numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/EIG/dhst01.f | 5840B | -rw-r--r-- |
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*> \brief \b DHST01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK, * LWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), H( LDH, * ), Q( LDQ, * ), * $ RESULT( 2 ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DHST01 tests the reduction of a general matrix A to upper Hessenberg *> form: A = Q*H*Q'. Two test ratios are computed; *> *> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ) *> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS ) *> *> The matrix Q is assumed to be given explicitly as it would be *> following DGEHRD + DORGHR. *> *> In this version, ILO and IHI are not used and are assumed to be 1 and *> N, respectively. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> A is assumed to be upper triangular in rows and columns *> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in *> rows and columns ILO+1:IHI. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The original n by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] H *> \verbatim *> H is DOUBLE PRECISION array, dimension (LDH,N) *> The upper Hessenberg matrix H from the reduction A = Q*H*Q' *> as computed by DGEHRD. H is assumed to be zero below the *> first subdiagonal. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[in] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> The orthogonal matrix Q from the reduction A = Q*H*Q' as *> computed by DGEHRD + DORGHR. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= 2*N*N. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (2) *> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ) *> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK, $ LWORK, RESULT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), H( LDH, * ), Q( LDQ, * ), $ RESULT( 2 ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER LDWORK DOUBLE PRECISION ANORM, EPS, OVFL, SMLNUM, UNFL, WNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DORT01 * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RETURN END IF * UNFL = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) OVFL = ONE / UNFL SMLNUM = UNFL*N / EPS * * Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ) * * Copy A to WORK * LDWORK = MAX( 1, N ) CALL DLACPY( ' ', N, N, A, LDA, WORK, LDWORK ) * * Compute Q*H * CALL DGEMM( 'No transpose', 'No transpose', N, N, N, ONE, Q, LDQ, $ H, LDH, ZERO, WORK( LDWORK*N+1 ), LDWORK ) * * Compute A - Q*H*Q' * CALL DGEMM( 'No transpose', 'Transpose', N, N, N, -ONE, $ WORK( LDWORK*N+1 ), LDWORK, Q, LDQ, ONE, WORK, $ LDWORK ) * ANORM = MAX( DLANGE( '1', N, N, A, LDA, WORK( LDWORK*N+1 ) ), $ UNFL ) WNORM = DLANGE( '1', N, N, WORK, LDWORK, WORK( LDWORK*N+1 ) ) * * Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS) * RESULT( 1 ) = MIN( WNORM, ANORM ) / MAX( SMLNUM, ANORM*EPS ) / N * * Test 2: Compute norm( I - Q'*Q ) / ( N * EPS ) * CALL DORT01( 'Columns', N, N, Q, LDQ, WORK, LWORK, RESULT( 2 ) ) * RETURN * * End of DHST01 * END