dapply_poly_sdia 

Apply polynomial preconditioner for symmetric diagonal storage (Serial and Parallel Versions)

FORMAT

  DAPPLY_POLY_SDIA
   (job, p, a, ia, ndim, nz, x, y, ndeg, n, iparam)

Arguments

  job                 integer*4
                      On entry, defines the operation to be performed:

                      job = 0 : y = inverse(Q) * x

                      job = 1 : y = inverse(transp(Q)) * x
                      where Q is the polynomial preconditioner.
                      On exit, job is unchanged.

  p                   real*8
                      On entry, a one-dimensional array of length at least
                      3*n that contains information for use by the polynomial
                      preconditioner and  workspace.
                      On exit, the part of array P that contains the
                      information related to the polynomial preconditioner is
                      unchanged. The part used as workspace is overwritten.

  a                   real*8
                      On entry, a two-dimensional array with dimensions ndim
                      by nz containing the nonzero elements of the matrix A.
                      On exit, a is unchanged.

  ia                  integer*4
                      On entry, a one-dimensional array of length at least
                      nz,  containing the distances of the diagonals from the
                      main diagonal.
                      On exit, ia is unchanged.

  ndim                integer*4
                      On entry, the leading dimension of array A, as declared
                      in the calling subprogram; ndim >= n.
                      On exit, ndim is unchanged.

  nz                  integer*4
                      On entry, the number of diagonals stored in array A.
                      On exit, nz is unchanged.

  x                   real*8
                      On entry, a one-dimensional array of length at least n,
                      containing the elements of vector x, accessed with unit
                      increment.
                      On exit, x is unchanged.

  y                   real*8
                      On entry, a one-dimensional array of length at least n.
                      On exit, array Y is overwritten by the output vector y.
                      The elements of array Y are accessed with unit
                      increment.

  ndeg                integer*4
                      On entry, the degree of the polynomial in the
                      polynomial preconditioner.
                      On exit, ndeg is unchanged.

  n                   integer*4
                      On entry, the order of the matrix A.
                      On exit, n is unchanged.

  iparam              integer*4
                      On entry, a one-dimensional array of length at least 50.
                      The variables in the IPARAM  array are assigned the values
                      listed in Table 10-4 of the CXML Reference Guide.  
                      Of the first 50 values, the 30th - 50th elements in IPARAM
                      are reserved for the use of CXML.

Description

  DAPPLY_POLY_SDIA applies the polynomial preconditioner for a sparse matrix
  stored using the symmetric diagonal storage scheme.  The input vector, p,
  contains information for use by the routine.  This vector is generated by a
  call to the routine DCREATE_POLY_SDIA prior to a call to one of the
  iterative solvers with polynomial preconditioning. Depending on the value
  of the input parameter job, DAPPLY_POLY_SDIA operates on either the
  preconditioning matrix or its transpose.

  This routine is available in both serial and parallel versions. The routine
  names and parameter list are identical for both versions. For information
  about linking to the serial or to the parallel library, refer to the CXML
  Reference Manual.