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)) }.

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.

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