cgemqr.f(3) LAPACK cgemqr.f(3)

cgemqr.f

# SYNOPSIS

## Functions/Subroutines

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

# Function/Subroutine Documentation

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

CGEMQR

Purpose:

```CGEMQR 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 (CGEQR)```

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 array, dimension (LDA,K)
Part of the data structure to represent Q as returned by CGEQR.```

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

TSIZE

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

C

```C is COMPLEX 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 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
CLATSQR or CGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, CGEQR will use either
CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
the QR factorization.
This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
multiply matrix Q by another matrix.
Further Details in CLAMTSQR or CGEMQRT.```

Definition at line 170 of file cgemqr.f.

# Author

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 Tue Jun 29 2021 Version 3.10.0