DCSDTS
Originally xGSVTS
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Adapted to DCSDTS
July 2010
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Adapted to DCSDTS
July 2010
Purpose
DCSDTS tests DORCSD, which, given an M-by-M partitioned orthogonal
matrix X,
Q M-Q
X = [ X11 X12 ] P ,
[ X21 X22 ] M-P
computes the CSD
[ U1 ]**T * [ X11 X12 ] * [ V1 ]
[ U2 ] [ X21 X22 ] [ V2 ]
[ I 0 0 | 0 0 0 ]
[ 0 C 0 | 0 -S 0 ]
[ 0 0 0 | 0 0 -I ]
= [---------------------] = [ D11 D12 ] .
[ 0 0 0 | I 0 0 ] [ D21 D22 ]
[ 0 S 0 | 0 C 0 ]
[ 0 0 I | 0 0 0 ]
matrix X,
Q M-Q
X = [ X11 X12 ] P ,
[ X21 X22 ] M-P
computes the CSD
[ U1 ]**T * [ X11 X12 ] * [ V1 ]
[ U2 ] [ X21 X22 ] [ V2 ]
[ I 0 0 | 0 0 0 ]
[ 0 C 0 | 0 -S 0 ]
[ 0 0 0 | 0 0 -I ]
= [---------------------] = [ D11 D12 ] .
[ 0 0 0 | I 0 0 ] [ D21 D22 ]
[ 0 S 0 | 0 C 0 ]
[ 0 0 I | 0 0 0 ]
Arguments
| M |
(input) INTEGER
The number of rows of the matrix X. M >= 0.
|
| P |
(input) INTEGER
The number of rows of the matrix X11. P >= 0.
|
| Q |
(input) INTEGER
The number of columns of the matrix X11. Q >= 0.
|
| X |
(input) DOUBLE PRECISION array, dimension (LDX,M)
The M-by-M matrix X.
|
| XF |
(output) DOUBLE PRECISION array, dimension (LDX,M)
Details of the CSD of X, as returned by DORCSD;
see DORCSD for further details. |
| LDX |
(input) INTEGER
The leading dimension of the arrays X and XF.
LDX >= max( 1,M ). |
| U1 |
(output) DOUBLE PRECISION array, dimension(LDU1,P)
The P-by-P orthogonal matrix U1.
|
| LDU1 |
(input) INTEGER
The leading dimension of the array U1. LDU >= max(1,P).
|
| U2 |
(output) DOUBLE PRECISION array, dimension(LDU2,M-P)
The (M-P)-by-(M-P) orthogonal matrix U2.
|
| LDU2 |
(input) INTEGER
The leading dimension of the array U2. LDU >= max(1,M-P).
|
| V1T |
(output) DOUBLE PRECISION array, dimension(LDV1T,Q)
The Q-by-Q orthogonal matrix V1T.
|
| LDV1T |
(input) INTEGER
The leading dimension of the array V1T. LDV1T >=
max(1,Q). |
| V2T |
(output) DOUBLE PRECISION array, dimension(LDV2T,M-Q)
The (M-Q)-by-(M-Q) orthogonal matrix V2T.
|
| LDV2T |
(input) INTEGER
The leading dimension of the array V2T. LDV2T >=
max(1,M-Q). |
| THETA |
(output) DOUBLE PRECISION array, dimension MIN(P,M-P,Q,M-Q)
The CS values of X; the essentially diagonal matrices C and
S are constructed from THETA; see subroutine DORCSD for details. |
| IWORK |
(workspace) INTEGER array, dimension (M)
|
| WORK |
(workspace) DOUBLE PRECISION array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK
|
| RWORK |
(workspace) DOUBLE PRECISION array
|
| RESULT |
(output) DOUBLE PRECISION array, dimension (9)
The test ratios:
RESULT(1) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 ) RESULT(2) = norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 ) RESULT(3) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 ) RESULT(4) = norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 ) RESULT(5) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP ) RESULT(6) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP ) RESULT(7) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP ) RESULT(8) = norm( I - V2T'*V2T ) / ( MAX(1,M-Q)*ULP ) RESULT(9) = 0 if THETA is in increasing order and all angles are in [0,pi/2]; = ULPINV otherwise. ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). ) |