cdrvst.f - Man Page

      CDRVST  checks the Hermitian eigenvalue problem drivers.

              CHEEVD computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix,
              using a divide-and-conquer algorithm.

              CHEEVX computes selected eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix.

              CHEEVR computes selected eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix
              using the Relatively Robust Representation where it can.

              CHPEVD computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix in packed
              storage, using a divide-and-conquer algorithm.

              CHPEVX computes selected eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix in packed
              storage.

              CHBEVD computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian band matrix,
              using a divide-and-conquer algorithm.

              CHBEVX computes selected eigenvalues and, optionally,
              eigenvectors of a complex Hermitian band matrix.

              CHEEV computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix.

              CHPEV computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian matrix in packed
              storage.

              CHBEV computes all eigenvalues and, optionally,
              eigenvectors of a complex Hermitian band matrix.

      When CDRVST 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 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 '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 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 'clustered' 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 'clustered' 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,
          CDRVST 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, CDRVST
          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 CDRVST to continue the same random number
          sequence.
          Modified.

  THRESH  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.
          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 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      REAL array, dimension (max(NN))
          The eigenvalues of A, as computed by CSTEQR simultaneously
          with Z.  On exit, the eigenvalues in D1 correspond with the
          matrix in A.
          Modified.

  D2      REAL array, dimension (max(NN))
          The eigenvalues of A, as computed by CSTEQR if Z is not
          computed.  On exit, the eigenvalues in D2 correspond with
          the matrix in A.
          Modified.

  D3      REAL array, dimension (max(NN))
          The eigenvalues of A, as computed by SSTERF.  On exit, the
          eigenvalues in D3 correspond with the matrix in A.
          Modified.

  WA1     REAL array, dimension

  WA2     REAL array, dimension

  WA3     REAL array, dimension

  U       COMPLEX array, dimension (LDU, max(NN))
          The unitary matrix computed by CHETRD + CUNGC3.
          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 array, dimension (LDU, max(NN))
          The Housholder vectors computed by CHETRD in reducing A to
          tridiagonal form.
          Modified.

  TAU     COMPLEX array, dimension (max(NN))
          The Householder factors computed by CHETRD in reducing A
          to tridiagonal form.
          Modified.

  Z       COMPLEX array, dimension (LDU, max(NN))
          The unitary matrix of eigenvectors computed by CHEEVD,
          CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX.
          Modified.

  WORK  - COMPLEX 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   REAL 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  REAL 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  SLATMR, SLATMS, CHETRD, SORGC3, CSTEQR, SSTERF,
              or SORMC2 returns an error code, the
              absolute value of it is returned.
          Modified.

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       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 SLAFTS).
       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 '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) )