# zgemqr.f - Man Page

SRC/zgemqr.f

## Synopsis

### Functions/Subroutines

subroutine zgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMQR

## Function/Subroutine Documentation

### subroutine zgemqr (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)

ZGEMQR

Purpose:

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

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**H * C       C * Q**H

where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by tall skinny
QR factorization (ZGEQR)```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.```

TRANS

```          TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'C':  Conjugate transpose, apply Q**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 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,K)
Part of the data structure to represent Q as returned by ZGEQR.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).```

T

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

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**H*C or C*Q**H 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

Univ. of Colorado Denver

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
ZLATSQR or ZGEQRT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGEQR will use either
ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute
the QR factorization.
This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to
multiply matrix Q by another matrix.
Further Details in ZLAMTSQR or ZGEMQRT.```

Definition at line 172 of file zgemqr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK