dgerqf man page on Scientific

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

NAME
DGERQF - computes an RQ factorization of a real M-by-N matrix A

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

INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE
DGERQF  computes an RQ factorization of a real M-by-N matrix A: A = R *
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, if m <= n,  the	 upper
triangle	 of  the  subarray  A(1:m,n-m+1:n) contains the M-by-M
upper triangular matrix R; if m >= n, the elements on and above
the  (m-n)-th  subdiagonal contain the M-by-N upper trapezoidal
matrix R; the remaining elements, with the array TAU, represent
the  orthogonal	matrix	Q  as a product of min(m,n) elementary
reflectors (see Further Details).  LDA	  (input) INTEGER  The
leading dimension 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored  on  exit  in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).

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