def test_genseralised_sparse_grid_aposteriori_error_based_refinement( self ):
from sparse_grid_cpp import AposterioriGeneralisedSparseGrid
num_dims = 1
quadrature_rule_1d = ClenshawCurtisQuadRule1D()
basis = LagrangePolynomialBasis()
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
m = AdjointModel()
print 'Initialised model'
forward_solution_num_DOF, adjoint_solution_num_DOF = m.get_num_dof()
print 'forward ndof: %d\n adjoint ndof: %d' %(forward_solution_num_DOF,
adjoint_solution_num_DOF)
domain = numpy.array( [-1.,1.], numpy.double )
sg = AposterioriGeneralisedSparseGrid()
sg.tolerance( 0.0 )
sg.max_num_points( 40 )
sg.max_level( 10 )
sg.forward_solution_num_DOF( int( forward_solution_num_DOF ) )
sg.adjoint_solution_num_DOF( int( adjoint_solution_num_DOF ) )
from utilities.visualisation import plot_surface_from_function
sg.initialise( m, domain, tpqr, 0 )
sg.build()
print 'sparse grid built successfully'
# need to set this before evaluate is called or
# quantities_of_interest will be whatever internal sg routines
# 3 have set it as. todo move this to the end of build
sg.quantities_of_interest( numpy.array( [0], numpy.int32 ) )
evaluate_enhanced_sparse_grid = lambda x: (sg.evaluate_set( x ) + \
sg.compute_error_estimates( x ) ).squeeze()
grid = sg.get_coordinates()
rng = numpy.random.RandomState( 0 )
test_pts = rng.uniform( -1., 1., ( num_dims, 1000 ) )
test_vals = m.evaluate_set( test_pts )[:,0]
sg_error = numpy.linalg.norm( test_vals -
sg.evaluate_set( test_pts ).squeeze() )
print 'done1'
print 'sparse grid error: ', sg_error
assert sg_error < 4e-10
enhanced_sg_error = numpy.linalg.norm( test_vals -
evaluate_enhanced_sparse_grid( test_pts ) )
print 'enhanced sparse grid error: ', enhanced_sg_error
assert enhanced_sg_error < 8e-15
print 'done'
num_dims = 2
quadrature_rule_1d = ClenshawCurtisQuadRule1D()
basis = LagrangePolynomialBasis()
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
m = AdjointModel()
print 'Initialised model'
forward_solution_num_DOF, adjoint_solution_num_DOF = m.get_num_dof()
print 'forward ndof: %d\n adjoint ndof: %d' %(forward_solution_num_DOF,
adjoint_solution_num_DOF)
domain = numpy.array( [-1.,1.,0.4,0.8], numpy.double )
sg = AposterioriGeneralisedSparseGrid()
sg.tolerance( 0.0 )
sg.max_num_points( 1000 )
sg.max_level( 10 )
sg.forward_solution_num_DOF( int( forward_solution_num_DOF ) )
sg.adjoint_solution_num_DOF( int( adjoint_solution_num_DOF ) )
from utilities.visualisation import plot_surface_from_function
sg.initialise( m, domain, tpqr, 0 )
sg.build()
print 'sparse grid built successfully'
# need to set this before evaluate is called or
# quantities_of_interest will be whatever internal sg routines
# 3 have set it as. todo move this to the end of build
sg.quantities_of_interest( numpy.array( [0], numpy.int32 ) )
evaluate_enhanced_sparse_grid = lambda x: (sg.evaluate_set( x ) + \
sg.compute_error_estimates( x ) ).squeeze()
grid = sg.get_coordinates()
rng = numpy.random.RandomState( 0 )
test_pts = rng.uniform( 0., 1., ( num_dims, 1000 ) )
from utilities.math_utils import map_from_unit_hypercube
test_pts = map_from_unit_hypercube( test_pts, domain )
test_vals = m.evaluate_set( test_pts )[:,0]
print test_pts.max(axis=1), test_pts.min(axis=1)
sg_error = numpy.linalg.norm( test_vals -
sg.evaluate_set( test_pts ).squeeze() )
print 'sparse grid error: ', sg_error
assert sg_error < 4e-10
enhanced_sg_error = numpy.linalg.norm( test_vals -
evaluate_enhanced_sparse_grid( test_pts ) )
print 'enhanced sparse grid error: ', enhanced_sg_error
assert enhanced_sg_error < 8e-15
#plot_surface_from_function( m.evaluate_set, domain, 100 )
import pylab
import mpl_toolkits.mplot3d.axes3d as p3
fig = pylab.figure( 1 )
ax = p3.Axes3D( fig )
grid = sg.get_coordinates()
fv = sg.get_function_values()
ax.scatter3D( grid[0,:], grid[1,:], fv[0,:] )
def generalised_sparse_grid_aposteriori_error_based_refinement():
num_dims = 2
quadrature_rule_1d = ClenshawCurtisQuadRule1D()
basis = LagrangePolynomialBasis()
tpqr = get_tensor_product_quadrature_rule_single(num_dims, quadrature_rule_1d, basis)
path = "/home/jdjakem/software/matlab/packages/" + "a-posteriori-error-estimation/work_stochastic/"
# last / is needed if path called from c code directly
# path = ''
# initiate model and run in the background
# os.system( 'python adjoint_file_model.py &' )
# m = CppAdjointFileModel( path )
m = AdjointMatlabModel()
m.add_matlab_paths(["/home/jdjakem/software/matlab/packages/" + "a-posteriori-error-estimation/ACES/", path])
# path needs to be specified last so that sample_input.m is the one
# in path and not one in the directores added earlier
m.initialise()
print "Initialised model"
forward_solution_num_DOF, adjoint_solution_num_DOF = m.get_num_dof()
print "forward ndof: %d\n adjoint ndof: %d" % (forward_solution_num_DOF, adjoint_solution_num_DOF)
domain = numpy.array([0.0, 1.0, 0.0, 1], numpy.double)
sg = AposterioriGeneralisedSparseGrid()
# todo this should be set automatically by model. Then can replace
# pt.getDegreesOfFreedom by grid.num_qoi()
# sg.quantities_of_interest( numpy.arange( forward_solution_num_DOF +
# adjoint_solution_num_DOF + num_dims + 2,
# dtype = numpy.int32 ) )
sg.tolerance(0.0)
sg.max_num_points(4000)
sg.max_level(20)
sg.forward_solution_num_DOF(int(forward_solution_num_DOF))
sg.adjoint_solution_num_DOF(int(adjoint_solution_num_DOF))
from utilities.visualisation import plot_surface_from_function
sg.initialise(m, domain, tpqr, 0)
sg.build()
print "sparse grid built successfully"
print "sparse grid has ", sg.num_points(), " points"
# need to set this before evaluate is called or
# quantities_of_interest will be whatever internal sg routines
# 3 have set it as. todo move this to the end of build
sg.quantities_of_interest(numpy.array([0], numpy.int32))
evaluate_enhanced_sparse_grid = lambda x: (sg.evaluate_set(x) + sg.compute_error_estimates(x)).squeeze()
grid = sg.get_coordinates()
rng = numpy.random.RandomState(0)
test_pts = rng.uniform(0.0, 1.0, (num_dims, 100))
test_vals = m.evaluate_set(test_pts)[:, 0]
print "sparse grid error: ", numpy.linalg.norm(test_vals - sg.evaluate_set(test_pts).squeeze()) / numpy.sqrt(
test_pts.shape[1]
)
print "enhanced sparse grid error: ", numpy.linalg.norm(
test_vals - evaluate_enhanced_sparse_grid(test_pts)
) / numpy.sqrt(test_pts.shape[1])
# plot_surface_from_function( evaluate_enhanced_sparse_grid, domain, 30 )
# m.terminate()
# plot_surface_from_function( sg.evaluate_set, domain, 30 )
import pylab
pylab.plot(grid[0, :], grid[1, :], "o")
pylab.xlim([0, 1])
pylab.ylim([0, 1])
pylab.show()