TESTING/EIG/zdrgvx.f(3)

NAME
TESTING/EIG/zdrgvx.f

SYNOPSIS

  Functions/Subroutines
subroutine zdrgvx (nsize, thresh, nin, nout, a, lda, b, ai, bi, alpha, beta, vl, vr, ilo, ihi, lscale, rscale, s, dtru, dif, diftru, work, lwork, rwork, iwork, liwork, result, bwork, info)
ZDRGVX

Function/Subroutine Documentation

  subroutine zdrgvx (integer nsize, double precision thresh, integer nin, integer nout, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) b, complex*16, dimension( lda, * ) ai, complex*16, dimension( lda, * ) bi, complex*16, dimension( * ) alpha, complex*16, dimension( * ) beta, complex*16, dimension( lda, * ) vl, complex*16, dimension( lda, * ) vr, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, double precision, dimension( * ) s, double precision, dimension( * ) dtru, double precision, dimension( * ) dif, double precision, dimension( * ) diftru, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer liwork, double precision, dimension( 4 ) result, logical, dimension( * ) bwork, integer info)

ZDRGVX

Purpose:

     ZDRGVX checks the nonsymmetric generalized eigenvalue problem
     expert driver ZGGEVX.
     ZGGEVX computes the generalized eigenvalues, (optionally) the left
     and/or right eigenvectors, (optionally) computes a balancing
     transformation to improve the conditioning, and (optionally)
     reciprocal condition numbers for the eigenvalues and eigenvectors.
     When ZDRGVX is called with NSIZE > 0, two types of test matrix pairs
     are generated by the subroutine DLATM6 and test the driver ZGGEVX.
     The test matrices have the known exact condition numbers for
     eigenvalues. For the condition numbers of the eigenvectors
     corresponding the first and last eigenvalues are also know
     ``exactly'' (see ZLATM6).
     For each matrix pair, the following tests will be performed and
     compared with the threshold THRESH.
     (1) max over all left eigenvalue/-vector pairs (beta/alpha,l) of
        | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )
         where l**H is the conjugate transpose of l.
     (2) max over all right eigenvalue/-vector pairs (beta/alpha,r) of
           | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
     (3) The condition number S(i) of eigenvalues computed by ZGGEVX
         differs less than a factor THRESH from the exact S(i) (see
         ZLATM6).
     (4) DIF(i) computed by ZTGSNA differs less than a factor 10*THRESH
         from the exact value (for the 1st and 5th vectors only).
     Test Matrices
     =============
     Two kinds of test matrix pairs
              (A, B) = inverse(YH) * (Da, Db) * inverse(X)
     are used in the tests:
     1: Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
              0   2+a   0    0    0         0   1   0   0   0
              0    0   3+a   0    0         0   0   1   0   0
              0    0    0   4+a   0         0   0   0   1   0
              0    0    0    0   5+a ,      0   0   0   0   1 , and
     2: Da =  1   -1    0    0    0    Db = 1   0   0   0   0
              1    1    0    0    0         0   1   0   0   0
              0    0    1    0    0         0   0   1   0   0
              0    0    0   1+a  1+b        0   0   0   1   0
              0    0    0  -1-b  1+a ,      0   0   0   0   1 .
     In both cases the same inverse(YH) and inverse(X) are used to compute
     (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
     YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
             0    1   -y    y   -y         0   1   x  -x  -x
             0    0    1    0    0         0   0   1   0   0
             0    0    0    1    0         0   0   0   1   0
             0    0    0    0    1,        0   0   0   0   1 , where
     a, b, x and y will have all values independently of each other from
     { sqrt(sqrt(ULP)),  0.1,  1,  10,  1/sqrt(sqrt(ULP)) }.

Parameters
    NSIZE

              NSIZE is INTEGER
              The number of sizes of matrices to use.  NSIZE must be at
              least zero. If it is zero, no randomly generated matrices
              are tested, but any test matrices read from NIN will be
              tested.  If it is not zero, then N = 5.

    THRESH

              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.

    NIN

              NIN is INTEGER
              The FORTRAN unit number for reading in the data file of
              problems to solve.

    NOUT

              NOUT 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*16 array, dimension (LDA, NSIZE)
              Used to hold the matrix whose eigenvalues are to be
              computed.  On exit, A contains the last matrix actually used.

    LDA

              LDA is INTEGER
              The leading dimension of A, B, AI, BI, Ao, and Bo.
              It must be at least 1 and at least NSIZE.

    B

              B is COMPLEX*16 array, dimension (LDA, NSIZE)
              Used to hold the matrix whose eigenvalues are to be
              computed.  On exit, B contains the last matrix actually used.

    AI

              AI is COMPLEX*16 array, dimension (LDA, NSIZE)
              Copy of A, modified by ZGGEVX.

    BI

              BI is COMPLEX*16 array, dimension (LDA, NSIZE)
              Copy of B, modified by ZGGEVX.

    ALPHA

              ALPHA is COMPLEX*16 array, dimension (NSIZE)

    BETA

              BETA is COMPLEX*16 array, dimension (NSIZE)
              On exit, ALPHA/BETA are the eigenvalues.

    VL

              VL is COMPLEX*16 array, dimension (LDA, NSIZE)
              VL holds the left eigenvectors computed by ZGGEVX.

    VR

              VR is COMPLEX*16 array, dimension (LDA, NSIZE)
              VR holds the right eigenvectors computed by ZGGEVX.

    ILO

            ILO is INTEGER

    IHI

            IHI is INTEGER

    LSCALE

            LSCALE is DOUBLE PRECISION array, dimension (N)

    RSCALE

            RSCALE is DOUBLE PRECISION array, dimension (N)

    S

            S is DOUBLE PRECISION array, dimension (N)

    DTRU

            DTRU is DOUBLE PRECISION array, dimension (N)

    DIF

            DIF is DOUBLE PRECISION array, dimension (N)

    DIFTRU

            DIFTRU is DOUBLE PRECISION array, dimension (N)

    WORK

              WORK is COMPLEX*16 array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
              Leading dimension of WORK.  LWORK >= 2*N*N + 2*N

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (6*N)

    IWORK

              IWORK is INTEGER array, dimension (LIWORK)

    LIWORK

              LIWORK is INTEGER
              Leading dimension of IWORK.  LIWORK >= N+2.

    RESULT

            RESULT is DOUBLE PRECISION array, dimension (4)

    BWORK

              BWORK is LOGICAL array, dimension (N)

    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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 293 of file zdrgvx.f.

Author

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