Contents
dgerqf - compute an RQ factorization of a real M-by-N matrix
A
SUBROUTINE DGERQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER M, N, LDA, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DGERQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER*8 M, N, LDA, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GERQF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER :: M, N, LDA, LDWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GERQF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER(8) :: M, N, LDA, LDWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dgerqf(int m, int n, double *a, int lda, double *tau,
int *info);
void dgerqf_64(long m, long n, double *a, long lda, double
*tau, long *info);
dgerqf computes an RQ factorization of a real M-by-N matrix
A: A = R * Q.
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 tra-
pezoidal matrix R; the remaining elements, with
the array TAU, represent the orthogonal 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 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 real scalar, and v is a real vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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).