def set_mean(self, mean):
'''
This function constructs the mean function
takes the following argument:
-> mean_type
'''
if mean.mean_type == 'Linear':
self.mean_function = ot.LinearBasisFactory(self.input_dim).build()
elif mean.mean_type == 'Constant':
self.mean_function = ot.ConstantBasisFactory(
self.input_dim).build()
elif mean.mean_type == 'Quadratic':
self.mean_function = ot.QuadraticBasisFactory(
self.input_dim).build()
elif mean.mean_type == 'Zero':
self.mean_function = ot.Basis()
else:
self.mean_function = "This library does not support the specified mean function"
# equal to # # .. math:: # dim = 4 # # # in the cantilever beam case. # # We observe that the number of coefficients in the trend is 5, which corresponds to: # # * 1 coefficient for the constant part, # * dim=4 coefficients for the linear part. # %% covarianceModel.setScale(X_train.getMax()) basis = ot.QuadraticBasisFactory(dimension).build() algo = ot.KrigingAlgorithm(X_train, Y_train, covarianceModel, basis) algo.setOptimizationBounds(scaleOptimizationBounds) algo.run() result = algo.getResult() krigingWithQuadraticTrend = result.getMetaModel() result.getTrendCoefficients() print(algo.getOptimizationBounds()) print(result.getCovarianceModel()) # %% # This time, the trend has 15 coefficients: # # * 1 coefficient for the constant part, # * 4 coefficients for the linear part, # * 10 coefficients for the quadratic part.
# Set precision
ot.PlatformInfo.SetNumericalPrecision(3)
# Calibration of default optimizer
ot.ResourceMap.SetAsScalar(
'GeneralLinearModelAlgorithm-DefaultOptimizationLowerBound', 1.0e-5)
ot.ResourceMap.SetAsScalar(
'GeneralLinearModelAlgorithm-DefaultOptimizationUpperBound', 100)
# Data & estimation
inputDimension = 1
X = ot.Normal().getSample(100)
X = X.sortAccordingToAComponent(0)
covarianceModel = ot.SquaredExponential([1.0], [1.0])
model = ot.SymbolicFunction(["x"], ["x - 0.6 * cos(x/3)"])
Y = model(X)
basis = ot.QuadraticBasisFactory(inputDimension).build()
algo = ot.GeneralLinearModelAlgorithm(X, Y, covarianceModel, basis, True)
algo.setOptimizationAlgorithm(ot.NLopt('LN_NELDERMEAD'))
algo.run()
# perform an evaluation
result = algo.getResult()
metaModel = result.getMetaModel()
conditionalCovariance = result.getCovarianceModel()
residual = metaModel(X) - Y
ott.assert_almost_equal(residual.computeCenteredMoment(2),
[1.06e-05], 1e-5, 1e-5)
ott.assert_almost_equal(conditionalCovariance.getParameter(),
[0.619144, 0.000937], 5e-3, 1e-3)
likelihood = algo.getObjectiveFunction()
assert likelihood.getInputDimension() == 1, "likelihood dim"
print("Test using NLOpt")
print("================")
# Calibration of default optimizer
ot.ResourceMap.SetAsNumericalScalar(
'GeneralizedLinearModelAlgorithm-DefaultOptimizationLowerBound',
1.0e-5)
ot.ResourceMap.SetAsNumericalScalar(
'GeneralizedLinearModelAlgorithm-DefaultOptimizationUpperBound', 100)
# Data & estimation
spatialDimension = 1
X = ot.Normal().getSample(100)
X = X.sortAccordingToAComponent(0)
covarianceModel = ot.SquaredExponential([1.0], [1.0])
model = ot.NumericalMathFunction(["x"], ["x - 0.6 * cos(x/3)"])
Y = model(X)
basis = ot.QuadraticBasisFactory(spatialDimension).build()
algo = ot.GeneralizedLinearModelAlgorithm(X, Y, covarianceModel, basis,
True)
algo.setOptimizationSolver(ot.NLopt('LN_NELDERMEAD'))
algo.run()
# perform an evaluation
result = algo.getResult()
metaModel = result.getMetaModel()
conditionalCovariance = result.getCovarianceModel()
residual = metaModel(X) - Y
assert_almost_equal(residual.computeCenteredMoment(2), [1.06e-05], 1e-5,
1e-5)
assert_almost_equal(conditionalCovariance.getParameter(),
[0.702138, 0.00137], 5e-3, 1e-3)
print("Test Ok")
print("x=", x)
factory = ot.ConstantBasisFactory(dim)
print("factory=", factory)
basis = factory.build()
print("basis=", basis)
f = ot.AggregatedFunction(basis)
y = f(x)
print("y=", y)
factory = ot.LinearBasisFactory(dim)
print("factory=", factory)
basis = factory.build()
print("basis=", basis)
f = ot.AggregatedFunction(basis)
y = f(x)
print("y=", y)
factory = ot.QuadraticBasisFactory(dim)
print("factory=", factory)
basis = factory.build()
print("basis=", basis)
f = ot.AggregatedFunction(basis)
y = f(x)
print("y=", y)
