221 lines
5.8 KiB
Fortran
221 lines
5.8 KiB
Fortran
*> \brief \b SHST01
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
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* LWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), H( LDH, * ), Q( LDQ, * ),
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* $ RESULT( 2 ), WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SHST01 tests the reduction of a general matrix A to upper Hessenberg
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*> form: A = Q*H*Q'. Two test ratios are computed;
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*>
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*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
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*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
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*>
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*> The matrix Q is assumed to be given explicitly as it would be
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*> following SGEHRD + SORGHR.
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*>
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*> In this version, ILO and IHI are not used and are assumed to be 1 and
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*> N, respectively.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] ILO
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*> \verbatim
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*> ILO is INTEGER
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*> \endverbatim
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*>
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*> \param[in] IHI
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*> \verbatim
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*> IHI is INTEGER
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*>
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*> A is assumed to be upper triangular in rows and columns
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*> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in
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*> rows and columns ILO+1:IHI.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The original n by n matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] H
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*> \verbatim
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*> H is REAL array, dimension (LDH,N)
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*> The upper Hessenberg matrix H from the reduction A = Q*H*Q'
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*> as computed by SGEHRD. H is assumed to be zero below the
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*> first subdiagonal.
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*> \endverbatim
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*>
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*> \param[in] LDH
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*> \verbatim
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*> LDH is INTEGER
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*> The leading dimension of the array H. LDH >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] Q
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*> \verbatim
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*> Q is REAL array, dimension (LDQ,N)
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*> The orthogonal matrix Q from the reduction A = Q*H*Q' as
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*> computed by SGEHRD + SORGHR.
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*> \endverbatim
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*>
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*> \param[in] LDQ
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*> \verbatim
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*> LDQ is INTEGER
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*> The leading dimension of the array Q. LDQ >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK >= 2*N*N.
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (2)
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*> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
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*> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
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$ LWORK, RESULT )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), H( LDH, * ), Q( LDQ, * ),
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$ RESULT( 2 ), WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER LDWORK
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REAL ANORM, EPS, OVFL, SMLNUM, UNFL, WNORM
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SLABAD, SLACPY, SORT01
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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RESULT( 1 ) = ZERO
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RESULT( 2 ) = ZERO
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RETURN
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END IF
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*
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UNFL = SLAMCH( 'Safe minimum' )
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EPS = SLAMCH( 'Precision' )
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OVFL = ONE / UNFL
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CALL SLABAD( UNFL, OVFL )
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SMLNUM = UNFL*N / EPS
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*
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* Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
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*
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* Copy A to WORK
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*
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LDWORK = MAX( 1, N )
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CALL SLACPY( ' ', N, N, A, LDA, WORK, LDWORK )
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*
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* Compute Q*H
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*
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CALL SGEMM( 'No transpose', 'No transpose', N, N, N, ONE, Q, LDQ,
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$ H, LDH, ZERO, WORK( LDWORK*N+1 ), LDWORK )
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*
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* Compute A - Q*H*Q'
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*
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CALL SGEMM( 'No transpose', 'Transpose', N, N, N, -ONE,
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$ WORK( LDWORK*N+1 ), LDWORK, Q, LDQ, ONE, WORK,
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$ LDWORK )
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*
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ANORM = MAX( SLANGE( '1', N, N, A, LDA, WORK( LDWORK*N+1 ) ),
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$ UNFL )
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WNORM = SLANGE( '1', N, N, WORK, LDWORK, WORK( LDWORK*N+1 ) )
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*
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* Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
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*
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RESULT( 1 ) = MIN( WNORM, ANORM ) / MAX( SMLNUM, ANORM*EPS ) / N
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*
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* Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
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*
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CALL SORT01( 'Columns', N, N, Q, LDQ, WORK, LWORK, RESULT( 2 ) )
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*
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RETURN
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*
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* End of SHST01
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*
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END
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