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. More...
Private Member Functions | |
subroutine | solve_least_squares_mtx (a, b, work, olwork, err) |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a QR or LQ factorization of the matrix A. Notice, it is assumed that matrix A has full rank. More... | |
subroutine | solve_least_squares_vec (a, b, work, olwork, err) |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns using a QR or LQ factorization of the matrix A. Notice, it is assumed that matrix A has full rank. More... | |
Solves the overdetermined or underdetermined system (A*X = B) of M equations of N unknowns.
Definition at line 351 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 QR or LQ factorization of the matrix A. Notice, it is assumed that matrix A has full rank.
[in,out] | a | On input, the M-by-N matrix A. On output, if M >= N, the QR factorization of A in the form as output by qr_factor; else, if M < N, the LQ factorization of A. |
[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] | 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 1966 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 QR or LQ factorization of the matrix A. Notice, it is assumed that matrix A has full rank.
[in,out] | a | On input, the M-by-N matrix A. On output, if M >= N, the QR factorization of A in the form as output by qr_factor; else, if M < N, the LQ factorization of A. |
[in,out] | b | If M >= N, the M-element array B. On output, the first N elements contain the N-element solution array X. If M < N, an N-element array with the first M elements containing the array B. On output, the N-element solution array X. |
[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 2072 of file linalg_solve.f90.