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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.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
$ LWORK, RESULT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. 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, DLABAD, 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
CALL DLABAD( UNFL, OVFL )
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
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