TESTING/EIG/cchkgg.f(3)

NAME
TESTING/EIG/cchkgg.f

SYNOPSIS

  Functions/Subroutines
subroutine cchkgg (nsizes, nn, ntypes, dotype, iseed, thresh, tstdif, thrshn, nounit, a, lda, b, h, t, s1, s2, p1, p2, u, ldu, v, q, z, alpha1, beta1, alpha3, beta3, evectl, evectr, work, lwork, rwork, llwork, result, info)
CCHKGG

Function/Subroutine Documentation

  subroutine cchkgg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, logical tstdif, real thrshn, integer nounit, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) b, complex, dimension( lda, * ) h, complex, dimension( lda, * ) t, complex, dimension( lda, * ) s1, complex, dimension( lda, * ) s2, complex, dimension( lda, * ) p1, complex, dimension( lda, * ) p2, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldu, * ) v, complex, dimension( ldu, * ) q, complex, dimension( ldu, * ) z, complex, dimension( * ) alpha1, complex, dimension( * ) beta1, complex, dimension( * ) alpha3, complex, dimension( * ) beta3, complex, dimension( ldu, * ) evectl, complex, dimension( ldu, * ) evectr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, logical, dimension( * ) llwork, real, dimension( 15 ) result, integer info)

CCHKGG

Purpose:

     CCHKGG  checks the nonsymmetric generalized eigenvalue problem
     routines.
                                    H          H        H
     CGGHRD factors A and B as U H V  and U T V , where   means conjugate
     transpose, H is hessenberg, T is triangular and U and V are unitary.
                                     H          H
     CHGEQZ factors H and T as  Q S Z  and Q P Z , where P and S are upper
     triangular and Q and Z are unitary.  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
     CTGEVC 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 CCHKGG 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, 13
     tests will be performed.  The first twelve 'test ratios' should be
     small -- O(1).  They will be compared with the threshold THRESH:
                      H
     (1)   | A - U H V  | / ( |A| n ulp )
                      H
     (2)   | B - U T V  | / ( |B| n ulp )
                   H
     (3)   | I - UU  | / ( n ulp )
                   H
     (4)   | I - VV  | / ( n ulp )
                      H
     (5)   | H - Q S Z  | / ( |H| n ulp )
                      H
     (6)   | T - Q P Z  | / ( |T| n ulp )
                   H
     (7)   | I - QQ  | / ( n ulp )
                   H
     (8)   | I - ZZ  | / ( n ulp )
     (9)   max over all left eigenvalue/-vector pairs (beta/alpha,l) of
                               H
           | (beta A - alpha B) l | / ( ulp max( |beta A|, |alpha B| ) )
     (10)  max over all left eigenvalue/-vector pairs (beta/alpha,l') of
                               H
           | (beta H - alpha T) l' | / ( ulp max( |beta H|, |alpha T| ) )
           where the eigenvectors l' are the result of passing Q to
           STGEVC and back transforming (JOB='B').
     (11)  max over all right eigenvalue/-vector pairs (beta/alpha,r) of
           | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
     (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
           STGEVC and back transforming (JOB='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 P*D1, P is a random unitary diagonal
                           matrix (i.e., with random magnitude 1 entries
                           on the diagonal), and D1=diag( 0, 1,..., N-1 )
                           (i.e., a diagonal matrix with D1(1,1)=0,
                           D1(2,2)=1, ..., D1(N,N)=N-1.)
     (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=P*diag( 0, 0, 1, ..., N-3, 0 ) and
                            D2=Q*diag( 0, N-3, N-4,..., 1, 0, 0 ), and
                            P and Q are random unitary diagonal matrices.
               t   t
     (16) U ( J , J ) V     where U and V are random unitary 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) =
                            P*( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
                            Q*( 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) = P*( 0, 0, 1, ..., N-3, 0 )
                                     diag(T2) = ( 0, 1, ..., 1, 0, 0 )
     (23) U ( small*T1, big*T2 ) V   diag(T1) = P*( 0, 0, 1, ..., N-3, 0 )
                                     diag(T2) = ( 0, 1, ..., 1, 0, 0 )
     (24) U ( small*T1, small*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 )
                                     diag(T2) = ( 0, 1, ..., 1, 0, 0 )
     (25) U ( big*T1, big*T2 ) V     diag(T1) = P*( 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.

Parameters
    NSIZES

              NSIZES is INTEGER
              The number of sizes of matrices to use.  If it is zero,
              CCHKGG does nothing.  It must be at least zero.

    NN

              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.

    NTYPES

              NTYPES is INTEGER
              The number of elements in DOTYPE.   If it is zero, CCHKGG
              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. .

    DOTYPE

              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.

    ISEED

              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 CCHKGG to continue the same random number
              sequence.

    THRESH

              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.  It must be at least zero.

    TSTDIF

              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.

    THRSHN

              THRSHN is REAL
              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.)

    NOUNIT

              NOUNIT is INTEGER
              The FORTRAN unit number for printing out error messages
              (e.g., if a routine returns IINFO not equal to 0.)

    A

              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.

    LDA

              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 ).

    B

              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.

    H

              H is COMPLEX array, dimension (LDA, max(NN))
              The upper Hessenberg matrix computed from A by CGGHRD.

    T

              T is COMPLEX array, dimension (LDA, max(NN))
              The upper triangular matrix computed from B by CGGHRD.

    S1

              S1 is COMPLEX array, dimension (LDA, max(NN))
              The Schur (upper triangular) matrix computed from H by CHGEQZ
              when Q and Z are also computed.

    S2

              S2 is COMPLEX array, dimension (LDA, max(NN))
              The Schur (upper triangular) matrix computed from H by CHGEQZ
              when Q and Z are not computed.

    P1

              P1 is COMPLEX array, dimension (LDA, max(NN))
              The upper triangular matrix computed from T by CHGEQZ
              when Q and Z are also computed.

    P2

              P2 is COMPLEX array, dimension (LDA, max(NN))
              The upper triangular matrix computed from T by CHGEQZ
              when Q and Z are not computed.

    U

              U is COMPLEX array, dimension (LDU, max(NN))
              The (left) unitary matrix computed by CGGHRD.

    LDU

              LDU is INTEGER
              The leading dimension of U, V, Q, Z, EVECTL, and EVECTR.  It
              must be at least 1 and at least max( NN ).

    V

              V is COMPLEX array, dimension (LDU, max(NN))
              The (right) unitary matrix computed by CGGHRD.

    Q

              Q is COMPLEX array, dimension (LDU, max(NN))
              The (left) unitary matrix computed by CHGEQZ.

    Z

              Z is COMPLEX array, dimension (LDU, max(NN))
              The (left) unitary matrix computed by CHGEQZ.

    ALPHA1

              ALPHA1 is COMPLEX array, dimension (max(NN))

    BETA1

              BETA1 is COMPLEX array, dimension (max(NN))
              The generalized eigenvalues of (A,B) computed by CHGEQZ
              when Q, Z, and the full Schur matrices are computed.

    ALPHA3

              ALPHA3 is COMPLEX array, dimension (max(NN))

    BETA3

              BETA3 is COMPLEX array, dimension (max(NN))
              The generalized eigenvalues of (A,B) computed by CHGEQZ
              when neither Q, Z, nor the Schur matrices are computed.

    EVECTL

              EVECTL is COMPLEX array, dimension (LDU, max(NN))
              The (lower triangular) left eigenvector matrix for the
              matrices in S1 and P1.

    EVECTR

              EVECTR is COMPLEX array, dimension (LDU, max(NN))
              The (upper triangular) right eigenvector matrix for the
              matrices in S1 and P1.

    WORK

              WORK is COMPLEX array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
              The number of entries in WORK.  This must be at least
              max( 4*N, 2 * N**2, 1 ), for all N=NN(j).

    RWORK

              RWORK is REAL array, dimension (2*max(NN))

    LLWORK

              LLWORK is LOGICAL array, dimension (max(NN))

    RESULT

              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.

    INFO

              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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 498 of file cchkgg.f.

Author

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