ZCSDTS
Originally xGSVTS
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2010
Adapted to ZCSDTS
July 2010
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2010
Adapted to ZCSDTS
July 2010
Purpose
ZCSDTS tests ZUNCSD, 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*16 array, dimension (LDX,M)
The M-by-M matrix X.
|
| XF |
(output) COMPLEX*16 array, dimension (LDX,M)
Details of the CSD of X, as returned by ZUNCSD;
see ZUNCSD for further details. |
| LDX |
(input) INTEGER
The leading dimension of the arrays X and XF.
LDX >= max( 1,M ). |
| U1 |
(output) COMPLEX*16 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*16 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*16 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*16 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) 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 ZUNCSD for details. |
| IWORK |
(workspace) INTEGER array, dimension (M)
|
| WORK |
(workspace) COMPLEX*16 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 ). ) |