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

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