# dgelq.f

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

## SYNOPSIS

### Functions/Subroutines

subroutine dgelq (M, N, A, LDA, T, TSIZE, WORK, LWORK, INFO)

## Function/Subroutine Documentation

### subroutine dgelq (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) T, integer TSIZE, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

DGELQ computes a LQ factorization of an M-by-N matrix A.

Parameters:

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 A.  N >= 0.
```

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-min(M,N) lower trapezoidal matrix L
(L is lower triangular if M <= N);
the elements above the diagonal are used to store part of the
data structure to represent Q.
```

LDA

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

T

```          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
On exit, if INFO = 0, T(1) returns optimal (or either minimal
or optimal, if query is assumed) TSIZE. See TSIZE for details.
Remaining T contains part of the data structure used to represent Q.
If one wants to apply or construct Q, then one needs to keep T
(in addition to A) and pass it to further subroutines.
```

TSIZE

```          TSIZE is INTEGER
If TSIZE >= 5, the dimension of the array T.
If TSIZE = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If TSIZE = -1, the routine calculates optimal size of T for the
optimum performance and returns this value in T(1).
If TSIZE = -2, the routine calculates minimal size of T and
returns this value in T(1).
```

WORK

```          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
```

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

The goal of the interface is to give maximum freedom to the developers for creating any LQ factorization algorithm they wish. The triangular (trapezoidal) L has to be stored in the lower part of A. The lower part of A and the array T can be used to store any relevant information for applying or constructing the Q factor. The WORK array can safely be discarded after exit.

Caution: One should not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However, for a given execution, the size of T and WORK are fixed and will not change from one query to the next.

Further Details particular to this LAPACK implementation:

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 short-and-wide) or DGELQT to compute the LQ factorization.

Definition at line 161 of file dgelq.f.

## Author

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