*> \brief \b SGET23 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, * A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, * LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, * RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, * WORK, LWORK, IWORK, INFO ) * * .. Scalar Arguments .. * LOGICAL COMP * CHARACTER BALANC * INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N, * $ NOUNIT * REAL THRESH * .. * .. Array Arguments .. * INTEGER ISEED( 4 ), IWORK( * ) * REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), * $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ), * $ RCNDV1( * ), RCONDE( * ), RCONDV( * ), * $ RESULT( 11 ), SCALE( * ), SCALE1( * ), * $ VL( LDVL, * ), VR( LDVR, * ), WI( * ), * $ WI1( * ), WORK( * ), WR( * ), WR1( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX. *> 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 block diagonal matrix, with a 1x1 block for each *> real eigenvalue and a 2x2 block for each complex conjugate *> pair. If eigenvalues j and j+1 are a complex conjugate pair, *> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the *> 2 x 2 block corresponding to the pair will be: *> *> ( wr wi ) *> ( -wi wr ) *> *> Such a block multiplying an n x 2 matrix ( ur ui ) on the *> right will be the same as multiplying ur + i*ui by wr + i*wi. *> *> (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 SGEEVX 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 SGEEVX 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMP *> \verbatim *> COMP is 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 *> \endverbatim *> *> \param[in] BALANC *> \verbatim *> BALANC is 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 *> \endverbatim *> *> \param[in] JTYPE *> \verbatim *> JTYPE is INTEGER *> Type of input matrix. Used to label output if error occurs. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> 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. *> \endverbatim *> *> \param[in] ISEED *> \verbatim *> ISEED is 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. *> \endverbatim *> *> \param[in] NOUNIT *> \verbatim *> NOUNIT is INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns INFO not equal to 0.) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of A. N must be at least 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> Used to hold the matrix whose eigenvalues are to be *> computed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of A, and H. LDA must be at *> least 1 and at least N. *> \endverbatim *> *> \param[out] H *> \verbatim *> H is REAL array, dimension (LDA,N) *> Another copy of the test matrix A, modified by SGEEVX. *> \endverbatim *> *> \param[out] WR *> \verbatim *> WR is REAL array, dimension (N) *> \endverbatim *> *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (N) *> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim *> *> \param[out] WR1 *> \verbatim *> WR1 is REAL array, dimension (N) *> \endverbatim *> *> \param[out] WI1 *> \verbatim *> WI1 is REAL array, dimension (N) *> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEEVX only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left *> and right eigenvectors. *> \endverbatim *> *> \param[out] VL *> \verbatim *> VL is REAL array, dimension (LDVL,N) *> VL holds the computed left eigenvectors. *> \endverbatim *> *> \param[in] LDVL *> \verbatim *> LDVL is INTEGER *> Leading dimension of VL. Must be at least max(1,N). *> \endverbatim *> *> \param[out] VR *> \verbatim *> VR is REAL array, dimension (LDVR,N) *> VR holds the computed right eigenvectors. *> \endverbatim *> *> \param[in] LDVR *> \verbatim *> LDVR is INTEGER *> Leading dimension of VR. Must be at least max(1,N). *> \endverbatim *> *> \param[out] LRE *> \verbatim *> LRE is REAL array, dimension (LDLRE,N) *> LRE holds the computed right or left eigenvectors. *> \endverbatim *> *> \param[in] LDLRE *> \verbatim *> LDLRE is INTEGER *> Leading dimension of LRE. Must be at least max(1,N). *> \endverbatim *> *> \param[out] RCONDV *> \verbatim *> RCONDV is REAL array, dimension (N) *> RCONDV holds the computed reciprocal condition numbers *> for eigenvectors. *> \endverbatim *> *> \param[out] RCNDV1 *> \verbatim *> RCNDV1 is REAL array, dimension (N) *> RCNDV1 holds more computed reciprocal condition numbers *> for eigenvectors. *> \endverbatim *> *> \param[in] RCDVIN *> \verbatim *> RCDVIN is REAL array, dimension (N) *> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal *> condition numbers for eigenvectors to be compared with *> RCONDV. *> \endverbatim *> *> \param[out] RCONDE *> \verbatim *> RCONDE is REAL array, dimension (N) *> RCONDE holds the computed reciprocal condition numbers *> for eigenvalues. *> \endverbatim *> *> \param[out] RCNDE1 *> \verbatim *> RCNDE1 is REAL array, dimension (N) *> RCNDE1 holds more computed reciprocal condition numbers *> for eigenvalues. *> \endverbatim *> *> \param[in] RCDEIN *> \verbatim *> RCDEIN is REAL array, dimension (N) *> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal *> condition numbers for eigenvalues to be compared with *> RCONDE. *> \endverbatim *> *> \param[out] SCALE *> \verbatim *> SCALE is REAL array, dimension (N) *> Holds information describing balancing of matrix. *> \endverbatim *> *> \param[out] SCALE1 *> \verbatim *> SCALE1 is REAL array, dimension (N) *> Holds information describing balancing of matrix. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (11) *> The values computed by the 11 tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The number of entries in WORK. This must be at least *> 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (2*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> If 0, successful exit. *> If <0, input parameter -INFO had an incorrect value. *> If >0, SGEEVX returned an error code, the absolute *> value of which is returned. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SGET23( COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, $ A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, $ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, $ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, $ WORK, LWORK, IWORK, INFO ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. LOGICAL COMP CHARACTER BALANC INTEGER INFO, JTYPE, LDA, LDLRE, LDVL, LDVR, LWORK, N, $ NOUNIT REAL THRESH * .. * .. Array Arguments .. INTEGER ISEED( 4 ), IWORK( * ) REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), $ RCDEIN( * ), RCDVIN( * ), RCNDE1( * ), $ RCNDV1( * ), RCONDE( * ), RCONDV( * ), $ RESULT( 11 ), SCALE( * ), SCALE1( * ), $ VL( LDVL, * ), VR( LDVR, * ), WI( * ), $ WI1( * ), WORK( * ), WR( * ), WR1( * ) * .. * * ===================================================================== * * * .. Parameters .. REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 ) REAL EPSIN PARAMETER ( EPSIN = 5.9605E-8 ) * .. * .. Local Scalars .. LOGICAL BALOK, NOBAL CHARACTER SENSE INTEGER I, IHI, IHI1, IINFO, ILO, ILO1, ISENS, ISENSM, $ J, JJ, KMIN REAL ABNRM, ABNRM1, EPS, SMLNUM, TNRM, TOL, TOLIN, $ ULP, ULPINV, V, VIMIN, VMAX, VMX, VRMIN, VRMX, $ VTST * .. * .. Local Arrays .. CHARACTER SENS( 2 ) REAL DUM( 1 ), RES( 2 ) * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLAPY2, SNRM2 EXTERNAL LSAME, SLAMCH, SLAPY2, SNRM2 * .. * .. External Subroutines .. EXTERNAL SGEEVX, SGET22, SLACPY, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, REAL * .. * .. 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( .NOT.BALOK ) THEN INFO = -2 ELSE IF( THRESH.LT.ZERO ) THEN INFO = -4 ELSE IF( NOUNIT.LE.0 ) THEN INFO = -6 ELSE IF( N.LT.0 ) THEN INFO = -7 ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN INFO = -9 ELSE IF( LDVL.LT.1 .OR. LDVL.LT.N ) THEN INFO = -16 ELSE IF( LDVR.LT.1 .OR. LDVR.LT.N ) THEN INFO = -18 ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.N ) THEN INFO = -20 ELSE IF( LWORK.LT.3*N .OR. ( COMP .AND. LWORK.LT.6*N+N*N ) ) THEN INFO = -31 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGET23', -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 = SLAMCH( 'Precision' ) SMLNUM = SLAMCH( 'S' ) ULPINV = ONE / ULP * * Compute eigenvalues and eigenvectors, and test them * IF( LWORK.GE.6*N+N*N ) THEN SENSE = 'B' ISENSM = 2 ELSE SENSE = 'E' ISENSM = 1 END IF CALL SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEVX( BALANC, 'V', 'V', SENSE, N, H, LDA, WR, WI, VL, LDVL, $ VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, $ WORK, LWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'SGEEVX1', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'SGEEVX1', IINFO, N, ISEED( 1 ) END IF INFO = ABS( IINFO ) RETURN END IF * * Do Test (1) * CALL SGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, WR, WI, WORK, $ RES ) RESULT( 1 ) = RES( 1 ) * * Do Test (2) * CALL SGET22( 'T', 'N', 'T', N, A, LDA, VL, LDVL, WR, WI, WORK, $ RES ) RESULT( 2 ) = RES( 1 ) * * Do Test (3) * DO 30 J = 1, N TNRM = ONE IF( WI( J ).EQ.ZERO ) THEN TNRM = SNRM2( N, VR( 1, J ), 1 ) ELSE IF( WI( J ).GT.ZERO ) THEN TNRM = SLAPY2( SNRM2( N, VR( 1, J ), 1 ), $ SNRM2( N, VR( 1, J+1 ), 1 ) ) END IF RESULT( 3 ) = MAX( RESULT( 3 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) IF( WI( J ).GT.ZERO ) THEN VMX = ZERO VRMX = ZERO DO 20 JJ = 1, N VTST = SLAPY2( VR( JJ, J ), VR( JJ, J+1 ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( VR( JJ, J+1 ).EQ.ZERO .AND. ABS( VR( JJ, J ) ).GT. $ VRMX )VRMX = ABS( VR( JJ, J ) ) 20 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 3 ) = ULPINV END IF 30 CONTINUE * * Do Test (4) * DO 50 J = 1, N TNRM = ONE IF( WI( J ).EQ.ZERO ) THEN TNRM = SNRM2( N, VL( 1, J ), 1 ) ELSE IF( WI( J ).GT.ZERO ) THEN TNRM = SLAPY2( SNRM2( N, VL( 1, J ), 1 ), $ SNRM2( N, VL( 1, J+1 ), 1 ) ) END IF RESULT( 4 ) = MAX( RESULT( 4 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) IF( WI( J ).GT.ZERO ) THEN VMX = ZERO VRMX = ZERO DO 40 JJ = 1, N VTST = SLAPY2( VL( JJ, J ), VL( JJ, J+1 ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( VL( JJ, J+1 ).EQ.ZERO .AND. ABS( VL( JJ, J ) ).GT. $ VRMX )VRMX = ABS( VL( JJ, J ) ) 40 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 4 ) = ULPINV END IF 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 SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEVX( BALANC, 'N', 'N', SENSE, N, H, LDA, WR1, WI1, DUM, $ 1, DUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1, $ RCNDV1, WORK, LWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'SGEEVX2', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'SGEEVX2', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) * DO 60 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( 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 SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEVX( BALANC, 'N', 'V', SENSE, N, H, LDA, WR1, WI1, DUM, $ 1, LRE, LDLRE, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1, $ RCNDV1, WORK, LWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'SGEEVX3', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'SGEEVX3', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) again * DO 90 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( 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 SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEVX( BALANC, 'V', 'N', SENSE, N, H, LDA, WR1, WI1, LRE, $ LDLRE, DUM, 1, ILO1, IHI1, SCALE1, ABNRM1, RCNDE1, $ RCNDV1, WORK, LWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'SGEEVX4', IINFO, N, JTYPE, $ BALANC, ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'SGEEVX4', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 190 END IF * * Do Test (5) again * DO 140 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( 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 SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEVX( 'N', 'V', 'V', 'B', N, H, LDA, WR, WI, VL, LDVL, $ VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, $ WORK, LWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'SGEEVX5', 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 VRMIN = WR( I ) VIMIN = WI( I ) DO 210 J = I + 1, N IF( WR( J ).LT.VRMIN ) THEN KMIN = J VRMIN = WR( J ) VIMIN = WI( J ) END IF 210 CONTINUE WR( KMIN ) = WR( I ) WI( KMIN ) = WI( I ) WR( I ) = VRMIN WI( I ) = VIMIN VRMIN = RCONDE( KMIN ) RCONDE( KMIN ) = RCONDE( I ) RCONDE( I ) = VRMIN VRMIN = RCONDV( KMIN ) RCONDV( KMIN ) = RCONDV( I ) RCONDV( I ) = VRMIN 220 CONTINUE * * Compare condition numbers for eigenvectors * taking their condition numbers into account * RESULT( 10 ) = ZERO EPS = MAX( EPSIN, ULP ) V = MAX( REAL( 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( ' SGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', INPUT EXAMPLE NUMBER = ', I4 ) 9998 FORMAT( ' SGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', BALANC = ', A, ', ISEED=(', $ 3( I5, ',' ), I5, ')' ) * RETURN * * End of SGET23 * END