numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/EIG/dget24.f | 32451B | -rw-r--r-- |
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*> \brief \b DGET24 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, * H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, * LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, * RESULT, WORK, LWORK, IWORK, BWORK, INFO ) * * .. Scalar Arguments .. * LOGICAL COMP * INTEGER INFO, JTYPE, LDA, LDVS, LWORK, N, NOUNIT, NSLCT * DOUBLE PRECISION RCDEIN, RCDVIN, THRESH * .. * .. Array Arguments .. * LOGICAL BWORK( * ) * INTEGER ISEED( 4 ), ISLCT( * ), IWORK( * ) * DOUBLE PRECISION A( LDA, * ), H( LDA, * ), HT( LDA, * ), * $ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ), * $ WI( * ), WIT( * ), WITMP( * ), WORK( * ), * $ WR( * ), WRT( * ), WRTMP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGET24 checks the nonsymmetric eigenvalue (Schur form) problem *> expert driver DGEESX. *> *> If COMP = .FALSE., the first 13 of the following tests will be *> be performed on the input matrix A, and also tests 14 and 15 *> if LWORK is sufficiently large. *> If COMP = .TRUE., all 17 test will be performed. *> *> (1) 0 if T is in Schur form, 1/ulp otherwise *> (no sorting of eigenvalues) *> *> (2) | A - VS T VS' | / ( n |A| ulp ) *> *> Here VS is the matrix of Schur eigenvectors, and T is in Schur *> form (no sorting of eigenvalues). *> *> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues). *> *> (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T *> 1/ulp otherwise *> (no sorting of eigenvalues) *> *> (5) 0 if T(with VS) = T(without VS), *> 1/ulp otherwise *> (no sorting of eigenvalues) *> *> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS), *> 1/ulp otherwise *> (no sorting of eigenvalues) *> *> (7) 0 if T is in Schur form, 1/ulp otherwise *> (with sorting of eigenvalues) *> *> (8) | A - VS T VS' | / ( n |A| ulp ) *> *> Here VS is the matrix of Schur eigenvectors, and T is in Schur *> form (with sorting of eigenvalues). *> *> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues). *> *> (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T *> 1/ulp otherwise *> If workspace sufficient, also compare WR, WI with and *> without reciprocal condition numbers *> (with sorting of eigenvalues) *> *> (11) 0 if T(with VS) = T(without VS), *> 1/ulp otherwise *> If workspace sufficient, also compare T with and without *> reciprocal condition numbers *> (with sorting of eigenvalues) *> *> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS), *> 1/ulp otherwise *> If workspace sufficient, also compare VS with and without *> reciprocal condition numbers *> (with sorting of eigenvalues) *> *> (13) if sorting worked and SDIM is the number of *> eigenvalues which were SELECTed *> If workspace sufficient, also compare SDIM with and *> without reciprocal condition numbers *> *> (14) if RCONDE the same no matter if VS and/or RCONDV computed *> *> (15) if RCONDV the same no matter if VS and/or RCONDE computed *> *> (16) |RCONDE - RCDEIN| / cond(RCONDE) *> *> RCONDE is the reciprocal average eigenvalue condition number *> computed by DGEESX 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. *> *> (17) |RCONDV - RCDVIN| / cond(RCONDV) *> *> RCONDV is the reciprocal right invariant subspace condition *> number computed by DGEESX 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. *> \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] JTYPE *> \verbatim *> JTYPE is INTEGER *> Type of input matrix. Used to label output if error occurs. *> \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] THRESH *> \verbatim *> THRESH is 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. *> \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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, N) *> Another copy of the test matrix A, modified by DGEESX. *> \endverbatim *> *> \param[out] HT *> \verbatim *> HT is DOUBLE PRECISION array, dimension (LDA, N) *> Yet another copy of the test matrix A, modified by DGEESX. *> \endverbatim *> *> \param[out] WR *> \verbatim *> WR is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION 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] WRT *> \verbatim *> WRT is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] WIT *> \verbatim *> WIT is DOUBLE PRECISION array, dimension (N) *> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEESX only computes a partial *> eigendecomposition, i.e. not Schur vectors *> \endverbatim *> *> \param[out] WRTMP *> \verbatim *> WRTMP is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] WITMP *> \verbatim *> WITMP is DOUBLE PRECISION array, dimension (N) *> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but sorted by increasing real part. *> \endverbatim *> *> \param[out] VS *> \verbatim *> VS is DOUBLE PRECISION array, dimension (LDVS, N) *> VS holds the computed Schur vectors. *> \endverbatim *> *> \param[in] LDVS *> \verbatim *> LDVS is INTEGER *> Leading dimension of VS. Must be at least max(1, N). *> \endverbatim *> *> \param[out] VS1 *> \verbatim *> VS1 is DOUBLE PRECISION array, dimension (LDVS, N) *> VS1 holds another copy of the computed Schur vectors. *> \endverbatim *> *> \param[in] RCDEIN *> \verbatim *> RCDEIN is DOUBLE PRECISION *> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal *> condition number for the average of selected eigenvalues. *> \endverbatim *> *> \param[in] RCDVIN *> \verbatim *> RCDVIN is DOUBLE PRECISION *> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal *> condition number for the selected right invariant subspace. *> \endverbatim *> *> \param[in] NSLCT *> \verbatim *> NSLCT is INTEGER *> When COMP = .TRUE. the number of selected eigenvalues *> corresponding to the precomputed values RCDEIN and RCDVIN. *> \endverbatim *> *> \param[in] ISLCT *> \verbatim *> ISLCT is INTEGER array, dimension (NSLCT) *> When COMP = .TRUE. ISLCT selects the eigenvalues of the *> input matrix corresponding to the precomputed values RCDEIN *> and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the *> eigenvalue with the J-th largest real part is selected. *> Not referenced if COMP = .FALSE. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (17) *> The values computed by the 17 tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The number of entries in WORK to be passed to DGEESX. This *> must be at least 3*N, and N+N**2 if tests 14--16 are to *> be performed. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (N*N) *> \endverbatim *> *> \param[out] BWORK *> \verbatim *> BWORK is LOGICAL array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> If 0, successful exit. *> If <0, input parameter -INFO had an incorrect value. *> If >0, DGEESX 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 double_eig * * ===================================================================== SUBROUTINE DGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, $ H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, $ LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, $ RESULT, WORK, LWORK, IWORK, BWORK, 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 INTEGER INFO, JTYPE, LDA, LDVS, LWORK, N, NOUNIT, NSLCT DOUBLE PRECISION RCDEIN, RCDVIN, THRESH * .. * .. Array Arguments .. LOGICAL BWORK( * ) INTEGER ISEED( 4 ), ISLCT( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), H( LDA, * ), HT( LDA, * ), $ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ), $ WI( * ), WIT( * ), WITMP( * ), WORK( * ), $ WR( * ), WRT( * ), WRTMP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION EPSIN PARAMETER ( EPSIN = 5.9605D-8 ) * .. * .. Local Scalars .. CHARACTER SORT INTEGER I, IINFO, ISORT, ITMP, J, KMIN, KNTEIG, LIWORK, $ RSUB, SDIM, SDIM1 DOUBLE PRECISION ANORM, EPS, RCNDE1, RCNDV1, RCONDE, RCONDV, $ SMLNUM, TMP, TOL, TOLIN, ULP, ULPINV, V, VIMIN, $ VRMIN, WNORM * .. * .. Local Arrays .. INTEGER IPNT( 20 ) * .. * .. Arrays in Common .. LOGICAL SELVAL( 20 ) DOUBLE PRECISION SELWI( 20 ), SELWR( 20 ) * .. * .. Scalars in Common .. INTEGER SELDIM, SELOPT * .. * .. Common blocks .. COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI * .. * .. External Functions .. LOGICAL DSLECT DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DSLECT, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEESX, DGEMM, DLACPY, DORT01, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SIGN, SQRT * .. * .. Executable Statements .. * * Check for errors * INFO = 0 IF( THRESH.LT.ZERO ) THEN INFO = -3 ELSE IF( NOUNIT.LE.0 ) THEN INFO = -5 ELSE IF( N.LT.0 ) THEN INFO = -6 ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN INFO = -8 ELSE IF( LDVS.LT.1 .OR. LDVS.LT.N ) THEN INFO = -18 ELSE IF( LWORK.LT.3*N ) THEN INFO = -26 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGET24', -INFO ) RETURN END IF * * Quick return if nothing to do * DO 10 I = 1, 17 RESULT( I ) = -ONE 10 CONTINUE * IF( N.EQ.0 ) $ RETURN * * Important constants * SMLNUM = DLAMCH( 'Safe minimum' ) ULP = DLAMCH( 'Precision' ) ULPINV = ONE / ULP * * Perform tests (1)-(13) * SELOPT = 0 LIWORK = N*N DO 120 ISORT = 0, 1 IF( ISORT.EQ.0 ) THEN SORT = 'N' RSUB = 0 ELSE SORT = 'S' RSUB = 6 END IF * * Compute Schur form and Schur vectors, and test them * CALL DLACPY( 'F', N, N, A, LDA, H, LDA ) CALL DGEESX( 'V', SORT, DSLECT, 'N', N, H, LDA, SDIM, WR, WI, $ VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK, $ LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 1+RSUB ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX1', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX1', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) RETURN END IF IF( ISORT.EQ.0 ) THEN CALL DCOPY( N, WR, 1, WRTMP, 1 ) CALL DCOPY( N, WI, 1, WITMP, 1 ) END IF * * Do Test (1) or Test (7) * RESULT( 1+RSUB ) = ZERO DO 30 J = 1, N - 2 DO 20 I = J + 2, N IF( H( I, J ).NE.ZERO ) $ RESULT( 1+RSUB ) = ULPINV 20 CONTINUE 30 CONTINUE DO 40 I = 1, N - 2 IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.ZERO ) $ RESULT( 1+RSUB ) = ULPINV 40 CONTINUE DO 50 I = 1, N - 1 IF( H( I+1, I ).NE.ZERO ) THEN IF( H( I, I ).NE.H( I+1, I+1 ) .OR. H( I, I+1 ).EQ. $ ZERO .OR. SIGN( ONE, H( I+1, I ) ).EQ. $ SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB ) = ULPINV END IF 50 CONTINUE * * Test (2) or (8): Compute norm(A - Q*H*Q') / (norm(A) * N * ULP) * * Copy A to VS1, used as workspace * CALL DLACPY( ' ', N, N, A, LDA, VS1, LDVS ) * * Compute Q*H and store in HT. * CALL DGEMM( 'No transpose', 'No transpose', N, N, N, ONE, VS, $ LDVS, H, LDA, ZERO, HT, LDA ) * * Compute A - Q*H*Q' * CALL DGEMM( 'No transpose', 'Transpose', N, N, N, -ONE, HT, $ LDA, VS, LDVS, ONE, VS1, LDVS ) * ANORM = MAX( DLANGE( '1', N, N, A, LDA, WORK ), SMLNUM ) WNORM = DLANGE( '1', N, N, VS1, LDVS, WORK ) * IF( ANORM.GT.WNORM ) THEN RESULT( 2+RSUB ) = ( WNORM / ANORM ) / ( N*ULP ) ELSE IF( ANORM.LT.ONE ) THEN RESULT( 2+RSUB ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / $ ( N*ULP ) ELSE RESULT( 2+RSUB ) = MIN( WNORM / ANORM, DBLE( N ) ) / $ ( N*ULP ) END IF END IF * * Test (3) or (9): Compute norm( I - Q'*Q ) / ( N * ULP ) * CALL DORT01( 'Columns', N, N, VS, LDVS, WORK, LWORK, $ RESULT( 3+RSUB ) ) * * Do Test (4) or Test (10) * RESULT( 4+RSUB ) = ZERO DO 60 I = 1, N IF( H( I, I ).NE.WR( I ) ) $ RESULT( 4+RSUB ) = ULPINV 60 CONTINUE IF( N.GT.1 ) THEN IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO ) $ RESULT( 4+RSUB ) = ULPINV IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO ) $ RESULT( 4+RSUB ) = ULPINV END IF DO 70 I = 1, N - 1 IF( H( I+1, I ).NE.ZERO ) THEN TMP = SQRT( ABS( H( I+1, I ) ) )* $ SQRT( ABS( H( I, I+1 ) ) ) RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ), $ ABS( WI( I )-TMP ) / $ MAX( ULP*TMP, SMLNUM ) ) RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ), $ ABS( WI( I+1 )+TMP ) / $ MAX( ULP*TMP, SMLNUM ) ) ELSE IF( I.GT.1 ) THEN IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.ZERO .AND. $ WI( I ).NE.ZERO )RESULT( 4+RSUB ) = ULPINV END IF 70 CONTINUE * * Do Test (5) or Test (11) * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'N', SORT, DSLECT, 'N', N, HT, LDA, SDIM, WRT, $ WIT, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK, $ LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 5+RSUB ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX2', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX2', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * RESULT( 5+RSUB ) = ZERO DO 90 J = 1, N DO 80 I = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 5+RSUB ) = ULPINV 80 CONTINUE 90 CONTINUE * * Do Test (6) or Test (12) * RESULT( 6+RSUB ) = ZERO DO 100 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 6+RSUB ) = ULPINV 100 CONTINUE * * Do Test (13) * IF( ISORT.EQ.1 ) THEN RESULT( 13 ) = ZERO KNTEIG = 0 DO 110 I = 1, N IF( DSLECT( WR( I ), WI( I ) ) .OR. $ DSLECT( WR( I ), -WI( I ) ) )KNTEIG = KNTEIG + 1 IF( I.LT.N ) THEN IF( ( DSLECT( WR( I+1 ), WI( I+1 ) ) .OR. $ DSLECT( WR( I+1 ), -WI( I+1 ) ) ) .AND. $ ( .NOT.( DSLECT( WR( I ), $ WI( I ) ) .OR. DSLECT( WR( I ), $ -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )RESULT( 13 ) $ = ULPINV END IF 110 CONTINUE IF( SDIM.NE.KNTEIG ) $ RESULT( 13 ) = ULPINV END IF * 120 CONTINUE * * If there is enough workspace, perform tests (14) and (15) * as well as (10) through (13) * IF( LWORK.GE.N+( N*N ) / 2 ) THEN * * Compute both RCONDE and RCONDV with VS * SORT = 'S' RESULT( 14 ) = ZERO RESULT( 15 ) = ZERO CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'V', SORT, DSLECT, 'B', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCONDE, RCONDV, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 14 ) = ULPINV RESULT( 15 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX3', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX3', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform tests (10), (11), (12), and (13) * DO 140 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 130 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 130 CONTINUE 140 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * * Compute both RCONDE and RCONDV without VS, and compare * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'N', SORT, DSLECT, 'B', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 14 ) = ULPINV RESULT( 15 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX4', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX4', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform tests (14) and (15) * IF( RCNDE1.NE.RCONDE ) $ RESULT( 14 ) = ULPINV IF( RCNDV1.NE.RCONDV ) $ RESULT( 15 ) = ULPINV * * Perform tests (10), (11), (12), and (13) * DO 160 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 150 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 150 CONTINUE 160 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * * Compute RCONDE with VS, and compare * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'V', SORT, DSLECT, 'E', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 14 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX5', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX5', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform test (14) * IF( RCNDE1.NE.RCONDE ) $ RESULT( 14 ) = ULPINV * * Perform tests (10), (11), (12), and (13) * DO 180 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 170 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 170 CONTINUE 180 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * * Compute RCONDE without VS, and compare * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'N', SORT, DSLECT, 'E', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 14 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX6', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX6', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform test (14) * IF( RCNDE1.NE.RCONDE ) $ RESULT( 14 ) = ULPINV * * Perform tests (10), (11), (12), and (13) * DO 200 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 190 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 190 CONTINUE 200 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * * Compute RCONDV with VS, and compare * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'V', SORT, DSLECT, 'V', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 15 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX7', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX7', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform test (15) * IF( RCNDV1.NE.RCONDV ) $ RESULT( 15 ) = ULPINV * * Perform tests (10), (11), (12), and (13) * DO 220 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 210 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 210 CONTINUE 220 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * * Compute RCONDV without VS, and compare * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'N', SORT, DSLECT, 'V', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 15 ) = ULPINV IF( JTYPE.NE.22 ) THEN WRITE( NOUNIT, FMT = 9998 )'DGEESX8', IINFO, N, JTYPE, $ ISEED ELSE WRITE( NOUNIT, FMT = 9999 )'DGEESX8', IINFO, N, $ ISEED( 1 ) END IF INFO = ABS( IINFO ) GO TO 250 END IF * * Perform test (15) * IF( RCNDV1.NE.RCONDV ) $ RESULT( 15 ) = ULPINV * * Perform tests (10), (11), (12), and (13) * DO 240 I = 1, N IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) ) $ RESULT( 10 ) = ULPINV DO 230 J = 1, N IF( H( I, J ).NE.HT( I, J ) ) $ RESULT( 11 ) = ULPINV IF( VS( I, J ).NE.VS1( I, J ) ) $ RESULT( 12 ) = ULPINV 230 CONTINUE 240 CONTINUE IF( SDIM.NE.SDIM1 ) $ RESULT( 13 ) = ULPINV * END IF * 250 CONTINUE * * If there are precomputed reciprocal condition numbers, compare * computed values with them. * IF( COMP ) THEN * * First set up SELOPT, SELDIM, SELVAL, SELWR, and SELWI so that * the logical function DSLECT selects the eigenvalues specified * by NSLCT and ISLCT. * SELDIM = N SELOPT = 1 EPS = MAX( ULP, EPSIN ) DO 260 I = 1, N IPNT( I ) = I SELVAL( I ) = .FALSE. SELWR( I ) = WRTMP( I ) SELWI( I ) = WITMP( I ) 260 CONTINUE DO 280 I = 1, N - 1 KMIN = I VRMIN = WRTMP( I ) VIMIN = WITMP( I ) DO 270 J = I + 1, N IF( WRTMP( J ).LT.VRMIN ) THEN KMIN = J VRMIN = WRTMP( J ) VIMIN = WITMP( J ) END IF 270 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 280 CONTINUE DO 290 I = 1, NSLCT SELVAL( IPNT( ISLCT( I ) ) ) = .TRUE. 290 CONTINUE * * Compute condition numbers * CALL DLACPY( 'F', N, N, A, LDA, HT, LDA ) CALL DGEESX( 'N', 'S', DSLECT, 'B', N, HT, LDA, SDIM1, WRT, $ WIT, VS1, LDVS, RCONDE, RCONDV, WORK, LWORK, $ IWORK, LIWORK, BWORK, IINFO ) IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN RESULT( 16 ) = ULPINV RESULT( 17 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGEESX9', IINFO, N, ISEED( 1 ) INFO = ABS( IINFO ) GO TO 300 END IF * * Compare condition number for average of selected eigenvalues * taking its condition number into account * ANORM = DLANGE( '1', N, N, A, LDA, WORK ) V = MAX( DBLE( N )*EPS*ANORM, SMLNUM ) IF( ANORM.EQ.ZERO ) $ V = ONE IF( V.GT.RCONDV ) THEN TOL = ONE ELSE TOL = V / RCONDV END IF IF( V.GT.RCDVIN ) THEN TOLIN = ONE ELSE TOLIN = V / RCDVIN END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( RCDEIN-TOLIN ).GT.RCONDE+TOL ) THEN RESULT( 16 ) = ULPINV ELSE IF( RCDEIN-TOLIN.GT.RCONDE+TOL ) THEN RESULT( 16 ) = ( RCDEIN-TOLIN ) / ( RCONDE+TOL ) ELSE IF( RCDEIN+TOLIN.LT.EPS*( RCONDE-TOL ) ) THEN RESULT( 16 ) = ULPINV ELSE IF( RCDEIN+TOLIN.LT.RCONDE-TOL ) THEN RESULT( 16 ) = ( RCONDE-TOL ) / ( RCDEIN+TOLIN ) ELSE RESULT( 16 ) = ONE END IF * * Compare condition numbers for right invariant subspace * taking its condition number into account * IF( V.GT.RCONDV*RCONDE ) THEN TOL = RCONDV ELSE TOL = V / RCONDE END IF IF( V.GT.RCDVIN*RCDEIN ) THEN TOLIN = RCDVIN ELSE TOLIN = V / RCDEIN END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( RCDVIN-TOLIN ).GT.RCONDV+TOL ) THEN RESULT( 17 ) = ULPINV ELSE IF( RCDVIN-TOLIN.GT.RCONDV+TOL ) THEN RESULT( 17 ) = ( RCDVIN-TOLIN ) / ( RCONDV+TOL ) ELSE IF( RCDVIN+TOLIN.LT.EPS*( RCONDV-TOL ) ) THEN RESULT( 17 ) = ULPINV ELSE IF( RCDVIN+TOLIN.LT.RCONDV-TOL ) THEN RESULT( 17 ) = ( RCONDV-TOL ) / ( RCDVIN+TOLIN ) ELSE RESULT( 17 ) = ONE END IF * 300 CONTINUE * END IF * 9999 FORMAT( ' DGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', INPUT EXAMPLE NUMBER = ', I4 ) 9998 FORMAT( ' DGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of DGET24 * END