859 lines
27 KiB
Fortran
859 lines
27 KiB
Fortran
*> \brief \b CGET23
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
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* NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
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* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
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* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
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* WORK, LWORK, RWORK, INFO )
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*
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* .. Scalar Arguments ..
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* LOGICAL COMP
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* CHARACTER BALANC
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* INTEGER INFO, ISRT, JTYPE, LDA, LDLRE, LDVL, LDVR,
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* $ LWORK, N, NOUNIT
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* REAL RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
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* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
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* $ RESULT( 11 ), RWORK( * ), SCALE( * ),
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* $ SCALE1( * )
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* COMPLEX A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
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* $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
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* $ WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX.
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*> If COMP = .FALSE., the first 8 of the following tests will be
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*> performed on the input matrix A, and also test 9 if LWORK is
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*> sufficiently large.
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*> if COMP is .TRUE. all 11 tests will be performed.
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*>
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*> (1) | A * VR - VR * W | / ( n |A| ulp )
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*>
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*> Here VR is the matrix of unit right eigenvectors.
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*> W is a diagonal matrix with diagonal entries W(j).
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*>
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*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp )
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*>
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*> Here VL is the matrix of unit left eigenvectors, A**H is the
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*> conjugate transpose of A, and W is as above.
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*>
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*> (3) | |VR(i)| - 1 | / ulp and largest component real
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*>
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*> VR(i) denotes the i-th column of VR.
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*>
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*> (4) | |VL(i)| - 1 | / ulp and largest component real
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*>
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*> VL(i) denotes the i-th column of VL.
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*>
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*> (5) 0 if W(full) = W(partial), 1/ulp otherwise
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*>
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*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV
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*> and RCONDE are also computed, and W(partial) denotes the
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*> eigenvalues computed when only some of VR, VL, RCONDV, and
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*> RCONDE are computed.
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*>
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*> (6) 0 if VR(full) = VR(partial), 1/ulp otherwise
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*>
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*> VR(full) denotes the right eigenvectors computed when VL, RCONDV
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*> and RCONDE are computed, and VR(partial) denotes the result
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*> when only some of VL and RCONDV are computed.
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*>
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*> (7) 0 if VL(full) = VL(partial), 1/ulp otherwise
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*>
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*> VL(full) denotes the left eigenvectors computed when VR, RCONDV
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*> and RCONDE are computed, and VL(partial) denotes the result
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*> when only some of VR and RCONDV are computed.
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*>
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*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) =
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*> SCALE, ILO, IHI, ABNRM (partial)
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*> 1/ulp otherwise
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*>
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*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
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*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and
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*> (partial) is when some are not computed.
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*>
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*> (9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise
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*>
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*> RCONDV(full) denotes the reciprocal condition numbers of the
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*> right eigenvectors computed when VR, VL and RCONDE are also
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*> computed. RCONDV(partial) denotes the reciprocal condition
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*> numbers when only some of VR, VL and RCONDE are computed.
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*>
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*> (10) |RCONDV - RCDVIN| / cond(RCONDV)
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*>
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*> RCONDV is the reciprocal right eigenvector condition number
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*> computed by CGEEVX and RCDVIN (the precomputed true value)
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*> is supplied as input. cond(RCONDV) is the condition number of
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*> RCONDV, and takes errors in computing RCONDV into account, so
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*> that the resulting quantity should be O(ULP). cond(RCONDV) is
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*> essentially given by norm(A)/RCONDE.
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*>
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*> (11) |RCONDE - RCDEIN| / cond(RCONDE)
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*>
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*> RCONDE is the reciprocal eigenvalue condition number
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*> computed by CGEEVX and RCDEIN (the precomputed true value)
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*> is supplied as input. cond(RCONDE) is the condition number
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*> of RCONDE, and takes errors in computing RCONDE into account,
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*> so that the resulting quantity should be O(ULP). cond(RCONDE)
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*> is essentially given by norm(A)/RCONDV.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] COMP
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*> \verbatim
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*> COMP is LOGICAL
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*> COMP describes which input tests to perform:
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*> = .FALSE. if the computed condition numbers are not to
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*> be tested against RCDVIN and RCDEIN
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*> = .TRUE. if they are to be compared
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*> \endverbatim
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*>
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*> \param[in] ISRT
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*> \verbatim
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*> ISRT is INTEGER
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*> If COMP = .TRUE., ISRT indicates in how the eigenvalues
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*> corresponding to values in RCDVIN and RCDEIN are ordered:
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*> = 0 means the eigenvalues are sorted by
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*> increasing real part
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*> = 1 means the eigenvalues are sorted by
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*> increasing imaginary part
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*> If COMP = .FALSE., ISRT is not referenced.
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*> \endverbatim
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*>
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*> \param[in] BALANC
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*> \verbatim
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*> BALANC is CHARACTER
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*> Describes the balancing option to be tested.
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*> = 'N' for no permuting or diagonal scaling
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*> = 'P' for permuting but no diagonal scaling
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*> = 'S' for no permuting but diagonal scaling
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*> = 'B' for permuting and diagonal scaling
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*> \endverbatim
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*>
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*> \param[in] JTYPE
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*> \verbatim
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*> JTYPE is INTEGER
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*> Type of input matrix. Used to label output if error occurs.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is REAL
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*> A test will count as "failed" if the "error", computed as
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*> described above, exceeds THRESH. Note that the error
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*> is scaled to be O(1), so THRESH should be a reasonably
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*> small multiple of 1, e.g., 10 or 100. In particular,
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*> it should not depend on the precision (single vs. double)
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*> or the size of the matrix. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> If COMP = .FALSE., the random number generator seed
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*> used to produce matrix.
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*> If COMP = .TRUE., ISEED(1) = the number of the example.
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*> Used to label output if error occurs.
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*> \endverbatim
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*>
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*> \param[in] NOUNIT
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*> \verbatim
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*> NOUNIT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns INFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The dimension of A. N must be at least 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,N)
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*> Used to hold the matrix whose eigenvalues are to be
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*> computed.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of A, and H. LDA must be at
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*> least 1 and at least N.
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*> \endverbatim
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*>
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*> \param[out] H
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*> \verbatim
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*> H is COMPLEX array, dimension (LDA,N)
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*> Another copy of the test matrix A, modified by CGEEVX.
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*> \endverbatim
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*>
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*> \param[out] W
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*> \verbatim
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*> W is COMPLEX array, dimension (N)
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*> Contains the eigenvalues of A.
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*> \endverbatim
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*>
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*> \param[out] W1
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*> \verbatim
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*> W1 is COMPLEX array, dimension (N)
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*> Like W, this array contains the eigenvalues of A,
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*> but those computed when CGEEVX only computes a partial
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*> eigendecomposition, i.e. not the eigenvalues and left
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*> and right eigenvectors.
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*> \endverbatim
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*>
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*> \param[out] VL
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*> \verbatim
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*> VL is COMPLEX array, dimension (LDVL,N)
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*> VL holds the computed left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDVL
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*> \verbatim
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*> LDVL is INTEGER
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*> Leading dimension of VL. Must be at least max(1,N).
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*> \endverbatim
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*>
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*> \param[out] VR
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*> \verbatim
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*> VR is COMPLEX array, dimension (LDVR,N)
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*> VR holds the computed right eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDVR
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*> \verbatim
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*> LDVR is INTEGER
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*> Leading dimension of VR. Must be at least max(1,N).
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*> \endverbatim
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*>
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*> \param[out] LRE
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*> \verbatim
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*> LRE is COMPLEX array, dimension (LDLRE,N)
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*> LRE holds the computed right or left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDLRE
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*> \verbatim
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*> LDLRE is INTEGER
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*> Leading dimension of LRE. Must be at least max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RCONDV
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*> \verbatim
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*> RCONDV is REAL array, dimension (N)
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*> RCONDV holds the computed reciprocal condition numbers
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*> for eigenvectors.
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*> \endverbatim
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*>
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*> \param[out] RCNDV1
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*> \verbatim
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*> RCNDV1 is REAL array, dimension (N)
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*> RCNDV1 holds more computed reciprocal condition numbers
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*> for eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] RCDVIN
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*> \verbatim
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*> RCDVIN is REAL array, dimension (N)
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*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
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*> condition numbers for eigenvectors to be compared with
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*> RCONDV.
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*> \endverbatim
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*>
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*> \param[out] RCONDE
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*> \verbatim
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*> RCONDE is REAL array, dimension (N)
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*> RCONDE holds the computed reciprocal condition numbers
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*> for eigenvalues.
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*> \endverbatim
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*>
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*> \param[out] RCNDE1
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*> \verbatim
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*> RCNDE1 is REAL array, dimension (N)
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*> RCNDE1 holds more computed reciprocal condition numbers
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*> for eigenvalues.
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*> \endverbatim
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*>
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*> \param[in] RCDEIN
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*> \verbatim
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*> RCDEIN is REAL array, dimension (N)
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*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
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*> condition numbers for eigenvalues to be compared with
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*> RCONDE.
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*> \endverbatim
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*>
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*> \param[out] SCALE
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*> \verbatim
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*> SCALE is REAL array, dimension (N)
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*> Holds information describing balancing of matrix.
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*> \endverbatim
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*>
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*> \param[out] SCALE1
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*> \verbatim
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*> SCALE1 is REAL array, dimension (N)
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*> Holds information describing balancing of matrix.
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (11)
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*> The values computed by the 11 tests described above.
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*> The values are currently limited to 1/ulp, to avoid
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*> overflow.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> 2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> If 0, successful exit.
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*> If <0, input parameter -INFO had an incorrect value.
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*> If >0, CGEEVX returned an error code, the absolute
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*> value of which is returned.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex_eig
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*
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* =====================================================================
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SUBROUTINE CGET23( COMP, ISRT, BALANC, JTYPE, THRESH, ISEED,
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$ NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR,
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$ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN,
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$ RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT,
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$ WORK, LWORK, RWORK, INFO )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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LOGICAL COMP
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CHARACTER BALANC
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INTEGER INFO, ISRT, JTYPE, LDA, LDLRE, LDVL, LDVR,
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$ LWORK, N, NOUNIT
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REAL THRESH
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
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$ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
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$ RESULT( 11 ), RWORK( * ), SCALE( * ),
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$ SCALE1( * )
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COMPLEX A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
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$ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
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$ WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
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REAL EPSIN
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PARAMETER ( EPSIN = 5.9605E-8 )
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* ..
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* .. Local Scalars ..
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LOGICAL BALOK, NOBAL
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CHARACTER SENSE
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INTEGER I, IHI, IHI1, IINFO, ILO, ILO1, ISENS, ISENSM,
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$ J, JJ, KMIN
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REAL ABNRM, ABNRM1, EPS, SMLNUM, TNRM, TOL, TOLIN,
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$ ULP, ULPINV, V, VMAX, VMX, VRICMP, VRIMIN,
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$ VRMX, VTST
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COMPLEX CTMP
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* ..
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* .. Local Arrays ..
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CHARACTER SENS( 2 )
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REAL RES( 2 )
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COMPLEX CDUM( 1 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SCNRM2, SLAMCH
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EXTERNAL LSAME, SCNRM2, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEEVX, CGET22, CLACPY, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, AIMAG, MAX, MIN, REAL
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* ..
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* .. Data statements ..
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DATA SENS / 'N', 'V' /
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* ..
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* .. Executable Statements ..
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*
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* Check for errors
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*
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NOBAL = LSAME( BALANC, 'N' )
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BALOK = NOBAL .OR. LSAME( BALANC, 'P' ) .OR.
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$ LSAME( BALANC, 'S' ) .OR. LSAME( BALANC, 'B' )
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INFO = 0
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IF( ISRT.NE.0 .AND. ISRT.NE.1 ) THEN
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INFO = -2
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ELSE IF( .NOT.BALOK ) THEN
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INFO = -3
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ELSE IF( THRESH.LT.ZERO ) THEN
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INFO = -5
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ELSE IF( NOUNIT.LE.0 ) THEN
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INFO = -7
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ELSE IF( N.LT.0 ) THEN
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INFO = -8
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ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN
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INFO = -10
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ELSE IF( LDVL.LT.1 .OR. LDVL.LT.N ) THEN
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INFO = -15
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ELSE IF( LDVR.LT.1 .OR. LDVR.LT.N ) THEN
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INFO = -17
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ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.N ) THEN
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INFO = -19
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ELSE IF( LWORK.LT.2*N .OR. ( COMP .AND. LWORK.LT.2*N+N*N ) ) THEN
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INFO = -30
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGET23', -INFO )
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RETURN
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END IF
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*
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* Quick return if nothing to do
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*
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DO 10 I = 1, 11
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RESULT( I ) = -ONE
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10 CONTINUE
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* More Important constants
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*
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ULP = SLAMCH( 'Precision' )
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SMLNUM = SLAMCH( 'S' )
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ULPINV = ONE / ULP
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*
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* Compute eigenvalues and eigenvectors, and test them
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*
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IF( LWORK.GE.2*N+N*N ) THEN
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SENSE = 'B'
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ISENSM = 2
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ELSE
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SENSE = 'E'
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ISENSM = 1
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END IF
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CALL CLACPY( 'F', N, N, A, LDA, H, LDA )
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CALL CGEEVX( BALANC, 'V', 'V', SENSE, N, H, LDA, W, VL, LDVL, VR,
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$ LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK,
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$ LWORK, RWORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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RESULT( 1 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'CGEEVX1', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'CGEEVX1', IINFO, N, ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do Test (1)
|
|
*
|
|
CALL CGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, W, WORK, RWORK,
|
|
$ RES )
|
|
RESULT( 1 ) = RES( 1 )
|
|
*
|
|
* Do Test (2)
|
|
*
|
|
CALL CGET22( '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 = SCNRM2( 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( AIMAG( VR( JJ, J ) ).EQ.ZERO .AND.
|
|
$ ABS( REAL( VR( JJ, J ) ) ).GT.VRMX )
|
|
$ VRMX = ABS( REAL( 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 = SCNRM2( 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( AIMAG( VL( JJ, J ) ).EQ.ZERO .AND.
|
|
$ ABS( REAL( VL( JJ, J ) ) ).GT.VRMX )
|
|
$ VRMX = ABS( REAL( 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 CLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL CGEEVX( 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 )'CGEEVX2', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'CGEEVX2', 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 CLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL CGEEVX( 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 )'CGEEVX3', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'CGEEVX3', 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 CLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL CGEEVX( 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 )'CGEEVX4', IINFO, N, JTYPE,
|
|
$ BALANC, ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'CGEEVX4', 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 CLACPY( 'F', N, N, A, LDA, H, LDA )
|
|
CALL CGEEVX( '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 )'CGEEVX5', 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 = REAL( W( I ) )
|
|
ELSE
|
|
VRIMIN = AIMAG( W( I ) )
|
|
END IF
|
|
DO 210 J = I + 1, N
|
|
IF( ISRT.EQ.0 ) THEN
|
|
VRICMP = REAL( W( J ) )
|
|
ELSE
|
|
VRICMP = AIMAG( 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( 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( ' CGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', INPUT EXAMPLE NUMBER = ', I4 )
|
|
9998 FORMAT( ' CGET23: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', BALANC = ', A, ', ISEED=(',
|
|
$ 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CGET23
|
|
*
|
|
END
|