Contents
cgeqlf - compute a QL factorization of a complex M-by-N
matrix A
SUBROUTINE CGEQLF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, LDA, LDWORK, INFO
SUBROUTINE CGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, LDA, LDWORK, INFO
F95 INTERFACE
SUBROUTINE GEQLF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, LDWORK, INFO
SUBROUTINE GEQLF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, LDWORK, INFO
C INTERFACE
#include <sunperf.h>
void cgeqlf(int m, int n, complex *a, int lda, complex *tau,
int *info);
void cgeqlf_64(long m, long n, complex *a, long lda, complex
*tau, long *info);
cgeqlf computes a QL factorization of a complex M-by-N
matrix A: A = Q * L.
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, if m >=
n, the lower triangle of the subarray 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 unitary 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,N). For optimum performance LDWORK >= N*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 complex scalar, and v is a complex 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).