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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgetsls.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine ZGETSLS (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)
    • ZGETSLS

👑 Function/Subroutine Documentation 👑

subroutine ZGETSLS (character trans, integer m, integer n, integer nrhs,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork,
    integer info)

ZGETSLS

🌸 Purpose 🌸

okay so ZGETSLS 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. 🫶

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 ||.
  1. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.
  2. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B.
  3. 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. no cap, that's the whole point. 🌈

💅 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*16 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 ZGEQR or ZGELQ.

LDA

LDA is INTEGER

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

B

B is COMPLEX*16 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*16 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.

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 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 160 of file zgetsls.f.

💖 Author 💖

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