cgerqf(3P) Sun Performance Library cgerqf(3P)NAMEcgerqf - compute an RQ factorization of a complex M-by-N matrix A
SYNOPSIS
SUBROUTINE CGERQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, LDA, LDWORK, INFO
SUBROUTINE CGERQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, LDA, LDWORK, INFO
F95 INTERFACE
SUBROUTINE GERQF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, LDWORK, INFO
SUBROUTINE GERQF_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 cgerqf(int m, int n, complex *a, int lda, complex *tau, int
*info);
void cgerqf_64(long m, long n, complex *a, long lda, complex *tau, long
*info);
PURPOSEcgerqf computes an RQ factorization of a complex M-by-N matrix A: A = R
* Q.
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, if m <= n, the upper
triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M
upper triangular matrix R; if m >= n, the elements on and
above the (m-n)-th subdiagonal contain the M-by-N upper
trapezoidal matrix R; the remaining elements, with the array
TAU, represent 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,M). For
optimum performance LDWORK >= M*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(n-
k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
6 Mar 2009 cgerqf(3P)
