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SUBROUTINE DCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
$ LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK,
$ RWORK, RESULT )
IMPLICIT NONE
*
* Originally xGSVTS
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* Adapted to DCSDTS
* July 2010
*
* .. Scalar Arguments ..
INTEGER LDX, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION RESULT( 9 ), RWORK( * ), THETA( * )
DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
$ V2T( LDV2T, * ), WORK( LWORK ), X( LDX, * ),
$ XF( LDX, * )
* ..
*
* 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 ]
*
* 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 ). )
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION PIOVER2, REALONE, REALZERO
PARAMETER ( PIOVER2 = 1.57079632679489662D0,
$ REALONE = 1.0D0, REALZERO = 0.0D0 )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, R
DOUBLE PRECISION EPS2, RESID, ULP, ULPINV
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY, DLASET, DORCSD, DSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
ULP = DLAMCH( 'Precision' )
ULPINV = REALONE / ULP
CALL DLASET( 'Full', M, M, ZERO, ONE, WORK, LDX )
CALL DSYRK( 'Upper', 'Conjugate transpose', M, M, -ONE, X, LDX,
$ ONE, WORK, LDX )
EPS2 = MAX( ULP,
$ DLANGE( '1', M, M, WORK, LDX, RWORK ) / DBLE( M ) )
R = MIN( P, M-P, Q, M-Q )
*
* Copy the matrix X to the array XF.
*
CALL DLACPY( 'Full', M, M, X, LDX, XF, LDX )
*
* Compute the CSD
*
CALL DORCSD( 'Y', 'Y', 'Y', 'Y', 'N', 'D', M, P, Q, XF(1,1), LDX,
$ XF(1,Q+1), LDX, XF(P+1,1), LDX, XF(P+1,Q+1), LDX,
$ THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T,
$ WORK, LWORK, IWORK, INFO )
*
* Compute X := diag(U1,U2)'*X*diag(V1,V2) - [D11 D12; D21 D22]
*
CALL DGEMM( 'No transpose', 'Conjugate transpose', P, Q, Q, ONE,
$ X, LDX, V1T, LDV1T, ZERO, WORK, LDX )
*
CALL DGEMM( 'Conjugate transpose', 'No transpose', P, Q, P, ONE,
$ U1, LDU1, WORK, LDX, ZERO, X, LDX )
*
DO I = 1, MIN(P,Q)-R
X(I,I) = X(I,I) - ONE
END DO
DO I = 1, R
X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) =
$ X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) - COS(THETA(I))
END DO
*
CALL DGEMM( 'No transpose', 'Conjugate transpose', P, M-Q, M-Q,
$ ONE, X(1,Q+1), LDX, V2T, LDV2T, ZERO, WORK, LDX )
*
CALL DGEMM( 'Conjugate transpose', 'No transpose', P, M-Q, P,
$ ONE, U1, LDU1, WORK, LDX, ZERO, X(1,Q+1), LDX )
*
DO I = 1, MIN(P,M-Q)-R
X(P-I+1,M-I+1) = X(P-I+1,M-I+1) + ONE
END DO
DO I = 1, R
X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) =
$ X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) +
$ SIN(THETA(R-I+1))
END DO
*
CALL DGEMM( 'No transpose', 'Conjugate transpose', M-P, Q, Q, ONE,
$ X(P+1,1), LDX, V1T, LDV1T, ZERO, WORK, LDX )
*
CALL DGEMM( 'Conjugate transpose', 'No transpose', M-P, Q, M-P,
$ ONE, U2, LDU2, WORK, LDX, ZERO, X(P+1,1), LDX )
*
DO I = 1, MIN(M-P,Q)-R
X(M-I+1,Q-I+1) = X(M-I+1,Q-I+1) - ONE
END DO
DO I = 1, R
X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) =
$ X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) -
$ SIN(THETA(R-I+1))
END DO
*
CALL DGEMM( 'No transpose', 'Conjugate transpose', M-P, M-Q, M-Q,
$ ONE, X(P+1,Q+1), LDX, V2T, LDV2T, ZERO, WORK, LDX )
*
CALL DGEMM( 'Conjugate transpose', 'No transpose', M-P, M-Q, M-P,
$ ONE, U2, LDU2, WORK, LDX, ZERO, X(P+1,Q+1), LDX )
*
DO I = 1, MIN(M-P,M-Q)-R
X(P+I,Q+I) = X(P+I,Q+I) - ONE
END DO
DO I = 1, R
X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) =
$ X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) -
$ COS(THETA(I))
END DO
*
* Compute norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 ) .
*
RESID = DLANGE( '1', P, Q, X, LDX, RWORK )
RESULT( 1 ) = ( RESID / DBLE(MAX(1,P,Q)) ) / EPS2
*
* Compute norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 ) .
*
RESID = DLANGE( '1', P, M-Q, X(1,Q+1), LDX, RWORK )
RESULT( 2 ) = ( RESID / DBLE(MAX(1,P,M-Q)) ) / EPS2
*
* Compute norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 ) .
*
RESID = DLANGE( '1', M-P, Q, X(P+1,1), LDX, RWORK )
RESULT( 3 ) = ( RESID / DBLE(MAX(1,M-P,Q)) ) / EPS2
*
* Compute norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 ) .
*
RESID = DLANGE( '1', M-P, M-Q, X(P+1,Q+1), LDX, RWORK )
RESULT( 4 ) = ( RESID / DBLE(MAX(1,M-P,M-Q)) ) / EPS2
*
* Compute I - U1'*U1
*
CALL DLASET( 'Full', P, P, ZERO, ONE, WORK, LDU1 )
CALL DSYRK( 'Upper', 'Conjugate transpose', P, P, -ONE, U1, LDU1,
$ ONE, WORK, LDU1 )
*
* Compute norm( I - U'*U ) / ( MAX(1,P) * ULP ) .
*
RESID = DLANSY( '1', 'Upper', P, WORK, LDU1, RWORK )
RESULT( 5 ) = ( RESID / DBLE(MAX(1,P)) ) / ULP
*
* Compute I - U2'*U2
*
CALL DLASET( 'Full', M-P, M-P, ZERO, ONE, WORK, LDU2 )
CALL DSYRK( 'Upper', 'Conjugate transpose', M-P, M-P, -ONE, U2,
$ LDU2, ONE, WORK, LDU2 )
*
* Compute norm( I - U2'*U2 ) / ( MAX(1,M-P) * ULP ) .
*
RESID = DLANSY( '1', 'Upper', M-P, WORK, LDU2, RWORK )
RESULT( 6 ) = ( RESID / DBLE(MAX(1,M-P)) ) / ULP
*
* Compute I - V1T*V1T'
*
CALL DLASET( 'Full', Q, Q, ZERO, ONE, WORK, LDV1T )
CALL DSYRK( 'Upper', 'No transpose', Q, Q, -ONE, V1T, LDV1T, ONE,
$ WORK, LDV1T )
*
* Compute norm( I - V1T*V1T' ) / ( MAX(1,Q) * ULP ) .
*
RESID = DLANSY( '1', 'Upper', Q, WORK, LDV1T, RWORK )
RESULT( 7 ) = ( RESID / DBLE(MAX(1,Q)) ) / ULP
*
* Compute I - V2T*V2T'
*
CALL DLASET( 'Full', M-Q, M-Q, ZERO, ONE, WORK, LDV2T )
CALL DSYRK( 'Upper', 'No transpose', M-Q, M-Q, -ONE, V2T, LDV2T,
$ ONE, WORK, LDV2T )
*
* Compute norm( I - V2T*V2T' ) / ( MAX(1,M-Q) * ULP ) .
*
RESID = DLANSY( '1', 'Upper', M-Q, WORK, LDV2T, RWORK )
RESULT( 8 ) = ( RESID / DBLE(MAX(1,M-Q)) ) / ULP
*
* Check sorting
*
RESULT(9) = REALZERO
DO I = 1, R
IF( THETA(I).LT.REALZERO .OR. THETA(I).GT.PIOVER2 ) THEN
RESULT(9) = ULPINV
END IF
IF( I.GT.1) THEN
IF ( THETA(I).LT.THETA(I-1) ) THEN
RESULT(9) = ULPINV
END IF
END IF
END DO
*
RETURN
*
* End of DCSDTS
*
END
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