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