Contents
sgelqf - compute an LQ factorization of a real M-by-N matrix
A
SUBROUTINE SGELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER M, N, LDA, LDWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
SUBROUTINE SGELQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER*8 M, N, LDA, LDWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GELQF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER :: M, N, LDA, LDWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
SUBROUTINE GELQF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER(8) :: M, N, LDA, LDWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void sgelqf(int m, int n, float *a, int lda, float *tau, int
*info);
void sgelqf_64(long m, long n, float *a, long lda, float
*tau, long *info);
sgelqf computes an LQ factorization of a real M-by-N matrix
A: A = L * Q.
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 ele-
ments on and below the diagonal of the array con-
tain 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, represent
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 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 LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
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).