cgetsls.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

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.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
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)
Author
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