_dgemv (CblasNoTrans, 1.0, Q, b, 0.0, x);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Solve x^T L = sol, storing x in-place */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_blas_dtrsv (CblasLower, CblasTrans, CblasNonUnit, L, x);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|