SRC/cgetsls.f(3)

🌸 NAME 🌸

SRC/cgetsls.f — bestie, this is the page from the Library Functions Manual, and it's all about the cgetsls subroutine. It's giving linear-solver main character energy 💅✨

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🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine cgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork,
    info)
    CGETSLS

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🦋 Function/Subroutine Documentation 🦋

subroutine cgetsls (character trans, integer m, integer n, integer nrhs,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
    ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer
    info)
    CGETSLS

Purpose

CGETSLS solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, using a tall skinny QR or short wide LQ factorization of A.

It is assumed that A has full rank, and only a rudimentary protection against rank-deficient matrices is provided. This subroutine only detects exact rank-deficiency, where a diagonal element of the triangular factor of A is exactly zero.

It is conceivable for one (or more) of the diagonal elements of the triangular factor of A to be subnormally tiny numbers without this subroutine signalling an error. The solutions computed for such almost-rank-deficient matrices may be less accurate due to a loss of numerical precision.

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B.
4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**T * X ||.

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.

Parameters

TRANS

TRANS is CHARACTER*1.

• = 'N': the linear system involves A;
• = 'C': the linear system involves A**H.

M

M is INTEGER. The number of rows of the matrix A. M >= 0.

N

N is INTEGER. The number of columns of the matrix A. N >= 0.

NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >=0.

A

A is COMPLEX array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A is overwritten by details of its QR or LQ factorization as returned by CGEQR or CGELQ.

LDA

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).

B

B is COMPLEX array, dimension (LDB,NRHS). On entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS if TRANS = 'C'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise:

• if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors.
• if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors;
• if TRANS = 'C' and m >= n, rows 1 to M of B contain the minimum norm solution vectors;
• if TRANS = 'C' and m < n, rows 1 to M of B contain the least squares solution vectors.

LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= MAX(1,M,N).

WORK

(workspace) COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details.

LWORK

LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1. If LWORK = -1 or -2, then a workspace query is assumed. If LWORK = -1, the routine calculates optimal size of WORK for the optimal performance and returns this value in WORK(1). If LWORK = -2, the routine calculates minimal size of WORK and returns this value in WORK(1).

INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: if INFO = i, the i-th diagonal element of the triangular factor of A is exactly zero, so that A does not have full rank; the least squares solution could not be computed.

Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 169 of file cgetsls.f.

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👑 Author 👑

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