zdrvst2stg3

!>
!>      ZDRVST2STG  checks the Hermitian eigenvalue problem drivers.
!>
!>              ZHEEVD computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix,
!>              using a divide-and-conquer algorithm.
!>
!>              ZHEEVX computes selected eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix.
!>
!>              ZHEEVR computes selected eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix
!>              using the Relatively Robust Representation where it can.
!>
!>              ZHPEVD computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix in packed
!>              storage, using a divide-and-conquer algorithm.
!>
!>              ZHPEVX computes selected eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix in packed
!>              storage.
!>
!>              ZHBEVD computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian band matrix,
!>              using a divide-and-conquer algorithm.
!>
!>              ZHBEVX computes selected eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian band matrix.
!>
!>              ZHEEV computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix.
!>
!>              ZHPEV computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian matrix in packed
!>              storage.
!>
!>              ZHBEV computes all eigenvalues and, optionally,
!>              eigenvectors of a complex Hermitian band matrix.
!>
!>      When ZDRVST2STG is called, a number of matrix  () and a
!>      number of matrix  are specified.  For each size ()
!>      and each type of matrix, one matrix will be generated and used
!>      to test the appropriate drivers.  For each matrix and each
!>      driver routine called, the following tests will be performed:
!>
!>      (1)     | A - Z D Z' | / ( |A| n ulp )
!>
!>      (2)     | I - Z Z' | / ( n ulp )
!>
!>      (3)     | D1 - D2 | / ( |D1| ulp )
!>
!>      where Z is the matrix of eigenvectors returned when the
!>      eigenvector option is given and D1 and D2 are the eigenvalues
!>      returned with and without the eigenvector option.
!>
!>      The  are specified by an array NN(1:NSIZES); the value of
!>      each element NN(j) specifies one size.
!>      The  are specified by a logical array DOTYPE( 1:NTYPES );
!>      if DOTYPE(j) is .TRUE., then matrix type  will be generated.
!>      Currently, the list of possible types is:
!>
!>      (1)  The zero matrix.
!>      (2)  The identity matrix.
!>
!>      (3)  A diagonal matrix with evenly spaced entries
!>           1, ..., ULP  and random signs.
!>           (ULP = (first number larger than 1) - 1 )
!>      (4)  A diagonal matrix with geometrically spaced entries
!>           1, ..., ULP  and random signs.
!>      (5)  A diagonal matrix with  entries 1, ULP, ..., ULP
!>           and random signs.
!>
!>      (6)  Same as (4), but multiplied by SQRT( overflow threshold )
!>      (7)  Same as (4), but multiplied by SQRT( underflow threshold )
!>
!>      (8)  A matrix of the form  U* D U, where U is unitary and
!>           D has evenly spaced entries 1, ..., ULP with random signs
!>           on the diagonal.
!>
!>      (9)  A matrix of the form  U* D U, where U is unitary and
!>           D has geometrically spaced entries 1, ..., ULP with random
!>           signs on the diagonal.
!>
!>      (10) A matrix of the form  U* D U, where U is unitary and
!>           D has  entries 1, ULP,..., ULP with random
!>           signs on the diagonal.
!>
!>      (11) Same as (8), but multiplied by SQRT( overflow threshold )
!>      (12) Same as (8), but multiplied by SQRT( underflow threshold )
!>
!>      (13) Symmetric matrix with random entries chosen from (-1,1).
!>      (14) Same as (13), but multiplied by SQRT( overflow threshold )
!>      (15) Same as (13), but multiplied by SQRT( underflow threshold )
!>      (16) A band matrix with half bandwidth randomly chosen between
!>           0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
!>           with random signs.
!>      (17) Same as (16), but multiplied by SQRT( overflow threshold )
!>      (18) Same as (16), but multiplied by SQRT( underflow threshold )
!> 

!>  NSIZES  INTEGER
!>          The number of sizes of matrices to use.  If it is zero,
!>          ZDRVST2STG 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, ZDRVST2STG
!>          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 ZDRVST2STG to continue the same random number
!>          sequence.
!>          Modified.
!>
!>  THRESH  DOUBLE PRECISION
!>          A test will count as  if the , 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.  It must be at
!>          least 1 and at least max( NN ).
!>          Not modified.
!>
!>  D1      DOUBLE PRECISION array, dimension (max(NN))
!>          The eigenvalues of A, as computed by ZSTEQR simultaneously
!>          with Z.  On exit, the eigenvalues in D1 correspond with the
!>          matrix in A.
!>          Modified.
!>
!>  D2      DOUBLE PRECISION array, dimension (max(NN))
!>          The eigenvalues of A, as computed by ZSTEQR if Z is not
!>          computed.  On exit, the eigenvalues in D2 correspond with
!>          the matrix in A.
!>          Modified.
!>
!>  D3      DOUBLE PRECISION array, dimension (max(NN))
!>          The eigenvalues of A, as computed by DSTERF.  On exit, the
!>          eigenvalues in D3 correspond with the matrix in A.
!>          Modified.
!>
!>  WA1     DOUBLE PRECISION array, dimension
!>
!>  WA2     DOUBLE PRECISION array, dimension
!>
!>  WA3     DOUBLE PRECISION array, dimension
!>
!>  U       COMPLEX*16 array, dimension (LDU, max(NN))
!>          The unitary matrix computed by ZHETRD + ZUNGC3.
!>          Modified.
!>
!>  LDU     INTEGER
!>          The leading dimension of U, Z, and V.  It must be at
!>          least 1 and at least max( NN ).
!>          Not modified.
!>
!>  V       COMPLEX*16 array, dimension (LDU, max(NN))
!>          The Housholder vectors computed by ZHETRD in reducing A to
!>          tridiagonal form.
!>          Modified.
!>
!>  TAU     COMPLEX*16 array, dimension (max(NN))
!>          The Householder factors computed by ZHETRD in reducing A
!>          to tridiagonal form.
!>          Modified.
!>
!>  Z       COMPLEX*16 array, dimension (LDU, max(NN))
!>          The unitary matrix of eigenvectors computed by ZHEEVD,
!>          ZHEEVX, ZHPEVD, CHPEVX, ZHBEVD, and CHBEVX.
!>          Modified.
!>
!>  WORK  - COMPLEX*16 array of dimension ( LWORK )
!>           Workspace.
!>           Modified.
!>
!>  LWORK - INTEGER
!>           The number of entries in WORK.  This must be at least
!>           2*max( NN(j), 2 )**2.
!>           Not modified.
!>
!>  RWORK   DOUBLE PRECISION array, dimension (3*max(NN))
!>           Workspace.
!>           Modified.
!>
!>  LRWORK - INTEGER
!>           The number of entries in RWORK.
!>
!>  IWORK   INTEGER array, dimension (6*max(NN))
!>          Workspace.
!>          Modified.
!>
!>  LIWORK - INTEGER
!>           The number of entries in IWORK.
!>
!>  RESULT  DOUBLE PRECISION array, dimension (??)
!>          The values computed by the 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
!>           -5: THRESH < 0
!>           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
!>          -16: LDU < 1 or LDU < NMAX.
!>          -21: LWORK too small.
!>          If  DLATMR, SLATMS, ZHETRD, DORGC3, ZSTEQR, DSTERF,
!>              or DORMC2 returns an error code, the
!>              absolute value of it is returned.
!>          Modified.
!>
!>-----------------------------------------------------------------------
!>
!>       Some Local Variables and Parameters:
!>       ---- ----- --------- --- ----------
!>       ZERO, ONE       Real 0 and 1.
!>       MAXTYP          The number of types defined.
!>       NTEST           The number of tests performed, or which can
!>                       be performed so far, for the current matrix.
!>       NTESTT          The total number of tests performed so far.
!>       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, 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  Square roots of the previous 2 values.
!>               The following four arrays decode JTYPE:
!>       KTYPE(j)        The general type (1-10) for type .
!>       KMODE(j)        The MODE value to be passed to the matrix
!>                       generator for type .
!>       KMAGN(j)        The order of magnitude ( O(1),
!>                       O(overflow^(1/2) ), O(underflow^(1/2) )
!> 

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