ZCHKHS  checks the nonsymmetric eigenvalue problem routines.
            ZGEHRD factors A as  U H U' , where ' means conjugate
            transpose, H is hessenberg, and U is unitary.
            ZUNGHR generates the unitary matrix U.
            ZUNMHR multiplies a matrix by the unitary matrix U.
            ZHSEQR factors H as  Z T Z' , where Z is unitary and T
            is upper triangular.  It also computes the eigenvalues,
            w(1), ..., w(n); we define a diagonal matrix W whose
            (diagonal) entries are the eigenvalues.
            ZTREVC computes the left eigenvector matrix L and the
            right eigenvector matrix R for the matrix T.  The
            columns of L are the complex conjugates of the left
            eigenvectors of T.  The columns of R are the right
            eigenvectors of T.  L is lower triangular, and R is
            upper triangular.
            ZHSEIN computes the left eigenvector matrix Y and the
            right eigenvector matrix X for the matrix H.  The
            columns of Y are the complex conjugates of the left
            eigenvectors of H.  The columns of X are the right
            eigenvectors of H.  Y is lower triangular, and X is
            upper triangular.
            ZTREVC3 computes left and right eigenvector matrices
            from a Schur matrix T and backtransforms them with Z
            to eigenvector matrices L and R for A. L and R are
            GE matrices.
    When ZCHKHS 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, 16
    tests will be performed:
    (1)     | A - U H U**H | / ( |A| n ulp )
    (2)     | I - UU**H | / ( n ulp )
    (3)     | H - Z T Z**H | / ( |H| n ulp )
    (4)     | I - ZZ**H | / ( n ulp )
    (5)     | A - UZ H (UZ)**H | / ( |A| n ulp )
    (6)     | I - UZ (UZ)**H | / ( n ulp )
    (7)     | T(Z computed) - T(Z not computed) | / ( |T| ulp )
    (8)     | W(Z computed) - W(Z not computed) | / ( |W| ulp )
    (9)     | TR - RW | / ( |T| |R| ulp )
    (10)    | L**H T - W**H L | / ( |T| |L| ulp )
    (11)    | HX - XW | / ( |H| |X| ulp )
    (12)    | Y**H H - W**H Y | / ( |H| |Y| ulp )
    (13)    | AX - XW | / ( |A| |X| ulp )
    (14)    | Y**H A - W**H Y | / ( |A| |Y| ulp )
    (15)    | AR - RW | / ( |A| |R| ulp )
    (16)    | LA - WL | / ( |A| |L| ulp )
    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 SQRT( overflow threshold )
    (8)  Same as (4), but multiplied by SQRT( 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 unitary 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 SQRT( overflow threshold )
    (18) Same as (16), but multiplied by SQRT( underflow threshold )
    (19) Nonsymmetric matrix with random entries chosen from |z| < 1
    (20) Same as (19), but multiplied by SQRT( overflow threshold )
    (21) Same as (19), but multiplied by SQRT( underflow threshold )

  NSIZES - INTEGER
           The number of sizes of matrices to use.  If it is zero,
           ZCHKHS does nothing.  It must be at least zero.
           Not modified.
  NN     - 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.
           Not modified.
  NTYPES - INTEGER
           The number of elements in DOTYPE.   If it is zero, ZCHKHS
           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. .
           Not modified.
  DOTYPE - 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.
           Not modified.
  ISEED  - 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 ZCHKHS to continue the same random number
           sequence.
           Modified.
  THRESH - 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.
           Not modified.
  NOUNIT - INTEGER
           The FORTRAN unit number for printing out error messages
           (e.g., if a routine returns IINFO not equal to 0.)
           Not modified.
  A      - 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.
           Modified.
  LDA    - INTEGER
           The leading dimension of A, H, T1 and T2.  It must be at
           least 1 and at least max( NN ).
           Not modified.
  H      - COMPLEX*16 array, dimension (LDA,max(NN))
           The upper hessenberg matrix computed by ZGEHRD.  On exit,
           H contains the Hessenberg form of the matrix in A.
           Modified.
  T1     - COMPLEX*16 array, dimension (LDA,max(NN))
           The Schur (='quasi-triangular') matrix computed by ZHSEQR
           if Z is computed.  On exit, T1 contains the Schur form of
           the matrix in A.
           Modified.
  T2     - COMPLEX*16 array, dimension (LDA,max(NN))
           The Schur matrix computed by ZHSEQR when Z is not computed.
           This should be identical to T1.
           Modified.
  LDU    - INTEGER
           The leading dimension of U, Z, UZ and UU.  It must be at
           least 1 and at least max( NN ).
           Not modified.
  U      - COMPLEX*16 array, dimension (LDU,max(NN))
           The unitary matrix computed by ZGEHRD.
           Modified.
  Z      - COMPLEX*16 array, dimension (LDU,max(NN))
           The unitary matrix computed by ZHSEQR.
           Modified.
  UZ     - COMPLEX*16 array, dimension (LDU,max(NN))
           The product of U times Z.
           Modified.
  W1     - COMPLEX*16 array, dimension (max(NN))
           The eigenvalues of A, as computed by a full Schur
           decomposition H = Z T Z'.  On exit, W1 contains the
           eigenvalues of the matrix in A.
           Modified.
  W3     - COMPLEX*16 array, dimension (max(NN))
           The eigenvalues of A, as computed by a partial Schur
           decomposition (Z not computed, T only computed as much
           as is necessary for determining eigenvalues).  On exit,
           W3 contains the eigenvalues of the matrix in A, possibly
           perturbed by ZHSEIN.
           Modified.
  EVECTL - COMPLEX*16 array, dimension (LDU,max(NN))
           The conjugate transpose of the (upper triangular) left
           eigenvector matrix for the matrix in T1.
           Modified.
  EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN))
           The (upper triangular) right eigenvector matrix for the
           matrix in T1.
           Modified.
  EVECTY - COMPLEX*16 array, dimension (LDU,max(NN))
           The conjugate transpose of the left eigenvector matrix
           for the matrix in H.
           Modified.
  EVECTX - COMPLEX*16 array, dimension (LDU,max(NN))
           The right eigenvector matrix for the matrix in H.
           Modified.
  UU     - COMPLEX*16 array, dimension (LDU,max(NN))
           Details of the unitary matrix computed by ZGEHRD.
           Modified.
  TAU    - COMPLEX*16 array, dimension (max(NN))
           Further details of the unitary matrix computed by ZGEHRD.
           Modified.
  WORK   - COMPLEX*16 array, dimension (NWORK)
           Workspace.
           Modified.
  NWORK  - INTEGER
           The number of entries in WORK.  NWORK >= 4*NN(j)*NN(j) + 2.
  RWORK  - DOUBLE PRECISION array, dimension (max(NN))
           Workspace.  Could be equivalenced to IWORK, but not SELECT.
           Modified.
  IWORK  - INTEGER array, dimension (max(NN))
           Workspace.
           Modified.
  SELECT - LOGICAL array, dimension (max(NN))
           Workspace.  Could be equivalenced to IWORK, but not RWORK.
           Modified.
  RESULT - DOUBLE PRECISION array, dimension (16)
           The values computed by the fourteen tests described above.
           The values are currently limited to 1/ulp, to avoid
           overflow.
           Modified.
  INFO   - 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) ).
           -14: LDU < 1 or LDU < NMAX.
           -26: NWORK too small.
           If  ZLATMR, CLATMS, or CLATME returns an error code, the
               absolute value of it is returned.
           If 1, then ZHSEQR could not find all the shifts.
           If 2, then the EISPACK code (for small blocks) failed.
           If >2, then 30*N iterations were not enough to find an
               eigenvalue or to decompose the problem.
           Modified.
-----------------------------------------------------------------------
     Some Local Variables and Parameters:
     ---- ----- --------- --- ----------
     ZERO, ONE       Real 0 and 1.
     MAXTYP          The number of types defined.
     MTEST           The number of tests defined: care must be taken
                     that (1) the size of RESULT, (2) the number of
                     tests actually performed, and (3) MTEST agree.
     NTEST           The number of tests performed on this matrix
                     so far.  This should be less than MTEST, and
                     equal to it by the last test.  It will be less
                     if any of the routines being tested indicates
                     that it could not compute the matrices that
                     would be tested.
     NMAX            Largest value in NN.
     NMATS           The number of matrices generated so far.
     NERRS           The number of tests which have exceeded THRESH
                     so far (computed by DLAFTS).
     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.
     RTOVFL, RTUNFL,
     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)       Selects whether CONDS is to be 1 or
                     1/sqrt(ulp).  (0 means irrelevant.)

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