SUBROUTINE ZGET37( 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 * ======= * * ZGET37 tests ZTRSNA, a routine for estimating condition numbers of * eigenvalues and/or right eigenvectors of a matrix. * * The test matrices are read from a file with logical unit number NIN. * * Arguments * ========== * * RMAX (output) DOUBLE PRECISION array, dimension (3) * Value of the largest test ratio. * RMAX(1) = largest ratio comparing different calls to ZTRSNA * 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 ZGEHRD returns INFO nonzero on example i, LMAX(1)=i * If ZHSEQR returns INFO nonzero on example i, LMAX(2)=i * If ZTRSNA returns INFO nonzero on example i, LMAX(3)=i * * NINFO (output) INTEGER array, dimension (3) * NINFO(1) = No. of times ZGEHRD returned INFO nonzero * NINFO(2) = No. of times ZHSEQR returned INFO nonzero * NINFO(3) = No. of times ZTRSNA 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 ) ) * .. * .. Local Scalars .. INTEGER I, ICMP, INFO, ISCL, ISRT, J, KMIN, M, N DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TNRM, TOL, TOLIN, V, \$ VCMIN, VMAX, VMIN, VMUL * .. * .. Local Arrays .. LOGICAL SELECT( LDT ) INTEGER LCMP( 3 ) DOUBLE PRECISION DUM( 1 ), RWORK( 2*LDT ), S( LDT ), SEP( LDT ), \$ SEPIN( LDT ), SEPTMP( LDT ), SIN( LDT ), \$ STMP( LDT ), VAL( 3 ), WIIN( LDT ), \$ WRIN( LDT ), WSRT( LDT ) COMPLEX*16 CDUM( 1 ), LE( LDT, LDT ), RE( LDT, LDT ), \$ T( LDT, LDT ), TMP( LDT, LDT ), W( LDT ), \$ WORK( LWORK ), WTMP( LDT ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE EXTERNAL DLAMCH, ZLANGE * .. * .. External Subroutines .. EXTERNAL DCOPY, DLABAD, DSCAL, ZCOPY, ZDSCAL, ZGEHRD, \$ ZHSEQR, ZLACPY, ZTREVC, ZTRSNA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DIMAG, 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( BIGNUM ) * * Read input data until N=0. Assume input eigenvalues are sorted * lexicographically (increasing by real part if ISRT = 0, * increasing by imaginary part if ISRT = 1) * 10 CONTINUE READ( NIN, FMT = * )N, ISRT IF( N.EQ.0 ) \$ RETURN DO 20 I = 1, N READ( NIN, FMT = * )( TMP( I, J ), J = 1, N ) 20 CONTINUE DO 30 I = 1, N READ( NIN, FMT = * )WRIN( I ), WIIN( I ), SIN( I ), SEPIN( I ) 30 CONTINUE TNRM = ZLANGE( 'M', N, N, TMP, LDT, RWORK ) DO 260 ISCL = 1, 3 * * Scale input matrix * KNT = KNT + 1 CALL ZLACPY( 'F', N, N, TMP, LDT, T, LDT ) VMUL = VAL( ISCL ) DO 40 I = 1, N CALL ZDSCAL( N, VMUL, T( 1, I ), 1 ) 40 CONTINUE IF( TNRM.EQ.ZERO ) \$ VMUL = ONE * * Compute eigenvalues and eigenvectors * CALL ZGEHRD( 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 260 END IF DO 60 J = 1, N - 2 DO 50 I = J + 2, N T( I, J ) = ZERO 50 CONTINUE 60 CONTINUE * * Compute Schur form * CALL ZHSEQR( 'S', 'N', N, 1, N, T, LDT, W, CDUM, 1, WORK, \$ LWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 2 ) = KNT NINFO( 2 ) = NINFO( 2 ) + 1 GO TO 260 END IF * * Compute eigenvectors * DO 70 I = 1, N SELECT( I ) = .TRUE. 70 CONTINUE CALL ZTREVC( 'B', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, N, \$ M, WORK, RWORK, INFO ) * * Compute condition numbers * CALL ZTRSNA( 'B', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, S, \$ SEP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF * * Sort eigenvalues and condition numbers lexicographically * to compare with inputs * CALL ZCOPY( N, W, 1, WTMP, 1 ) IF( ISRT.EQ.0 ) THEN * * Sort by increasing real part * DO 80 I = 1, N WSRT( I ) = DBLE( W( I ) ) 80 CONTINUE ELSE * * Sort by increasing imaginary part * DO 90 I = 1, N WSRT( I ) = DIMAG( W( I ) ) 90 CONTINUE END IF CALL DCOPY( N, S, 1, STMP, 1 ) CALL DCOPY( N, SEP, 1, SEPTMP, 1 ) CALL DSCAL( N, ONE / VMUL, SEPTMP, 1 ) DO 110 I = 1, N - 1 KMIN = I VMIN = WSRT( I ) DO 100 J = I + 1, N IF( WSRT( J ).LT.VMIN ) THEN KMIN = J VMIN = WSRT( J ) END IF 100 CONTINUE WSRT( KMIN ) = WSRT( I ) WSRT( I ) = VMIN VCMIN = WTMP( I ) WTMP( I ) = W( KMIN ) WTMP( KMIN ) = VCMIN VMIN = STMP( KMIN ) STMP( KMIN ) = STMP( I ) STMP( I ) = VMIN VMIN = SEPTMP( KMIN ) SEPTMP( KMIN ) = SEPTMP( I ) SEPTMP( I ) = VMIN 110 CONTINUE * * Compare condition numbers for eigenvalues * taking their condition numbers into account * V = MAX( TWO*DBLE( N )*EPS*TNRM, SMLNUM ) IF( TNRM.EQ.ZERO ) \$ V = ONE DO 120 I = 1, N IF( V.GT.SEPTMP( I ) ) THEN TOL = ONE ELSE TOL = V / SEPTMP( I ) END IF IF( V.GT.SEPIN( I ) ) THEN TOLIN = ONE ELSE TOLIN = V / SEPIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( SIN( I )-TOLIN ).GT.STMP( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( SIN( I )-TOLIN.GT.STMP( I )+TOL ) THEN VMAX = ( SIN( I )-TOLIN ) / ( STMP( I )+TOL ) ELSE IF( SIN( I )+TOLIN.LT.EPS*( STMP( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I )+TOLIN.LT.STMP( I )-TOL ) THEN VMAX = ( STMP( I )-TOL ) / ( SIN( I )+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 120 CONTINUE * * Compare condition numbers for eigenvectors * taking their condition numbers into account * DO 130 I = 1, N IF( V.GT.SEPTMP( I )*STMP( I ) ) THEN TOL = SEPTMP( I ) ELSE TOL = V / STMP( I ) END IF IF( V.GT.SEPIN( I )*SIN( I ) ) THEN TOLIN = SEPIN( I ) ELSE TOLIN = V / SIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( SEPIN( I )-TOLIN ).GT.SEPTMP( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I )-TOLIN.GT.SEPTMP( I )+TOL ) THEN VMAX = ( SEPIN( I )-TOLIN ) / ( SEPTMP( I )+TOL ) ELSE IF( SEPIN( I )+TOLIN.LT.EPS*( SEPTMP( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I )+TOLIN.LT.SEPTMP( I )-TOL ) THEN VMAX = ( SEPTMP( I )-TOL ) / ( SEPIN( I )+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 130 CONTINUE * * Compare condition numbers for eigenvalues * without taking their condition numbers into account * DO 140 I = 1, N IF( SIN( I ).LE.DBLE( 2*N )*EPS .AND. STMP( I ).LE. \$ DBLE( 2*N )*EPS ) THEN VMAX = ONE ELSE IF( EPS*SIN( I ).GT.STMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I ).GT.STMP( I ) ) THEN VMAX = SIN( I ) / STMP( I ) ELSE IF( SIN( I ).LT.EPS*STMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I ).LT.STMP( I ) ) THEN VMAX = STMP( I ) / SIN( I ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 3 ) ) THEN RMAX( 3 ) = VMAX IF( NINFO( 3 ).EQ.0 ) \$ LMAX( 3 ) = KNT END IF 140 CONTINUE * * Compare condition numbers for eigenvectors * without taking their condition numbers into account * DO 150 I = 1, N IF( SEPIN( I ).LE.V .AND. SEPTMP( I ).LE.V ) THEN VMAX = ONE ELSE IF( EPS*SEPIN( I ).GT.SEPTMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I ).GT.SEPTMP( I ) ) THEN VMAX = SEPIN( I ) / SEPTMP( I ) ELSE IF( SEPIN( I ).LT.EPS*SEPTMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I ).LT.SEPTMP( I ) ) THEN VMAX = SEPTMP( I ) / SEPIN( I ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 3 ) ) THEN RMAX( 3 ) = VMAX IF( NINFO( 3 ).EQ.0 ) \$ LMAX( 3 ) = KNT END IF 150 CONTINUE * * Compute eigenvalue condition numbers only and compare * VMAX = ZERO DUM( 1 ) = -ONE CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'E', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 160 I = 1, N IF( STMP( I ).NE.S( I ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS 160 CONTINUE * * Compute eigenvector condition numbers only and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'V', 'A', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 170 I = 1, N IF( STMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( I ) ) \$ VMAX = ONE / EPS 170 CONTINUE * * Compute all condition numbers using SELECT and compare * DO 180 I = 1, N SELECT( I ) = .TRUE. 180 CONTINUE CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'B', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 190 I = 1, N IF( SEPTMP( I ).NE.SEP( I ) ) \$ VMAX = ONE / EPS IF( STMP( I ).NE.S( I ) ) \$ VMAX = ONE / EPS 190 CONTINUE * * Compute eigenvalue condition numbers using SELECT and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'E', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 200 I = 1, N IF( STMP( I ).NE.S( I ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS 200 CONTINUE * * Compute eigenvector condition numbers using SELECT and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'V', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 210 I = 1, N IF( STMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( I ) ) \$ VMAX = ONE / EPS 210 CONTINUE IF( VMAX.GT.RMAX( 1 ) ) THEN RMAX( 1 ) = VMAX IF( NINFO( 1 ).EQ.0 ) \$ LMAX( 1 ) = KNT END IF * * Select second and next to last eigenvalues * DO 220 I = 1, N SELECT( I ) = .FALSE. 220 CONTINUE ICMP = 0 IF( N.GT.1 ) THEN ICMP = 1 LCMP( 1 ) = 2 SELECT( 2 ) = .TRUE. CALL ZCOPY( N, RE( 1, 2 ), 1, RE( 1, 1 ), 1 ) CALL ZCOPY( N, LE( 1, 2 ), 1, LE( 1, 1 ), 1 ) END IF IF( N.GT.3 ) THEN ICMP = 2 LCMP( 2 ) = N - 1 SELECT( N-1 ) = .TRUE. CALL ZCOPY( N, RE( 1, N-1 ), 1, RE( 1, 2 ), 1 ) CALL ZCOPY( N, LE( 1, N-1 ), 1, LE( 1, 2 ), 1 ) END IF * * Compute all selected condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'B', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 230 I = 1, ICMP J = LCMP( I ) IF( SEPTMP( I ).NE.SEP( J ) ) \$ VMAX = ONE / EPS IF( STMP( I ).NE.S( J ) ) \$ VMAX = ONE / EPS 230 CONTINUE * * Compute selected eigenvalue condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'E', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 240 I = 1, ICMP J = LCMP( I ) IF( STMP( I ).NE.S( J ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS 240 CONTINUE * * Compute selected eigenvector condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL ZTRSNA( 'V', 'S', SELECT, N, T, LDT, LE, LDT, RE, LDT, \$ STMP, SEPTMP, N, M, WORK, N, RWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 260 END IF DO 250 I = 1, ICMP J = LCMP( I ) IF( STMP( I ).NE.DUM( 1 ) ) \$ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( J ) ) \$ VMAX = ONE / EPS 250 CONTINUE IF( VMAX.GT.RMAX( 1 ) ) THEN RMAX( 1 ) = VMAX IF( NINFO( 1 ).EQ.0 ) \$ LMAX( 1 ) = KNT END IF 260 CONTINUE GO TO 10 * * End of ZGET37 * END