Contents
zgeqrf - compute a QR factorization of a complex M-by-N
matrix A
SUBROUTINE ZGEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, LDA, LDWORK, INFO
SUBROUTINE ZGEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, LDA, LDWORK, INFO
F95 INTERFACE
SUBROUTINE GEQRF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, LDWORK, INFO
SUBROUTINE GEQRF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, LDWORK, INFO
C INTERFACE
#include <sunperf.h>
void zgeqrf(int m, int n, doublecomplex *a, int lda, doub-
lecomplex *tau, int *info);
void zgeqrf_64(long m, long n, doublecomplex *a, long lda,
doublecomplex *tau, long *info);
zgeqrf computes a QR factorization of a complex M-by-N
matrix A: A = Q * R.
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 above the diagonal of the array con-
tain the min(M,N)-by-N upper trapezoidal matrix R
(R is upper triangular if m >= n); the elements
below the diagonal, with the array TAU, represent
the unitary matrix Q as a product of min(m,n) ele-
mentary 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(1) H(2) . . . H(k), 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit
in A(i+1:m,i), and tau in TAU(i).