ZDRVES checks the nonsymmetric eigenvalue (Schur form) problem
    driver ZGEES.
    When ZDRVES 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:
    (1)     0 if T is in Schur form, 1/ulp otherwise
           (no sorting of eigenvalues)
    (2)     | A - VS T VS' | / ( n |A| ulp )
      Here VS is the matrix of Schur eigenvectors, and T is in Schur
      form  (no sorting of eigenvalues).
    (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
    (4)     0     if W are eigenvalues of T
            1/ulp otherwise
            (no sorting of eigenvalues)
    (5)     0     if T(with VS) = T(without VS),
            1/ulp otherwise
            (no sorting of eigenvalues)
    (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
            1/ulp otherwise
            (no sorting of eigenvalues)
    (7)     0 if T is in Schur form, 1/ulp otherwise
            (with sorting of eigenvalues)
    (8)     | A - VS T VS' | / ( n |A| ulp )
      Here VS is the matrix of Schur eigenvectors, and T is in Schur
      form  (with sorting of eigenvalues).
    (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
    (10)    0     if W are eigenvalues of T
            1/ulp otherwise
            (with sorting of eigenvalues)
    (11)    0     if T(with VS) = T(without VS),
            1/ulp otherwise
            (with sorting of eigenvalues)
    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
            1/ulp otherwise
            (with sorting of eigenvalues)
    (13)    if sorting worked and SDIM is the number of
            eigenvalues which were SELECTed
    The 'sizes' 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)  The zero matrix.
    (2)  The identity matrix.
    (3)  A (transposed) Jordan block, with 1's on the diagonal.
    (4)  A diagonal matrix with evenly spaced entries
         1, ..., ULP  and random complex angles.
         (ULP = (first number larger than 1) - 1 )
    (5)  A diagonal matrix with geometrically spaced entries
         1, ..., ULP  and random complex angles.
    (6)  A diagonal matrix with 'clustered' entries 1, ULP, ..., ULP
         and random complex angles.
    (7)  Same as (4), but multiplied by a constant near
         the overflow threshold
    (8)  Same as (4), but multiplied by a constant near
         the underflow threshold
    (9)  A matrix of the form  U' T U, where U is unitary and
         T has evenly spaced entries 1, ..., ULP with random
         complex angles on the diagonal and random O(1) entries in
         the upper triangle.
    (10) A matrix of the form  U' T U, where U is unitary and
         T has geometrically spaced entries 1, ..., ULP with random
         complex angles on the diagonal and random O(1) entries in
         the upper triangle.
    (11) A matrix of the form  U' T U, where U is orthogonal and
         T has 'clustered' entries 1, ULP,..., ULP with random
         complex angles on the diagonal and random O(1) entries in
         the upper triangle.
    (12) A matrix of the form  U' T U, where U is unitary and
         T has complex eigenvalues randomly chosen from
         ULP < |z| < 1   and random O(1) entries in the upper
         triangle.
    (13) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
         with random complex angles on the diagonal and random O(1)
         entries in the upper triangle.
    (14) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has geometrically spaced entries
         1, ..., ULP with random complex angles on the diagonal
         and random O(1) entries in the upper triangle.
    (15) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has 'clustered' entries 1, ULP,..., ULP
         with random complex angles on the diagonal and random O(1)
         entries in the upper triangle.
    (16) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has complex eigenvalues randomly chosen
         from ULP < |z| < 1 and random O(1) entries in the upper
         triangle.
    (17) Same as (16), but multiplied by a constant
         near the overflow threshold
    (18) Same as (16), but multiplied by a constant
         near the underflow threshold
    (19) Nonsymmetric matrix with random entries chosen from (-1,1).
         If N is at least 4, all entries in first two rows and last
         row, and first column and last two columns are zero.
    (20) Same as (19), but multiplied by a constant
         near the overflow threshold
    (21) Same as (19), but multiplied by a constant
         near the underflow threshold

NSIZES

          NSIZES is INTEGER
          The number of sizes of matrices to use.  If it is zero,
          ZDRVES 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, ZDRVES
          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 ZDRVES to continue the same random number
          sequence.

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.

NOUNIT

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

A

          A is COMPLEX*16 array, dimension (LDA, max(NN))
          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, and H. LDA must be at
          least 1 and at least max( NN ).

H

          H is COMPLEX*16 array, dimension (LDA, max(NN))
          Another copy of the test matrix A, modified by ZGEES.

HT

          HT is COMPLEX*16 array, dimension (LDA, max(NN))
          Yet another copy of the test matrix A, modified by ZGEES.

W

          W is COMPLEX*16 array, dimension (max(NN))
          The computed eigenvalues of A.

WT

          WT is COMPLEX*16 array, dimension (max(NN))
          Like W, this array contains the eigenvalues of A,
          but those computed when ZGEES only computes a partial
          eigendecomposition, i.e. not Schur vectors

VS

          VS is COMPLEX*16 array, dimension (LDVS, max(NN))
          VS holds the computed Schur vectors.

LDVS

          LDVS is INTEGER
          Leading dimension of VS. Must be at least max(1,max(NN)).

RESULT

          RESULT is DOUBLE PRECISION array, dimension (13)
          The values computed by the 13 tests described above.
          The values are currently limited to 1/ulp, to avoid overflow.

WORK

          WORK is COMPLEX*16 array, dimension (NWORK)

NWORK

          NWORK is INTEGER
          The number of entries in WORK.  This must be at least
          5*NN(j)+2*NN(j)**2 for all j.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (max(NN))

IWORK

          IWORK is INTEGER array, dimension (max(NN))

BWORK

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

INFO

          INFO is INTEGER
          If 0, then everything ran OK.
           -1: NSIZES < 0
           -2: Some NN(j) < 0
           -3: NTYPES < 0
           -6: THRESH < 0
           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
          -15: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
          -18: NWORK too small.
          If  ZLATMR, CLATMS, CLATME or ZGEES returns an error code,
              the absolute value of it is returned.
-----------------------------------------------------------------------
     Some Local Variables and Parameters:
     ---- ----- --------- --- ----------
     ZERO, ONE       Real 0 and 1.
     MAXTYP          The number of types defined.
     NMAX            Largest value in NN.
     NERRS           The number of tests which have exceeded THRESH
     COND, CONDS,
     IMODE           Values to be passed to the matrix generators.
     ANORM           Norm of A; passed to matrix generators.
     OVFL, UNFL      Overflow and underflow thresholds.
     ULP, ULPINV     Finest relative precision and its inverse.
     RTULP, RTULPI   Square roots of the previous 4 values.
             The following four arrays decode JTYPE:
     KTYPE(j)        The general type (1-10) for type 'j'.
     KMODE(j)        The MODE value to be passed to the matrix
                     generator for type 'j'.
     KMAGN(j)        The order of magnitude ( O(1),
                     O(overflow^(1/2) ), O(underflow^(1/2) )
     KCONDS(j)       Select whether CONDS is to be 1 or
                     1/sqrt(ulp).  (0 means irrelevant.)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.