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_isotropic_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 ) ) #test_pts = numpy.vstack( ( numpy.zeros( (1, 3 ) ), numpy.linspace( -1., 1., 3 ).reshape(1,3) ) ) x = test_pts test_vals = m.evaluate_set( test_pts ) max_levels = range( 5, 9 ) #max_levels = range( 1, 9 ) num_pts = [145,321,705,1537,3329,7169] 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() assert sg.num_points() == num_pts[i] assert numpy.allclose( test_vals, sg.evaluate_set( test_pts ) ) sg.clear() num_dims = 5 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,-1.,1,-1.,1,-1.,1.], numpy.double ) sg = GeneralisedSparseGrid() test_pts = rng.uniform( -1., 1., ( num_dims, 100) ) test_vals = m.evaluate_set( test_pts ) max_levels = range( 1, 6 ) num_pts = [11,61,241,801,2433] 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() assert sg.num_points() == num_pts[i] if ( max_level > 3 ): assert numpy.allclose( test_vals, sg.evaluate_set( test_pts ) ) sg.clear() num_dims = 2 quadrature_rule_1d = GaussPattersonQuadRule1D() 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, 6 ) num_pts = [5, 17, 49, 129, 321, 769] 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() assert sg.num_points() == num_pts[i] if ( max_level > 2 ): assert numpy.allclose( test_vals, sg.evaluate_set( test_pts ) ) sg.clear()