
sgerqf.f(3) LAPACK sgerqf.f(3)
NAME
sgerqf.f 
SYNOPSIS
Functions/Subroutines
subroutine sgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF
Function/Subroutine Documentation
subroutine sgerqf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real,
dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)
SGERQF
Purpose:
SGERQF computes an RQ factorization of a real MbyN matrix A:
A = R * Q.
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 REAL array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit,
if m <= n, the upper triangle of the subarray
A(1:m,nm+1:n) contains the MbyM upper triangular matrix R;
if m >= n, the elements on and above the (mn)th subdiagonal
contain the MbyN 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU
TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is
the optimal blocksize.
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
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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**T
where tau is a real scalar, and v is a real vector with
v(nk+i+1:n) = 0 and v(nk+i) = 1; v(1:nk+i1) is stored on exit in
A(mk+i,1:nk+i1), and tau in TAU(i).
Definition at line 139 of file sgerqf.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgerqf.f(3) 
