CCSDTS
Originally xGSVTS
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2010
Adapted to CCSDTS by
July 2010
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2010
Adapted to CCSDTS by
July 2010
Purpose
CCSDTS tests CUNCSD, which, given an M-by-M partitioned unitary
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) COMPLEX array, dimension (LDX,M)
The M-by-M matrix X.
|
| XF |
(output) COMPLEX array, dimension (LDX,M)
Details of the CSD of X, as returned by CUNCSD;
see CUNCSD for further details. |
| LDX |
(input) INTEGER
The leading dimension of the arrays X and XF.
LDX >= max( 1,M ). |
| U1 |
(output) COMPLEX array, dimension(LDU1,P)
The P-by-P unitary matrix U1.
|
| LDU1 |
(input) INTEGER
The leading dimension of the array U1. LDU >= max(1,P).
|
| U2 |
(output) COMPLEX array, dimension(LDU2,M-P)
The (M-P)-by-(M-P) unitary matrix U2.
|
| LDU2 |
(input) INTEGER
The leading dimension of the array U2. LDU >= max(1,M-P).
|
| V1T |
(output) COMPLEX array, dimension(LDV1T,Q)
The Q-by-Q unitary matrix V1T.
|
| LDV1T |
(input) INTEGER
The leading dimension of the array V1T. LDV1T >=
max(1,Q). |
| V2T |
(output) COMPLEX array, dimension(LDV2T,M-Q)
The (M-Q)-by-(M-Q) unitary matrix V2T.
|
| LDV2T |
(input) INTEGER
The leading dimension of the array V2T. LDV2T >=
max(1,M-Q). |
| THETA |
(output) REAL 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 CUNCSD for details. |
| IWORK |
(workspace) INTEGER array, dimension (M)
|
| WORK |
(workspace) COMPLEX array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK
|
| RWORK |
(workspace) REAL array
|
| RESULT |
(output) REAL 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 ). ) |