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511 lines
16 KiB
511 lines
16 KiB
*> \brief \b DGET38
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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 DGET38( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, NIN
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* ..
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* .. Array Arguments ..
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* INTEGER LMAX( 3 ), NINFO( 3 )
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* DOUBLE PRECISION RMAX( 3 )
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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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*> DGET38 tests DTRSEN, a routine for estimating condition numbers of a
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*> cluster of eigenvalues and/or its associated right invariant subspace
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*>
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*> The test matrices are read from a file with logical unit number NIN.
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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[out] RMAX
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*> \verbatim
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*> RMAX is DOUBLE PRECISION array, dimension (3)
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*> Values of the largest test ratios.
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*> RMAX(1) = largest residuals from DHST01 or comparing
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*> different calls to DTRSEN
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*> RMAX(2) = largest error in reciprocal condition
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*> numbers taking their conditioning into account
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*> RMAX(3) = largest error in reciprocal condition
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*> numbers not taking their conditioning into
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*> account (may be larger than RMAX(2))
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*> \endverbatim
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*>
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*> \param[out] LMAX
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*> \verbatim
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*> LMAX is INTEGER array, dimension (3)
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*> LMAX(i) is example number where largest test ratio
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*> RMAX(i) is achieved. Also:
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*> If DGEHRD returns INFO nonzero on example i, LMAX(1)=i
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*> If DHSEQR returns INFO nonzero on example i, LMAX(2)=i
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*> If DTRSEN returns INFO nonzero on example i, LMAX(3)=i
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*> \endverbatim
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*>
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*> \param[out] NINFO
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*> \verbatim
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*> NINFO is INTEGER array, dimension (3)
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*> NINFO(1) = No. of times DGEHRD returned INFO nonzero
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*> NINFO(2) = No. of times DHSEQR returned INFO nonzero
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*> NINFO(3) = No. of times DTRSEN returned INFO nonzero
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*> \endverbatim
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*>
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*> \param[out] KNT
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*> \verbatim
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*> KNT is INTEGER
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*> Total number of examples tested.
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*> \endverbatim
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*>
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*> \param[in] NIN
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*> \verbatim
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*> NIN is INTEGER
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*> Input logical unit number.
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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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*> \ingroup double_eig
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*
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* =====================================================================
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SUBROUTINE DGET38( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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INTEGER KNT, NIN
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* ..
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* .. Array Arguments ..
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INTEGER LMAX( 3 ), NINFO( 3 )
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DOUBLE PRECISION RMAX( 3 )
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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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DOUBLE PRECISION ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
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DOUBLE PRECISION EPSIN
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PARAMETER ( EPSIN = 5.9605D-8 )
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INTEGER LDT, LWORK
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PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) )
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INTEGER LIWORK
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PARAMETER ( LIWORK = LDT*LDT )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, ISCL, ITMP, J, KMIN, M, N, NDIM
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DOUBLE PRECISION BIGNUM, EPS, S, SEP, SEPIN, SEPTMP, SIN,
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$ SMLNUM, STMP, TNRM, TOL, TOLIN, V, VIMIN, VMAX,
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$ VMUL, VRMIN
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* ..
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* .. Local Arrays ..
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LOGICAL SELECT( LDT )
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INTEGER IPNT( LDT ), ISELEC( LDT ), IWORK( LIWORK )
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DOUBLE PRECISION Q( LDT, LDT ), QSAV( LDT, LDT ),
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$ QTMP( LDT, LDT ), RESULT( 2 ), T( LDT, LDT ),
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$ TMP( LDT, LDT ), TSAV( LDT, LDT ),
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$ TSAV1( LDT, LDT ), TTMP( LDT, LDT ), VAL( 3 ),
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$ WI( LDT ), WITMP( LDT ), WORK( LWORK ),
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$ WR( LDT ), WRTMP( LDT )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLANGE
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EXTERNAL DLAMCH, DLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL DCOPY, DGEHRD, DHSEQR, DHST01, DLACPY, DORGHR,
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$ DSCAL, DTRSEN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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EPS = DLAMCH( 'P' )
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SMLNUM = DLAMCH( 'S' ) / EPS
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BIGNUM = ONE / SMLNUM
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*
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* EPSIN = 2**(-24) = precision to which input data computed
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*
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EPS = MAX( EPS, EPSIN )
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RMAX( 1 ) = ZERO
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RMAX( 2 ) = ZERO
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RMAX( 3 ) = ZERO
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LMAX( 1 ) = 0
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LMAX( 2 ) = 0
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LMAX( 3 ) = 0
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KNT = 0
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NINFO( 1 ) = 0
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NINFO( 2 ) = 0
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NINFO( 3 ) = 0
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*
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VAL( 1 ) = SQRT( SMLNUM )
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VAL( 2 ) = ONE
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VAL( 3 ) = SQRT( SQRT( BIGNUM ) )
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*
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* Read input data until N=0. Assume input eigenvalues are sorted
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* lexicographically (increasing by real part, then decreasing by
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* imaginary part)
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*
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10 CONTINUE
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READ( NIN, FMT = * )N, NDIM
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IF( N.EQ.0 )
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$ RETURN
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READ( NIN, FMT = * )( ISELEC( I ), I = 1, NDIM )
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DO 20 I = 1, N
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READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
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20 CONTINUE
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READ( NIN, FMT = * )SIN, SEPIN
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*
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TNRM = DLANGE( 'M', N, N, TMP, LDT, WORK )
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DO 160 ISCL = 1, 3
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*
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* Scale input matrix
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*
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KNT = KNT + 1
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CALL DLACPY( 'F', N, N, TMP, LDT, T, LDT )
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VMUL = VAL( ISCL )
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DO 30 I = 1, N
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CALL DSCAL( N, VMUL, T( 1, I ), 1 )
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30 CONTINUE
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IF( TNRM.EQ.ZERO )
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$ VMUL = ONE
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CALL DLACPY( 'F', N, N, T, LDT, TSAV, LDT )
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*
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* Compute Schur form
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*
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CALL DGEHRD( N, 1, N, T, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N,
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$ INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 1 ) = KNT
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NINFO( 1 ) = NINFO( 1 ) + 1
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GO TO 160
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END IF
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*
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* Generate orthogonal matrix
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*
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CALL DLACPY( 'L', N, N, T, LDT, Q, LDT )
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CALL DORGHR( N, 1, N, Q, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N,
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$ INFO )
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*
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* Compute Schur form
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*
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CALL DHSEQR( 'S', 'V', N, 1, N, T, LDT, WR, WI, Q, LDT, WORK,
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$ LWORK, INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 2 ) = KNT
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NINFO( 2 ) = NINFO( 2 ) + 1
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GO TO 160
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END IF
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*
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* Sort, select eigenvalues
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*
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DO 40 I = 1, N
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IPNT( I ) = I
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SELECT( I ) = .FALSE.
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40 CONTINUE
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CALL DCOPY( N, WR, 1, WRTMP, 1 )
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CALL DCOPY( N, WI, 1, WITMP, 1 )
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DO 60 I = 1, N - 1
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KMIN = I
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VRMIN = WRTMP( I )
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VIMIN = WITMP( I )
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DO 50 J = I + 1, N
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IF( WRTMP( J ).LT.VRMIN ) THEN
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KMIN = J
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VRMIN = WRTMP( J )
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VIMIN = WITMP( J )
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END IF
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50 CONTINUE
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WRTMP( KMIN ) = WRTMP( I )
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WITMP( KMIN ) = WITMP( I )
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WRTMP( I ) = VRMIN
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WITMP( I ) = VIMIN
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ITMP = IPNT( I )
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IPNT( I ) = IPNT( KMIN )
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IPNT( KMIN ) = ITMP
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60 CONTINUE
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DO 70 I = 1, NDIM
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SELECT( IPNT( ISELEC( I ) ) ) = .TRUE.
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70 CONTINUE
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*
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* Compute condition numbers
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*
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CALL DLACPY( 'F', N, N, Q, LDT, QSAV, LDT )
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CALL DLACPY( 'F', N, N, T, LDT, TSAV1, LDT )
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CALL DTRSEN( 'B', 'V', SELECT, N, T, LDT, Q, LDT, WRTMP, WITMP,
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$ M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 3 ) = KNT
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NINFO( 3 ) = NINFO( 3 ) + 1
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GO TO 160
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END IF
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SEPTMP = SEP / VMUL
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STMP = S
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*
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* Compute residuals
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*
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CALL DHST01( N, 1, N, TSAV, LDT, T, LDT, Q, LDT, WORK, LWORK,
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$ RESULT )
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VMAX = MAX( RESULT( 1 ), RESULT( 2 ) )
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IF( VMAX.GT.RMAX( 1 ) ) THEN
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RMAX( 1 ) = VMAX
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IF( NINFO( 1 ).EQ.0 )
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$ LMAX( 1 ) = KNT
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END IF
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*
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* Compare condition number for eigenvalue cluster
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* taking its condition number into account
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*
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V = MAX( TWO*DBLE( N )*EPS*TNRM, SMLNUM )
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IF( TNRM.EQ.ZERO )
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$ V = ONE
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IF( V.GT.SEPTMP ) THEN
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TOL = ONE
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ELSE
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TOL = V / SEPTMP
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END IF
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IF( V.GT.SEPIN ) THEN
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TOLIN = ONE
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ELSE
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TOLIN = V / SEPIN
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END IF
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TOL = MAX( TOL, SMLNUM / EPS )
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TOLIN = MAX( TOLIN, SMLNUM / EPS )
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IF( EPS*( SIN-TOLIN ).GT.STMP+TOL ) THEN
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VMAX = ONE / EPS
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ELSE IF( SIN-TOLIN.GT.STMP+TOL ) THEN
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VMAX = ( SIN-TOLIN ) / ( STMP+TOL )
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ELSE IF( SIN+TOLIN.LT.EPS*( STMP-TOL ) ) THEN
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VMAX = ONE / EPS
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ELSE IF( SIN+TOLIN.LT.STMP-TOL ) THEN
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VMAX = ( STMP-TOL ) / ( SIN+TOLIN )
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ELSE
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VMAX = ONE
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END IF
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IF( VMAX.GT.RMAX( 2 ) ) THEN
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RMAX( 2 ) = VMAX
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IF( NINFO( 2 ).EQ.0 )
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$ LMAX( 2 ) = KNT
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END IF
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*
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* Compare condition numbers for invariant subspace
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* taking its condition number into account
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*
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IF( V.GT.SEPTMP*STMP ) THEN
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TOL = SEPTMP
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ELSE
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TOL = V / STMP
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END IF
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IF( V.GT.SEPIN*SIN ) THEN
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TOLIN = SEPIN
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ELSE
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TOLIN = V / SIN
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END IF
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TOL = MAX( TOL, SMLNUM / EPS )
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TOLIN = MAX( TOLIN, SMLNUM / EPS )
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IF( EPS*( SEPIN-TOLIN ).GT.SEPTMP+TOL ) THEN
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VMAX = ONE / EPS
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ELSE IF( SEPIN-TOLIN.GT.SEPTMP+TOL ) THEN
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VMAX = ( SEPIN-TOLIN ) / ( SEPTMP+TOL )
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ELSE IF( SEPIN+TOLIN.LT.EPS*( SEPTMP-TOL ) ) THEN
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VMAX = ONE / EPS
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ELSE IF( SEPIN+TOLIN.LT.SEPTMP-TOL ) THEN
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VMAX = ( SEPTMP-TOL ) / ( SEPIN+TOLIN )
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ELSE
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VMAX = ONE
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END IF
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IF( VMAX.GT.RMAX( 2 ) ) THEN
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RMAX( 2 ) = VMAX
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IF( NINFO( 2 ).EQ.0 )
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$ LMAX( 2 ) = KNT
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END IF
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*
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* Compare condition number for eigenvalue cluster
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* without taking its condition number into account
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*
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IF( SIN.LE.DBLE( 2*N )*EPS .AND. STMP.LE.DBLE( 2*N )*EPS ) THEN
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VMAX = ONE
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ELSE IF( EPS*SIN.GT.STMP ) THEN
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VMAX = ONE / EPS
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ELSE IF( SIN.GT.STMP ) THEN
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VMAX = SIN / STMP
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ELSE IF( SIN.LT.EPS*STMP ) THEN
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VMAX = ONE / EPS
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ELSE IF( SIN.LT.STMP ) THEN
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VMAX = STMP / SIN
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ELSE
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VMAX = ONE
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END IF
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IF( VMAX.GT.RMAX( 3 ) ) THEN
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RMAX( 3 ) = VMAX
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IF( NINFO( 3 ).EQ.0 )
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$ LMAX( 3 ) = KNT
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END IF
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*
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* Compare condition numbers for invariant subspace
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* without taking its condition number into account
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*
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IF( SEPIN.LE.V .AND. SEPTMP.LE.V ) THEN
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VMAX = ONE
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ELSE IF( EPS*SEPIN.GT.SEPTMP ) THEN
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VMAX = ONE / EPS
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ELSE IF( SEPIN.GT.SEPTMP ) THEN
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VMAX = SEPIN / SEPTMP
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ELSE IF( SEPIN.LT.EPS*SEPTMP ) THEN
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VMAX = ONE / EPS
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ELSE IF( SEPIN.LT.SEPTMP ) THEN
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VMAX = SEPTMP / SEPIN
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ELSE
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VMAX = ONE
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END IF
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IF( VMAX.GT.RMAX( 3 ) ) THEN
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RMAX( 3 ) = VMAX
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IF( NINFO( 3 ).EQ.0 )
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$ LMAX( 3 ) = KNT
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END IF
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*
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* Compute eigenvalue condition number only and compare
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* Update Q
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*
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VMAX = ZERO
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CALL DLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
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CALL DLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
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SEPTMP = -ONE
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STMP = -ONE
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CALL DTRSEN( 'E', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
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$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 3 ) = KNT
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NINFO( 3 ) = NINFO( 3 ) + 1
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GO TO 160
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END IF
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IF( S.NE.STMP )
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$ VMAX = ONE / EPS
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IF( -ONE.NE.SEPTMP )
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$ VMAX = ONE / EPS
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DO 90 I = 1, N
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DO 80 J = 1, N
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IF( TTMP( I, J ).NE.T( I, J ) )
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$ VMAX = ONE / EPS
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IF( QTMP( I, J ).NE.Q( I, J ) )
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$ VMAX = ONE / EPS
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80 CONTINUE
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90 CONTINUE
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*
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* Compute invariant subspace condition number only and compare
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* Update Q
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*
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CALL DLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
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CALL DLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
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SEPTMP = -ONE
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STMP = -ONE
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CALL DTRSEN( 'V', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
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$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 3 ) = KNT
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NINFO( 3 ) = NINFO( 3 ) + 1
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GO TO 160
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END IF
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IF( -ONE.NE.STMP )
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$ VMAX = ONE / EPS
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IF( SEP.NE.SEPTMP )
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$ VMAX = ONE / EPS
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DO 110 I = 1, N
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DO 100 J = 1, N
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IF( TTMP( I, J ).NE.T( I, J ) )
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$ VMAX = ONE / EPS
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IF( QTMP( I, J ).NE.Q( I, J ) )
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$ VMAX = ONE / EPS
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100 CONTINUE
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110 CONTINUE
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*
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* Compute eigenvalue condition number only and compare
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* Do not update Q
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*
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CALL DLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
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CALL DLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
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SEPTMP = -ONE
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STMP = -ONE
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CALL DTRSEN( 'E', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
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$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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IF( INFO.NE.0 ) THEN
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LMAX( 3 ) = KNT
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NINFO( 3 ) = NINFO( 3 ) + 1
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GO TO 160
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END IF
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IF( S.NE.STMP )
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$ VMAX = ONE / EPS
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IF( -ONE.NE.SEPTMP )
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$ VMAX = ONE / EPS
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DO 130 I = 1, N
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DO 120 J = 1, N
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IF( TTMP( I, J ).NE.T( I, J ) )
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$ VMAX = ONE / EPS
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IF( QTMP( I, J ).NE.QSAV( I, J ) )
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$ VMAX = ONE / EPS
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120 CONTINUE
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130 CONTINUE
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*
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* Compute invariant subspace condition number only and compare
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* Do not update Q
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*
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CALL DLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
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CALL DLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
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SEPTMP = -ONE
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|
STMP = -ONE
|
|
CALL DTRSEN( 'V', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
|
|
$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
|
|
$ LIWORK, INFO )
|
|
IF( INFO.NE.0 ) THEN
|
|
LMAX( 3 ) = KNT
|
|
NINFO( 3 ) = NINFO( 3 ) + 1
|
|
GO TO 160
|
|
END IF
|
|
IF( -ONE.NE.STMP )
|
|
$ VMAX = ONE / EPS
|
|
IF( SEP.NE.SEPTMP )
|
|
$ VMAX = ONE / EPS
|
|
DO 150 I = 1, N
|
|
DO 140 J = 1, N
|
|
IF( TTMP( I, J ).NE.T( I, J ) )
|
|
$ VMAX = ONE / EPS
|
|
IF( QTMP( I, J ).NE.QSAV( I, J ) )
|
|
$ VMAX = ONE / EPS
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
IF( VMAX.GT.RMAX( 1 ) ) THEN
|
|
RMAX( 1 ) = VMAX
|
|
IF( NINFO( 1 ).EQ.0 )
|
|
$ LMAX( 1 ) = KNT
|
|
END IF
|
|
160 CONTINUE
|
|
GO TO 10
|
|
*
|
|
* End of DGET38
|
|
*
|
|
END
|
|
|