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
#
# %%
factoryCollection = [
ot.OrthogonalUniVariatePolynomialFunctionFactory(
ot.StandardDistributionPolynomialFactory(_)) for _ in [E, F, L, I]
]
functionFactory = ot.OrthogonalProductFunctionFactory(factoryCollection)
nk = [4, 15, 3, 2]
maxRank = 1
# %%
# Finally we might launch the algorithm:
# %%
algo = ot.TensorApproximationAlgorithm(X_train, Y_train, myDistribution,
functionFactory, nk, maxRank)
algo.run()
result = algo.getResult()
metamodel = result.getMetaModel()
# %%
# The `run` method has optimized the hyperparameters of the metamodel (:math:`\beta` coefficients).
#
# We can then print the coefficients which have been estimated using a double loop.
# %%
tensor = result.getTensor()
for j in range(myDistribution.getDimension()):
print("j =", j)
for i in range(maxRank):
for k in range(nk[j]):
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
# ArcsineMuSigma parameter ave
ams_parameters = ot.ArcsineMuSigma(8.4, 2.25)
myStudy.add('ams_parameters', ams_parameters)
# BetaMuSigma parameter save
bms_parameters = ot.BetaMuSigma(0.2, 0.6, -1, 2)
myStudy.add('bms_parameters', bms_parameters)
# GammaMuSigma parameter save
dim = 1
f = ot.SymbolicFunction(['x'], ['x*sin(x)'])
uniform = ot.Uniform(0.0, 10.0)
distribution = ot.ComposedDistribution([uniform] * dim)
factoryCollection = [
ot.OrthogonalUniVariateFunctionFamily(
ot.OrthogonalUniVariatePolynomialFunctionFactory(
ot.StandardDistributionPolynomialFactory(uniform)))
] * dim
functionFactory = ot.OrthogonalProductFunctionFactory(factoryCollection)
size = 10
sampleX = [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0], [7.0], [8.0]]
sampleY = f(sampleX)
nk = [5] * dim
maxRank = 1
algo = ot.TensorApproximationAlgorithm(sampleX, sampleY, distribution,
functionFactory, nk, maxRank)
algo.run()
result = algo.getResult()
metamodel = result.getMetaModel()
graph = f.draw(0.0, 10.0)
graph.add(metamodel.draw(0.0, 10.0))
graph.add(ot.Cloud(sampleX, sampleY))
graph.setColors(['blue', 'red', 'black'])
graph.setLegends(['model', 'meta model', 'sample'])
graph.setLegendPosition('topleft')
graph.setTitle('y(x)=x*sin(x)')
graph.setYTitle('y')
View(graph, figure_kw={'figsize': (8, 4)})
