zgeqrf(3P) Sun Performance Library zgeqrf(3P)NAMEzgeqrf - compute a QR factorization of a complex M-by-N matrix A
SYNOPSIS
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, doublecomplex
*tau, int *info);
void zgeqrf_64(long m, long n, doublecomplex *a, long lda, doublecom‐
plex *tau, long *info);
PURPOSEzgeqrf computes a QR factorization of a complex M-by-N matrix A: A = Q
* R.
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
above the diagonal of the array contain 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, repre‐
sent the unitary matrix Q as a product of min(m,n) 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 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(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).
6 Mar 2009 zgeqrf(3P)