SUBROUTINE CGET38( 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 ) REAL RMAX( 3 ) * .. * * Purpose * ======= * * CGET38 tests CTRSEN, 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) REAL array, dimension (3) * Values of the largest test ratios. * RMAX(1) = largest residuals from CHST01 or comparing * different calls to CTRSEN * 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 CGEHRD returns INFO nonzero on example i, LMAX(1)=i * If CHSEQR returns INFO nonzero on example i, LMAX(2)=i * If CTRSEN returns INFO nonzero on example i, LMAX(3)=i * * NINFO (output) INTEGER array, dimension (3) * NINFO(1) = No. of times CGEHRD returned INFO nonzero * NINFO(2) = No. of times CHSEQR returned INFO nonzero * NINFO(3) = No. of times CTRSEN returned INFO nonzero * * KNT (output) INTEGER * Total number of examples tested. * * NIN (input) INTEGER * Input logical unit number. * * ===================================================================== * * .. Parameters .. INTEGER LDT, LWORK PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) ) REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 ) REAL EPSIN PARAMETER ( EPSIN = 5.9605E-8 ) COMPLEX CZERO PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, ISCL, ISRT, ITMP, J, KMIN, M, N, NDIM REAL BIGNUM, EPS, S, SEP, SEPIN, SEPTMP, SIN, \$ SMLNUM, STMP, TNRM, TOL, TOLIN, V, VMAX, VMIN, \$ VMUL * .. * .. Local Arrays .. LOGICAL SELECT( LDT ) INTEGER IPNT( LDT ), ISELEC( LDT ) REAL RESULT( 2 ), RWORK( LDT ), VAL( 3 ), \$ WSRT( LDT ) COMPLEX Q( LDT, LDT ), QSAV( LDT, LDT ), \$ QTMP( LDT, LDT ), T( LDT, LDT ), \$ TMP( LDT, LDT ), TSAV( LDT, LDT ), \$ TSAV1( LDT, LDT ), TTMP( LDT, LDT ), W( LDT ), \$ WORK( LWORK ), WTMP( LDT ) * .. * .. External Functions .. REAL CLANGE, SLAMCH EXTERNAL CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEHRD, CHSEQR, CHST01, CLACPY, CSSCAL, CTRSEN, \$ CUNGHR, SLABAD * .. * .. Intrinsic Functions .. INTRINSIC AIMAG, MAX, REAL, SQRT * .. * .. Executable Statements .. * EPS = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM CALL SLABAD( 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, ISRT 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 = CLANGE( 'M', N, N, TMP, LDT, RWORK ) DO 200 ISCL = 1, 3 * * Scale input matrix * KNT = KNT + 1 CALL CLACPY( 'F', N, N, TMP, LDT, T, LDT ) VMUL = VAL( ISCL ) DO 30 I = 1, N CALL CSSCAL( N, VMUL, T( 1, I ), 1 ) 30 CONTINUE IF( TNRM.EQ.ZERO ) \$ VMUL = ONE CALL CLACPY( 'F', N, N, T, LDT, TSAV, LDT ) * * Compute Schur form * CALL CGEHRD( 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 200 END IF * * Generate unitary matrix * CALL CLACPY( 'L', N, N, T, LDT, Q, LDT ) CALL CUNGHR( N, 1, N, Q, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N, \$ INFO ) * * Compute Schur form * DO 50 J = 1, N - 2 DO 40 I = J + 2, N T( I, J ) = CZERO 40 CONTINUE 50 CONTINUE CALL CHSEQR( 'S', 'V', N, 1, N, T, LDT, W, Q, LDT, WORK, LWORK, \$ INFO ) IF( INFO.NE.0 ) THEN LMAX( 2 ) = KNT NINFO( 2 ) = NINFO( 2 ) + 1 GO TO 200 END IF * * Sort, select eigenvalues * DO 60 I = 1, N IPNT( I ) = I SELECT( I ) = .FALSE. 60 CONTINUE IF( ISRT.EQ.0 ) THEN DO 70 I = 1, N WSRT( I ) = REAL( W( I ) ) 70 CONTINUE ELSE DO 80 I = 1, N WSRT( I ) = AIMAG( W( I ) ) 80 CONTINUE END IF DO 100 I = 1, N - 1 KMIN = I VMIN = WSRT( I ) DO 90 J = I + 1, N IF( WSRT( J ).LT.VMIN ) THEN KMIN = J VMIN = WSRT( J ) END IF 90 CONTINUE WSRT( KMIN ) = WSRT( I ) WSRT( I ) = VMIN ITMP = IPNT( I ) IPNT( I ) = IPNT( KMIN ) IPNT( KMIN ) = ITMP 100 CONTINUE DO 110 I = 1, NDIM SELECT( IPNT( ISELEC( I ) ) ) = .TRUE. 110 CONTINUE * * Compute condition numbers * CALL CLACPY( 'F', N, N, Q, LDT, QSAV, LDT ) CALL CLACPY( 'F', N, N, T, LDT, TSAV1, LDT ) CALL CTRSEN( 'B', 'V', SELECT, N, T, LDT, Q, LDT, WTMP, M, S, \$ SEP, WORK, LWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 200 END IF SEPTMP = SEP / VMUL STMP = S * * Compute residuals * CALL CHST01( N, 1, N, TSAV, LDT, T, LDT, Q, LDT, WORK, LWORK, \$ RWORK, 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*REAL( 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.REAL( 2*N )*EPS .AND. STMP.LE.REAL( 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 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