dgeqrf man page on Scientific

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

NAME
DGEQRF - computes a QR factorization of a real M-by-N matrix A

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

INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE
DGEQRF  computes	 a QR factorization of a real M-by-N matrix A: A = Q *
R.

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
above the diagonal of the array contain the min(M,N)-by-N upper
trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
elements	 below the diagonal, with the array TAU, represent the
orthogonal matrix Q as a product of min(m,n) elementary reflec‐
tors (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,N).  For opti‐
mum performance LWORK >= N*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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on	 exit  in  A(i+1:m,i),
and tau in TAU(i).

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