"""

Test the convergence of a small diffusion problem discretized with the local
discontinuous Galerkin method.  The polynomial order is 5.  To utilize the
visualization capabilities, you need to have Paraview and scikits.delaunay
installed.

References
----------
[1] <NAME> and <NAME>.  Smoothed Aggregation Multigrid Solvers for
High-Order Discontinuous Galerkin Methods.  Journal of Computational Physics.
Submitted 2010. 

"""
import numpy
import scipy

from pyamg.gallery import load_example
from pyamg import smoothed_aggregation_solver

from convergence_tools import print_cycle_history

if __name__ == '__main__':

    print "\nDiffusion problem discretized with p=5 and the local\n" + \
          "discontinuous Galerkin method."

    # Discontinuous Galerkin Diffusion Problem
    data = load_example('local_disc_galerkin_diffusion')
    A = data['A'].tocsr()
    B = data['B']
    elements = data['elements']
    vertices = data['vertices']
    numpy.random.seed(625)
    x0 = scipy.rand(A.shape[0])
    b = numpy.zeros_like(x0)
    
    ##
    # For demonstration, show that a naive SA solver 
    # yields unsatisfactory convergence
    smooth=('jacobi', {'filter' : True})
    strength=('symmetric', {'theta' : 0.1})
    SA_solve_args={'cycle':'W', 'maxiter':20, 'tol':1e-8, 'accel' : 'cg'}
    SA_build_args={'max_levels':10, 'max_coarse':25, 'coarse_solver':'pinv2', \
            'symmetry':'hermitian', 'keep':True}
    presmoother =('gauss_seidel', {'sweep':'symmetric', 'iterations':1})
    postsmoother=('gauss_seidel', {'sweep':'symmetric', 'iterations':1})
    
    ##
    # Construct solver and solve
    sa = smoothed_aggregation_solver(A, B=B, smooth=smooth, \
             strength=strength, presmoother=presmoother, \
             postsmoother=postsmoother, **SA_build_args)
    resvec = []
    x = sa.solve(b, x0=x0, residuals=resvec, **SA_solve_args)
    print "\n*************************************************************"
    print "*************************************************************"
    print "Observe that standard SA parameters for this p=5 discontinuous \n" + \
          "Galerkin system yield an inefficient solver.\n"
    print_cycle_history(resvec, sa, verbose=True, plotting=False)

    ##
    # Now, construct and solve with appropriate parameters 
    p = 5
    Bimprove = [('block_gauss_seidel', {'sweep':'symmetric', 'iterations':p}),
                ('gauss_seidel', {'sweep':'symmetric', 'iterations':p})]   
    aggregate = ['naive', 'standard']
    # the initial conforming aggregation step requires no prolongation smoothing
    smooth=[None, ('energy', {'krylov' : 'cg', 'maxiter' : p})]
    strength =[('distance', {'V' : data['vertices'], 'theta':5e-5, 'relative_drop':False}),\
               ('evolution', {'k':4, 'proj_type':'l2', 'epsilon':2.0})]
    sa = smoothed_aggregation_solver(A, B=B, smooth=smooth, Bimprove=Bimprove,\
             strength=strength, presmoother=presmoother, aggregate=aggregate,\
             postsmoother=postsmoother, **SA_build_args)
    resvec = []
    x = sa.solve(b, x0=x0, residuals=resvec, **SA_solve_args)
    print "\n*************************************************************"
    print "*************************************************************"
    print "Now use appropriate parameters, especially \'energy\' prolongation\n" + \
          "smoothing and a distance based strength measure on level 0.  This\n" + \
          "yields a much more efficient solver.\n"
    print_cycle_history(resvec, sa, verbose=True, plotting=False)


##
# check for scikits and print message about needing to have paraview in order
# to view the visualization files
try:
    from scikits import delaunay
except:
    print "Must install scikits.delaunay to generate the visualization files (.vtu for paraview)."
# generate visualization files    
print "\n\n*************************************************************"
print "*************************************************************"
print "Generating visualization files in .vtu format for use with Paraview."
print "\nAll values from coarse levels are interpolated using the aggregates,\n" +\
      "i.e., there is no fixed geometric hierarchy.  Additionally, the mesh\n" +\
      "has been artificially shrunk towards each element's barycenter, in order\n" +\
      "to highlight the discontinuous nature of the discretization.\n"
print "-- Near null-space mode from level * is in the file\n"+\
      "   DG_Example_B_variable0_lvl*.vtu"
print "-- Aggregtes from level * are in the two file\n"+\
      "   DG_Example_aggs_lvl*_point-aggs,  and \n"+\
      "   DG_Example_aggs_lvl*_aggs.vtu"
print "-- The mesh from from level * is in the file\n"+\
      "   DG_Example_mesh_lvl*.vtu"
print "-- The error is in file\n"+\
      "   DG_Example_error_variable0.vtu"
print ""
from my_vis import shrink_elmts, my_vis
elements2,vertices2 =  shrink_elmts(elements, vertices)
my_vis(sa, vertices2, error=x, fname="DG_Example_", E2V=elements2[:,0:3])





"""

Test the convergence of a small diffusion problem discretized with the local
discontinuous Galerkin method.  The polynomial order is 5.  To utilize the
visualization capabilities, you need to have Paraview and scikits.delaunay
installed.

References
----------
[1] <NAME> and <NAME>.  Smoothed Aggregation Multigrid Solvers for
High-Order Discontinuous Galerkin Methods.  Journal of Computational Physics.
Submitted 2010. 

"""
import numpy
import scipy

from pyamg.gallery import load_example
from pyamg import smoothed_aggregation_solver

from convergence_tools import print_cycle_history

if __name__ == '__main__':

    print "\nDiffusion problem discretized with p=5 and the local\n" + \
          "discontinuous Galerkin method."

    # Discontinuous Galerkin Diffusion Problem
    data = load_example('local_disc_galerkin_diffusion')
    A = data['A'].tocsr()
    B = data['B']
    elements = data['elements']
    vertices = data['vertices']
    numpy.random.seed(625)
    x0 = scipy.rand(A.shape[0])
    b = numpy.zeros_like(x0)
    
    ##
    # For demonstration, show that a naive SA solver 
    # yields unsatisfactory convergence
    smooth=('jacobi', {'filter' : True})
    strength=('symmetric', {'theta' : 0.1})
    SA_solve_args={'cycle':'W', 'maxiter':20, 'tol':1e-8, 'accel' : 'cg'}
    SA_build_args={'max_levels':10, 'max_coarse':25, 'coarse_solver':'pinv2', \
            'symmetry':'hermitian', 'keep':True}
    presmoother =('gauss_seidel', {'sweep':'symmetric', 'iterations':1})
    postsmoother=('gauss_seidel', {'sweep':'symmetric', 'iterations':1})
    
    ##
    # Construct solver and solve
    sa = smoothed_aggregation_solver(A, B=B, smooth=smooth, \
             strength=strength, presmoother=presmoother, \
             postsmoother=postsmoother, **SA_build_args)
    resvec = []
    x = sa.solve(b, x0=x0, residuals=resvec, **SA_solve_args)
    print "\n*************************************************************"
    print "*************************************************************"
    print "Observe that standard SA parameters for this p=5 discontinuous \n" + \
          "Galerkin system yield an inefficient solver.\n"
    print_cycle_history(resvec, sa, verbose=True, plotting=False)

    ##
    # Now, construct and solve with appropriate parameters 
    p = 5
    Bimprove = [('block_gauss_seidel', {'sweep':'symmetric', 'iterations':p}),
                ('gauss_seidel', {'sweep':'symmetric', 'iterations':p})]   
    aggregate = ['naive', 'standard']
    # the initial conforming aggregation step requires no prolongation smoothing
    smooth=[None, ('energy', {'krylov' : 'cg', 'maxiter' : p})]
    strength =[('distance', {'V' : data['vertices'], 'theta':5e-5, 'relative_drop':False}),\
               ('evolution', {'k':4, 'proj_type':'l2', 'epsilon':2.0})]
    sa = smoothed_aggregation_solver(A, B=B, smooth=smooth, Bimprove=Bimprove,\
             strength=strength, presmoother=presmoother, aggregate=aggregate,\
             postsmoother=postsmoother, **SA_build_args)
    resvec = []
    x = sa.solve(b, x0=x0, residuals=resvec, **SA_solve_args)
    print "\n*************************************************************"
    print "*************************************************************"
    print "Now use appropriate parameters, especially \'energy\' prolongation\n" + \
          "smoothing and a distance based strength measure on level 0.  This\n" + \
          "yields a much more efficient solver.\n"
    print_cycle_history(resvec, sa, verbose=True, plotting=False)


##
# check for scikits and print message about needing to have paraview in order
# to view the visualization files
try:
    from scikits import delaunay
except:
    print "Must install scikits.delaunay to generate the visualization files (.vtu for paraview)."
# generate visualization files    
print "\n\n*************************************************************"
print "*************************************************************"
print "Generating visualization files in .vtu format for use with Paraview."
print "\nAll values from coarse levels are interpolated using the aggregates,\n" +\
      "i.e., there is no fixed geometric hierarchy.  Additionally, the mesh\n" +\
      "has been artificially shrunk towards each element's barycenter, in order\n" +\
      "to highlight the discontinuous nature of the discretization.\n"
print "-- Near null-space mode from level * is in the file\n"+\
      "   DG_Example_B_variable0_lvl*.vtu"
print "-- Aggregtes from level * are in the two file\n"+\
      "   DG_Example_aggs_lvl*_point-aggs,  and \n"+\
      "   DG_Example_aggs_lvl*_aggs.vtu"
print "-- The mesh from from level * is in the file\n"+\
      "   DG_Example_mesh_lvl*.vtu"
print "-- The error is in file\n"+\
      "   DG_Example_error_variable0.vtu"
print ""
from my_vis import shrink_elmts, my_vis
elements2,vertices2 =  shrink_elmts(elements, vertices)
my_vis(sa, vertices2, error=x, fname="DG_Example_", E2V=elements2[:,0:3])





Test the convergence of a small diffusion problem discretized with the local discontinuous Galerkin method.  The polynomial order is 5.  To utilize the visualization capabilities, you need to have Paraview and scikits.delaunay installed.  References ---------- [1] <NAME> and <NAME>.  Smoothed Aggregation Multigrid Solvers for High-Order Discontinuous Galerkin Methods.  Journal of Computational Physics. Submitted 2010. # Discontinuous Galerkin Diffusion Problem ## # For demonstration, show that a naive SA solver # yields unsatisfactory convergence ## # Construct solver and solve ## # Now, construct and solve with appropriate parameters # the initial conforming aggregation step requires no prolongation smoothing ## # check for scikits and print message about needing to have paraview in order # to view the visualization files # generate visualization files