sgeqlf - compute a QL factorization of a real M-by-N matrix A
SUBROUTINE SGEQLF( M, N, A, LDA, TAU, WORK, LDWORK, INFO) INTEGER M, N, LDA, LDWORK, INFO REAL A(LDA,*), TAU(*), WORK(*)
SUBROUTINE SGEQLF_64( M, N, A, LDA, TAU, WORK, LDWORK, INFO) INTEGER*8 M, N, LDA, LDWORK, INFO REAL A(LDA,*), TAU(*), WORK(*)
SUBROUTINE GEQLF( [M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO]) INTEGER :: M, N, LDA, LDWORK, INFO REAL, DIMENSION(:) :: TAU, WORK REAL, DIMENSION(:,:) :: A
SUBROUTINE GEQLF_64( [M], [N], A, [LDA], TAU, [WORK], [LDWORK], * [INFO]) INTEGER(8) :: M, N, LDA, LDWORK, INFO REAL, DIMENSION(:) :: TAU, WORK REAL, DIMENSION(:,:) :: A
#include <sunperf.h>
void sgeqlf(int m, int n, float *a, int lda, float *tau, int *info);
void sgeqlf_64(long m, long n, float *a, long lda, float *tau, long *info);
sgeqlf computes a QL factorization of a real M-by-N matrix A: A = Q * L.
A(m-n+1:m,1:n)
contains the N-by-N lower triangular matrix L;
if m < = n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N 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).
WORK(1)
returns the optimal LDWORK.
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.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal 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(m-k+i+1:m)
= 0 and v(m-k+i)
= 1; v(1:m-k+i-1)
is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).