dgelqf(3P) Sun Performance Library dgelqf(3P)NAMEdgelqf - compute an LQ factorization of a real M-by-N matrix A
SYNOPSIS
SUBROUTINE DGELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER M, N, LDA, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DGELQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER*8 M, N, LDA, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GELQF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER :: M, N, LDA, LDWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GELQF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER(8) :: M, N, LDA, LDWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dgelqf(int m, int n, double *a, int lda, double *tau, int *info);
void dgelqf_64(long m, long n, double *a, long lda, double *tau, long
*info);
PURPOSEdgelqf computes an LQ factorization of a real M-by-N matrix A: A = L *
Q.
ARGUMENTS
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
A (input/output)
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, repre‐
sent the orthogonal matrix Q as a product of elementary
reflectors (see Further Details).
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
TAU (output)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,M). For
optimum performance LDWORK >= M*NB, where NB is the optimal
blocksize.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 LDWORK is issued by XERBLA.
INFO (output)
= 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).
6 Mar 2009 dgelqf(3P)
