sgeqrt - N matrix A using the compact WY representation of Q
SUBROUTINE SGEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER INFO, LDA, LDT, M, N, NB REAL A(LDA,*), T(LDT,*), WORK(*) SUBROUTINE SGEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER*8 INFO, LDA, LDT, M, N, NB REAL A(LDA,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE GEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) REAL, DIMENSION(:,:) :: A, T INTEGER :: M, N, NB, LDA, LDT, INFO REAL, DIMENSION(:) :: WORK SUBROUTINE GEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) REAL, DIMENSION(:,:) :: A, T INTEGER(8) :: M, N, NB, LDA, LDT, INFO REAL, DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void sgeqrt (int m, int n, int nb, float *a, int lda, float *t, int ldt, int *info); void sgeqrt_64 (long m, long n, long nb, float *a, long lda, float *t, long ldt, long *info);
Oracle Solaris Studio Performance Library sgeqrt(3P)
NAME
sgeqrt - compute a blocked QR factorization of a real M-by-N matrix A
using the compact WY representation of Q
SYNOPSIS
SUBROUTINE SGEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO)
INTEGER INFO, LDA, LDT, M, N, NB
REAL A(LDA,*), T(LDT,*), WORK(*)
SUBROUTINE SGEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO)
INTEGER*8 INFO, LDA, LDT, M, N, NB
REAL A(LDA,*), T(LDT,*), WORK(*)
F95 INTERFACE
SUBROUTINE GEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO)
REAL, DIMENSION(:,:) :: A, T
INTEGER :: M, N, NB, LDA, LDT, INFO
REAL, DIMENSION(:) :: WORK
SUBROUTINE GEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO)
REAL, DIMENSION(:,:) :: A, T
INTEGER(8) :: M, N, NB, LDA, LDT, INFO
REAL, DIMENSION(:) :: WORK
C INTERFACE
#include <sunperf.h>
void sgeqrt (int m, int n, int nb, float *a, int lda, float *t, int
ldt, int *info);
void sgeqrt_64 (long m, long n, long nb, float *a, long lda, float *t,
long ldt, long *info);
PURPOSE
sgeqrt computes a blocked QR factorization of a real M-by-N matrix A
using the compact WY representation of Q.
ARGUMENTS
M (input)
M is INTEGER
The number of rows of the matrix A. M >= 0.
N (input)
N is INTEGER
The number of columns of the matrix A. N >= 0.
NB (input)
NB is INTEGER
The block size to be used in the blocked QR.
MIN(M,N) >= NB >= 1.
A (input/output)
A is REAL array, dimension (LDA,N)
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
are the columns of V.
LDA (input)
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,M).
T (output)
T is REAL array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below for fur-
ther details.
LDT (input)
LDT is INTEGER
The leading dimension of the array T.
LDT >= NB.
WORK (output)
WORK is REAL array, dimension (NB*N)
INFO (output)
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each
block is of order NB except for the last block, which is of order
IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
for the last block) T's are stored in the NB-by-N matrix T as
T = (T1 T2 ... TB).
7 Nov 2015 sgeqrt(3P)