SGRQTS
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SGRQTS tests SGGRQF, which computes the GRQ factorization of an
M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
Arguments
| M |
(input) INTEGER
The number of rows of the matrix A. M >= 0.
|
| P |
(input) INTEGER
The number of rows of the matrix B. P >= 0.
|
| N |
(input) INTEGER
The number of columns of the matrices A and B. N >= 0.
|
| A |
(input) REAL array, dimension (LDA,N)
The M-by-N matrix A.
|
| AF |
(output) REAL array, dimension (LDA,N)
Details of the GRQ factorization of A and B, as returned
by SGGRQF, see SGGRQF for further details. |
| Q |
(output) REAL array, dimension (LDA,N)
The N-by-N orthogonal matrix Q.
|
| R |
(workspace) REAL array, dimension (LDA,MAX(M,N))
|
| LDA |
(input) INTEGER
The leading dimension of the arrays A, AF, R and Q.
LDA >= max(M,N). |
| TAUA |
(output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGGQRC. |
| B |
(input) REAL array, dimension (LDB,N)
On entry, the P-by-N matrix A.
|
| BF |
(output) REAL array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by SGGRQF, see SGGRQF for further details. |
| Z |
(output) REAL array, dimension (LDB,P)
The P-by-P orthogonal matrix Z.
|
| T |
(workspace) REAL array, dimension (LDB,max(P,N))
|
| BWK |
(workspace) REAL array, dimension (LDB,N)
|
| LDB |
(input) INTEGER
The leading dimension of the arrays B, BF, Z and T.
LDB >= max(P,N). |
| TAUB |
(output) REAL array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by SGGRQF. |
| WORK |
(workspace) REAL array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK, LWORK >= max(M,P,N)**2.
|
| RWORK |
(workspace) REAL array, dimension (M)
|
| RESULT |
(output) REAL array, dimension (4)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP) RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP) RESULT(3) = norm( I - Q'*Q ) / ( N*ULP ) RESULT(4) = norm( I - Z'*Z ) / ( P*ULP ) |