for i in range(10): f = basis.build(i) print('i=', i, 'f(X)=', f(x)) # Using multi-indices enum = basis.getEnumerateFunction() for i in range(10): indices = enum(i) f = basis.build(indices) print('indices=', indices, 'f(X)=', f(x)) # Other factories factoryCollection = [ ot.OrthogonalUniVariatePolynomialFunctionFactory(ot.LaguerreFactory(2.5)), ot.HaarWaveletFactory(), ot.FourierSeriesFactory() ] dim = len(factoryCollection) basisFactory = ot.OrthogonalProductFunctionFactory(factoryCollection) basis = ot.OrthogonalBasis(basisFactory) print('basis=', basis) x = [0.5] * dim for i in range(10): f = basis.build(i) print('i=', i, 'f(X)=', f(x)) # Using multi-indices enum = basis.getEnumerateFunction() for i in range(10): indices = enum(i) f = basis.build(indices)
# Create a GeneralLinearModelResult generalizedLinearModelResult = ot.GeneralLinearModelResult() generalizedLinearModelResult.setName('generalizedLinearModelResult') myStudy.add('generalizedLinearModelResult', generalizedLinearModelResult) # KDTree sample = ot.Normal(3).getSample(10) kDTree = ot.KDTree(sample) myStudy.add('kDTree', kDTree) # TensorApproximationAlgorithm/Result dim = 1 model = ot.SymbolicFunction(['x'], ['x*sin(x)']) distribution = ot.ComposedDistribution([ot.Uniform()] * dim) factoryCollection = [ot.FourierSeriesFactory()] * dim functionFactory = ot.OrthogonalProductFunctionFactory(factoryCollection) size = 10 X = distribution.getSample(size) Y = model(X) nk = [5] * dim rank = 1 algo = ot.TensorApproximationAlgorithm(X, Y, distribution, functionFactory, nk, rank) algo.run() tensorResult = algo.getResult() myStudy.add('tensorResult', tensorResult) tensorIn = [0.4] tensorRef = tensorResult.getMetaModel()(tensorIn) # Distribution parameters
x = [0.5] * dim for i in range(10): f = basis.build(i) print('i=', i, 'f(X)=', f(x)) # Using multi-indices enum = basis.getEnumerateFunction() for i in range(10): indices = enum(i) f = basis.build(indices) print('indices=', indices, 'f(X)=', f(x)) # Other factories factoryCollection = [ot.OrthogonalUniVariatePolynomialFunctionFactory( ot.LaguerreFactory(2.5)), ot.HaarWaveletFactory(), ot.FourierSeriesFactory()] dim = len(factoryCollection) basisFactory = ot.OrthogonalProductFunctionFactory(factoryCollection) basis = ot.OrthogonalBasis(basisFactory) print('basis=', basis) x = [0.5] * dim for i in range(10): f = basis.build(i) print('i=', i, 'f(X)=', f(x)) # Using multi-indices enum = basis.getEnumerateFunction() for i in range(10): indices = enum(i) f = basis.build(indices) print('indices=', indices, 'f(X)=', f(x))
import openturns as ot from matplotlib import pyplot as plt from openturns.viewer import View from math import sqrt domain = ot.Interval(-1.0, 1.0) basis = ot.OrthogonalProductFunctionFactory([ot.FourierSeriesFactory()]) basisSize = 10 experiment = ot.GaussProductExperiment(basis.getMeasure(), [20]) mustScale = False threshold = 0.001 model = ot.AbsoluteExponential([1.0]) algo = ot.KarhunenLoeveQuadratureAlgorithm(domain, domain, model, experiment, basis, basisSize, mustScale, threshold) algo.run() ev = algo.getResult().getEigenValues() functions = algo.getResult().getScaledModes() g = ot.Graph() g.setXTitle("$t$") g.setYTitle("$\sqrt{\lambda_n}\phi_n$") for i in range(functions.getSize()): g.add(functions.build(i).draw(-1.0, 1.0, 256)) g.setColors(ot.Drawable.BuildDefaultPalette(functions.getSize())) fig = plt.figure(figsize=(6, 4)) plt.suptitle("Quadrature approx. of KL expansion for $C(s,t)=e^{-|s-t|}$") axis = fig.add_subplot(111) axis.set_xlim(auto=True) View(g, figure=fig, axes=[axis], add_legend=False)
import openturns as ot import numpy as np from matplotlib import pyplot as plt n_functions = 8 function_factory = ot.FourierSeriesFactory() if function_factory.getClassName() == 'KrawtchoukFactory': function_factory = ot.FourierSeriesFactory(n_functions, .5) functions = [function_factory.build(i) for i in range(n_functions)] measure = function_factory.getMeasure() if hasattr(measure, 'getA') and hasattr(measure, 'getB'): x_min = measure.getA() x_max = measure.getB() else: x_min = measure.computeQuantile(1e-3)[0] x_max = measure.computeQuantile(1. - 1e-3)[0] n_points = 200 meshed_support = np.linspace(x_min, x_max, n_points) fig = plt.figure() ax = fig.add_subplot(111) for i in range(n_functions): plt.plot(meshed_support, [functions[i](x) for x in meshed_support], lw=1.5, label='$\phi_{' + str(i) + '}(x)$') plt.xlabel('$x$') plt.ylabel('$\phi_i(x)$') plt.xlim(x_min, x_max) plt.grid() box = ax.get_position() ax.set_position([box.x0, box.y0, box.width, box.height * 0.9]) plt.legend(loc='upper center', bbox_to_anchor=(.5, 1.25), ncol=4)