
sgeqlf.f(3) LAPACK sgeqlf.f(3)
NAME
sgeqlf.f 
SYNOPSIS
Functions/Subroutines
subroutine sgeqlf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQLF
Function/Subroutine Documentation
subroutine sgeqlf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real,
dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)
SGEQLF
Purpose:
SGEQLF computes a QL factorization of a real MbyN matrix A:
A = Q * L.
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 lower triangle of the subarray
A(mn+1:m,1:n) contains the NbyN lower triangular matrix L;
if m <= n, the elements on and below the (nm)th
superdiagonal contain the MbyN lower trapezoidal matrix L;
the remaining elements, with the array TAU, represent the
orthogonal matrix Q as a product of 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,N).
For optimum performance LWORK >= N*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(k) . . . H(2) H(1), 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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in
A(1:mk+i1,nk+i), and tau in TAU(i).
Definition at line 139 of file sgeqlf.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgeqlf.f(3) 
