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SUBROUTINE DGET38( RMAX, LMAX, NINFO, KNT, NIN )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER KNT, NIN * .. * .. Array Arguments .. INTEGER LMAX( 3 ), NINFO( 3 ) DOUBLE PRECISION RMAX( 3 ) * .. * * Purpose * ======= * * 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. * * Arguments * ========== * * RMAX (output) 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)) * * LMAX (output) 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 * * NINFO (output) 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 * * KNT (output) INTEGER * Total number of examples tested. * * NIN (input) INTEGER * Input logical unit number. * * ===================================================================== * * .. 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 |