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- /* 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 "gsl_mode.h"
- #include "gsl_permutation.h"
- #include "gsl_vector.h"
- #include "gsl_matrix.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);
- /* 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);
- /* 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_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);
- /* 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);
- /* 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 * Q,
- 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);
- __END_DECLS
- #endif /* __GSL_LINALG_H__ */
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