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Diffstat (limited to 'gsl-1.9/linalg/luc.c')
-rw-r--r-- | gsl-1.9/linalg/luc.c | 334 |
1 files changed, 334 insertions, 0 deletions
diff --git a/gsl-1.9/linalg/luc.c b/gsl-1.9/linalg/luc.c new file mode 100644 index 0000000..5360679 --- /dev/null +++ b/gsl-1.9/linalg/luc.c @@ -0,0 +1,334 @@ +/* linalg/luc.c + * + * Copyright (C) 2001 Brian Gough + * + * 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 2 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 <stdlib.h> +#include <string.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_vector.h> +#include <gsl/gsl_matrix.h> +#include <gsl/gsl_complex.h> +#include <gsl/gsl_complex_math.h> +#include <gsl/gsl_permute_vector.h> +#include <gsl/gsl_blas.h> +#include <gsl/gsl_complex_math.h> + +#include <gsl/gsl_linalg.h> + +/* Factorise a general N x N complex matrix A into, + * + * P A = L U + * + * where P is a permutation matrix, L is unit lower triangular and U + * is upper triangular. + * + * L is stored in the strict lower triangular part of the input + * matrix. The diagonal elements of L are unity and are not stored. + * + * U is stored in the diagonal and upper triangular part of the + * input matrix. + * + * P is stored in the permutation p. Column j of P is column k of the + * identity matrix, where k = permutation->data[j] + * + * signum gives the sign of the permutation, (-1)^n, where n is the + * number of interchanges in the permutation. + * + * See Golub & Van Loan, Matrix Computations, Algorithm 3.4.1 (Gauss + * Elimination with Partial Pivoting). + */ + +int +gsl_linalg_complex_LU_decomp (gsl_matrix_complex * A, gsl_permutation * p, int *signum) +{ + if (A->size1 != A->size2) + { + GSL_ERROR ("LU decomposition requires square matrix", GSL_ENOTSQR); + } + else if (p->size != A->size1) + { + GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN); + } + else + { + const size_t N = A->size1; + size_t i, j, k; + + *signum = 1; + gsl_permutation_init (p); + + for (j = 0; j < N - 1; j++) + { + /* Find maximum in the j-th column */ + + gsl_complex ajj = gsl_matrix_complex_get (A, j, j); + double max = gsl_complex_abs (ajj); + size_t i_pivot = j; + + for (i = j + 1; i < N; i++) + { + gsl_complex aij = gsl_matrix_complex_get (A, i, j); + double ai = gsl_complex_abs (aij); + + if (ai > max) + { + max = ai; + i_pivot = i; + } + } + + if (i_pivot != j) + { + gsl_matrix_complex_swap_rows (A, j, i_pivot); + gsl_permutation_swap (p, j, i_pivot); + *signum = -(*signum); + } + + ajj = gsl_matrix_complex_get (A, j, j); + + if (!(GSL_REAL(ajj) == 0.0 && GSL_IMAG(ajj) == 0.0)) + { + for (i = j + 1; i < N; i++) + { + gsl_complex aij_orig = gsl_matrix_complex_get (A, i, j); + gsl_complex aij = gsl_complex_div (aij_orig, ajj); + gsl_matrix_complex_set (A, i, j, aij); + + for (k = j + 1; k < N; k++) + { + gsl_complex aik = gsl_matrix_complex_get (A, i, k); + gsl_complex ajk = gsl_matrix_complex_get (A, j, k); + + /* aik = aik - aij * ajk */ + + gsl_complex aijajk = gsl_complex_mul (aij, ajk); + gsl_complex aik_new = gsl_complex_sub (aik, aijajk); + + gsl_matrix_complex_set (A, i, k, aik_new); + } + } + } + } + + return GSL_SUCCESS; + } +} + +int +gsl_linalg_complex_LU_solve (const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x) +{ + if (LU->size1 != LU->size2) + { + GSL_ERROR ("LU matrix must be square", GSL_ENOTSQR); + } + else if (LU->size1 != p->size) + { + GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN); + } + else if (LU->size1 != b->size) + { + GSL_ERROR ("matrix size must match b size", GSL_EBADLEN); + } + else if (LU->size2 != x->size) + { + GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN); + } + else + { + /* Copy x <- b */ + + gsl_vector_complex_memcpy (x, b); + + /* Solve for x */ + + gsl_linalg_complex_LU_svx (LU, p, x); + + return GSL_SUCCESS; + } +} + + +int +gsl_linalg_complex_LU_svx (const gsl_matrix_complex * LU, const gsl_permutation * p, gsl_vector_complex * x) +{ + if (LU->size1 != LU->size2) + { + GSL_ERROR ("LU matrix must be square", GSL_ENOTSQR); + } + else if (LU->size1 != p->size) + { + GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN); + } + else if (LU->size1 != x->size) + { + GSL_ERROR ("matrix size must match solution/rhs size", GSL_EBADLEN); + } + else + { + /* Apply permutation to RHS */ + + gsl_permute_vector_complex (p, x); + + /* Solve for c using forward-substitution, L c = P b */ + + gsl_blas_ztrsv (CblasLower, CblasNoTrans, CblasUnit, LU, x); + + /* Perform back-substitution, U x = c */ + + gsl_blas_ztrsv (CblasUpper, CblasNoTrans, CblasNonUnit, LU, x); + + return GSL_SUCCESS; + } +} + + +int +gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A, const gsl_matrix_complex * LU, const gsl_permutation * p, const gsl_vector_complex * b, gsl_vector_complex * x, gsl_vector_complex * residual) +{ + if (A->size1 != A->size2) + { + GSL_ERROR ("matrix a must be square", GSL_ENOTSQR); + } + if (LU->size1 != LU->size2) + { + GSL_ERROR ("LU matrix must be square", GSL_ENOTSQR); + } + else if (A->size1 != LU->size2) + { + GSL_ERROR ("LU matrix must be decomposition of a", GSL_ENOTSQR); + } + else if (LU->size1 != p->size) + { + GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN); + } + else if (LU->size1 != b->size) + { + GSL_ERROR ("matrix size must match b size", GSL_EBADLEN); + } + else if (LU->size1 != x->size) + { + GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN); + } + else + { + /* Compute residual, residual = (A * x - b) */ + + gsl_vector_complex_memcpy (residual, b); + + { + gsl_complex one = GSL_COMPLEX_ONE; + gsl_complex negone = GSL_COMPLEX_NEGONE; + gsl_blas_zgemv (CblasNoTrans, one, A, x, negone, residual); + } + + /* Find correction, delta = - (A^-1) * residual, and apply it */ + + gsl_linalg_complex_LU_svx (LU, p, residual); + + { + gsl_complex negone= GSL_COMPLEX_NEGONE; + gsl_blas_zaxpy (negone, residual, x); + } + + return GSL_SUCCESS; + } +} + +int +gsl_linalg_complex_LU_invert (const gsl_matrix_complex * LU, const gsl_permutation * p, gsl_matrix_complex * inverse) +{ + size_t i, n = LU->size1; + + int status = GSL_SUCCESS; + + gsl_matrix_complex_set_identity (inverse); + + for (i = 0; i < n; i++) + { + gsl_vector_complex_view c = gsl_matrix_complex_column (inverse, i); + int status_i = gsl_linalg_complex_LU_svx (LU, p, &(c.vector)); + + if (status_i) + status = status_i; + } + + return status; +} + +gsl_complex +gsl_linalg_complex_LU_det (gsl_matrix_complex * LU, int signum) +{ + size_t i, n = LU->size1; + + gsl_complex det = gsl_complex_rect((double) signum, 0.0); + + for (i = 0; i < n; i++) + { + gsl_complex zi = gsl_matrix_complex_get (LU, i, i); + det = gsl_complex_mul (det, zi); + } + + return det; +} + + +double +gsl_linalg_complex_LU_lndet (gsl_matrix_complex * LU) +{ + size_t i, n = LU->size1; + + double lndet = 0.0; + + for (i = 0; i < n; i++) + { + gsl_complex z = gsl_matrix_complex_get (LU, i, i); + lndet += log (gsl_complex_abs (z)); + } + + return lndet; +} + + +gsl_complex +gsl_linalg_complex_LU_sgndet (gsl_matrix_complex * LU, int signum) +{ + size_t i, n = LU->size1; + + gsl_complex phase = gsl_complex_rect((double) signum, 0.0); + + for (i = 0; i < n; i++) + { + gsl_complex z = gsl_matrix_complex_get (LU, i, i); + + double r = gsl_complex_abs(z); + + if (r == 0) + { + phase = gsl_complex_rect(0.0, 0.0); + break; + } + else + { + z = gsl_complex_div_real(z, r); + phase = gsl_complex_mul(phase, z); + } + } + + return phase; +} |