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()
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 build_sparse_grid_cpp( quadrature_rule_1d, basis, domain, f,
num_dims, max_level, max_num_points,
tolerance = 0., test_pts = None,
test_vals = None, breaks = None ):
tpqr = get_tensor_product_quadrature_rule_single( num_dims,
quadrature_rule_1d,
basis )
sg = GeneralisedSparseGrid()
sg.quantities_of_interest( numpy.array( [0], dtype = numpy.int32 ) )
sg.tolerance( 0.0 )
sg.max_num_points( max_num_points )
sg.max_level( max_level )
break_cnt = 0
if breaks is None:
breaks = numpy.logspace( 1, numpy.log10( max_num_points ), 10 )
if test_pts is not None and test_vals is None:
test_vals = f( test_pts ).squeeze()
error = []
num_pts = []
sg.initialise( f, domain, tpqr, 0 )
#sg.build()
sg.initialise_build();
while ( True ):
sg.prioritise();
if ( not sg.grid_warrants_refinement() ): break;
sg.refine();
if ( test_pts is not None and break_cnt < breaks.shape[0] and sg.num_points() > breaks[break_cnt] ):
pred_vals = sg.evaluate_set( test_pts ).squeeze()
l2_error = get_l2_error( test_vals, pred_vals )
error.append( l2_error )
num_pts.append( sg.num_points() )
#print 'e', error
#print 'n', sg.num_points()
break_cnt += 1
tmp = SubSpaceVector()
sg.get_subspaces( tmp )
if ( test_pts is not None ):
pred_vals = sg.evaluate_set( test_pts ).squeeze()
l2_error = get_l2_error( test_vals, pred_vals )
error.append( l2_error )
num_pts.append( sg.num_points() )
return sg, numpy.asarray( error ), numpy.asarray( num_pts )