Header wrapper for bidiag_base.h. More...
#include <o2scl/err_hnd.h>#include <o2scl/permutation.h>#include <o2scl/cblas.h>#include <o2scl/householder.h>#include <o2scl/givens.h>#include "bidiag_base.h"Go to the source code of this file.
Namespaces | |
| o2scl_linalg | |
| The namespace for linear algebra classes and functions. | |
| o2scl_linalg_bracket | |
| The namespace for linear algebra classes and functions with operator() | |
Macros | |
| #define | O2SCL_IX(V, i) V[i] |
| #define | O2SCL_IX2(M, i, j) M(i,j) |
| #define | O2SCL_IX(V, i) V[i] |
| #define | O2SCL_IX2(M, i, j) M[i][j] |
Functions | |
| template<class mat_t , class vec_t , class vec2_t > | |
| int | o2scl_linalg::o2scl_linalg::bidiag_decomp (size_t M, size_t N, mat_t &A, vec_t &tau_U, vec2_t &tau_V) |
| Factor a matrix into bidiagonal form. More... | |
| template<class mat_t , class vec_t , class mat2_t , class vec2_t , class mat3_t , class vec3_t , class vec4_t > | |
| int | o2scl_linalg::o2scl_linalg::bidiag_unpack (size_t M, size_t N, const mat_t &A, const vec_t &tau_U, mat2_t &U, const vec2_t &tau_V, mat3_t &V, vec3_t &diag, vec4_t &superdiag) |
Unpack a matrix A with the bidiagonal decomposition and create matrices U, V, diagonal diag and superdiagonal superdiag. More... | |
| template<class mat_t , class vec_t , class vec2_t , class mat2_t > | |
| int | o2scl_linalg::o2scl_linalg::bidiag_unpack2 (size_t M, size_t N, mat_t &A, vec_t &tau_U, vec2_t &tau_V, mat2_t &V) |
Unpack a matrix A with the bidiagonal decomposition and create matrix V. | |
| template<class mat_t , class vec_t , class vec2_t > | |
| int | o2scl_linalg::o2scl_linalg::bidiag_unpack_B (size_t M, size_t N, const mat_t &A, vec_t &diag, vec2_t &superdiag) |
Unpack the diagonal and superdiagonal of the bidiagonal decomposition of A into diag and superdiag. | |
| template<class mat_t , class vec_t , class vec2_t > | |
| int | o2scl_linalg_bracket::o2scl_linalg::bidiag_decomp (size_t M, size_t N, mat_t &A, vec_t &tau_U, vec2_t &tau_V) |
| Factor a matrix into bidiagonal form. More... | |
| template<class mat_t , class vec_t , class mat2_t , class vec2_t , class mat3_t , class vec3_t , class vec4_t > | |
| int | o2scl_linalg_bracket::o2scl_linalg::bidiag_unpack (size_t M, size_t N, const mat_t &A, const vec_t &tau_U, mat2_t &U, const vec2_t &tau_V, mat3_t &V, vec3_t &diag, vec4_t &superdiag) |
Unpack a matrix A with the bidiagonal decomposition and create matrices U, V, diagonal diag and superdiagonal superdiag. More... | |
| template<class mat_t , class vec_t , class vec2_t , class mat2_t > | |
| int | o2scl_linalg_bracket::o2scl_linalg::bidiag_unpack2 (size_t M, size_t N, mat_t &A, vec_t &tau_U, vec2_t &tau_V, mat2_t &V) |
Unpack a matrix A with the bidiagonal decomposition and create matrix V. | |
| template<class mat_t , class vec_t , class vec2_t > | |
| int | o2scl_linalg_bracket::o2scl_linalg::bidiag_unpack_B (size_t M, size_t N, const mat_t &A, vec_t &diag, vec2_t &superdiag) |
Unpack the diagonal and superdiagonal of the bidiagonal decomposition of A into diag and superdiag. | |
Function Documentation
◆ bidiag_decomp() [1/2]
| int o2scl_linalg::o2scl_linalg::bidiag_decomp | ( | size_t | M, |
| size_t | N, | ||
| mat_t & | A, | ||
| vec_t & | tau_U, | ||
| vec2_t & | tau_V | ||
| ) |
Factor matrix A of size (M,N) with 
into 
where U and V are orthogonal and B is upper bidiagonal.
After the function call, the matrix 
is stored the diagonal and first superdiagonal of A. The matrices 
and 
are stored as packed sets of Householder transformations in the lower and upper triangular parts of A, respectively.
Adapted from the GSL version which was based on algorithm 5.4.2 in Golub96.
◆ bidiag_decomp() [2/2]
| int o2scl_linalg_bracket::o2scl_linalg::bidiag_decomp | ( | size_t | M, |
| size_t | N, | ||
| mat_t & | A, | ||
| vec_t & | tau_U, | ||
| vec2_t & | tau_V | ||
| ) |
Factor matrix A of size (M,N) with into where U and V are orthogonal and B is upper bidiagonal.
After the function call, the matrix is stored the diagonal and first superdiagonal of A. The matrices and are stored as packed sets of Householder transformations in the lower and upper triangular parts of A, respectively.
Adapted from the GSL version which was based on algorithm 5.4.2 in Golub96.
◆ bidiag_unpack() [1/2]
| int o2scl_linalg::o2scl_linalg::bidiag_unpack | ( | size_t | M, |
| size_t | N, | ||
| const mat_t & | A, | ||
| const vec_t & | tau_U, | ||
| mat2_t & | U, | ||
| const vec2_t & | tau_V, | ||
| mat3_t & | V, | ||
| vec3_t & | diag, | ||
| vec4_t & | superdiag | ||
| ) |
Given a matrix A of size (M,N) with 
created by bidiag_decomp(), this function creates the matrix U of size (M,N), the matrix V of size (N,N), the diagonal diag of size N and the super-diagonal superdiag of size N-1.
◆ bidiag_unpack() [2/2]
| int o2scl_linalg_bracket::o2scl_linalg::bidiag_unpack | ( | size_t | M, |
| size_t | N, | ||
| const mat_t & | A, | ||
| const vec_t & | tau_U, | ||
| mat2_t & | U, | ||
| const vec2_t & | tau_V, | ||
| mat3_t & | V, | ||
| vec3_t & | diag, | ||
| vec4_t & | superdiag | ||
| ) |
Given a matrix A of size (M,N) with created by bidiag_decomp(), this function creates the matrix U of size (M,N), the matrix V of size (N,N), the diagonal diag of size N and the super-diagonal superdiag of size N-1.