SGSVTS
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SGSVTS tests SGGSVD, which computes the GSVD of an M-by-N matrix A
and a P-by-N matrix B:
U'*A*Q = D1*R and V'*B*Q = D2*R.
and a P-by-N matrix B:
U'*A*Q = D1*R and V'*B*Q = D2*R.
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,M)
The M-by-N matrix A.
|
| AF |
(output) REAL array, dimension (LDA,N)
Details of the GSVD of A and B, as returned by SGGSVD,
see SGGSVD for further details. |
| LDA |
(input) INTEGER
The leading dimension of the arrays A and AF.
LDA >= max( 1,M ). |
| B |
(input) REAL array, dimension (LDB,P)
On entry, the P-by-N matrix B.
|
| BF |
(output) REAL array, dimension (LDB,N)
Details of the GSVD of A and B, as returned by SGGSVD,
see SGGSVD for further details. |
| LDB |
(input) INTEGER
The leading dimension of the arrays B and BF.
LDB >= max(1,P). |
| U |
(output) REAL array, dimension(LDU,M)
The M by M orthogonal matrix U.
|
| LDU |
(input) INTEGER
The leading dimension of the array U. LDU >= max(1,M).
|
| V |
(output) REAL array, dimension(LDV,M)
The P by P orthogonal matrix V.
|
| LDV |
(input) INTEGER
The leading dimension of the array V. LDV >= max(1,P).
|
| Q |
(output) REAL array, dimension(LDQ,N)
The N by N orthogonal matrix Q.
|
| LDQ |
(input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
|
| ALPHA |
(output) REAL array, dimension (N)
|
| BETA |
(output) REAL array, dimension (N)
The generalized singular value pairs of A and B, the
``diagonal'' matrices D1 and D2 are constructed from ALPHA and BETA, see subroutine SGGSVD for details. |
| R |
(output) REAL array, dimension(LDQ,N)
The upper triangular matrix R.
|
| LDR |
(input) INTEGER
The leading dimension of the array R. LDR >= max(1,N).
|
| IWORK |
(workspace) INTEGER array, dimension (N)
|
| WORK |
(workspace) REAL array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK,
LWORK >= max(M,P,N)*max(M,P,N). |
| RWORK |
(workspace) REAL array, dimension (max(M,P,N))
|
| RESULT |
(output) REAL array, dimension (6)
The test ratios:
RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP) RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP) RESULT(3) = norm( I - U'*U ) / ( M*ULP ) RESULT(4) = norm( I - V'*V ) / ( P*ULP ) RESULT(5) = norm( I - Q'*Q ) / ( N*ULP ) RESULT(6) = 0 if ALPHA is in decreasing order; = ULPINV otherwise. |