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Cloned library LAPACK-3.11.0 with extra build files for internal package management.
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LAPACK-3.11.0/TESTING/EIG/cdrges3.f

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*> \brief \b CDRGES3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CDRGES3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
* BETA, WORK, LWORK, RWORK, RESULT, BWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL BWORK( * ), DOTYPE( * )
* INTEGER ISEED( 4 ), NN( * )
* REAL RESULT( 13 ), RWORK( * )
* COMPLEX A( LDA, * ), ALPHA( * ), B( LDA, * ),
* $ BETA( * ), Q( LDQ, * ), S( LDA, * ),
* $ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CDRGES3 checks the nonsymmetric generalized eigenvalue (Schur form)
*> problem driver CGGES3.
*>
*> CGGES3 factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate
*> transpose, S and T are upper triangular (i.e., in generalized Schur
*> form), and Q and Z are unitary. It also computes the generalized
*> eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus,
*> w(j) = alpha(j)/beta(j) is a root of the characteristic equation
*>
*> det( A - w(j) B ) = 0
*>
*> Optionally it also reorder the eigenvalues so that a selected
*> cluster of eigenvalues appears in the leading diagonal block of the
*> Schur forms.
*>
*> When CDRGES3 is called, a number of matrix "sizes" ("N's") and a
*> number of matrix "TYPES" are specified. For each size ("N")
*> and each TYPE of matrix, a pair of matrices (A, B) will be generated
*> and used for testing. For each matrix pair, the following 13 tests
*> will be performed and compared with the threshold THRESH except
*> the tests (5), (11) and (13).
*>
*>
*> (1) | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues)
*>
*>
*> (2) | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues)
*>
*>
*> (3) | I - QQ' | / ( n ulp ) (no sorting of eigenvalues)
*>
*>
*> (4) | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues)
*>
*> (5) if A is in Schur form (i.e. triangular form) (no sorting of
*> eigenvalues)
*>
*> (6) if eigenvalues = diagonal elements of the Schur form (S, T),
*> i.e., test the maximum over j of D(j) where:
*>
*> |alpha(j) - S(j,j)| |beta(j) - T(j,j)|
*> D(j) = ------------------------ + -----------------------
*> max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
*>
*> (no sorting of eigenvalues)
*>
*> (7) | (A,B) - Q (S,T) Z' | / ( |(A,B)| n ulp )
*> (with sorting of eigenvalues).
*>
*> (8) | I - QQ' | / ( n ulp ) (with sorting of eigenvalues).
*>
*> (9) | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues).
*>
*> (10) if A is in Schur form (i.e. quasi-triangular form)
*> (with sorting of eigenvalues).
*>
*> (11) if eigenvalues = diagonal elements of the Schur form (S, T),
*> i.e. test the maximum over j of D(j) where:
*>
*> |alpha(j) - S(j,j)| |beta(j) - T(j,j)|
*> D(j) = ------------------------ + -----------------------
*> max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
*>
*> (with sorting of eigenvalues).
*>
*> (12) if sorting worked and SDIM is the number of eigenvalues
*> which were CELECTed.
*>
*> Test Matrices
*> =============
*>
*> The sizes of the test matrices are specified by an array
*> NN(1:NSIZES); the value of each element NN(j) specifies one size.
*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
*> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
*> Currently, the list of possible types is:
*>
*> (1) ( 0, 0 ) (a pair of zero matrices)
*>
*> (2) ( I, 0 ) (an identity and a zero matrix)
*>
*> (3) ( 0, I ) (an identity and a zero matrix)
*>
*> (4) ( I, I ) (a pair of identity matrices)
*>
*> t t
*> (5) ( J , J ) (a pair of transposed Jordan blocks)
*>
*> t ( I 0 )
*> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
*> ( 0 I ) ( 0 J )
*> and I is a k x k identity and J a (k+1)x(k+1)
*> Jordan block; k=(N-1)/2
*>
*> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
*> matrix with those diagonal entries.)
*> (8) ( I, D )
*>
*> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big
*>
*> (10) ( small*D, big*I )
*>
*> (11) ( big*I, small*D )
*>
*> (12) ( small*I, big*D )
*>
*> (13) ( big*D, big*I )
*>
*> (14) ( small*D, small*I )
*>
*> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
*> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
*> t t
*> (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices.
*>
*> (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
*> with random O(1) entries above the diagonal
*> and diagonal entries diag(T1) =
*> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
*> ( 0, N-3, N-4,..., 1, 0, 0 )
*>
*> (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
*> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
*> s = machine precision.
*>
*> (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
*>
*> N-5
*> (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
*>
*> (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
*> where r1,..., r(N-4) are random.
*>
*> (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
*> matrices.
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> NSIZES is INTEGER
*> The number of sizes of matrices to use. If it is zero,
*> SDRGES3 does nothing. NSIZES >= 0.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER array, dimension (NSIZES)
*> An array containing the sizes to be used for the matrices.
*> Zero values will be skipped. NN >= 0.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*> NTYPES is INTEGER
*> The number of elements in DOTYPE. If it is zero, SDRGES3
*> does nothing. It must be at least zero. If it is MAXTYP+1
*> and NSIZES is 1, then an additional type, MAXTYP+1 is
*> defined, which is to use whatever matrix is in A on input.
*> This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
*> DOTYPE(MAXTYP+1) is .TRUE. .
*> \endverbatim
*>
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> If DOTYPE(j) is .TRUE., then for each size in NN a
*> matrix of that size and of type j will be generated.
*> If NTYPES is smaller than the maximum number of types
*> defined (PARAMETER MAXTYP), then types NTYPES+1 through
*> MAXTYP will not be generated. If NTYPES is larger
*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
*> will be ignored.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is INTEGER array, dimension (4)
*> On entry ISEED specifies the seed of the random number
*> generator. The array elements should be between 0 and 4095;
*> if not they will be reduced mod 4096. Also, ISEED(4) must
*> be odd. The random number generator uses a linear
*> congruential sequence limited to small integers, and so
*> should produce machine independent random numbers. The
*> values of ISEED are changed on exit, and can be used in the
*> next call to SDRGES3 to continue the same random number
*> sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> A test will count as "failed" if the "error", computed as
*> described above, exceeds THRESH. Note that the error is
*> scaled to be O(1), so THRESH should be a reasonably small
*> multiple of 1, e.g., 10 or 100. In particular, it should
*> not depend on the precision (single vs. double) or the size
*> of the matrix. THRESH >= 0.
*> \endverbatim
*>
*> \param[in] NOUNIT
*> \verbatim
*> NOUNIT is INTEGER
*> The FORTRAN unit number for printing out error messages
*> (e.g., if a routine returns IINFO not equal to 0.)
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension(LDA, max(NN))
*> Used to hold the original A matrix. Used as input only
*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
*> DOTYPE(MAXTYP+1)=.TRUE.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A, B, S, and T.
*> It must be at least 1 and at least max( NN ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension(LDA, max(NN))
*> Used to hold the original B matrix. Used as input only
*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
*> DOTYPE(MAXTYP+1)=.TRUE.
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is COMPLEX array, dimension (LDA, max(NN))
*> The Schur form matrix computed from A by CGGES3. On exit, S
*> contains the Schur form matrix corresponding to the matrix
*> in A.
*> \endverbatim
*>
*> \param[out] T
*> \verbatim
*> T is COMPLEX array, dimension (LDA, max(NN))
*> The upper triangular matrix computed from B by CGGES3.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDQ, max(NN))
*> The (left) orthogonal matrix computed by CGGES3.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of Q and Z. It must
*> be at least 1 and at least max( NN ).
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is COMPLEX array, dimension( LDQ, max(NN) )
*> The (right) orthogonal matrix computed by CGGES3.
*> \endverbatim
*>
*> \param[out] ALPHA
*> \verbatim
*> ALPHA is COMPLEX array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> BETA is COMPLEX array, dimension (max(NN))
*>
*> The generalized eigenvalues of (A,B) computed by CGGES3.
*> ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A
*> and B.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= 3*N*N.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension ( 8*N )
*> Real workspace.
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (15)
*> The values computed by the tests described above.
*> The values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
*>
*> \param[out] BWORK
*> \verbatim
*> BWORK is LOGICAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: A routine returned an error code. INFO is the
*> absolute value of the INFO value returned.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_eig
*
* =====================================================================
SUBROUTINE CDRGES3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
$ BETA, WORK, LWORK, RWORK, RESULT, BWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL BWORK( * ), DOTYPE( * )
INTEGER ISEED( 4 ), NN( * )
REAL RESULT( 13 ), RWORK( * )
COMPLEX A( LDA, * ), ALPHA( * ), B( LDA, * ),
$ BETA( * ), Q( LDQ, * ), S( LDA, * ),
$ T( LDA, * ), WORK( * ), Z( LDQ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 26 )
* ..
* .. Local Scalars ..
LOGICAL BADNN, ILABAD
CHARACTER SORT
INTEGER I, IADD, IINFO, IN, ISORT, J, JC, JR, JSIZE,
$ JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES, N, N1,
$ NB, NERRS, NMATS, NMAX, NTEST, NTESTT, RSUB,
$ SDIM
REAL SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
COMPLEX CTEMP, X
* ..
* .. Local Arrays ..
LOGICAL LASIGN( MAXTYP ), LBSIGN( MAXTYP )
INTEGER IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
$ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
$ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
$ KBZERO( MAXTYP ), KCLASS( MAXTYP ),
$ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
REAL RMAGN( 0: 3 )
* ..
* .. External Functions ..
LOGICAL CLCTES
INTEGER ILAENV
REAL SLAMCH
COMPLEX CLARND
EXTERNAL CLCTES, ILAENV, SLAMCH, CLARND
* ..
* .. External Subroutines ..
EXTERNAL ALASVM, CGET51, CGET54, CGGES3, CLACPY, CLARFG,
$ CLASET, CLATM4, CUNM2R, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, CONJG, MAX, MIN, REAL, SIGN
* ..
* .. Statement Functions ..
REAL ABS1
* ..
* .. Statement Function definitions ..
ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
* ..
* .. Data statements ..
DATA KCLASS / 15*1, 10*2, 1*3 /
DATA KZ1 / 0, 1, 2, 1, 3, 3 /
DATA KZ2 / 0, 0, 1, 2, 1, 1 /
DATA KADD / 0, 0, 0, 0, 3, 2 /
DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
$ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
$ 1, 1, -4, 2, -4, 8*8, 0 /
DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
$ 4*5, 4*3, 1 /
DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
$ 4*6, 4*4, 1 /
DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
$ 2, 1 /
DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
$ 2, 1 /
DATA KTRIAN / 16*0, 10*1 /
DATA LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
$ 2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
$ 3*.FALSE., 5*.TRUE., .FALSE. /
DATA LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
$ 2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
$ 9*.FALSE. /
* ..
* .. Executable Statements ..
*
* Check for errors
*
INFO = 0
*
BADNN = .FALSE.
NMAX = 1
DO 10 J = 1, NSIZES
NMAX = MAX( NMAX, NN( J ) )
IF( NN( J ).LT.0 )
$ BADNN = .TRUE.
10 CONTINUE
*
IF( NSIZES.LT.0 ) THEN
INFO = -1
ELSE IF( BADNN ) THEN
INFO = -2
ELSE IF( NTYPES.LT.0 ) THEN
INFO = -3
ELSE IF( THRESH.LT.ZERO ) THEN
INFO = -6
ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
INFO = -9
ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
INFO = -14
END IF
*
* Compute workspace
* (Note: Comments in the code beginning "Workspace:" describe the
* minimal amount of workspace needed at that point in the code,
* as well as the preferred amount for good performance.
* NB refers to the optimal block size for the immediately
* following subroutine, as returned by ILAENV.
*
MINWRK = 1
IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
MINWRK = 3*NMAX*NMAX
NB = MAX( 1, ILAENV( 1, 'CGEQRF', ' ', NMAX, NMAX, -1, -1 ),
$ ILAENV( 1, 'CUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
$ ILAENV( 1, 'CUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
MAXWRK = MAX( NMAX+NMAX*NB, 3*NMAX*NMAX)
WORK( 1 ) = MAXWRK
END IF
*
IF( LWORK.LT.MINWRK )
$ INFO = -19
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CDRGES3', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ RETURN
*
ULP = SLAMCH( 'Precision' )
SAFMIN = SLAMCH( 'Safe minimum' )
SAFMIN = SAFMIN / ULP
SAFMAX = ONE / SAFMIN
ULPINV = ONE / ULP
*
* The values RMAGN(2:3) depend on N, see below.
*
RMAGN( 0 ) = ZERO
RMAGN( 1 ) = ONE
*
* Loop over matrix sizes
*
NTESTT = 0
NERRS = 0
NMATS = 0
*
DO 190 JSIZE = 1, NSIZES
N = NN( JSIZE )
N1 = MAX( 1, N )
RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
RMAGN( 3 ) = SAFMIN*ULPINV*REAL( N1 )
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
* Loop over matrix types
*
DO 180 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 180
NMATS = NMATS + 1
NTEST = 0
*
* Save ISEED in case of an error.
*
DO 20 J = 1, 4
IOLDSD( J ) = ISEED( J )
20 CONTINUE
*
* Initialize RESULT
*
DO 30 J = 1, 13
RESULT( J ) = ZERO
30 CONTINUE
*
* Generate test matrices A and B
*
* Description of control parameters:
*
* KCLASS: =1 means w/o rotation, =2 means w/ rotation,
* =3 means random.
* KATYPE: the "type" to be passed to CLATM4 for computing A.
* KAZERO: the pattern of zeros on the diagonal for A:
* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
* non-zero entries.)
* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
* =2: large, =3: small.
* LASIGN: .TRUE. if the diagonal elements of A are to be
* multiplied by a random magnitude 1 number.
* KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
* KTRIAN: =0: don't fill in the upper triangle, =1: do.
* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
* RMAGN: used to implement KAMAGN and KBMAGN.
*
IF( MTYPES.GT.MAXTYP )
$ GO TO 110
IINFO = 0
IF( KCLASS( JTYPE ).LT.3 ) THEN
*
* Generate A (w/o rotation)
*
IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
IN = 2*( ( N-1 ) / 2 ) + 1
IF( IN.NE.N )
$ CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
ELSE
IN = N
END IF
CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
$ KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
$ RMAGN( KAMAGN( JTYPE ) ), ULP,
$ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
$ ISEED, A, LDA )
IADD = KADD( KAZERO( JTYPE ) )
IF( IADD.GT.0 .AND. IADD.LE.N )
$ A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
*
* Generate B (w/o rotation)
*
IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
IN = 2*( ( N-1 ) / 2 ) + 1
IF( IN.NE.N )
$ CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
ELSE
IN = N
END IF
CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
$ KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
$ RMAGN( KBMAGN( JTYPE ) ), ONE,
$ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
$ ISEED, B, LDA )
IADD = KADD( KBZERO( JTYPE ) )
IF( IADD.NE.0 .AND. IADD.LE.N )
$ B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
*
IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
*
* Include rotations
*
* Generate Q, Z as Householder transformations times
* a diagonal matrix.
*
DO 50 JC = 1, N - 1
DO 40 JR = JC, N
Q( JR, JC ) = CLARND( 3, ISEED )
Z( JR, JC ) = CLARND( 3, ISEED )
40 CONTINUE
CALL CLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
$ WORK( JC ) )
WORK( 2*N+JC ) = SIGN( ONE, REAL( Q( JC, JC ) ) )
Q( JC, JC ) = CONE
CALL CLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
$ WORK( N+JC ) )
WORK( 3*N+JC ) = SIGN( ONE, REAL( Z( JC, JC ) ) )
Z( JC, JC ) = CONE
50 CONTINUE
CTEMP = CLARND( 3, ISEED )
Q( N, N ) = CONE
WORK( N ) = CZERO
WORK( 3*N ) = CTEMP / ABS( CTEMP )
CTEMP = CLARND( 3, ISEED )
Z( N, N ) = CONE
WORK( 2*N ) = CZERO
WORK( 4*N ) = CTEMP / ABS( CTEMP )
*
* Apply the diagonal matrices
*
DO 70 JC = 1, N
DO 60 JR = 1, N
A( JR, JC ) = WORK( 2*N+JR )*
$ CONJG( WORK( 3*N+JC ) )*
$ A( JR, JC )
B( JR, JC ) = WORK( 2*N+JR )*
$ CONJG( WORK( 3*N+JC ) )*
$ B( JR, JC )
60 CONTINUE
70 CONTINUE
CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
$ LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
$ A, LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
$ LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
$ B, LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
END IF
ELSE
*
* Random matrices
*
DO 90 JC = 1, N
DO 80 JR = 1, N
A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
$ CLARND( 4, ISEED )
B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
$ CLARND( 4, ISEED )
80 CONTINUE
90 CONTINUE
END IF
*
100 CONTINUE
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
110 CONTINUE
*
DO 120 I = 1, 13
RESULT( I ) = -ONE
120 CONTINUE
*
* Test with and without sorting of eigenvalues
*
DO 150 ISORT = 0, 1
IF( ISORT.EQ.0 ) THEN
SORT = 'N'
RSUB = 0
ELSE
SORT = 'S'
RSUB = 5
END IF
*
* Call XLAENV to set the parameters used in CLAQZ0
*
CALL XLAENV( 12, 10 )
CALL XLAENV( 13, 12 )
CALL XLAENV( 14, 13 )
CALL XLAENV( 15, 2 )
CALL XLAENV( 17, 10 )
*
* Call CGGES3 to compute H, T, Q, Z, alpha, and beta.
*
CALL CLACPY( 'Full', N, N, A, LDA, S, LDA )
CALL CLACPY( 'Full', N, N, B, LDA, T, LDA )
NTEST = 1 + RSUB + ISORT
RESULT( 1+RSUB+ISORT ) = ULPINV
CALL CGGES3( 'V', 'V', SORT, CLCTES, N, S, LDA, T, LDA,
$ SDIM, ALPHA, BETA, Q, LDQ, Z, LDQ, WORK,
$ LWORK, RWORK, BWORK, IINFO )
IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
RESULT( 1+RSUB+ISORT ) = ULPINV
WRITE( NOUNIT, FMT = 9999 )'CGGES3', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 160
END IF
*
NTEST = 4 + RSUB
*
* Do tests 1--4 (or tests 7--9 when reordering )
*
IF( ISORT.EQ.0 ) THEN
CALL CGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ,
$ WORK, RWORK, RESULT( 1 ) )
CALL CGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ,
$ WORK, RWORK, RESULT( 2 ) )
ELSE
CALL CGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q,
$ LDQ, Z, LDQ, WORK, RESULT( 2+RSUB ) )
END IF
*
CALL CGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
$ RWORK, RESULT( 3+RSUB ) )
CALL CGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
$ RWORK, RESULT( 4+RSUB ) )
*
* Do test 5 and 6 (or Tests 10 and 11 when reordering):
* check Schur form of A and compare eigenvalues with
* diagonals.
*
NTEST = 6 + RSUB
TEMP1 = ZERO
*
DO 130 J = 1, N
ILABAD = .FALSE.
TEMP2 = ( ABS1( ALPHA( J )-S( J, J ) ) /
$ MAX( SAFMIN, ABS1( ALPHA( J ) ), ABS1( S( J,
$ J ) ) )+ABS1( BETA( J )-T( J, J ) ) /
$ MAX( SAFMIN, ABS1( BETA( J ) ), ABS1( T( J,
$ J ) ) ) ) / ULP
*
IF( J.LT.N ) THEN
IF( S( J+1, J ).NE.ZERO ) THEN
ILABAD = .TRUE.
RESULT( 5+RSUB ) = ULPINV
END IF
END IF
IF( J.GT.1 ) THEN
IF( S( J, J-1 ).NE.ZERO ) THEN
ILABAD = .TRUE.
RESULT( 5+RSUB ) = ULPINV
END IF
END IF
TEMP1 = MAX( TEMP1, TEMP2 )
IF( ILABAD ) THEN
WRITE( NOUNIT, FMT = 9998 )J, N, JTYPE, IOLDSD
END IF
130 CONTINUE
RESULT( 6+RSUB ) = TEMP1
*
IF( ISORT.GE.1 ) THEN
*
* Do test 12
*
NTEST = 12
RESULT( 12 ) = ZERO
KNTEIG = 0
DO 140 I = 1, N
IF( CLCTES( ALPHA( I ), BETA( I ) ) )
$ KNTEIG = KNTEIG + 1
140 CONTINUE
IF( SDIM.NE.KNTEIG )
$ RESULT( 13 ) = ULPINV
END IF
*
150 CONTINUE
*
* End of Loop -- Check for RESULT(j) > THRESH
*
160 CONTINUE
*
NTESTT = NTESTT + NTEST
*
* Print out tests which fail.
*
DO 170 JR = 1, NTEST
IF( RESULT( JR ).GE.THRESH ) THEN
*
* If this is the first test to fail,
* print a header to the data file.
*
IF( NERRS.EQ.0 ) THEN
WRITE( NOUNIT, FMT = 9997 )'CGS'
*
* Matrix types
*
WRITE( NOUNIT, FMT = 9996 )
WRITE( NOUNIT, FMT = 9995 )
WRITE( NOUNIT, FMT = 9994 )'Unitary'
*
* Tests performed
*
WRITE( NOUNIT, FMT = 9993 )'unitary', '''',
$ 'transpose', ( '''', J = 1, 8 )
*
END IF
NERRS = NERRS + 1
IF( RESULT( JR ).LT.10000.0 ) THEN
WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
$ RESULT( JR )
ELSE
WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
$ RESULT( JR )
END IF
END IF
170 CONTINUE
*
180 CONTINUE
190 CONTINUE
*
* Summary
*
CALL ALASVM( 'CGS', NOUNIT, NERRS, NTESTT, 0 )
*
WORK( 1 ) = MAXWRK
*
RETURN
*
9999 FORMAT( ' CDRGES3: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' )
*
9998 FORMAT( ' CDRGES3: S not in Schur form at eigenvalue ', I6, '.',
$ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
$ I5, ')' )
*
9997 FORMAT( / 1X, A3, ' -- Complex Generalized Schur from problem ',
$ 'driver' )
*
9996 FORMAT( ' Matrix types (see CDRGES3 for details): ' )
*
9995 FORMAT( ' Special Matrices:', 23X,
$ '(J''=transposed Jordan block)',
$ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
$ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
$ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
$ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
$ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
$ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
$ / ' 16=Transposed Jordan Blocks 19=geometric ',
$ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
$ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
$ 'alpha, beta=0,1 21=random alpha, beta=0,1',
$ / ' Large & Small Matrices:', / ' 22=(large, small) ',
$ '23=(small,large) 24=(small,small) 25=(large,large)',
$ / ' 26=random O(1) matrices.' )
*
9993 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ',
$ 'Q and Z are ', A, ',', / 19X,
$ 'l and r are the appropriate left and right', / 19X,
$ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
$ ' means ', A, '.)', / ' Without ordering: ',
$ / ' 1 = | A - Q S Z', A,
$ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A,
$ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
$ ' | / ( n ulp ) 4 = | I - ZZ', A,
$ ' | / ( n ulp )', / ' 5 = A is in Schur form S',
$ / ' 6 = difference between (alpha,beta)',
$ ' and diagonals of (S,T)', / ' With ordering: ',
$ / ' 7 = | (A,B) - Q (S,T) Z', A, ' | / ( |(A,B)| n ulp )',
$ / ' 8 = | I - QQ', A,
$ ' | / ( n ulp ) 9 = | I - ZZ', A,
$ ' | / ( n ulp )', / ' 10 = A is in Schur form S',
$ / ' 11 = difference between (alpha,beta) and diagonals',
$ ' of (S,T)', / ' 12 = SDIM is the correct number of ',
$ 'selected eigenvalues', / )
9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
$ 4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
$ 4( I4, ',' ), ' result ', I2, ' is', 1P, E10.3 )
*
* End of CDRGES3
*
END