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SUBROUTINE DGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
$ LDV, WORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N DOUBLE PRECISION RESULT * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( LDS, * ), $ T( LDT, * ), U( LDU, * ), V( LDV, * ), $ WORK( * ) * .. * * Purpose * ======= * * DGET54 checks a generalized decomposition of the form * * A = U*S*V' and B = U*T* V' * * where ' means transpose and U and V are orthogonal. * * Specifically, * * RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp ) * * Arguments * ========= * * N (input) INTEGER * The size of the matrix. If it is zero, DGET54 does nothing. * It must be at least zero. * * A (input) DOUBLE PRECISION array, dimension (LDA, N) * The original (unfactored) matrix A. * * LDA (input) INTEGER * The leading dimension of A. It must be at least 1 * and at least N. * * B (input) DOUBLE PRECISION array, dimension (LDB, N) * The original (unfactored) matrix B. * * LDB (input) INTEGER * The leading dimension of B. It must be at least 1 * and at least N. * * S (input) DOUBLE PRECISION array, dimension (LDS, N) * The factored matrix S. * * LDS (input) INTEGER * The leading dimension of S. It must be at least 1 * and at least N. * * T (input) DOUBLE PRECISION array, dimension (LDT, N) * The factored matrix T. * * LDT (input) INTEGER * The leading dimension of T. It must be at least 1 * and at least N. * * U (input) DOUBLE PRECISION array, dimension (LDU, N) * The orthogonal matrix on the left-hand side in the * decomposition. * * LDU (input) INTEGER * The leading dimension of U. LDU must be at least N and * at least 1. * * V (input) DOUBLE PRECISION array, dimension (LDV, N) * The orthogonal matrix on the left-hand side in the * decomposition. * * LDV (input) INTEGER * The leading dimension of V. LDV must be at least N and * at least 1. * * WORK (workspace) DOUBLE PRECISION array, dimension (3*N**2) * * RESULT (output) DOUBLE PRECISION * The value RESULT, It is currently limited to 1/ulp, to * avoid overflow. Errors are flagged by RESULT=10/ulp. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. DOUBLE PRECISION ABNORM, ULP, UNFL, WNORM * .. * .. Local Arrays .. DOUBLE PRECISION DUM( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * RESULT = ZERO IF( N.LE.0 ) $ RETURN * * Constants * UNFL = DLAMCH( 'Safe minimum' ) ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' ) * * compute the norm of (A,B) * CALL DLACPY( 'Full', N, N, A, LDA, WORK, N ) CALL DLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N ) ABNORM = MAX( DLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL ) * * Compute W1 = A - U*S*V', and put in the array WORK(1:N*N) * CALL DLACPY( ' ', N, N, A, LDA, WORK, N ) CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, S, LDS, ZERO, $ WORK( N*N+1 ), N ) * CALL DGEMM( 'N', 'C', N, N, N, -ONE, WORK( N*N+1 ), N, V, LDV, $ ONE, WORK, N ) * * Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N) * CALL DLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N ) CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, T, LDT, ZERO, $ WORK( 2*N*N+1 ), N ) * CALL DGEMM( 'N', 'C', N, N, N, -ONE, WORK( 2*N*N+1 ), N, V, LDV, $ ONE, WORK( N*N+1 ), N ) * * Compute norm(W)/ ( ulp*norm((A,B)) ) * WNORM = DLANGE( '1', N, 2*N, WORK, N, DUM ) * IF( ABNORM.GT.WNORM ) THEN RESULT = ( WNORM / ABNORM ) / ( 2*N*ULP ) ELSE IF( ABNORM.LT.ONE ) THEN RESULT = ( MIN( WNORM, 2*N*ABNORM ) / ABNORM ) / ( 2*N*ULP ) ELSE RESULT = MIN( WNORM / ABNORM, DBLE( 2*N ) ) / ( 2*N*ULP ) END IF END IF * RETURN * * End of DGET54 * END |