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)
