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516 lines
15 KiB
516 lines
15 KiB
2 years ago
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*> \brief \b CGET38
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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 CGET38( 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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* REAL 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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*> CGET38 tests CTRSEN, 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 REAL array, dimension (3)
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*> Values of the largest test ratios.
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*> RMAX(1) = largest residuals from CHST01 or comparing
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*> different calls to CTRSEN
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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 CGEHRD returns INFO nonzero on example i, LMAX(1)=i
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*> If CHSEQR returns INFO nonzero on example i, LMAX(2)=i
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*> If CTRSEN 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 CGEHRD returned INFO nonzero
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*> NINFO(2) = No. of times CHSEQR returned INFO nonzero
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*> NINFO(3) = No. of times CTRSEN 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 complex_eig
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*
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* =====================================================================
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SUBROUTINE CGET38( 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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REAL 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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INTEGER LDT, LWORK
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PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) )
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REAL ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
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REAL EPSIN
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PARAMETER ( EPSIN = 5.9605E-8 )
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COMPLEX CZERO
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, ISCL, ISRT, ITMP, J, KMIN, M, N, NDIM
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REAL BIGNUM, EPS, S, SEP, SEPIN, SEPTMP, SIN,
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$ SMLNUM, STMP, TNRM, TOL, TOLIN, V, VMAX, VMIN,
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$ VMUL
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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 )
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REAL RESULT( 2 ), RWORK( LDT ), VAL( 3 ),
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$ WSRT( LDT )
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COMPLEX Q( LDT, LDT ), QSAV( LDT, LDT ),
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$ QTMP( LDT, LDT ), T( LDT, LDT ),
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$ TMP( LDT, LDT ), TSAV( LDT, LDT ),
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$ TSAV1( LDT, LDT ), TTMP( LDT, LDT ), W( LDT ),
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$ WORK( LWORK ), WTMP( LDT )
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* ..
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* .. External Functions ..
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REAL CLANGE, SLAMCH
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EXTERNAL CLANGE, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEHRD, CHSEQR, CHST01, CLACPY, CSSCAL, CTRSEN,
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$ CUNGHR
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC AIMAG, MAX, REAL, SQRT
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'P' )
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SMLNUM = SLAMCH( '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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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, ISRT
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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 = CLANGE( 'M', N, N, TMP, LDT, RWORK )
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DO 200 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 CLACPY( '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 CSSCAL( 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 CLACPY( '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 CGEHRD( 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 200
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END IF
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*
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* Generate unitary matrix
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*
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CALL CLACPY( 'L', N, N, T, LDT, Q, LDT )
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CALL CUNGHR( 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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DO 50 J = 1, N - 2
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DO 40 I = J + 2, N
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T( I, J ) = CZERO
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40 CONTINUE
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50 CONTINUE
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CALL CHSEQR( 'S', 'V', N, 1, N, T, LDT, W, Q, LDT, WORK, LWORK,
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$ 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 200
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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 60 I = 1, N
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IPNT( I ) = I
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SELECT( I ) = .FALSE.
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60 CONTINUE
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IF( ISRT.EQ.0 ) THEN
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DO 70 I = 1, N
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WSRT( I ) = REAL( W( I ) )
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70 CONTINUE
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ELSE
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DO 80 I = 1, N
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WSRT( I ) = AIMAG( W( I ) )
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80 CONTINUE
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END IF
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DO 100 I = 1, N - 1
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KMIN = I
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VMIN = WSRT( I )
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DO 90 J = I + 1, N
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IF( WSRT( J ).LT.VMIN ) THEN
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KMIN = J
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VMIN = WSRT( J )
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END IF
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90 CONTINUE
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WSRT( KMIN ) = WSRT( I )
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WSRT( I ) = VMIN
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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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100 CONTINUE
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DO 110 I = 1, NDIM
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SELECT( IPNT( ISELEC( I ) ) ) = .TRUE.
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110 CONTINUE
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*
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* Compute condition numbers
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*
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CALL CLACPY( 'F', N, N, Q, LDT, QSAV, LDT )
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CALL CLACPY( 'F', N, N, T, LDT, TSAV1, LDT )
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CALL CTRSEN( 'B', 'V', SELECT, N, T, LDT, Q, LDT, WTMP, M, S,
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$ SEP, WORK, LWORK, 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 200
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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 CHST01( N, 1, N, TSAV, LDT, T, LDT, Q, LDT, WORK, LWORK,
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$ RWORK, 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*REAL( 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.REAL( 2*N )*EPS .AND. STMP.LE.REAL( 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
|
||
|
|
ELSE IF( SIN.LT.EPS*STMP ) THEN
|
||
|
|
VMAX = ONE / EPS
|
||
|
|
ELSE IF( SIN.LT.STMP ) THEN
|
||
|
|
VMAX = STMP / SIN
|
||
|
|
ELSE
|
||
|
|
VMAX = ONE
|
||
|
|
END IF
|
||
|
|
IF( VMAX.GT.RMAX( 3 ) ) THEN
|
||
|
|
RMAX( 3 ) = VMAX
|
||
|
|
IF( NINFO( 3 ).EQ.0 )
|
||
|
|
$ LMAX( 3 ) = KNT
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compare condition numbers for invariant subspace
|
||
|
|
* without taking its condition number into account
|
||
|
|
*
|
||
|
|
IF( SEPIN.LE.V .AND. SEPTMP.LE.V ) THEN
|
||
|
|
VMAX = ONE
|
||
|
|
ELSE IF( EPS*SEPIN.GT.SEPTMP ) THEN
|
||
|
|
VMAX = ONE / EPS
|
||
|
|
ELSE IF( SEPIN.GT.SEPTMP ) THEN
|
||
|
|
VMAX = SEPIN / SEPTMP
|
||
|
|
ELSE IF( SEPIN.LT.EPS*SEPTMP ) THEN
|
||
|
|
VMAX = ONE / EPS
|
||
|
|
ELSE IF( SEPIN.LT.SEPTMP ) THEN
|
||
|
|
VMAX = SEPTMP / SEPIN
|
||
|
|
ELSE
|
||
|
|
VMAX = ONE
|
||
|
|
END IF
|
||
|
|
IF( VMAX.GT.RMAX( 3 ) ) THEN
|
||
|
|
RMAX( 3 ) = VMAX
|
||
|
|
IF( NINFO( 3 ).EQ.0 )
|
||
|
|
$ LMAX( 3 ) = KNT
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Compute eigenvalue condition number only and compare
|
||
|
|
* Update Q
|
||
|
|
*
|
||
|
|
VMAX = ZERO
|
||
|
|
CALL CLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
|
||
|
|
CALL CLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
|
||
|
|
SEPTMP = -ONE
|
||
|
|
STMP = -ONE
|
||
|
|
CALL CTRSEN( 'E', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WTMP,
|
||
|
|
$ M, STMP, SEPTMP, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
LMAX( 3 ) = KNT
|
||
|
|
NINFO( 3 ) = NINFO( 3 ) + 1
|
||
|
|
GO TO 200
|
||
|
|
END IF
|
||
|
|
IF( S.NE.STMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
IF( -ONE.NE.SEPTMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
DO 130 I = 1, N
|
||
|
|
DO 120 J = 1, N
|
||
|
|
IF( TTMP( I, J ).NE.T( I, J ) )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
IF( QTMP( I, J ).NE.Q( I, J ) )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
120 CONTINUE
|
||
|
|
130 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute invariant subspace condition number only and compare
|
||
|
|
* Update Q
|
||
|
|
*
|
||
|
|
CALL CLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
|
||
|
|
CALL CLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
|
||
|
|
SEPTMP = -ONE
|
||
|
|
STMP = -ONE
|
||
|
|
CALL CTRSEN( 'V', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WTMP,
|
||
|
|
$ M, STMP, SEPTMP, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
LMAX( 3 ) = KNT
|
||
|
|
NINFO( 3 ) = NINFO( 3 ) + 1
|
||
|
|
GO TO 200
|
||
|
|
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.Q( I, J ) )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
140 CONTINUE
|
||
|
|
150 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute eigenvalue condition number only and compare
|
||
|
|
* Do not update Q
|
||
|
|
*
|
||
|
|
CALL CLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
|
||
|
|
CALL CLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
|
||
|
|
SEPTMP = -ONE
|
||
|
|
STMP = -ONE
|
||
|
|
CALL CTRSEN( 'E', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WTMP,
|
||
|
|
$ M, STMP, SEPTMP, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
LMAX( 3 ) = KNT
|
||
|
|
NINFO( 3 ) = NINFO( 3 ) + 1
|
||
|
|
GO TO 200
|
||
|
|
END IF
|
||
|
|
IF( S.NE.STMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
IF( -ONE.NE.SEPTMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
DO 170 I = 1, N
|
||
|
|
DO 160 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
|
||
|
|
160 CONTINUE
|
||
|
|
170 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute invariant subspace condition number only and compare
|
||
|
|
* Do not update Q
|
||
|
|
*
|
||
|
|
CALL CLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
|
||
|
|
CALL CLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
|
||
|
|
SEPTMP = -ONE
|
||
|
|
STMP = -ONE
|
||
|
|
CALL CTRSEN( 'V', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WTMP,
|
||
|
|
$ M, STMP, SEPTMP, WORK, LWORK, INFO )
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
LMAX( 3 ) = KNT
|
||
|
|
NINFO( 3 ) = NINFO( 3 ) + 1
|
||
|
|
GO TO 200
|
||
|
|
END IF
|
||
|
|
IF( -ONE.NE.STMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
IF( SEP.NE.SEPTMP )
|
||
|
|
$ VMAX = ONE / EPS
|
||
|
|
DO 190 I = 1, N
|
||
|
|
DO 180 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
|
||
|
|
180 CONTINUE
|
||
|
|
190 CONTINUE
|
||
|
|
IF( VMAX.GT.RMAX( 1 ) ) THEN
|
||
|
|
RMAX( 1 ) = VMAX
|
||
|
|
IF( NINFO( 1 ).EQ.0 )
|
||
|
|
$ LMAX( 1 ) = KNT
|
||
|
|
END IF
|
||
|
|
200 CONTINUE
|
||
|
|
GO TO 10
|
||
|
|
*
|
||
|
|
* End of CGET38
|
||
|
|
*
|
||
|
|
END
|