def fit(self, X, y, **fit_params):
input_dimension = X.shape[1]
if self.distribution is None:
self.distribution = BuildDistribution(X)
factoryCollection = [ot.OrthogonalUniVariateFunctionFamily( ot.OrthogonalUniVariatePolynomialFunctionFactory(ot.StandardDistributionPolynomialFactory(self.distribution.getMarginal(i)))) for i in range(input_dimension)]
functionFactory = ot.OrthogonalProductFunctionFactory(factoryCollection)
algo = ot.TensorApproximationAlgorithm(X, y.reshape(-1, 1), self.distribution, functionFactory, [self.nk]*input_dimension, self.max_rank)
algo.run()
self._result = algo.getResult()
return self
def fit(self, X, y, **fit_params):
"""Fit Tensor regression model.
Parameters
----------
X : array-like, shape = (n_samples, n_features)
Training data.
y : array-like, shape = (n_samples, [n_output_dims])
Target values.
Returns
-------
self : returns an instance of self.
"""
if len(X) == 0:
raise ValueError(
"Can not perform a tensor approximation with empty sample")
# check data type is accurate
if (len(np.shape(X)) != 2):
raise ValueError("X has incorrect shape.")
input_dimension = len(X[1])
if (len(np.shape(y)) != 2):
raise ValueError("y has incorrect shape.")
if self.distribution is None:
self.distribution = BuildDistribution(X)
factoryCollection = [
ot.OrthogonalUniVariateFunctionFamily(
ot.OrthogonalUniVariatePolynomialFunctionFactory(
ot.StandardDistributionPolynomialFactory(
self.distribution.getMarginal(i))))
for i in range(input_dimension)
]
functionFactory = ot.OrthogonalProductFunctionFactory(
factoryCollection)
algo = ot.TensorApproximationAlgorithm(X, y, self.distribution,
functionFactory,
[self.nk] * input_dimension,
self.max_rank)
algo.run()
self.result_ = algo.getResult()
return self
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)
