# dgemlq.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgemlq.f

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

Purpose:

DGEMLQ 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 (DGELQ)

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

TSIZE

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

C

```          C is DOUBLE PRECISION 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) DOUBLE PRECISION 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 unlikely not 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 DLASWLQ or DGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGELQ will use either DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute the LQ factorization. This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to multiply matrix Q by another matrix. Further Details in DLAMSWLQ or DGEMLQT.

Definition at line 170 of file dgemlq.f.

## Author

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