cgetsls.f man page

cgetsls.f

Synopsis

Functions/Subroutines

subroutine cgetsls (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)

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)

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.

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.
          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.

Date:

June 2017

Definition at line 162 of file cgetsls.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page cgetsls(3) is an alias of cgetsls.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK