def test_least_interpolant_generalised_sparse_grid( self ):
def f( x ):
if ( x.ndim == 1) :
x = x.reshape( x.shape[0], 1 )
assert x.shape[0] > 1
y = numpy.sum( x**10+1, axis = 0 ) + \
numpy.sum( x[1:,:]**2 * x[:-1,:], axis = 0 )
if y.shape[0] == 1: return numpy.array( y[0] )
else: return y
m = CppModel( f )
rng = numpy.random.RandomState( 0 )
num_dims = 2
quadrature_rule_1d = ClenshawCurtisQuadRule1D()
basis = LagrangePolynomialBasis()
tpqr = self.get_tensor_product_quadrature_rule_single(num_dims,
quadrature_rule_1d,
basis )
tol = 0.
domain = numpy.array( [-1.,1,-1.,1], numpy.double )
sg = GeneralisedSparseGrid()
test_pts = rng.uniform( -1., 1., ( num_dims, 100 ) )
x = test_pts
test_vals = m.evaluate_set( test_pts )
max_levels = range( 1, 8 )
for i, max_level in enumerate( max_levels ):
sg.max_num_points( numpy.iinfo( numpy.int32 ).max )
sg.tolerance( tol )
sg.max_level( max_level )
sg.initialise_default( m, domain, tpqr )
sg.build()
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]
sg_error = numpy.linalg.norm( test_vals -
sg.evaluate_set( test_pts ).squeeze() )
#print 'sparse grid error: ', sg_error
#print 'num sparse grid points: ', sg.num_points()
poly_1d = [ LegendrePolynomial1D() ]
basis = TensorProductBasis( num_dims, poly_1d )
domain_py = TensorProductDomain( num_dims, [[-1,1]] )
pce = convert_sparse_grid_to_pce( sg, basis, domain_py )
pce_error = numpy.linalg.norm( test_vals -
pce.evaluate_set( test_pts ).squeeze() )
#print 'pce error: ', pce_error
assert numpy.allclose( pce_error, sg_error )
sg.clear()
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,:] )
