Contents
sgeqrf - compute a QR factorization of a real M-by-N matrix
A
SUBROUTINE SGEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER M, N, LDA, LDWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
SUBROUTINE SGEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)
INTEGER*8 M, N, LDA, LDWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GEQRF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER :: M, N, LDA, LDWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
SUBROUTINE GEQRF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
INTEGER(8) :: M, N, LDA, LDWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void sgeqrf(int m, int n, float *a, int lda, float *tau, int
*info);
void sgeqrf_64(long m, long n, float *a, long lda, float
*tau, long *info);
sgeqrf computes a QR factorization of a real 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 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,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 real scalar, and v is a real 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).