GSL科学计算函数库(GNU Scientific Library)

/* linalg/gsl_linalg.h * * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007, 2019 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> #include <gsl/gsl_blas.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); double gsl_linalg_householder_transform2 (double * alpha, 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_left(const double tau, const gsl_vector * v, gsl_matrix * A, gsl_vector * work); int gsl_linalg_householder_right(const double tau, const gsl_vector * v, gsl_matrix * A, gsl_vector * work); 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); int gsl_linalg_complex_householder_left (const gsl_complex tau, const gsl_vector_complex * v, gsl_matrix_complex * A, gsl_vector_complex * work); /* 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); /* 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 * work); int gsl_linalg_LU_invert (const gsl_matrix * LU, const gsl_permutation * p, gsl_matrix * inverse); int gsl_linalg_LU_invx (gsl_matrix * LU, const gsl_permutation * p); 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); /* Banded LU decomposition */ int gsl_linalg_LU_band_decomp (const size_t M, const size_t lb, const size_t ub, gsl_matrix * AB, gsl_vector_uint * piv); int gsl_linalg_LU_band_solve (const size_t lb, const size_t ub, const gsl_matrix * LUB, const gsl_vector_uint * piv, const gsl_vector * b, gsl_vector * x); int gsl_linalg_LU_band_svx (const size_t lb, const size_t ub, const gsl_matrix * LUB, const gsl_vector_uint * piv, gsl_vector * x); int gsl_linalg_LU_band_unpack (const siz