# zgemlq.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zgemlq (character SIDE, character TRANS, integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) T, integer TSIZE, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

ZGEMLQ

Purpose:

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

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H
where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by short wide
LQ factorization (ZGELQ)```
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 COMPLEX*16 array, dimension
(LDA,M) if SIDE = 'L',
(LDA,N) if SIDE = 'R'
Part of the data structure to represent Q as returned by ZGELQ.```

LDA

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

T

```          T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by ZGELQ.```

TSIZE

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

C

```          C is COMPLEX*16 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) COMPLEX*16 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
ZLASWLQ or ZGELQT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGELQ will use either
ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
the LQ factorization.
This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
multiply matrix Q by another matrix.
Further Details in ZLAMSWLQ or ZGEMLQT.```

Definition at line 167 of file zgemlq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Thu Apr 1 2021 Version 3.9.1 LAPACK