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SUBROUTINE ZGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
$ NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR, $ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, $ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, $ WORK, LWORK, RWORK, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL COMP CHARACTER BALANC INTEGER INFO, ISRT, JTYPE, LDA, LDLRE, LDVL, LDVR, $ LWORK, N, NOUNIT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ), $ RCNDV1( * ), RCONDE( * ), RCONDV( * ), $ RESULT( 11 ), RWORK( * ), SCALE( * ), $ SCALE1( * ) COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ), $ WORK( * ) * .. * * Purpose * ======= * * ZGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX. * If COMP = .FALSE., the first 8 of the following tests will be * performed on the input matrix A, and also test 9 if LWORK is * sufficiently large. * if COMP is .TRUE. all 11 tests will be performed. * * (1) | A * VR - VR * W | / ( n |A| ulp ) * * Here VR is the matrix of unit right eigenvectors. * W is a diagonal matrix with diagonal entries W(j). * * (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) * * Here VL is the matrix of unit left eigenvectors, A**H is the * conjugate transpose of A, and W is as above. * * (3) | |VR(i)| - 1 | / ulp and largest component real * * VR(i) denotes the i-th column of VR. * * (4) | |VL(i)| - 1 | / ulp and largest component real * * VL(i) denotes the i-th column of VL. * * (5) 0 if W(full) = W(partial), 1/ulp otherwise * * W(full) denotes the eigenvalues computed when VR, VL, RCONDV * and RCONDE are also computed, and W(partial) denotes the * eigenvalues computed when only some of VR, VL, RCONDV, and * RCONDE are computed. * * (6) 0 if VR(full) = VR(partial), 1/ulp otherwise * * VR(full) denotes the right eigenvectors computed when VL, RCONDV * and RCONDE are computed, and VR(partial) denotes the result * when only some of VL and RCONDV are computed. * * (7) 0 if VL(full) = VL(partial), 1/ulp otherwise * * VL(full) denotes the left eigenvectors computed when VR, RCONDV * and RCONDE are computed, and VL(partial) denotes the result * when only some of VR and RCONDV are computed. * * (8) 0 if SCALE, ILO, IHI, ABNRM (full) = * SCALE, ILO, IHI, ABNRM (partial) * 1/ulp otherwise * * SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. * (full) is when VR, VL, RCONDE and RCONDV are also computed, and * (partial) is when some are not computed. * * (9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise * * RCONDV(full) denotes the reciprocal condition numbers of the * right eigenvectors computed when VR, VL and RCONDE are also * computed. RCONDV(partial) denotes the reciprocal condition * numbers when only some of VR, VL and RCONDE are computed. * * (10) |RCONDV - RCDVIN| / cond(RCONDV) * * RCONDV is the reciprocal right eigenvector condition number * computed by ZGEEVX and RCDVIN (the precomputed true value) * is supplied as input. cond(RCONDV) is the condition number of * RCONDV, and takes errors in computing RCONDV into account, so * that the resulting quantity should be O(ULP). cond(RCONDV) is * essentially given by norm(A)/RCONDE. * * (11) |RCONDE - RCDEIN| / cond(RCONDE) * * RCONDE is the reciprocal eigenvalue condition number * computed by ZGEEVX and RCDEIN (the precomputed true value) * is supplied as input. cond(RCONDE) is the condition number * of RCONDE, and takes errors in computing RCONDE into account, * so that the resulting quantity should be O(ULP). cond(RCONDE) * is essentially given by norm(A)/RCONDV. * * Arguments * ========= * * COMP (input) LOGICAL * COMP describes which input tests to perform: * = .FALSE. if the computed condition numbers are not to * be tested against RCDVIN and RCDEIN * = .TRUE. if they are to be compared * * ISRT (input) INTEGER * If COMP = .TRUE., ISRT indicates in how the eigenvalues * corresponding to values in RCDVIN and RCDEIN are ordered: * = 0 means the eigenvalues are sorted by * increasing real part * = 1 means the eigenvalues are sorted by * increasing imaginary part * If COMP = .FALSE., ISRT is not referenced. * * BALANC (input) CHARACTER * Describes the balancing option to be tested. * = 'N' for no permuting or diagonal scaling * = 'P' for permuting but no diagonal scaling * = 'S' for no permuting but diagonal scaling * = 'B' for permuting and diagonal scaling * * JTYPE (input) INTEGER * Type of input matrix. Used to label output if error occurs. * * THRESH (input) DOUBLE PRECISION * A test will count as "failed" if the "error", computed as * described above, exceeds THRESH. Note that the error * is scaled to be O(1), so THRESH should be a reasonably * small multiple of 1, e.g., 10 or 100. In particular, * it should not depend on the precision (single vs. double) * or the size of the matrix. It must be at least zero. * * ISEED (input) INTEGER array, dimension (4) * If COMP = .FALSE., the random number generator seed * used to produce matrix. * If COMP = .TRUE., ISEED(1) = the number of the example. * Used to label output if error occurs. * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns INFO not equal to 0.) * * N (input) INTEGER * The dimension of A. N must be at least 0. * * A (input/output) COMPLEX*16 array, dimension (LDA,N) * Used to hold the matrix whose eigenvalues are to be * computed. * * LDA (input) INTEGER * The leading dimension of A, and H. LDA must be at * least 1 and at least N. * * H (workspace) COMPLEX*16 array, dimension (LDA,N) * Another copy of the test matrix A, modified by ZGEEVX. * * W (workspace) COMPLEX*16 array, dimension (N) * Contains the eigenvalues of A. * * W1 (workspace) COMPLEX*16 array, dimension (N) * Like W, this array contains the eigenvalues of A, * but those computed when ZGEEVX only computes a partial * eigendecomposition, i.e. not the eigenvalues and left * and right eigenvectors. * * VL (workspace) COMPLEX*16 array, dimension (LDVL,N) * VL holds the computed left eigenvectors. * * LDVL (input) INTEGER * Leading dimension of VL. Must be at least max(1,N). * * VR (workspace) COMPLEX*16 array, dimension (LDVR,N) * VR holds the computed right eigenvectors. * * LDVR (input) INTEGER * Leading dimension of VR. Must be at least max(1,N). * * LRE (workspace) COMPLEX*16 array, dimension (LDLRE,N) * LRE holds the computed right or left eigenvectors. * * LDLRE (input) INTEGER * Leading dimension of LRE. Must be at least max(1,N). * * RCONDV (workspace) DOUBLE PRECISION array, dimension (N) * RCONDV holds the computed reciprocal condition numbers * for eigenvectors. * * RCNDV1 (workspace) DOUBLE PRECISION array, dimension (N) * RCNDV1 holds more computed reciprocal condition numbers * for eigenvectors. * * RCDVIN (input) DOUBLE PRECISION array, dimension (N) * When COMP = .TRUE. RCDVIN holds the precomputed reciprocal * condition numbers for eigenvectors to be compared with * RCONDV. * * RCONDE (workspace) DOUBLE PRECISION array, dimension (N) * RCONDE holds the computed reciprocal condition numbers * for eigenvalues. * * RCNDE1 (workspace) DOUBLE PRECISION array, dimension (N) * RCNDE1 holds more computed reciprocal condition numbers * for eigenvalues. * * RCDEIN (input) DOUBLE PRECISION array, dimension (N) * When COMP = .TRUE. RCDEIN holds the precomputed reciprocal * condition numbers for eigenvalues to be compared with * RCONDE. * * SCALE (workspace) DOUBLE PRECISION array, dimension (N) * Holds information describing balancing of matrix. * * SCALE1 (workspace) DOUBLE PRECISION array, dimension (N) * Holds information describing balancing of matrix. * * RESULT (output) DOUBLE PRECISION array, dimension (11) * The values computed by the 11 tests described above. * The values are currently limited to 1/ulp, to avoid * overflow. * * WORK (workspace) COMPLEX*16 array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * 2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed. * * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) * * INFO (output) INTEGER * If 0, successful exit. * If <0, input parameter -INFO had an incorrect value. * If >0, ZGEEVX returned an error code, the absolute * value of which is returned. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) DOUBLE PRECISION EPSIN PARAMETER ( EPSIN = 5.9605D-8 ) * .. * .. Local Scalars .. LOGICAL BALOK, NOBAL CHARACTER SENSE INTEGER I, IHI, IHI1, IINFO, ILO, ILO1, ISENS, ISENSM, $ J, JJ, KMIN DOUBLE PRECISION ABNRM, ABNRM1, EPS, SMLNUM, TNRM, TOL, TOLIN, $ ULP, ULPINV, V, VMAX, VMX, VRICMP, VRIMIN, $ VRMX, VTST COMPLEX*16 CTMP * .. * .. Local Arrays .. CHARACTER SENS( 2 ) DOUBLE PRECISION RES( 2 ) COMPLEX*16 CDUM( 1 ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DZNRM2 EXTERNAL LSAME, DLAMCH, DZNRM2 * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEEVX, ZGET22, ZLACPY * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG, MAX, MIN * .. * .. Data statements .. DATA SENS / 'N', 'V' / * .. * .. Executable Statements .. * * Check for errors * NOBAL = LSAME( BALANC, 'N' ) BALOK = NOBAL .OR. LSAME( BALANC, 'P' ) .OR. $ LSAME( BALANC, 'S' ) .OR. LSAME( BALANC, 'B' ) INFO = 0 IF( ISRT.NE.0 .AND. ISRT.NE.1 ) THEN INFO = -2 ELSE IF( .NOT.BALOK ) THEN INFO = -3 ELSE IF( THRESH.LT.ZERO ) THEN INFO = -5 ELSE IF( NOUNIT.LE.0 ) THEN INFO = -7 ELSE IF( N.LT.0 ) THEN INFO = -8 ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN INFO = -10 ELSE IF( LDVL.LT.1 .OR. LDVL.LT.N ) THEN INFO = -15 ELSE IF( LDVR.LT.1 .OR. LDVR.LT.N ) THEN INFO = -17 ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.N ) THEN INFO = -19 ELSE IF( LWORK.LT.2*N .OR. ( COMP .AND. LWORK.LT.2*N+N*N ) ) THEN INFO = -30 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGET23', -INFO ) RETURN END IF * * Quick return if nothing to do * DO 10 I = 1, 11 RESULT( I ) = -ONE 10 CONTINUE * IF( N.EQ.0 ) $ RETURN * * More Important constants * ULP = DLAMCH( 'Precision' ) SMLNUM = DLAMCH( 'S' ) ULPINV = ONE / ULP * * Compute eigenvalues and eigenvectors, and test them * IF( LWORK.GE.2*N+N*N ) THEN SENSE = 'B' ISENSM = 2 ELSE SENSE = 'E' ISENSM = 1 END IF CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEVX( BALANC, 'V', 'V', SENSE, N, H, LDA, W, VL, LDVL, VR, $ LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, $ LWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'ZGEEVX1', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'ZGEEVX1', IINFO, N, ISEED( 1 ) END IF INFO = ABS( IINFO ) RETURN END IF * * Do Test (1) * CALL ZGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, W, WORK, RWORK, $ RES ) RESULT( 1 ) = RES( 1 ) * * Do Test (2) * CALL ZGET22( 'C', 'N', 'C', N, A, LDA, VL, LDVL, W, WORK, RWORK, $ RES ) RESULT( 2 ) = RES( 1 ) * * Do Test (3) * DO 30 J = 1, N TNRM = DZNRM2( N, VR( 1, J ), 1 ) RESULT( 3 ) = MAX( RESULT( 3 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) VMX = ZERO VRMX = ZERO DO 20 JJ = 1, N VTST = ABS( VR( JJ, J ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( DIMAG( VR( JJ, J ) ).EQ.ZERO .AND. $ ABS( DBLE( VR( JJ, J ) ) ).GT.VRMX ) $ VRMX = ABS( DBLE( VR( JJ, J ) ) ) 20 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 3 ) = ULPINV 30 CONTINUE * * Do Test (4) * DO 50 J = 1, N TNRM = DZNRM2( N, VL( 1, J ), 1 ) RESULT( 4 ) = MAX( RESULT( 4 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) VMX = ZERO VRMX = ZERO DO 40 JJ = 1, N VTST = ABS( VL( JJ, J ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( DIMAG( VL( JJ, J ) ).EQ.ZERO .AND. $ ABS( DBLE( VL( JJ, J ) ) ).GT.VRMX ) $ VRMX = ABS( DBLE( VL( JJ, J ) ) ) 40 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 4 ) = ULPINV 50 CONTINUE * * Test for all options of computing condition numbers * DO 200 ISENS = 1, ISENSM * SENSE = SENS( ISENS ) * * Compute eigenvalues only, and test them * CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEVX( BALANC, 'N', 'N', SENSE, N, H, LDA, W1, CDUM, 1, $ CDUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1, $ RCNDV1, WORK, LWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'ZGEEVX2', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'ZGEEVX2', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) * DO 60 J = 1, N IF( W( J ).NE.W1( J ) ) $ RESULT( 5 ) = ULPINV 60 CONTINUE * * Do Test (8) * IF( .NOT.NOBAL ) THEN DO 70 J = 1, N IF( SCALE( J ).NE.SCALE1( J ) ) $ RESULT( 8 ) = ULPINV 70 CONTINUE IF( ILO.NE.ILO1 ) $ RESULT( 8 ) = ULPINV IF( IHI.NE.IHI1 ) $ RESULT( 8 ) = ULPINV IF( ABNRM.NE.ABNRM1 ) $ RESULT( 8 ) = ULPINV END IF * * Do Test (9) * IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN DO 80 J = 1, N IF( RCONDV( J ).NE.RCNDV1( J ) ) $ RESULT( 9 ) = ULPINV 80 CONTINUE END IF * * Compute eigenvalues and right eigenvectors, and test them * CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEVX( BALANC, 'N', 'V', SENSE, N, H, LDA, W1, CDUM, 1, $ LRE, LDLRE, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1, $ RCNDV1, WORK, LWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'ZGEEVX3', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'ZGEEVX3', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) again * DO 90 J = 1, N IF( W( J ).NE.W1( J ) ) $ RESULT( 5 ) = ULPINV 90 CONTINUE * * Do Test (6) * DO 110 J = 1, N DO 100 JJ = 1, N IF( VR( J, JJ ).NE.LRE( J, JJ ) ) $ RESULT( 6 ) = ULPINV 100 CONTINUE 110 CONTINUE * * Do Test (8) again * IF( .NOT.NOBAL ) THEN DO 120 J = 1, N IF( SCALE( J ).NE.SCALE1( J ) ) $ RESULT( 8 ) = ULPINV 120 CONTINUE IF( ILO.NE.ILO1 ) $ RESULT( 8 ) = ULPINV IF( IHI.NE.IHI1 ) $ RESULT( 8 ) = ULPINV IF( ABNRM.NE.ABNRM1 ) $ RESULT( 8 ) = ULPINV END IF * * Do Test (9) again * IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN DO 130 J = 1, N IF( RCONDV( J ).NE.RCNDV1( J ) ) $ RESULT( 9 ) = ULPINV 130 CONTINUE END IF * * Compute eigenvalues and left eigenvectors, and test them * CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEVX( BALANC, 'V', 'N', SENSE, N, H, LDA, W1, LRE, $ LDLRE, CDUM, 1, ILO1, IHI1, SCALE1, ABNRM1, $ RCNDE1, RCNDV1, WORK, LWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'ZGEEVX4', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'ZGEEVX4', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) again * DO 140 J = 1, N IF( W( J ).NE.W1( J ) ) $ RESULT( 5 ) = ULPINV 140 CONTINUE * * Do Test (7) * DO 160 J = 1, N DO 150 JJ = 1, N IF( VL( J, JJ ).NE.LRE( J, JJ ) ) $ RESULT( 7 ) = ULPINV 150 CONTINUE 160 CONTINUE * * Do Test (8) again * IF( .NOT.NOBAL ) THEN DO 170 J = 1, N IF( SCALE( J ).NE.SCALE1( J ) ) $ RESULT( 8 ) = ULPINV 170 CONTINUE IF( ILO.NE.ILO1 ) $ RESULT( 8 ) = ULPINV IF( IHI.NE.IHI1 ) $ RESULT( 8 ) = ULPINV IF( ABNRM.NE.ABNRM1 ) $ RESULT( 8 ) = ULPINV END IF * * Do Test (9) again * IF( ISENS.EQ.2 .AND. N.GT.1 ) THEN DO 180 J = 1, N IF( RCONDV( J ).NE.RCNDV1( J ) ) $ RESULT( 9 ) = ULPINV 180 CONTINUE END IF * 190 CONTINUE * 200 CONTINUE * * If COMP, compare condition numbers to precomputed ones * IF( COMP ) THEN CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEVX( 'N', 'V', 'V', 'B', N, H, LDA, W, VL, LDVL, VR, $ LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, $ WORK, LWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'ZGEEVX5', IINFO, N, ISEED( 1 ) INFO = ABS( IINFO ) GO TO 250 END IF * * Sort eigenvalues and condition numbers lexicographically * to compare with inputs * DO 220 I = 1, N - 1 KMIN = I IF( ISRT.EQ.0 ) THEN VRIMIN = DBLE( W( I ) ) ELSE VRIMIN = DIMAG( W( I ) ) END IF DO 210 J = I + 1, N IF( ISRT.EQ.0 ) THEN VRICMP = DBLE( W( J ) ) ELSE VRICMP = DIMAG( W( J ) ) END IF IF( VRICMP.LT.VRIMIN ) THEN KMIN = J VRIMIN = VRICMP END IF 210 CONTINUE CTMP = W( KMIN ) W( KMIN ) = W( I ) W( I ) = CTMP VRIMIN = RCONDE( KMIN ) RCONDE( KMIN ) = RCONDE( I ) RCONDE( I ) = VRIMIN VRIMIN = RCONDV( KMIN ) RCONDV( KMIN ) = RCONDV( I ) RCONDV( I ) = VRIMIN 220 CONTINUE * * Compare condition numbers for eigenvectors * taking their condition numbers into account * RESULT( 10 ) = ZERO EPS = MAX( EPSIN, ULP ) V = MAX( DBLE( N )*EPS*ABNRM, SMLNUM ) IF( ABNRM.EQ.ZERO ) $ V = ONE DO 230 I = 1, N IF( V.GT.RCONDV( I )*RCONDE( I ) ) THEN TOL = RCONDV( I ) ELSE TOL = V / RCONDE( I ) END IF IF( V.GT.RCDVIN( I )*RCDEIN( I ) ) THEN TOLIN = RCDVIN( I ) ELSE TOLIN = V / RCDEIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( RCDVIN( I )-TOLIN ).GT.RCONDV( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( RCDVIN( I )-TOLIN.GT.RCONDV( I )+TOL ) THEN VMAX = ( RCDVIN( I )-TOLIN ) / ( RCONDV( I )+TOL ) ELSE IF( RCDVIN( I )+TOLIN.LT.EPS*( RCONDV( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( RCDVIN( I )+TOLIN.LT.RCONDV( I )-TOL ) THEN VMAX = ( RCONDV( I )-TOL ) / ( RCDVIN( I )+TOLIN ) ELSE VMAX = ONE END IF RESULT( 10 ) = MAX( RESULT( 10 ), VMAX ) 230 CONTINUE * * Compare condition numbers for eigenvalues * taking their condition numbers into account * RESULT( 11 ) = ZERO DO 240 I = 1, N IF( V.GT.RCONDV( I ) ) THEN TOL = ONE ELSE TOL = V / RCONDV( I ) END IF IF( V.GT.RCDVIN( I ) ) THEN TOLIN = ONE ELSE TOLIN = V / RCDVIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( RCDEIN( I )-TOLIN ).GT.RCONDE( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( RCDEIN( I )-TOLIN.GT.RCONDE( I )+TOL ) THEN VMAX = ( RCDEIN( I )-TOLIN ) / ( RCONDE( I )+TOL ) ELSE IF( RCDEIN( I )+TOLIN.LT.EPS*( RCONDE( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( RCDEIN( I )+TOLIN.LT.RCONDE( I )-TOL ) THEN VMAX = ( RCONDE( I )-TOL ) / ( RCDEIN( I )+TOLIN ) ELSE VMAX = ONE END IF RESULT( 11 ) = MAX( RESULT( 11 ), VMAX ) 240 CONTINUE 250 CONTINUE * END IF * 9999 FORMAT( ' ZGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', INPUT EXAMPLE NUMBER = ', I4 ) 9998 FORMAT( ' ZGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', BALANC = ', A, ', ISEED=(', $ 3( I5, ',' ), I5, ')' ) * RETURN * * End of ZGET23 * END |