TESTING/EIG/cdrgvx.f(3)

NAME
TESTING/EIG/cdrgvx.f

SYNOPSIS

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

Function/Subroutine Documentation

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

CDRGVX

Purpose:

     CDRGVX checks the nonsymmetric generalized eigenvalue problem
     expert driver CGGEVX.
     CGGEVX 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 CDRGVX is called with NSIZE > 0, two types of test matrix pairs
     are generated by the subroutine SLATM6 and test the driver CGGEVX.
     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 CLATM6).
     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 CGGEVX
         differs less than a factor THRESH from the exact S(i) (see
         CLATM6).
     (4) DIF(i) computed by CTGSNA 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 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.

    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 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 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 array, dimension (LDA, NSIZE)
              Copy of A, modified by CGGEVX.

    BI

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

    ALPHA

              ALPHA is COMPLEX array, dimension (NSIZE)

    BETA

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

    VL

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

    VR

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

    ILO

            ILO is INTEGER

    IHI

            IHI is INTEGER

    LSCALE

            LSCALE is REAL array, dimension (N)

    RSCALE

            RSCALE is REAL array, dimension (N)

    S

            S is REAL array, dimension (N)

    STRU

            STRU is REAL array, dimension (N)

    DIF

            DIF is REAL array, dimension (N)

    DIFTRU

            DIFTRU is REAL array, dimension (N)

    WORK

              WORK is COMPLEX array, dimension (LWORK)

    LWORK

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

    RWORK

              RWORK is REAL 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 REAL 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 294 of file cdrgvx.f.

Author

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