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Diffstat (limited to 'thirdparty/includes/GSL/gsl/gsl_linalg.h')
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diff --git a/thirdparty/includes/GSL/gsl/gsl_linalg.h b/thirdparty/includes/GSL/gsl/gsl_linalg.h deleted file mode 100644 index ac3e6433..00000000 --- a/thirdparty/includes/GSL/gsl/gsl_linalg.h +++ /dev/null @@ -1,650 +0,0 @@ -/* linalg/gsl_linalg.h - * - * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007 Gerard Jungman, Brian Gough, 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. - */ - -#ifndef __GSL_LINALG_H__ -#define __GSL_LINALG_H__ - -#include <stdlib.h> -#include <gsl/gsl_mode.h> -#include <gsl/gsl_permutation.h> -#include <gsl/gsl_vector.h> -#include <gsl/gsl_matrix.h> -#include <gsl/gsl_math.h> -#include <gsl/gsl_inline.h> - -#undef __BEGIN_DECLS -#undef __END_DECLS -#ifdef __cplusplus -#define __BEGIN_DECLS extern "C" { -#define __END_DECLS } -#else -#define __BEGIN_DECLS /* empty */ -#define __END_DECLS /* empty */ -#endif - -__BEGIN_DECLS - -typedef enum - { - GSL_LINALG_MOD_NONE = 0, - GSL_LINALG_MOD_TRANSPOSE = 1, - GSL_LINALG_MOD_CONJUGATE = 2 - } -gsl_linalg_matrix_mod_t; - - -/* Note: You can now use the gsl_blas_dgemm function instead of matmult */ - -/* Simple implementation of matrix multiply. - * Calculates C = A.B - * - * exceptions: GSL_EBADLEN - */ -int gsl_linalg_matmult (const gsl_matrix * A, - const gsl_matrix * B, - gsl_matrix * C); - - -/* Simple implementation of matrix multiply. - * Allows transposition of either matrix, so it - * can compute A.B or Trans(A).B or A.Trans(B) or Trans(A).Trans(B) - * - * exceptions: GSL_EBADLEN - */ -int gsl_linalg_matmult_mod (const gsl_matrix * A, - gsl_linalg_matrix_mod_t modA, - const gsl_matrix * B, - gsl_linalg_matrix_mod_t modB, - gsl_matrix * C); - -/* Calculate the matrix exponential by the scaling and - * squaring method described in Moler + Van Loan, - * SIAM Rev 20, 801 (1978). The mode argument allows - * choosing an optimal strategy, from the table - * given in the paper, for a given precision. - * - * exceptions: GSL_ENOTSQR, GSL_EBADLEN - */ -int gsl_linalg_exponential_ss( - const gsl_matrix * A, - gsl_matrix * eA, - gsl_mode_t mode - ); - - -/* Householder Transformations */ - -double gsl_linalg_householder_transform (gsl_vector * v); -gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * v); - -int gsl_linalg_householder_hm (double tau, - const gsl_vector * v, - gsl_matrix * A); - -int gsl_linalg_householder_mh (double tau, - const gsl_vector * v, - gsl_matrix * A); - -int gsl_linalg_householder_hv (double tau, - const gsl_vector * v, - gsl_vector * w); - -int gsl_linalg_householder_hm1 (double tau, - gsl_matrix * A); - -int gsl_linalg_complex_householder_hm (gsl_complex tau, - const gsl_vector_complex * v, - gsl_matrix_complex * A); - -int gsl_linalg_complex_householder_mh (gsl_complex tau, - const gsl_vector_complex * v, - gsl_matrix_complex * A); - -int gsl_linalg_complex_householder_hv (gsl_complex tau, - const gsl_vector_complex * v, - gsl_vector_complex * w); - -/* Hessenberg reduction */ - -int gsl_linalg_hessenberg_decomp(gsl_matrix *A, gsl_vector *tau); -int gsl_linalg_hessenberg_unpack(gsl_matrix * H, gsl_vector * tau, - gsl_matrix * U); -int gsl_linalg_hessenberg_unpack_accum(gsl_matrix * H, gsl_vector * tau, - gsl_matrix * U); -int gsl_linalg_hessenberg_set_zero(gsl_matrix * H); -int gsl_linalg_hessenberg_submatrix(gsl_matrix *M, gsl_matrix *A, - size_t top, gsl_vector *tau); - -/* To support gsl-1.9 interface: DEPRECATED */ -int gsl_linalg_hessenberg(gsl_matrix *A, gsl_vector *tau); - - -/* Hessenberg-Triangular reduction */ - -int gsl_linalg_hesstri_decomp(gsl_matrix * A, gsl_matrix * B, - gsl_matrix * U, gsl_matrix * V, - gsl_vector * work); - -/* Singular Value Decomposition - - * exceptions: - */ - -int -gsl_linalg_SV_decomp (gsl_matrix * A, - gsl_matrix * V, - gsl_vector * S, - gsl_vector * work); - -int -gsl_linalg_SV_decomp_mod (gsl_matrix * A, - gsl_matrix * X, - gsl_matrix * V, - gsl_vector * S, - gsl_vector * work); - -int gsl_linalg_SV_decomp_jacobi (gsl_matrix * A, - gsl_matrix * Q, - gsl_vector * S); - -int -gsl_linalg_SV_solve (const gsl_matrix * U, - const gsl_matrix * Q, - const gsl_vector * S, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_SV_leverage(const gsl_matrix *U, gsl_vector *h); - - -/* LU Decomposition, Gaussian elimination with partial pivoting - */ - -int gsl_linalg_LU_decomp (gsl_matrix * A, gsl_permutation * p, int *signum); - -int gsl_linalg_LU_solve (const gsl_matrix * LU, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_LU_svx (const gsl_matrix * LU, - const gsl_permutation * p, - gsl_vector * x); - -int gsl_linalg_LU_refine (const gsl_matrix * A, - const gsl_matrix * LU, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x, - gsl_vector * residual); - -int gsl_linalg_LU_invert (const gsl_matrix * LU, - const gsl_permutation * p, - gsl_matrix * inverse); - -double gsl_linalg_LU_det (gsl_matrix * LU, int signum); -double gsl_linalg_LU_lndet (gsl_matrix * LU); -int gsl_linalg_LU_sgndet (gsl_matrix * lu, int signum); - -/* Complex LU Decomposition */ - -int gsl_linalg_complex_LU_decomp (gsl_matrix_complex * A, - gsl_permutation * p, - int *signum); - -int gsl_linalg_complex_LU_solve (const gsl_matrix_complex * LU, - const gsl_permutation * p, - const gsl_vector_complex * b, - gsl_vector_complex * x); - -int gsl_linalg_complex_LU_svx (const gsl_matrix_complex * LU, - const gsl_permutation * p, - gsl_vector_complex * x); - -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); - -int gsl_linalg_complex_LU_invert (const gsl_matrix_complex * LU, - const gsl_permutation * p, - gsl_matrix_complex * inverse); - -gsl_complex gsl_linalg_complex_LU_det (gsl_matrix_complex * LU, - int signum); - -double gsl_linalg_complex_LU_lndet (gsl_matrix_complex * LU); - -gsl_complex gsl_linalg_complex_LU_sgndet (gsl_matrix_complex * LU, - int signum); - -/* QR decomposition */ - -int gsl_linalg_QR_decomp (gsl_matrix * A, - gsl_vector * tau); - -int gsl_linalg_QR_solve (const gsl_matrix * QR, - const gsl_vector * tau, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_QR_svx (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_vector * x); - -int gsl_linalg_QR_lssolve (const gsl_matrix * QR, - const gsl_vector * tau, - const gsl_vector * b, - gsl_vector * x, - gsl_vector * residual); - - -int gsl_linalg_QR_QRsolve (gsl_matrix * Q, - gsl_matrix * R, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_QR_Rsolve (const gsl_matrix * QR, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_QR_Rsvx (const gsl_matrix * QR, - gsl_vector * x); - -int gsl_linalg_QR_update (gsl_matrix * Q, - gsl_matrix * R, - gsl_vector * w, - const gsl_vector * v); - -int gsl_linalg_QR_QTvec (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_vector * v); - -int gsl_linalg_QR_Qvec (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_vector * v); - -int gsl_linalg_QR_QTmat (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_matrix * A); - -int gsl_linalg_QR_matQ (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_matrix * A); - -int gsl_linalg_QR_unpack (const gsl_matrix * QR, - const gsl_vector * tau, - gsl_matrix * Q, - gsl_matrix * R); - -int gsl_linalg_R_solve (const gsl_matrix * R, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_R_svx (const gsl_matrix * R, - gsl_vector * x); - - -/* Q R P^T decomposition */ - -int gsl_linalg_QRPT_decomp (gsl_matrix * A, - gsl_vector * tau, - gsl_permutation * p, - int *signum, - gsl_vector * norm); - -int gsl_linalg_QRPT_decomp2 (const gsl_matrix * A, - gsl_matrix * q, gsl_matrix * r, - gsl_vector * tau, - gsl_permutation * p, - int *signum, - gsl_vector * norm); - -int gsl_linalg_QRPT_solve (const gsl_matrix * QR, - const gsl_vector * tau, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - - -int gsl_linalg_QRPT_svx (const gsl_matrix * QR, - const gsl_vector * tau, - const gsl_permutation * p, - gsl_vector * x); - -int gsl_linalg_QRPT_QRsolve (const gsl_matrix * Q, - const gsl_matrix * R, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_QRPT_Rsolve (const gsl_matrix * QR, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_QRPT_Rsvx (const gsl_matrix * QR, - const gsl_permutation * p, - gsl_vector * x); - -int gsl_linalg_QRPT_update (gsl_matrix * Q, - gsl_matrix * R, - const gsl_permutation * p, - gsl_vector * u, - const gsl_vector * v); - -/* LQ decomposition */ - -int gsl_linalg_LQ_decomp (gsl_matrix * A, gsl_vector * tau); - -int gsl_linalg_LQ_solve_T (const gsl_matrix * LQ, const gsl_vector * tau, - const gsl_vector * b, gsl_vector * x); - -int gsl_linalg_LQ_svx_T (const gsl_matrix * LQ, const gsl_vector * tau, - gsl_vector * x); - -int gsl_linalg_LQ_lssolve_T (const gsl_matrix * LQ, const gsl_vector * tau, - const gsl_vector * b, gsl_vector * x, - gsl_vector * residual); - -int gsl_linalg_LQ_Lsolve_T (const gsl_matrix * LQ, const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_LQ_Lsvx_T (const gsl_matrix * LQ, gsl_vector * x); - -int gsl_linalg_L_solve_T (const gsl_matrix * L, const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_LQ_vecQ (const gsl_matrix * LQ, const gsl_vector * tau, - gsl_vector * v); - -int gsl_linalg_LQ_vecQT (const gsl_matrix * LQ, const gsl_vector * tau, - gsl_vector * v); - -int gsl_linalg_LQ_unpack (const gsl_matrix * LQ, const gsl_vector * tau, - gsl_matrix * Q, gsl_matrix * L); - -int gsl_linalg_LQ_update (gsl_matrix * Q, gsl_matrix * R, - const gsl_vector * v, gsl_vector * w); -int gsl_linalg_LQ_LQsolve (gsl_matrix * Q, gsl_matrix * L, - const gsl_vector * b, gsl_vector * x); - -/* P^T L Q decomposition */ - -int gsl_linalg_PTLQ_decomp (gsl_matrix * A, gsl_vector * tau, - gsl_permutation * p, int *signum, - gsl_vector * norm); - -int gsl_linalg_PTLQ_decomp2 (const gsl_matrix * A, gsl_matrix * q, - gsl_matrix * r, gsl_vector * tau, - gsl_permutation * p, int *signum, - gsl_vector * norm); - -int gsl_linalg_PTLQ_solve_T (const gsl_matrix * QR, - const gsl_vector * tau, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_PTLQ_svx_T (const gsl_matrix * LQ, - const gsl_vector * tau, - const gsl_permutation * p, - gsl_vector * x); - -int gsl_linalg_PTLQ_LQsolve_T (const gsl_matrix * Q, const gsl_matrix * L, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_PTLQ_Lsolve_T (const gsl_matrix * LQ, - const gsl_permutation * p, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_PTLQ_Lsvx_T (const gsl_matrix * LQ, - const gsl_permutation * p, - gsl_vector * x); - -int gsl_linalg_PTLQ_update (gsl_matrix * Q, gsl_matrix * L, - const gsl_permutation * p, - const gsl_vector * v, gsl_vector * w); - -/* Cholesky Decomposition */ - -int gsl_linalg_cholesky_decomp (gsl_matrix * A); - -int gsl_linalg_cholesky_solve (const gsl_matrix * cholesky, - const gsl_vector * b, - gsl_vector * x); - -int gsl_linalg_cholesky_svx (const gsl_matrix * cholesky, - gsl_vector * x); - -int gsl_linalg_cholesky_invert(gsl_matrix * cholesky); - -/* Cholesky decomposition with unit-diagonal triangular parts. - * A = L D L^T, where diag(L) = (1,1,...,1). - * Upon exit, A contains L and L^T as for Cholesky, and - * the diagonal of A is (1,1,...,1). The vector Dis set - * to the diagonal elements of the diagonal matrix D. - */ -int gsl_linalg_cholesky_decomp_unit(gsl_matrix * A, gsl_vector * D); - -/* Complex Cholesky Decomposition */ - -int gsl_linalg_complex_cholesky_decomp (gsl_matrix_complex * A); - -int gsl_linalg_complex_cholesky_solve (const gsl_matrix_complex * cholesky, - const gsl_vector_complex * b, - gsl_vector_complex * x); - -int gsl_linalg_complex_cholesky_svx (const gsl_matrix_complex * cholesky, - gsl_vector_complex * x); - -int gsl_linalg_complex_cholesky_invert(gsl_matrix_complex * cholesky); - - -/* Symmetric to symmetric tridiagonal decomposition */ - -int gsl_linalg_symmtd_decomp (gsl_matrix * A, - gsl_vector * tau); - -int gsl_linalg_symmtd_unpack (const gsl_matrix * A, - const gsl_vector * tau, - gsl_matrix * Q, - gsl_vector * diag, - gsl_vector * subdiag); - -int gsl_linalg_symmtd_unpack_T (const gsl_matrix * A, - gsl_vector * diag, - gsl_vector * subdiag); - -/* Hermitian to symmetric tridiagonal decomposition */ - -int gsl_linalg_hermtd_decomp (gsl_matrix_complex * A, - gsl_vector_complex * tau); - -int gsl_linalg_hermtd_unpack (const gsl_matrix_complex * A, - const gsl_vector_complex * tau, - gsl_matrix_complex * U, - gsl_vector * diag, - gsl_vector * sudiag); - -int gsl_linalg_hermtd_unpack_T (const gsl_matrix_complex * A, - gsl_vector * diag, - gsl_vector * subdiag); - -/* Linear Solve Using Householder Transformations - - * exceptions: - */ - -int gsl_linalg_HH_solve (gsl_matrix * A, const gsl_vector * b, gsl_vector * x); -int gsl_linalg_HH_svx (gsl_matrix * A, gsl_vector * x); - -/* Linear solve for a symmetric tridiagonal system. - - * The input vectors represent the NxN matrix as follows: - * - * diag[0] offdiag[0] 0 ... - * offdiag[0] diag[1] offdiag[1] ... - * 0 offdiag[1] diag[2] ... - * 0 0 offdiag[2] ... - * ... ... ... ... - */ -int gsl_linalg_solve_symm_tridiag (const gsl_vector * diag, - const gsl_vector * offdiag, - const gsl_vector * b, - gsl_vector * x); - -/* Linear solve for a nonsymmetric tridiagonal system. - - * The input vectors represent the NxN matrix as follows: - * - * diag[0] abovediag[0] 0 ... - * belowdiag[0] diag[1] abovediag[1] ... - * 0 belowdiag[1] diag[2] ... - * 0 0 belowdiag[2] ... - * ... ... ... ... - */ -int gsl_linalg_solve_tridiag (const gsl_vector * diag, - const gsl_vector * abovediag, - const gsl_vector * belowdiag, - const gsl_vector * b, - gsl_vector * x); - - -/* Linear solve for a symmetric cyclic tridiagonal system. - - * The input vectors represent the NxN matrix as follows: - * - * diag[0] offdiag[0] 0 ..... offdiag[N-1] - * offdiag[0] diag[1] offdiag[1] ..... - * 0 offdiag[1] diag[2] ..... - * 0 0 offdiag[2] ..... - * ... ... - * offdiag[N-1] ... - */ -int gsl_linalg_solve_symm_cyc_tridiag (const gsl_vector * diag, - const gsl_vector * offdiag, - const gsl_vector * b, - gsl_vector * x); - -/* Linear solve for a nonsymmetric cyclic tridiagonal system. - - * The input vectors represent the NxN matrix as follows: - * - * diag[0] abovediag[0] 0 ..... belowdiag[N-1] - * belowdiag[0] diag[1] abovediag[1] ..... - * 0 belowdiag[1] diag[2] - * 0 0 belowdiag[2] ..... - * ... ... - * abovediag[N-1] ... - */ -int gsl_linalg_solve_cyc_tridiag (const gsl_vector * diag, - const gsl_vector * abovediag, - const gsl_vector * belowdiag, - const gsl_vector * b, - gsl_vector * x); - - -/* Bidiagonal decomposition */ - -int gsl_linalg_bidiag_decomp (gsl_matrix * A, - gsl_vector * tau_U, - gsl_vector * tau_V); - -int gsl_linalg_bidiag_unpack (const gsl_matrix * A, - const gsl_vector * tau_U, - gsl_matrix * U, - const gsl_vector * tau_V, - gsl_matrix * V, - gsl_vector * diag, - gsl_vector * superdiag); - -int gsl_linalg_bidiag_unpack2 (gsl_matrix * A, - gsl_vector * tau_U, - gsl_vector * tau_V, - gsl_matrix * V); - -int gsl_linalg_bidiag_unpack_B (const gsl_matrix * A, - gsl_vector * diag, - gsl_vector * superdiag); - -/* Balancing */ - -int gsl_linalg_balance_matrix (gsl_matrix * A, gsl_vector * D); -int gsl_linalg_balance_accum (gsl_matrix * A, gsl_vector * D); -int gsl_linalg_balance_columns (gsl_matrix * A, gsl_vector * D); - -INLINE_DECL void gsl_linalg_givens (const double a, const double b, - double *c, double *s); -INLINE_DECL void gsl_linalg_givens_gv (gsl_vector * v, const size_t i, - const size_t j, const double c, - const double s); - -#ifdef HAVE_INLINE - -/* Generate a Givens rotation (cos,sin) which takes v=(x,y) to (|v|,0) - From Golub and Van Loan, "Matrix Computations", Section 5.1.8 */ -INLINE_FUN -void -gsl_linalg_givens (const double a, const double b, double *c, double *s) -{ - if (b == 0) - { - *c = 1; - *s = 0; - } - else if (fabs (b) > fabs (a)) - { - double t = -a / b; - double s1 = 1.0 / sqrt (1 + t * t); - *s = s1; - *c = s1 * t; - } - else - { - double t = -b / a; - double c1 = 1.0 / sqrt (1 + t * t); - *c = c1; - *s = c1 * t; - } -} /* gsl_linalg_givens() */ - -INLINE_FUN -void -gsl_linalg_givens_gv (gsl_vector * v, const size_t i, const size_t j, - const double c, const double s) -{ - /* Apply rotation to vector v' = G^T v */ - - double vi = gsl_vector_get (v, i); - double vj = gsl_vector_get (v, j); - gsl_vector_set (v, i, c * vi - s * vj); - gsl_vector_set (v, j, s * vi + c * vj); -} - -#endif /* HAVE_INLINE */ - -__END_DECLS - -#endif /* __GSL_LINALG_H__ */ |