gsl_linalg.h

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

                           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_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);

/* 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);

/* 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_columns (gsl_matrix * A, gsl_vector * D);


__END_DECLS

#endif /* __GSL_LINALG_H__ */