lib
/
LAPACK-3.11.0
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Cloned library LAPACK-3.11.0 with extra build files for internal package management.
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
3 Commits
1 Branch
0 Tags
5.8 MiB
 
 
 
 
 
Tag: Branch: Tree: main
Branches Tags
${ item.name }
Create tag ${ searchTerm }
Create branch ${ searchTerm }
from 'main'
${ noResults }
LAPACK-3.11.0/TESTING/EIG/dchkgg.f

1240 lines
44 KiB
Raw Permalink Blame History

*> \brief \b DCHKGG
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
* TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
* S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1,
* BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR,
* WORK, LWORK, LLWORK, RESULT, INFO )
*
* .. Scalar Arguments ..
* LOGICAL TSTDIF
* INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
* DOUBLE PRECISION THRESH, THRSHN
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * ), LLWORK( * )
* INTEGER ISEED( 4 ), NN( * )
* DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI3( * ),
* $ ALPHR1( * ), ALPHR3( * ), B( LDA, * ),
* $ BETA1( * ), BETA3( * ), EVECTL( LDU, * ),
* $ EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ),
* $ P2( LDA, * ), Q( LDU, * ), RESULT( 15 ),
* $ S1( LDA, * ), S2( LDA, * ), T( LDA, * ),
* $ U( LDU, * ), V( LDU, * ), WORK( * ),
* $ Z( LDU, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCHKGG checks the nonsymmetric generalized eigenvalue problem
*> routines.
*> T T T
*> DGGHRD factors A and B as U H V and U T V , where means
*> transpose, H is hessenberg, T is triangular and U and V are
*> orthogonal.
*> T T
*> DHGEQZ factors H and T as Q S Z and Q P Z , where P is upper
*> triangular, S is in generalized Schur form (block upper triangular,
*> with 1x1 and 2x2 blocks on the diagonal, the 2x2 blocks
*> corresponding to complex conjugate pairs of generalized
*> eigenvalues), and Q and Z are orthogonal. It also computes the
*> generalized eigenvalues (alpha(1),beta(1)),...,(alpha(n),beta(n)),
*> where alpha(j)=S(j,j) and beta(j)=P(j,j) -- thus,
*> w(j) = alpha(j)/beta(j) is a root of the generalized eigenvalue
*> problem
*>
*> det( A - w(j) B ) = 0
*>
*> and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
*> problem
*>
*> det( m(j) A - B ) = 0
*>
*> DTGEVC computes the matrix L of left eigenvectors and the matrix R
*> of right eigenvectors for the matrix pair ( S, P ). In the
*> description below, l and r are left and right eigenvectors
*> corresponding to the generalized eigenvalues (alpha,beta).
*>
*> When DCHKGG 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, one matrix will be generated and used
*> to test the nonsymmetric eigenroutines. For each matrix, 15
*> tests will be performed. The first twelve "test ratios" should be
*> small -- O(1). They will be compared with the threshold THRESH:
*>
*> T
*> (1) | A - U H V | / ( |A| n ulp )
*>
*> T
*> (2) | B - U T V | / ( |B| n ulp )
*>
*> T
*> (3) | I - UU | / ( n ulp )
*>
*> T
*> (4) | I - VV | / ( n ulp )
*>
*> T
*> (5) | H - Q S Z | / ( |H| n ulp )
*>
*> T
*> (6) | T - Q P Z | / ( |T| n ulp )
*>
*> T
*> (7) | I - QQ | / ( n ulp )
*>
*> T
*> (8) | I - ZZ | / ( n ulp )
*>
*> (9) max over all left eigenvalue/-vector pairs (beta/alpha,l) of
*>
*> | l**H * (beta S - alpha P) | / ( ulp max( |beta S|, |alpha P| ) )
*>
*> (10) max over all left eigenvalue/-vector pairs (beta/alpha,l') of
*> T
*> | l'**H * (beta H - alpha T) | / ( ulp max( |beta H|, |alpha T| ) )
*>
*> where the eigenvectors l' are the result of passing Q to
*> DTGEVC and back transforming (HOWMNY='B').
*>
*> (11) max over all right eigenvalue/-vector pairs (beta/alpha,r) of
*>
*> | (beta S - alpha T) r | / ( ulp max( |beta S|, |alpha T| ) )
*>
*> (12) max over all right eigenvalue/-vector pairs (beta/alpha,r') of
*>
*> | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) )
*>
*> where the eigenvectors r' are the result of passing Z to
*> DTGEVC and back transforming (HOWMNY='B').
*>
*> The last three test ratios will usually be small, but there is no
*> mathematical requirement that they be so. They are therefore
*> compared with THRESH only if TSTDIF is .TRUE.
*>
*> (13) | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp )
*>
*> (14) | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp )
*>
*> (15) max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| ,
*> |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp
*>
*> In addition, the normalization of L and R are checked, and compared
*> with the threshold THRSHN.
*>
*> 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) U ( J , J ) V where U and V are random orthogonal matrices.
*>
*> (17) U ( T1, T2 ) V 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) U ( T1, T2 ) V diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
*> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
*> s = machine precision.
*>
*> (19) U ( T1, T2 ) V 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) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
*>
*> (21) U ( T1, T2 ) V 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) U ( big*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (23) U ( small*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (24) U ( small*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (25) U ( big*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
*> diag(T2) = ( 0, 1, ..., 1, 0, 0 )
*>
*> (26) U ( T1, T2 ) V 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,
*> DCHKGG does nothing. It must be at least zero.
*> \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. The values must be at least
*> zero.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*> NTYPES is INTEGER
*> The number of elements in DOTYPE. If it is zero, DCHKGG
*> 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. 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 DCHKGG to continue the same random number
*> sequence.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is DOUBLE PRECISION
*> A test will count as "failed" if the "error", computed as
*> described above, exceeds THRESH. Note that the error is
*> scaled to be O(1), so THRESH should be a reasonably small
*> multiple of 1, e.g., 10 or 100. In particular, it should
*> not depend on the precision (single vs. double) or the size
*> of the matrix. It must be at least zero.
*> \endverbatim
*>
*> \param[in] TSTDIF
*> \verbatim
*> TSTDIF is LOGICAL
*> Specifies whether test ratios 13-15 will be computed and
*> compared with THRESH.
*> = .FALSE.: Only test ratios 1-12 will be computed and tested.
*> Ratios 13-15 will be set to zero.
*> = .TRUE.: All the test ratios 1-15 will be computed and
*> tested.
*> \endverbatim
*>
*> \param[in] THRSHN
*> \verbatim
*> THRSHN is DOUBLE PRECISION
*> Threshold for reporting eigenvector normalization error.
*> If the normalization of any eigenvector differs from 1 by
*> more than THRSHN*ulp, then a special error message will be
*> printed. (This is handled separately from the other tests,
*> since only a compiler or programming error should cause an
*> error message, at least if THRSHN is at least 5--10.)
*> \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 DOUBLE PRECISION 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, H, T, S1, P1, S2, and P2.
*> It must be at least 1 and at least max( NN ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION 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] H
*> \verbatim
*> H is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The upper Hessenberg matrix computed from A by DGGHRD.
*> \endverbatim
*>
*> \param[out] T
*> \verbatim
*> T is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The upper triangular matrix computed from B by DGGHRD.
*> \endverbatim
*>
*> \param[out] S1
*> \verbatim
*> S1 is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The Schur (block upper triangular) matrix computed from H by
*> DHGEQZ when Q and Z are also computed.
*> \endverbatim
*>
*> \param[out] S2
*> \verbatim
*> S2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The Schur (block upper triangular) matrix computed from H by
*> DHGEQZ when Q and Z are not computed.
*> \endverbatim
*>
*> \param[out] P1
*> \verbatim
*> P1 is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The upper triangular matrix computed from T by DHGEQZ
*> when Q and Z are also computed.
*> \endverbatim
*>
*> \param[out] P2
*> \verbatim
*> P2 is DOUBLE PRECISION array, dimension (LDA, max(NN))
*> The upper triangular matrix computed from T by DHGEQZ
*> when Q and Z are not computed.
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (left) orthogonal matrix computed by DGGHRD.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U, V, Q, Z, EVECTL, and EVEZTR. It
*> must be at least 1 and at least max( NN ).
*> \endverbatim
*>
*> \param[out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (right) orthogonal matrix computed by DGGHRD.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (left) orthogonal matrix computed by DHGEQZ.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (left) orthogonal matrix computed by DHGEQZ.
*> \endverbatim
*>
*> \param[out] ALPHR1
*> \verbatim
*> ALPHR1 is DOUBLE PRECISION array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] ALPHI1
*> \verbatim
*> ALPHI1 is DOUBLE PRECISION array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] BETA1
*> \verbatim
*> BETA1 is DOUBLE PRECISION array, dimension (max(NN))
*>
*> The generalized eigenvalues of (A,B) computed by DHGEQZ
*> when Q, Z, and the full Schur matrices are computed.
*> On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th
*> generalized eigenvalue of the matrices in A and B.
*> \endverbatim
*>
*> \param[out] ALPHR3
*> \verbatim
*> ALPHR3 is DOUBLE PRECISION array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] ALPHI3
*> \verbatim
*> ALPHI3 is DOUBLE PRECISION array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] BETA3
*> \verbatim
*> BETA3 is DOUBLE PRECISION array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] EVECTL
*> \verbatim
*> EVECTL is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (block lower triangular) left eigenvector matrix for
*> the matrices in S1 and P1. (See DTGEVC for the format.)
*> \endverbatim
*>
*> \param[out] EVECTR
*> \verbatim
*> EVECTR is DOUBLE PRECISION array, dimension (LDU, max(NN))
*> The (block upper triangular) right eigenvector matrix for
*> the matrices in S1 and P1. (See DTGEVC for the format.)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The number of entries in WORK. This must be at least
*> max( 2 * N**2, 6*N, 1 ), for all N=NN(j).
*> \endverbatim
*>
*> \param[out] LLWORK
*> \verbatim
*> LLWORK is LOGICAL array, dimension (max(NN))
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION 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] 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 double_eig
*
* =====================================================================
SUBROUTINE DCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
$ S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1,
$ BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR,
$ WORK, LWORK, LLWORK, RESULT, INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
LOGICAL TSTDIF
INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
DOUBLE PRECISION THRESH, THRSHN
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * ), LLWORK( * )
INTEGER ISEED( 4 ), NN( * )
DOUBLE PRECISION A( LDA, * ), ALPHI1( * ), ALPHI3( * ),
$ ALPHR1( * ), ALPHR3( * ), B( LDA, * ),
$ BETA1( * ), BETA3( * ), EVECTL( LDU, * ),
$ EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ),
$ P2( LDA, * ), Q( LDU, * ), RESULT( 15 ),
$ S1( LDA, * ), S2( LDA, * ), T( LDA, * ),
$ U( LDU, * ), V( LDU, * ), WORK( * ),
$ Z( LDU, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 26 )
* ..
* .. Local Scalars ..
LOGICAL BADNN
INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
$ LWKOPT, MTYPES, N, N1, NERRS, NMATS, NMAX,
$ NTEST, NTESTT
DOUBLE PRECISION ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2,
$ ULP, ULPINV
* ..
* .. Local Arrays ..
INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
$ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
$ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
$ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
$ KBZERO( MAXTYP ), KCLASS( MAXTYP ),
$ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
DOUBLE PRECISION DUMMA( 4 ), RMAGN( 0: 3 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLARND
EXTERNAL DLAMCH, DLANGE, DLARND
* ..
* .. External Subroutines ..
EXTERNAL DGEQR2, DGET51, DGET52, DGGHRD, DHGEQZ, DLACPY,
$ DLARFG, DLASET, DLASUM, DLATM4, DORM2R, DTGEVC,
$ XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, SIGN
* ..
* .. 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 IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
$ 5*2, 0 /
DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
* ..
* .. 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
*
* Maximum blocksize and shift -- we assume that blocksize and number
* of shifts are monotone increasing functions of N.
*
LWKOPT = MAX( 6*NMAX, 2*NMAX*NMAX, 1 )
*
* Check for errors
*
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 = -10
ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN
INFO = -19
ELSE IF( LWKOPT.GT.LWORK ) THEN
INFO = -30
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DCHKGG', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
$ RETURN
*
SAFMIN = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
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 sizes, types
*
NTESTT = 0
NERRS = 0
NMATS = 0
*
DO 240 JSIZE = 1, NSIZES
N = NN( JSIZE )
N1 = MAX( 1, N )
RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
RMAGN( 3 ) = SAFMIN*ULPINV*N1
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 230 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 230
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, 15
RESULT( J ) = ZERO
30 CONTINUE
*
* Compute A and B
*
* Description of control parameters:
*
* KZLASS: =1 means w/o rotation, =2 means w/ rotation,
* =3 means random.
* KATYPE: the "type" to be passed to DLATM4 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.
* IASIGN: 1 if the diagonal elements of A are to be
* multiplied by a random magnitude 1 number, =2 if
* randomly chosen diagonal blocks are to be rotated
* to form 2x2 blocks.
* KBTYPE, KBZERO, KBMAGN, IBSIGN: 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 DLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
ELSE
IN = N
END IF
CALL DLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
$ KZ2( KAZERO( JTYPE ) ), IASIGN( 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 DLASET( 'Full', N, N, ZERO, ZERO, B, LDA )
ELSE
IN = N
END IF
CALL DLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
$ KZ2( KBZERO( JTYPE ) ), IBSIGN( 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 U, V as Householder transformations times
* a diagonal matrix.
*
DO 50 JC = 1, N - 1
DO 40 JR = JC, N
U( JR, JC ) = DLARND( 3, ISEED )
V( JR, JC ) = DLARND( 3, ISEED )
40 CONTINUE
CALL DLARFG( N+1-JC, U( JC, JC ), U( JC+1, JC ), 1,
$ WORK( JC ) )
WORK( 2*N+JC ) = SIGN( ONE, U( JC, JC ) )
U( JC, JC ) = ONE
CALL DLARFG( N+1-JC, V( JC, JC ), V( JC+1, JC ), 1,
$ WORK( N+JC ) )
WORK( 3*N+JC ) = SIGN( ONE, V( JC, JC ) )
V( JC, JC ) = ONE
50 CONTINUE
U( N, N ) = ONE
WORK( N ) = ZERO
WORK( 3*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
V( N, N ) = ONE
WORK( 2*N ) = ZERO
WORK( 4*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
*
* Apply the diagonal matrices
*
DO 70 JC = 1, N
DO 60 JR = 1, N
A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
$ A( JR, JC )
B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
$ B( JR, JC )
60 CONTINUE
70 CONTINUE
CALL DORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, A,
$ LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL DORM2R( 'R', 'T', N, N, N-1, V, LDU, WORK( N+1 ),
$ A, LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL DORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, B,
$ LDA, WORK( 2*N+1 ), IINFO )
IF( IINFO.NE.0 )
$ GO TO 100
CALL DORM2R( 'R', 'T', N, N, N-1, V, LDU, 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 ) )*
$ DLARND( 2, ISEED )
B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
$ DLARND( 2, ISEED )
80 CONTINUE
90 CONTINUE
END IF
*
ANORM = DLANGE( '1', N, N, A, LDA, WORK )
BNORM = DLANGE( '1', N, N, B, LDA, WORK )
*
100 CONTINUE
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
110 CONTINUE
*
* Call DGEQR2, DORM2R, and DGGHRD to compute H, T, U, and V
*
CALL DLACPY( ' ', N, N, A, LDA, H, LDA )
CALL DLACPY( ' ', N, N, B, LDA, T, LDA )
NTEST = 1
RESULT( 1 ) = ULPINV
*
CALL DGEQR2( N, N, T, LDA, WORK, WORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DGEQR2', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DORM2R( 'L', 'T', N, N, N, T, LDA, WORK, H, LDA,
$ WORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DORM2R', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DLASET( 'Full', N, N, ZERO, ONE, U, LDU )
CALL DORM2R( 'R', 'N', N, N, N, T, LDA, WORK, U, LDU,
$ WORK( N+1 ), IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DORM2R', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DGGHRD( 'V', 'I', N, 1, N, H, LDA, T, LDA, U, LDU, V,
$ LDU, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DGGHRD', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
NTEST = 4
*
* Do tests 1--4
*
CALL DGET51( 1, N, A, LDA, H, LDA, U, LDU, V, LDU, WORK,
$ RESULT( 1 ) )
CALL DGET51( 1, N, B, LDA, T, LDA, U, LDU, V, LDU, WORK,
$ RESULT( 2 ) )
CALL DGET51( 3, N, B, LDA, T, LDA, U, LDU, U, LDU, WORK,
$ RESULT( 3 ) )
CALL DGET51( 3, N, B, LDA, T, LDA, V, LDU, V, LDU, WORK,
$ RESULT( 4 ) )
*
* Call DHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests.
*
* Compute T1 and UZ
*
* Eigenvalues only
*
CALL DLACPY( ' ', N, N, H, LDA, S2, LDA )
CALL DLACPY( ' ', N, N, T, LDA, P2, LDA )
NTEST = 5
RESULT( 5 ) = ULPINV
*
CALL DHGEQZ( 'E', 'N', 'N', N, 1, N, S2, LDA, P2, LDA,
$ ALPHR3, ALPHI3, BETA3, Q, LDU, Z, LDU, WORK,
$ LWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(E)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
* Eigenvalues and Full Schur Form
*
CALL DLACPY( ' ', N, N, H, LDA, S2, LDA )
CALL DLACPY( ' ', N, N, T, LDA, P2, LDA )
*
CALL DHGEQZ( 'S', 'N', 'N', N, 1, N, S2, LDA, P2, LDA,
$ ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK,
$ LWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(S)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
* Eigenvalues, Schur Form, and Schur Vectors
*
CALL DLACPY( ' ', N, N, H, LDA, S1, LDA )
CALL DLACPY( ' ', N, N, T, LDA, P1, LDA )
*
CALL DHGEQZ( 'S', 'I', 'I', N, 1, N, S1, LDA, P1, LDA,
$ ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK,
$ LWORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(V)', IINFO, N, JTYPE,
$ IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
NTEST = 8
*
* Do Tests 5--8
*
CALL DGET51( 1, N, H, LDA, S1, LDA, Q, LDU, Z, LDU, WORK,
$ RESULT( 5 ) )
CALL DGET51( 1, N, T, LDA, P1, LDA, Q, LDU, Z, LDU, WORK,
$ RESULT( 6 ) )
CALL DGET51( 3, N, T, LDA, P1, LDA, Q, LDU, Q, LDU, WORK,
$ RESULT( 7 ) )
CALL DGET51( 3, N, T, LDA, P1, LDA, Z, LDU, Z, LDU, WORK,
$ RESULT( 8 ) )
*
* Compute the Left and Right Eigenvectors of (S1,P1)
*
* 9: Compute the left eigenvector Matrix without
* back transforming:
*
NTEST = 9
RESULT( 9 ) = ULPINV
*
* To test "SELECT" option, compute half of the eigenvectors
* in one call, and half in another
*
I1 = N / 2
DO 120 J = 1, I1
LLWORK( J ) = .TRUE.
120 CONTINUE
DO 130 J = I1 + 1, N
LLWORK( J ) = .FALSE.
130 CONTINUE
*
CALL DTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, EVECTL,
$ LDU, DUMMA, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,S1)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
I1 = IN
DO 140 J = 1, I1
LLWORK( J ) = .FALSE.
140 CONTINUE
DO 150 J = I1 + 1, N
LLWORK( J ) = .TRUE.
150 CONTINUE
*
CALL DTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA,
$ EVECTL( 1, I1+1 ), LDU, DUMMA, LDU, N, IN,
$ WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,S2)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DGET52( .TRUE., N, S1, LDA, P1, LDA, EVECTL, LDU,
$ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
RESULT( 9 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRSHN ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'DTGEVC(HOWMNY=S)',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* 10: Compute the left eigenvector Matrix with
* back transforming:
*
NTEST = 10
RESULT( 10 ) = ULPINV
CALL DLACPY( 'F', N, N, Q, LDU, EVECTL, LDU )
CALL DTGEVC( 'L', 'B', LLWORK, N, S1, LDA, P1, LDA, EVECTL,
$ LDU, DUMMA, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,B)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DGET52( .TRUE., N, H, LDA, T, LDA, EVECTL, LDU, ALPHR1,
$ ALPHI1, BETA1, WORK, DUMMA( 1 ) )
RESULT( 10 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRSHN ) THEN
WRITE( NOUNIT, FMT = 9998 )'Left', 'DTGEVC(HOWMNY=B)',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* 11: Compute the right eigenvector Matrix without
* back transforming:
*
NTEST = 11
RESULT( 11 ) = ULPINV
*
* To test "SELECT" option, compute half of the eigenvectors
* in one call, and half in another
*
I1 = N / 2
DO 160 J = 1, I1
LLWORK( J ) = .TRUE.
160 CONTINUE
DO 170 J = I1 + 1, N
LLWORK( J ) = .FALSE.
170 CONTINUE
*
CALL DTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
$ LDU, EVECTR, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,S1)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
I1 = IN
DO 180 J = 1, I1
LLWORK( J ) = .FALSE.
180 CONTINUE
DO 190 J = I1 + 1, N
LLWORK( J ) = .TRUE.
190 CONTINUE
*
CALL DTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
$ LDU, EVECTR( 1, I1+1 ), LDU, N, IN, WORK,
$ IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,S2)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DGET52( .FALSE., N, S1, LDA, P1, LDA, EVECTR, LDU,
$ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
RESULT( 11 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'DTGEVC(HOWMNY=S)',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* 12: Compute the right eigenvector Matrix with
* back transforming:
*
NTEST = 12
RESULT( 12 ) = ULPINV
CALL DLACPY( 'F', N, N, Z, LDU, EVECTR, LDU )
CALL DTGEVC( 'R', 'B', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
$ LDU, EVECTR, LDU, N, IN, WORK, IINFO )
IF( IINFO.NE.0 ) THEN
WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,B)', IINFO, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
GO TO 210
END IF
*
CALL DGET52( .FALSE., N, H, LDA, T, LDA, EVECTR, LDU,
$ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
RESULT( 12 ) = DUMMA( 1 )
IF( DUMMA( 2 ).GT.THRESH ) THEN
WRITE( NOUNIT, FMT = 9998 )'Right', 'DTGEVC(HOWMNY=B)',
$ DUMMA( 2 ), N, JTYPE, IOLDSD
END IF
*
* Tests 13--15 are done only on request
*
IF( TSTDIF ) THEN
*
* Do Tests 13--14
*
CALL DGET51( 2, N, S1, LDA, S2, LDA, Q, LDU, Z, LDU,
$ WORK, RESULT( 13 ) )
CALL DGET51( 2, N, P1, LDA, P2, LDA, Q, LDU, Z, LDU,
$ WORK, RESULT( 14 ) )
*
* Do Test 15
*
TEMP1 = ZERO
TEMP2 = ZERO
DO 200 J = 1, N
TEMP1 = MAX( TEMP1, ABS( ALPHR1( J )-ALPHR3( J ) )+
$ ABS( ALPHI1( J )-ALPHI3( J ) ) )
TEMP2 = MAX( TEMP2, ABS( BETA1( J )-BETA3( J ) ) )
200 CONTINUE
*
TEMP1 = TEMP1 / MAX( SAFMIN, ULP*MAX( TEMP1, ANORM ) )
TEMP2 = TEMP2 / MAX( SAFMIN, ULP*MAX( TEMP2, BNORM ) )
RESULT( 15 ) = MAX( TEMP1, TEMP2 )
NTEST = 15
ELSE
RESULT( 13 ) = ZERO
RESULT( 14 ) = ZERO
RESULT( 15 ) = ZERO
NTEST = 12
END IF
*
* End of Loop -- Check for RESULT(j) > THRESH
*
210 CONTINUE
*
NTESTT = NTESTT + NTEST
*
* Print out tests which fail.
*
DO 220 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 )'DGG'
*
* Matrix types
*
WRITE( NOUNIT, FMT = 9996 )
WRITE( NOUNIT, FMT = 9995 )
WRITE( NOUNIT, FMT = 9994 )'Orthogonal'
*
* Tests performed
*
WRITE( NOUNIT, FMT = 9993 )'orthogonal', '''',
$ 'transpose', ( '''', J = 1, 10 )
*
END IF
NERRS = NERRS + 1
IF( RESULT( JR ).LT.10000.0D0 ) 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
220 CONTINUE
*
230 CONTINUE
240 CONTINUE
*
* Summary
*
CALL DLASUM( 'DGG', NOUNIT, NERRS, NTESTT )
RETURN
*
9999 FORMAT( ' DCHKGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
*
9998 FORMAT( ' DCHKGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
$ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
$ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
$ ')' )
*
9997 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem' )
*
9996 FORMAT( ' Matrix types (see DCHKGG 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: (H is Hessenberg, S is Schur, B, ',
$ 'T, P are triangular,', / 20X, 'U, V, Q, and Z are ', A,
$ ', l and r are the', / 20X,
$ 'appropriate left and right eigenvectors, resp., a is',
$ / 20X, 'alpha, b is beta, and ', A, ' means ', A, '.)',
$ / ' 1 = | A - U H V', A,
$ ' | / ( |A| n ulp ) 2 = | B - U T V', A,
$ ' | / ( |B| n ulp )', / ' 3 = | I - UU', A,
$ ' | / ( n ulp ) 4 = | I - VV', A,
$ ' | / ( n ulp )', / ' 5 = | H - Q S Z', A,
$ ' | / ( |H| n ulp )', 6X, '6 = | T - Q P Z', A,
$ ' | / ( |T| n ulp )', / ' 7 = | I - QQ', A,
$ ' | / ( n ulp ) 8 = | I - ZZ', A,
$ ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', A,
$ ' l | / const. 10 = max | ( b H - a T )', A,
$ ' l | / const.', /
$ ' 11= max | ( b S - a P ) r | / const. 12 = max | ( b H',
$ ' - a T ) r | / const.', / 1X )
*
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, D10.3 )
*
* End of DCHKGG
*
END