dgelqf man page on Scientific

```DGELQF(1)		 LAPACK routine (version 3.2)		     DGELQF(1)

NAME
DGELQF - computes an LQ factorization of a real M-by-N matrix A

SYNOPSIS
SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER	  INFO, LDA, LWORK, M, N

DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
DGELQF  computes an LQ factorization of a real M-by-N matrix A: A = L *
Q.

ARGUMENTS
M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns of the matrix A.  N >= 0.

A       (input/output) 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, with the array TAU, represent the
orthogonal matrix Q as a product of elementary reflectors  (see
Further	Details).   LDA	    (input) INTEGER The leading dimen‐
sion of the array A.  LDA >= max(1,M).

TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary  reflectors	 (see  Further
Details).

WORK	  (workspace/output)   DOUBLE	PRECISION   array,   dimension
(MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.	 LWORK >= max(1,M).  For opti‐
mum  performance	 LWORK >= M*NB, where NB is the optimal block‐
size.  If LWORK = -1, then a workspace query  is	 assumed;  the
routine	only  calculates  the  optimal size of the WORK array,
returns this value as the first entry of the WORK array, and no
error message related to LWORK is issued by XERBLA.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1)	 =  0  and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).

LAPACK routine (version 3.2)	 November 2008			     DGELQF(1)
```
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