ex11.py: 2-D Laplacian eigenproblem solved with contour integral
================================================================

This example is similar to ``ex2.py``, but employs a contour integral
solver. It illustrates how to define a region of the complex plane
using an `RG` object.

The full source code for this demo can be `downloaded here
<../_static/ex11.py>`__.

Initialization is similar to previous examples.

::

  try: range = xrange
  except: pass

  import sys, slepc4py
  slepc4py.init(sys.argv)

  from petsc4py import PETSc
  from slepc4py import SLEPc

  Print = PETSc.Sys.Print

Build the finite-difference 2-D Laplacian matrix.

::

  def construct_operator(m, n):
      # Create matrix for 2D Laplacian operator
      A = PETSc.Mat().create()
      A.setSizes([m*n, m*n])
      A.setFromOptions()
      # Fill matrix
      hx = 1.0/(m-1) # x grid spacing
      hy = 1.0/(n-1) # y grid spacing
      diagv = 2.0*hy/hx + 2.0*hx/hy
      offdx = -1.0*hy/hx
      offdy = -1.0*hx/hy
      Istart, Iend = A.getOwnershipRange()
      for I in range(Istart, Iend) :
          A[I,I] = diagv
          i = I//n    # map row number to
          j = I - i*n # grid coordinates
          if i> 0  : J = I-n; A[I,J] = offdx
          if i< m-1: J = I+n; A[I,J] = offdx
          if j> 0  : J = I-1; A[I,J] = offdy
          if j< n-1: J = I+1; A[I,J] = offdy
      A.assemble()
      return A

In the main function, first two command-line options are processed to
set the grid dimensions. Then the matrix is built and passed to the
solver object. In this case, the solver is configured to use the contour
integral method. Next, the region of interest is defined, in this case
an ellipse centered at the origin, with radius 0.2 and vertical scaling
of 0.1. Finally, the solver is run. In this example, we illustrate how to
print the solution using the solver method `errorView() <EPS.errorView()>`.

::

  def main():
      opts = PETSc.Options()
      n = opts.getInt('n', 32)
      m = opts.getInt('m', 32)
      Print("2-D Laplacian Eigenproblem solved with contour integral, "
            "N=%d (%dx%d grid)\n" % (m*n, m, n))
      A = construct_operator(m,n)

      E = SLEPc.EPS().create()
      E.setOperators(A)
      E.setProblemType(SLEPc.EPS.ProblemType.HEP)
      E.setType(SLEPc.EPS.Type.CISS)

      R = E.getRG()
      R.setType(SLEPc.RG.Type.ELLIPSE)
      R.setEllipseParameters(0.0,0.2,0.1)
      E.setFromOptions()

      E.solve()

      vw = PETSc.Viewer.STDOUT()
      vw.pushFormat(PETSc.Viewer.Format.ASCII_INFO_DETAIL)
      E.errorView(viewer=vw)
      vw.popFormat()

  if __name__ == '__main__':
      main()