def xtest_isotropic_adaptive_sparse_grid( self ):
f = lambda x: numpy.sum( x**2+1, axis = 0 )
m = CppModel( f )
num_dims = 2
quadrature_rule_1d = ClosedEquidistantQuadRule1D()
basis = ClosedPiecewisePolynomialBasis()
basis.degree( 2 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 5, 11 )
num_pts = [145,321,705,1537,3329,7169]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 1 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 3
quadrature_rule_1d = ClosedEquidistantQuadRule1D()
basis = ClosedPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1,-1.,1.], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 8 )
num_pts = [7,25,69,177,441,1073,2561]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 1 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 4
quadrature_rule_1d = ClosedEquidistantQuadRule1D()
basis = ClosedPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1,-1.,1.,-1.,1.], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 7 )
num_pts = [9,41,137,401,1105,2929]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 1 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 5
quadrature_rule_1d = ClosedEquidistantQuadRule1D()
basis = ClosedPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1,-1.,1.,-1.,1.,-1.,1.], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 6 )
num_pts = [11,61,241,801,2433]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 1 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 2
quadrature_rule_1d = OpenEquidistantQuadRule1D()
basis = OpenPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 6 )
num_pts = [5,17,49,129,321,769]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 0 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 6
quadrature_rule_1d = OpenEquidistantQuadRule1D()
basis = OpenPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1,-1.,1.,-1.,1.,-1.,1.,-1.,1.],
numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 5 )
num_pts = [13,97,545,2561]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 0 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
num_dims = 10
quadrature_rule_1d = OpenEquidistantQuadRule1D()
basis = OpenPiecewisePolynomialBasis()
basis.degree( 1 )
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance( 0.0 )
domain = numpy.array( [-1.,1,-1.,1,-1.,1.,-1.,1.,-1.,1.,
-1.,1,-1.,1,-1.,1.,-1.,1.,-1.,1.], numpy.double )
sg = AdaptiveSparseGrid()
max_levels = range( 1, 4 )
num_pts = [21,241,2001]
for i, max_level in enumerate( max_levels ):
refinement_manager.maxLevel( max_level )
sg.initialise( m, domain, tpqr, refinement_manager, 0 )
sg.build()
assert sg.num_points() == num_pts[i]
sg.clear()
def adaptive_sparse_grid_aposteriori_error_based_refinement():
num_dims = 2
quadrature_rule_1d = ClosedEquidistantQuadRule1D()
basis = ClosedPiecewisePolynomialBasis()
basis.degree(1)
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 = MatlabModel()
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.capture_matlab_buffer( 100 )
m.initialise()
# m.print_matlab_buffer()
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)
# refinement_manager = AposterioriErrorRefinementManager()
# refinement_manager.path( path );
# refinement_manager.forward_solution_num_DOF( int(forward_solution_num_DOF) )
# refinement_manager.adjoint_solution_num_DOF( int(adjoint_solution_num_DOF) )
refinement_manager = HierarchicalSurplusRefinementManager()
refinement_manager.tolerance(0.0)
refinement_manager.maxPoints(2000)
refinement_manager.maxLevel(20)
domain = numpy.array([0.0, 1.0, 0.0, 1], numpy.double)
sg = AdaptiveSparseGrid()
from utilities.visualisation import plot_surface_from_function
sg.initialise(m, domain, tpqr, refinement_manager, 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 ) + \
# refinement_manager.compute_error_estimates( x, sg, m )).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()
from sparse_grid_cpp import AposterioriGeneralisedSparseGrid