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SUBROUTINE SCSDTS( 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 SCSDTS * July 2010 * * .. Scalar Arguments .. INTEGER LDX, LDU1, LDU2, LDV1T, LDV2T, LWORK, M, P, Q * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL RESULT( 9 ), RWORK( * ), THETA( * ) REAL U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), $ V2T( LDV2T, * ), WORK( LWORK ), X( LDX, * ), $ XF( LDX, * ) * .. * * Purpose * ======= * * SCSDTS tests SORCSD, 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) REAL array, dimension (LDX,M) * The M-by-M matrix X. * * XF (output) REAL array, dimension (LDX,M) * Details of the CSD of X, as returned by SORCSD; * see SORCSD for further details. * * LDX (input) INTEGER * The leading dimension of the arrays X and XF. * LDX >= max( 1,M ). * * U1 (output) REAL 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) REAL 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) REAL 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) REAL 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) 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 SORCSD for * details. * * IWORK (workspace) INTEGER array, dimension (M) * * WORK (workspace) REAL 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 ). ) * * ===================================================================== * * .. Parameters .. REAL PIOVER2, REALONE, REALZERO PARAMETER ( PIOVER2 = 1.57079632679489662E0, $ REALONE = 1.0E0, REALZERO = 0.0E0 ) REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, INFO, R REAL EPS2, RESID, ULP, ULPINV * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM, SLACPY, SLASET, SORCSD, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC REAL, MAX, MIN * .. * .. Executable Statements .. * ULP = SLAMCH( 'Precision' ) ULPINV = REALONE / ULP CALL SLASET( 'Full', M, M, ZERO, ONE, WORK, LDX ) CALL SSYRK( 'Upper', 'Conjugate transpose', M, M, -ONE, X, LDX, $ ONE, WORK, LDX ) EPS2 = MAX( ULP, $ SLANGE( '1', M, M, WORK, LDX, RWORK ) / REAL( M ) ) R = MIN( P, M-P, Q, M-Q ) * * Copy the matrix X to the array XF. * CALL SLACPY( 'Full', M, M, X, LDX, XF, LDX ) * * Compute the CSD * CALL SORCSD( '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 SGEMM( 'No transpose', 'Conjugate transpose', P, Q, Q, ONE, $ X, LDX, V1T, LDV1T, ZERO, WORK, LDX ) * CALL SGEMM( '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 SGEMM( 'No transpose', 'Conjugate transpose', P, M-Q, M-Q, $ ONE, X(1,Q+1), LDX, V2T, LDV2T, ZERO, WORK, LDX ) * CALL SGEMM( '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 SGEMM( 'No transpose', 'Conjugate transpose', M-P, Q, Q, ONE, $ X(P+1,1), LDX, V1T, LDV1T, ZERO, WORK, LDX ) * CALL SGEMM( '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 SGEMM( 'No transpose', 'Conjugate transpose', M-P, M-Q, M-Q, $ ONE, X(P+1,Q+1), LDX, V2T, LDV2T, ZERO, WORK, LDX ) * CALL SGEMM( '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 = SLANGE( '1', P, Q, X, LDX, RWORK ) RESULT( 1 ) = ( RESID / REAL(MAX(1,P,Q)) ) / EPS2 * * Compute norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 ) . * RESID = SLANGE( '1', P, M-Q, X(1,Q+1), LDX, RWORK ) RESULT( 2 ) = ( RESID / REAL(MAX(1,P,M-Q)) ) / EPS2 * * Compute norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 ) . * RESID = SLANGE( '1', M-P, Q, X(P+1,1), LDX, RWORK ) RESULT( 3 ) = ( RESID / REAL(MAX(1,M-P,Q)) ) / EPS2 * * Compute norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 ) . * RESID = SLANGE( '1', M-P, M-Q, X(P+1,Q+1), LDX, RWORK ) RESULT( 4 ) = ( RESID / REAL(MAX(1,M-P,M-Q)) ) / EPS2 * * Compute I - U1'*U1 * CALL SLASET( 'Full', P, P, ZERO, ONE, WORK, LDU1 ) CALL SSYRK( 'Upper', 'Conjugate transpose', P, P, -ONE, U1, LDU1, $ ONE, WORK, LDU1 ) * * Compute norm( I - U'*U ) / ( MAX(1,P) * ULP ) . * RESID = SLANSY( '1', 'Upper', P, WORK, LDU1, RWORK ) RESULT( 5 ) = ( RESID / REAL(MAX(1,P)) ) / ULP * * Compute I - U2'*U2 * CALL SLASET( 'Full', M-P, M-P, ZERO, ONE, WORK, LDU2 ) CALL SSYRK( 'Upper', 'Conjugate transpose', M-P, M-P, -ONE, U2, $ LDU2, ONE, WORK, LDU2 ) * * Compute norm( I - U2'*U2 ) / ( MAX(1,M-P) * ULP ) . * RESID = SLANSY( '1', 'Upper', M-P, WORK, LDU2, RWORK ) RESULT( 6 ) = ( RESID / REAL(MAX(1,M-P)) ) / ULP * * Compute I - V1T*V1T' * CALL SLASET( 'Full', Q, Q, ZERO, ONE, WORK, LDV1T ) CALL SSYRK( 'Upper', 'No transpose', Q, Q, -ONE, V1T, LDV1T, ONE, $ WORK, LDV1T ) * * Compute norm( I - V1T*V1T' ) / ( MAX(1,Q) * ULP ) . * RESID = SLANSY( '1', 'Upper', Q, WORK, LDV1T, RWORK ) RESULT( 7 ) = ( RESID / REAL(MAX(1,Q)) ) / ULP * * Compute I - V2T*V2T' * CALL SLASET( 'Full', M-Q, M-Q, ZERO, ONE, WORK, LDV2T ) CALL SSYRK( 'Upper', 'No transpose', M-Q, M-Q, -ONE, V2T, LDV2T, $ ONE, WORK, LDV2T ) * * Compute norm( I - V2T*V2T' ) / ( MAX(1,M-Q) * ULP ) . * RESID = SLANSY( '1', 'Upper', M-Q, WORK, LDV2T, RWORK ) RESULT( 8 ) = ( RESID / REAL(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 SCSDTS * END |