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957 lines
30 KiB
957 lines
30 KiB
*> \brief \b ZGET24
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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 ZGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
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* H, HT, W, WT, WTMP, VS, LDVS, VS1, RCDEIN,
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* RCDVIN, NSLCT, ISLCT, ISRT, RESULT, WORK,
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* LWORK, RWORK, BWORK, INFO )
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*
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* .. Scalar Arguments ..
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* LOGICAL COMP
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* INTEGER INFO, ISRT, JTYPE, LDA, LDVS, LWORK, N, NOUNIT,
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* $ NSLCT
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* DOUBLE PRECISION RCDEIN, RCDVIN, THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL BWORK( * )
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* INTEGER ISEED( 4 ), ISLCT( * )
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* DOUBLE PRECISION RESULT( 17 ), RWORK( * )
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* COMPLEX*16 A( LDA, * ), H( LDA, * ), HT( LDA, * ),
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* $ VS( LDVS, * ), VS1( LDVS, * ), W( * ),
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* $ WORK( * ), WT( * ), WTMP( * )
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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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*> ZGET24 checks the nonsymmetric eigenvalue (Schur form) problem
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*> expert driver ZGEESX.
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*>
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*> If COMP = .FALSE., the first 13 of the following tests will be
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*> be performed on the input matrix A, and also tests 14 and 15
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*> if LWORK is sufficiently large.
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*> If COMP = .TRUE., all 17 test will be performed.
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*>
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*> (1) 0 if T is in Schur form, 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (2) | A - VS T VS' | / ( n |A| ulp )
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*>
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*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
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*> form (no sorting of eigenvalues).
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*>
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*> (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
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*>
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*> (4) 0 if W are eigenvalues of T
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (5) 0 if T(with VS) = T(without VS),
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
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*> 1/ulp otherwise
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*> (no sorting of eigenvalues)
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*>
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*> (7) 0 if T is in Schur form, 1/ulp otherwise
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*> (with sorting of eigenvalues)
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*>
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*> (8) | A - VS T VS' | / ( n |A| ulp )
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*>
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*> Here VS is the matrix of Schur eigenvectors, and T is in Schur
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*> form (with sorting of eigenvalues).
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*>
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*> (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
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*>
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*> (10) 0 if W are eigenvalues of T
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare W with and
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*> without reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (11) 0 if T(with VS) = T(without VS),
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare T with and without
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*> reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
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*> 1/ulp otherwise
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*> If workspace sufficient, also compare VS with and without
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*> reciprocal condition numbers
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*> (with sorting of eigenvalues)
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*>
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*> (13) if sorting worked and SDIM is the number of
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*> eigenvalues which were SELECTed
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*> If workspace sufficient, also compare SDIM with and
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*> without reciprocal condition numbers
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*>
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*> (14) if RCONDE the same no matter if VS and/or RCONDV computed
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*>
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*> (15) if RCONDV the same no matter if VS and/or RCONDE computed
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*>
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*> (16) |RCONDE - RCDEIN| / cond(RCONDE)
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*>
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*> RCONDE is the reciprocal average eigenvalue condition number
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*> computed by ZGEESX 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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*>
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*> (17) |RCONDV - RCDVIN| / cond(RCONDV)
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*>
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*> RCONDV is the reciprocal right invariant subspace condition
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*> number computed by ZGEESX and RCDVIN (the precomputed true
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*> value) is supplied as input. cond(RCONDV) is the condition
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*> number of RCONDV, and takes errors in computing RCONDV into
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*> account, so that the resulting quantity should be O(ULP).
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*> cond(RCONDV) is essentially given by norm(A)/RCONDE.
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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] 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] 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] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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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] 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*16 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*16 array, dimension (LDA, N)
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*> Another copy of the test matrix A, modified by ZGEESX.
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*> \endverbatim
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*>
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*> \param[out] HT
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*> \verbatim
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*> HT is COMPLEX*16 array, dimension (LDA, N)
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*> Yet another copy of the test matrix A, modified by ZGEESX.
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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*16 array, dimension (N)
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*> The computed eigenvalues of A.
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*> \endverbatim
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*>
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*> \param[out] WT
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*> \verbatim
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*> WT is COMPLEX*16 array, dimension (N)
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*> Like W, this array contains the eigenvalues of A,
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*> but those computed when ZGEESX only computes a partial
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*> eigendecomposition, i.e. not Schur vectors
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*> \endverbatim
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*>
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*> \param[out] WTMP
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*> \verbatim
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*> WTMP is COMPLEX*16 array, dimension (N)
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*> Like W, this array contains the eigenvalues of A,
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*> but sorted by increasing real or imaginary part.
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*> \endverbatim
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*>
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*> \param[out] VS
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*> \verbatim
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*> VS is COMPLEX*16 array, dimension (LDVS, N)
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*> VS holds the computed Schur vectors.
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*> \endverbatim
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*>
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*> \param[in] LDVS
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*> \verbatim
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*> LDVS is INTEGER
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*> Leading dimension of VS. Must be at least max(1, N).
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*> \endverbatim
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*>
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*> \param[out] VS1
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*> \verbatim
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*> VS1 is COMPLEX*16 array, dimension (LDVS, N)
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*> VS1 holds another copy of the computed Schur vectors.
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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 DOUBLE PRECISION
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*> When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
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*> condition number for the average of selected eigenvalues.
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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 DOUBLE PRECISION
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*> When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
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*> condition number for the selected right invariant subspace.
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*> \endverbatim
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*>
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*> \param[in] NSLCT
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*> \verbatim
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*> NSLCT is INTEGER
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*> When COMP = .TRUE. the number of selected eigenvalues
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*> corresponding to the precomputed values RCDEIN and RCDVIN.
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*> \endverbatim
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*>
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*> \param[in] ISLCT
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*> \verbatim
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*> ISLCT is INTEGER array, dimension (NSLCT)
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*> When COMP = .TRUE. ISLCT selects the eigenvalues of the
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*> input matrix corresponding to the precomputed values RCDEIN
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*> and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the
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*> eigenvalue with the J-th largest real or imaginary part is
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*> selected. The real part is used if ISRT = 0, and the
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*> imaginary part if ISRT = 1.
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*> Not referenced if COMP = .FALSE.
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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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*> When COMP = .TRUE., ISRT describes how ISLCT is used to
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*> choose a subset of the spectrum.
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*> Not referenced if COMP = .FALSE.
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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 DOUBLE PRECISION array, dimension (17)
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*> The values computed by the 17 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*16 array, dimension (2*N*N)
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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 to be passed to ZGEESX. This
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*> must be at least 2*N, and N*(N+1)/2 if tests 14--16 are to
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*> 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 DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] BWORK
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*> \verbatim
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*> BWORK is LOGICAL array, dimension (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, ZGEESX 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 complex16_eig
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*
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* =====================================================================
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SUBROUTINE ZGET24( COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA,
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$ H, HT, W, WT, WTMP, VS, LDVS, VS1, RCDEIN,
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$ RCDVIN, NSLCT, ISLCT, ISRT, RESULT, WORK,
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$ LWORK, RWORK, BWORK, 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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INTEGER INFO, ISRT, JTYPE, LDA, LDVS, LWORK, N, NOUNIT,
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$ NSLCT
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DOUBLE PRECISION RCDEIN, RCDVIN, THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL BWORK( * )
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INTEGER ISEED( 4 ), ISLCT( * )
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DOUBLE PRECISION RESULT( 17 ), RWORK( * )
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COMPLEX*16 A( LDA, * ), H( LDA, * ), HT( LDA, * ),
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$ VS( LDVS, * ), VS1( LDVS, * ), W( * ),
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$ WORK( * ), WT( * ), WTMP( * )
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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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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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DOUBLE PRECISION EPSIN
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PARAMETER ( EPSIN = 5.9605D-8 )
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* ..
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* .. Local Scalars ..
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CHARACTER SORT
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INTEGER I, IINFO, ISORT, ITMP, J, KMIN, KNTEIG, RSUB,
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$ SDIM, SDIM1
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DOUBLE PRECISION ANORM, EPS, RCNDE1, RCNDV1, RCONDE, RCONDV,
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$ SMLNUM, TOL, TOLIN, ULP, ULPINV, V, VRICMP,
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$ VRIMIN, WNORM
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COMPLEX*16 CTMP
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* ..
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* .. Local Arrays ..
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INTEGER IPNT( 20 )
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* ..
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* .. External Functions ..
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LOGICAL ZSLECT
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DOUBLE PRECISION DLAMCH, ZLANGE
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EXTERNAL ZSLECT, DLAMCH, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZCOPY, ZGEESX, ZGEMM, ZLACPY, ZUNT01
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
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* ..
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* .. Arrays in Common ..
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LOGICAL SELVAL( 20 )
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DOUBLE PRECISION SELWI( 20 ), SELWR( 20 )
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* ..
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* .. Scalars in Common ..
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INTEGER SELDIM, SELOPT
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* ..
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* .. Common blocks ..
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COMMON / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
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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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INFO = 0
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IF( THRESH.LT.ZERO ) THEN
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INFO = -3
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ELSE IF( NOUNIT.LE.0 ) THEN
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INFO = -5
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ELSE IF( N.LT.0 ) THEN
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INFO = -6
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ELSE IF( LDA.LT.1 .OR. LDA.LT.N ) THEN
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INFO = -8
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ELSE IF( LDVS.LT.1 .OR. LDVS.LT.N ) THEN
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INFO = -15
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ELSE IF( LWORK.LT.2*N ) THEN
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INFO = -24
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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( 'ZGET24', -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, 17
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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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* Important constants
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*
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SMLNUM = DLAMCH( 'Safe minimum' )
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ULP = DLAMCH( 'Precision' )
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ULPINV = ONE / ULP
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*
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* Perform tests (1)-(13)
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*
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SELOPT = 0
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DO 90 ISORT = 0, 1
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IF( ISORT.EQ.0 ) THEN
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SORT = 'N'
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RSUB = 0
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ELSE
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SORT = 'S'
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RSUB = 6
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END IF
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*
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* Compute Schur form and Schur vectors, and test them
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*
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CALL ZLACPY( 'F', N, N, A, LDA, H, LDA )
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CALL ZGEESX( 'V', SORT, ZSLECT, 'N', N, H, LDA, SDIM, W, VS,
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$ LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK,
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$ IINFO )
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IF( IINFO.NE.0 ) THEN
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RESULT( 1+RSUB ) = ULPINV
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IF( JTYPE.NE.22 ) THEN
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WRITE( NOUNIT, FMT = 9998 )'ZGEESX1', IINFO, N, JTYPE,
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$ ISEED
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ELSE
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WRITE( NOUNIT, FMT = 9999 )'ZGEESX1', IINFO, N,
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$ ISEED( 1 )
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END IF
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INFO = ABS( IINFO )
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RETURN
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END IF
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IF( ISORT.EQ.0 ) THEN
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CALL ZCOPY( N, W, 1, WTMP, 1 )
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END IF
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*
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* Do Test (1) or Test (7)
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*
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RESULT( 1+RSUB ) = ZERO
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DO 30 J = 1, N - 1
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DO 20 I = J + 1, N
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IF( H( I, J ).NE.CZERO )
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$ RESULT( 1+RSUB ) = ULPINV
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20 CONTINUE
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30 CONTINUE
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*
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* Test (2) or (8): Compute norm(A - Q*H*Q') / (norm(A) * N * ULP)
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*
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* Copy A to VS1, used as workspace
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*
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CALL ZLACPY( ' ', N, N, A, LDA, VS1, LDVS )
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*
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* Compute Q*H and store in HT.
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*
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CALL ZGEMM( 'No transpose', 'No transpose', N, N, N, CONE, VS,
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$ LDVS, H, LDA, CZERO, HT, LDA )
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*
|
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* Compute A - Q*H*Q'
|
|
*
|
|
CALL ZGEMM( 'No transpose', 'Conjugate transpose', N, N, N,
|
|
$ -CONE, HT, LDA, VS, LDVS, CONE, VS1, LDVS )
|
|
*
|
|
ANORM = MAX( ZLANGE( '1', N, N, A, LDA, RWORK ), SMLNUM )
|
|
WNORM = ZLANGE( '1', N, N, VS1, LDVS, RWORK )
|
|
*
|
|
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 ZUNT01( 'Columns', N, N, VS, LDVS, WORK, LWORK, RWORK,
|
|
$ RESULT( 3+RSUB ) )
|
|
*
|
|
* Do Test (4) or Test (10)
|
|
*
|
|
RESULT( 4+RSUB ) = ZERO
|
|
DO 40 I = 1, N
|
|
IF( H( I, I ).NE.W( I ) )
|
|
$ RESULT( 4+RSUB ) = ULPINV
|
|
40 CONTINUE
|
|
*
|
|
* Do Test (5) or Test (11)
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'N', SORT, ZSLECT, 'N', N, HT, LDA, SDIM, WT, VS,
|
|
$ LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK,
|
|
$ IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 5+RSUB ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX2', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX2', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
RESULT( 5+RSUB ) = ZERO
|
|
DO 60 J = 1, N
|
|
DO 50 I = 1, N
|
|
IF( H( I, J ).NE.HT( I, J ) )
|
|
$ RESULT( 5+RSUB ) = ULPINV
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
*
|
|
* Do Test (6) or Test (12)
|
|
*
|
|
RESULT( 6+RSUB ) = ZERO
|
|
DO 70 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 6+RSUB ) = ULPINV
|
|
70 CONTINUE
|
|
*
|
|
* Do Test (13)
|
|
*
|
|
IF( ISORT.EQ.1 ) THEN
|
|
RESULT( 13 ) = ZERO
|
|
KNTEIG = 0
|
|
DO 80 I = 1, N
|
|
IF( ZSLECT( W( I ) ) )
|
|
$ KNTEIG = KNTEIG + 1
|
|
IF( I.LT.N ) THEN
|
|
IF( ZSLECT( W( I+1 ) ) .AND.
|
|
$ ( .NOT.ZSLECT( W( I ) ) ) )RESULT( 13 ) = ULPINV
|
|
END IF
|
|
80 CONTINUE
|
|
IF( SDIM.NE.KNTEIG )
|
|
$ RESULT( 13 ) = ULPINV
|
|
END IF
|
|
*
|
|
90 CONTINUE
|
|
*
|
|
* If there is enough workspace, perform tests (14) and (15)
|
|
* as well as (10) through (13)
|
|
*
|
|
IF( LWORK.GE.( N*( N+1 ) ) / 2 ) THEN
|
|
*
|
|
* Compute both RCONDE and RCONDV with VS
|
|
*
|
|
SORT = 'S'
|
|
RESULT( 14 ) = ZERO
|
|
RESULT( 15 ) = ZERO
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'V', SORT, ZSLECT, 'B', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 14 ) = ULPINV
|
|
RESULT( 15 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX3', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX3', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Perform tests (10), (11), (12), and (13)
|
|
*
|
|
DO 110 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 100 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
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
* Compute both RCONDE and RCONDV without VS, and compare
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'N', SORT, ZSLECT, 'B', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 14 ) = ULPINV
|
|
RESULT( 15 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX4', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX4', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
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 130 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 120 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
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
* Compute RCONDE with VS, and compare
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'V', SORT, ZSLECT, 'E', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 14 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX5', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX5', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Perform test (14)
|
|
*
|
|
IF( RCNDE1.NE.RCONDE )
|
|
$ RESULT( 14 ) = ULPINV
|
|
*
|
|
* Perform tests (10), (11), (12), and (13)
|
|
*
|
|
DO 150 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 140 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
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
* Compute RCONDE without VS, and compare
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'N', SORT, ZSLECT, 'E', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 14 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX6', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX6', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Perform test (14)
|
|
*
|
|
IF( RCNDE1.NE.RCONDE )
|
|
$ RESULT( 14 ) = ULPINV
|
|
*
|
|
* Perform tests (10), (11), (12), and (13)
|
|
*
|
|
DO 170 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 160 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
|
|
160 CONTINUE
|
|
170 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
* Compute RCONDV with VS, and compare
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'V', SORT, ZSLECT, 'V', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 15 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX7', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX7', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Perform test (15)
|
|
*
|
|
IF( RCNDV1.NE.RCONDV )
|
|
$ RESULT( 15 ) = ULPINV
|
|
*
|
|
* Perform tests (10), (11), (12), and (13)
|
|
*
|
|
DO 190 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 180 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
|
|
180 CONTINUE
|
|
190 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
* Compute RCONDV without VS, and compare
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'N', SORT, ZSLECT, 'V', N, HT, LDA, SDIM1, WT,
|
|
$ VS1, LDVS, RCNDE1, RCNDV1, WORK, LWORK, RWORK,
|
|
$ BWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 15 ) = ULPINV
|
|
IF( JTYPE.NE.22 ) THEN
|
|
WRITE( NOUNIT, FMT = 9998 )'ZGEESX8', IINFO, N, JTYPE,
|
|
$ ISEED
|
|
ELSE
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX8', IINFO, N,
|
|
$ ISEED( 1 )
|
|
END IF
|
|
INFO = ABS( IINFO )
|
|
GO TO 220
|
|
END IF
|
|
*
|
|
* Perform test (15)
|
|
*
|
|
IF( RCNDV1.NE.RCONDV )
|
|
$ RESULT( 15 ) = ULPINV
|
|
*
|
|
* Perform tests (10), (11), (12), and (13)
|
|
*
|
|
DO 210 I = 1, N
|
|
IF( W( I ).NE.WT( I ) )
|
|
$ RESULT( 10 ) = ULPINV
|
|
DO 200 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
|
|
200 CONTINUE
|
|
210 CONTINUE
|
|
IF( SDIM.NE.SDIM1 )
|
|
$ RESULT( 13 ) = ULPINV
|
|
*
|
|
END IF
|
|
*
|
|
220 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 ZSLECT selects the eigenvalues specified
|
|
* by NSLCT, ISLCT and ISRT.
|
|
*
|
|
SELDIM = N
|
|
SELOPT = 1
|
|
EPS = MAX( ULP, EPSIN )
|
|
DO 230 I = 1, N
|
|
IPNT( I ) = I
|
|
SELVAL( I ) = .FALSE.
|
|
SELWR( I ) = DBLE( WTMP( I ) )
|
|
SELWI( I ) = DIMAG( WTMP( I ) )
|
|
230 CONTINUE
|
|
DO 250 I = 1, N - 1
|
|
KMIN = I
|
|
IF( ISRT.EQ.0 ) THEN
|
|
VRIMIN = DBLE( WTMP( I ) )
|
|
ELSE
|
|
VRIMIN = DIMAG( WTMP( I ) )
|
|
END IF
|
|
DO 240 J = I + 1, N
|
|
IF( ISRT.EQ.0 ) THEN
|
|
VRICMP = DBLE( WTMP( J ) )
|
|
ELSE
|
|
VRICMP = DIMAG( WTMP( J ) )
|
|
END IF
|
|
IF( VRICMP.LT.VRIMIN ) THEN
|
|
KMIN = J
|
|
VRIMIN = VRICMP
|
|
END IF
|
|
240 CONTINUE
|
|
CTMP = WTMP( KMIN )
|
|
WTMP( KMIN ) = WTMP( I )
|
|
WTMP( I ) = CTMP
|
|
ITMP = IPNT( I )
|
|
IPNT( I ) = IPNT( KMIN )
|
|
IPNT( KMIN ) = ITMP
|
|
250 CONTINUE
|
|
DO 260 I = 1, NSLCT
|
|
SELVAL( IPNT( ISLCT( I ) ) ) = .TRUE.
|
|
260 CONTINUE
|
|
*
|
|
* Compute condition numbers
|
|
*
|
|
CALL ZLACPY( 'F', N, N, A, LDA, HT, LDA )
|
|
CALL ZGEESX( 'N', 'S', ZSLECT, 'B', N, HT, LDA, SDIM1, WT, VS1,
|
|
$ LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK,
|
|
$ IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
RESULT( 16 ) = ULPINV
|
|
RESULT( 17 ) = ULPINV
|
|
WRITE( NOUNIT, FMT = 9999 )'ZGEESX9', IINFO, N, ISEED( 1 )
|
|
INFO = ABS( IINFO )
|
|
GO TO 270
|
|
END IF
|
|
*
|
|
* Compare condition number for average of selected eigenvalues
|
|
* taking its condition number into account
|
|
*
|
|
ANORM = ZLANGE( '1', N, N, A, LDA, RWORK )
|
|
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
|
|
*
|
|
270 CONTINUE
|
|
*
|
|
END IF
|
|
*
|
|
9999 FORMAT( ' ZGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', INPUT EXAMPLE NUMBER = ', I4 )
|
|
9998 FORMAT( ' ZGET24: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
|
|
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZGET24
|
|
*
|
|
END
|
|
|