# sgemlq.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine sgemlq (SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
SGEMLQ

## Function/Subroutine Documentation

### subroutine sgemlq (character SIDE, character TRANS, integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) T, integer TSIZE, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO)

SGEMLQ

Purpose:

```     SGEMLQ overwrites the general real M-by-N matrix C with

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T
where Q is a real orthogonal matrix defined as the product
of blocked elementary reflectors computed by short wide LQ
factorization (SGELQ)```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.```

TRANS

```          TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'T':  Transpose, apply Q**T.```

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 C. N >= 0.```

K

```          K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.```

A

```          A is REAL array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
Part of the data structure to represent Q as returned by DGELQ.```

LDA

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

T

```          T is REAL array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by SGELQ.```

TSIZE

```          TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.```

C

```          C is REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.```

LDC

```          LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).```

WORK

`         (workspace) REAL array, dimension (MAX(1,LWORK))`

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
is issued by XERBLA.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Further Details

``` These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
SLASWLQ or SGELQT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGELQ will use either
SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
the LQ factorization.
This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
multiply matrix Q by another matrix.
Further Details in SLAMSWLQ or SGEMLQT.```

Definition at line 168 of file sgemlq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Thu Apr 1 2021 Version 3.9.1 LAPACK