def test_least_interpolant( self ):
num_dims = 2
func_domain = TensorProductDomain( num_dims, [[-1,1]] )
x = -numpy.cos( numpy.linspace( 0., 1., 10 ) * numpy.pi );
[X,Y] = numpy.meshgrid( x, x )
build_points = numpy.vstack( ( X.reshape(( 1,X.shape[0]*X.shape[1])),
Y.reshape(( 1, Y.shape[0]*Y.shape[1]))))
build_values = matlab_peaks( build_points )
poly_1d = [ LegendrePolynomial1D() ]
basis = TensorProductBasis( num_dims, poly_1d )
linear_solver = LeastInterpolation()
predictor = PCE( build_points.shape[0], basis = basis,
linear_solver = linear_solver )
predictor.function_domain( func_domain )
predictor.build( build_points, build_values )
result = predictor.evaluate_set( build_points )
if ( result.ndim > 1 ): result = result.reshape( result.shape[0] )
error = result - build_values
l2_error = numpy.sqrt( numpy.dot( error.T, error ) / \
build_points.shape[1] )
print 'error at nodes: %1.15e' %l2_error
assert l2_error < self.eps
poly_1d = [ JacobiPolynomial1D( 0.5, 0.5 ) ]
basis = TensorProductBasis( num_dims, poly_1d )
linear_solver = LeastInterpolation()
predictor = PCE( build_points.shape[0], basis = basis,
linear_solver = linear_solver )
predictor.function_domain( func_domain )
predictor.build( build_points, build_values )
result = predictor.evaluate_set( build_points )
if ( result.ndim > 1 ): result = result.reshape( result.shape[0] )
num_dims = 2
poly_1d = [ LegendrePolynomial1D() ]
basis = TensorProductBasis( num_dims, poly_1d )
domain = TensorProductDomain( num_dims, ranges = [[-1.,1.]] )
#linear_solver = LARSSolver( solver = CSSolvers.LASSO_REGRESSION )
linear_solver = LARSSolver( solver = CSSolvers.LEAST_ANGLE_REGRESSION )
#linear_solver = OMPSolver()
#linear_solver = LeastSquaresSolver()
pce = PolynomialChaosExpansion( num_dims, basis, order, domain,
linear_solver = linear_solver )
print pce.num_terms
f = lambda x: numpy.sum( x**5, axis = 0 )
# f = lambda x: numpy.sum( 1/2.*(3*x**2-1.), axis = 0 )
from examples.test_functions import matlab_peaks
f = lambda x: matlab_peaks( x )
#rng = numpy.random
seed = 0
rng = numpy.random.RandomState( seed )
build_pts = rng.uniform( -1, 1, ( 2, 1000 ) )
build_vals = f( build_pts )
from utilities.math_utils import nchoosek
pce.build( build_pts, build_vals )
test_pts = rng.uniform( -1, 1, ( 2, 10000 ) )
test_vals = f( test_pts )
print numpy.linalg.norm( test_vals - pce.evaluate_set( test_pts ) ) / numpy.sqrt( test_pts.shape[1] )
me, te, ie = pce.get_sensitivities()
