linalg
1.4.3
A linear algebra library that provides a user-friendly interface to several BLAS and LAPACK routines.
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Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A. More...
Private Member Functions | |
subroutine | solve_least_squares_mtx_svd (a, b, s, arnk, work, olwork, err) |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A. More... | |
subroutine | solve_least_squares_vec_svd (a, b, s, arnk, work, olwork, err) |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A. More... | |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A.
Definition at line 457 of file linalg_solve.f90.
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private |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A.
[in,out] | a | On input, the M-by-N matrix A. On output, the matrix is overwritten by the details of its complete orthogonal factorization. |
[in,out] | b | If M >= N, the M-by-NRHS matrix B. On output, the first N rows contain the N-by-NRHS solution matrix X. If M < N, an N-by-NRHS matrix with the first M rows containing the matrix B. On output, the N-by-NRHS solution matrix X. |
[out] | arnk | An optional output, that if provided, will return the rank of a . |
[out] | s | An optional MIN(M, N)-element array that on output contains the singular values of a in descending order. Notice, the condition number of a can be determined by S(1) / S(MIN(M, N)). |
[out] | arnk | An optional output, that if provided, will return the rank of a . |
[out] | work | An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork . |
[out] | olwork | An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work , and returns without performing any actual calculations. |
[out] | err | An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.
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Definition at line 2472 of file linalg_solve.f90.
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private |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a singular value decomposition of matrix A.
[in,out] | a | On input, the M-by-N matrix A. On output, the matrix is overwritten by the details of its complete orthogonal factorization. |
[in,out] | b | If M >= N, the M-by-NRHS matrix B. On output, the first N rows contain the N-by-NRHS solution matrix X. If M < N, an N-by-NRHS matrix with the first M rows containing the matrix B. On output, the N-by-NRHS solution matrix X. |
[out] | s | An optional MIN(M, N)-element array that on output contains the singular values of a in descending order. Notice, the condition number of a can be determined by S(1) / S(MIN(M, N)). |
[out] | arnk | An optional output, that if provided, will return the rank of a . |
[out] | work | An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork . |
[out] | olwork | An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work , and returns without performing any actual calculations. |
[out] | err | An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.
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Definition at line 2619 of file linalg_solve.f90.