def test_active_parameter():
# Define product of matern 1d
cov_model_1d = ot.MaternModel([0.5], 2.5)
print("1D Full parameter : ", cov_model_1d.getFullParameter())
print("1D active cov. param.: ", [cov_model_1d.getFullParameterDescription()[
i] for i in cov_model_1d.getActiveParameter()])
print("Activate nu parameter")
cov_model_1d.setActiveParameter([0, 1, 2])
print("active cov. param.: ", [cov_model_1d.getFullParameterDescription()[
i] for i in cov_model_1d.getActiveParameter()])
print("Matern d-dimensional covariance as product")
d = 3
cov_model = ot.ProductCovarianceModel([cov_model_1d]*d)
marginal0 = cov_model.getMarginal(0)
assert marginal0.getInputDimension() == d, "wrong marginal input dim"
assert marginal0.getOutputDimension() == 1, "wrong marginal output dim"
print("Full parameter : ", cov_model.getFullParameter())
print("active cov. param.: ", [cov_model.getFullParameterDescription()[
i] for i in cov_model.getActiveParameter()])
print("Disable nu for marginals 0 & 1 parameter : ",
cov_model.getFullParameter())
cov_model.setActiveParameter([0, 1, 2, 3, 6])
print("active cov. param.: ", [cov_model.getFullParameterDescription()[
i] for i in cov_model.getActiveParameter()])
print("Check that active parameter is correctly propagated")
for k in range(3):
print("Model ", k, " : active cov. param.: ", [cov_model.getCollection()[
k].getFullParameterDescription()[i] for i in cov_model.getCollection()[k].getActiveParameter()])
def test_active_amplitude_parameter():
# Define product of matern 1d
model1 = ot.MaternModel([1.0], 2.5)
print("Model 1 : ", model1.getFullParameterDescription())
print("Activate nu parameter and disable sigma2")
model1.setActiveParameter([0, 2])
print("model1 active parameter: ", [
model1.getFullParameterDescription()[i]
for i in model1.getActiveParameter()
])
model2 = ot.ExponentiallyDampedCosineModel()
print("Model 2 : ", model2.getFullParameterDescription())
print("Activate freq parameter")
model2.setActiveParameter([0, 1, 2])
print("model2 active parameter: ", [
model2.getFullParameterDescription()[i]
for i in model2.getActiveParameter()
])
print("Product covariance model")
d = 3
cov_model = ot.ProductCovarianceModel([model1, model2])
print("Full parameter : ", cov_model.getFullParameter())
print("active cov. param.: ", [
cov_model.getFullParameterDescription()[i]
for i in cov_model.getActiveParameter()
])
def _buildKrigingAlgo(self, inputSample, outputSample):
"""
Build the functional chaos algorithm without running it.
"""
if self._basis is None:
# create linear basis only for the defect parameter (1st parameter),
# constant otherwise
input = ['x' + str(i) for i in range(self._dim)]
functions = []
# constant
functions.append(ot.NumericalMathFunction(input, ['y'], ['1']))
# linear for the first parameter only
functions.append(ot.NumericalMathFunction(input, ['y'],
[input[0]]))
self._basis = ot.Basis(functions)
if self._covarianceModel is None:
# anisotropic squared exponential covariance model
covColl = ot.CovarianceModelCollection(self._dim)
for i in range(self._dim):
if LooseVersion(ot.__version__) == '1.6':
covColl[i] = ot.SquaredExponential(1, 1.)
elif LooseVersion(ot.__version__) > '1.6':
covColl[i] = ot.SquaredExponential([1], [1.])
self._covarianceModel = ot.ProductCovarianceModel(covColl)
if LooseVersion(ot.__version__) == "1.9":
algoKriging = ot.KrigingAlgorithm(inputSample, outputSample,
self._covarianceModel,
self._basis)
else:
algoKriging = ot.KrigingAlgorithm(inputSample, outputSample,
self._basis,
self._covarianceModel, True)
algoKriging.run()
return algoKriging
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.MaternModel().__class__.__name__ == 'ExponentialModel':
covarianceModel = ot.ExponentialModel([0.5], [5.0])
elif ot.MaternModel().__class__.__name__ == 'GeneralizedExponential':
covarianceModel = ot.GeneralizedExponential([2.0], [3.0], 1.5)
elif ot.MaternModel().__class__.__name__ == 'ProductCovarianceModel':
amplitude = [1.0]
scale1 = [4.0]
scale2 = [4.0]
cov1 = ot.ExponentialModel(scale1, amplitude)
cov2 = ot.ExponentialModel(scale2, amplitude)
covarianceModel = ot.ProductCovarianceModel([cov1, cov2])
elif ot.MaternModel().__class__.__name__ == 'RankMCovarianceModel':
variance = [1.0, 2.0]
basis = ot.LinearBasisFactory().build()
covarianceModel = ot.RankMCovarianceModel(variance, basis)
else:
covarianceModel = ot.MaternModel()
title = str(covarianceModel)[:100]
if covarianceModel.getInputDimension() == 1:
scale = covarianceModel.getScale()[0]
if covarianceModel.isStationary():
def f(x):
return [covarianceModel(x)[0, 0]]
func = ot.PythonFunction(1, 1, f)
func.setDescription(['$tau$', '$cov$'])
cov_graph = func.draw(-3.0 * scale, 3.0 * scale, 129)
def test_parameters_iso():
scale = []
amplitude = 1.0
extraParameter = []
# model 1
atom_ex = ot.IsotropicCovarianceModel(ot.MaternModel(), 2)
atom_ex.setScale([5])
atom_ex.setAmplitude([1.5])
scale.append(5)
amplitude *= 1.5
extraParameter.append(atom_ex.getKernel().getFullParameter()[-1])
# model2
m = ot.MaternModel()
m.setNu(2.5)
m.setScale([3])
m.setAmplitude([3])
scale.append(3)
amplitude *= 3
extraParameter.append(m.getNu())
# model 3
atom = ot.IsotropicCovarianceModel(ot.AbsoluteExponential(), 2)
atom.setScale([2])
atom.setAmplitude([2.5])
scale.append(2)
amplitude *= 2.5
model = ot.ProductCovarianceModel([atom_ex, m, atom])
ott.assert_almost_equal(model.getScale(), scale, 1e-16, 1e-16)
ott.assert_almost_equal(model.getAmplitude(), [amplitude], 1e-16, 1e-16)
ott.assert_almost_equal(model.getFullParameter(),
scale + [amplitude] + extraParameter, 1e-16, 1e-16)
# active parameter should be scale + amplitude
ott.assert_almost_equal(model.getActiveParameter(),
[0, 1, 2, 3], 1e-16, 1e-16)
# setting new parameters
extraParameter = [2.5, 0.5]
model.setFullParameter([6, 7, 8, 2] + extraParameter)
ott.assert_almost_equal(model.getCollection()[
0].getScale()[0], 6, 1e-16, 1e-16)
ott.assert_almost_equal(model.getCollection()[
1].getScale()[0], 7, 1e-16, 1e-16)
ott.assert_almost_equal(model.getCollection()[
2].getScale()[0], 8, 1e-16, 1e-16)
ott.assert_almost_equal(model.getAmplitude()[0], 2, 1e-16, 1e-16)
ott.assert_almost_equal(model.getCollection(
)[0].getFullParameter()[-1], extraParameter[0], 1e-16, 1e-16)
ott.assert_almost_equal(model.getCollection(
)[1].getFullParameter()[-1], extraParameter[1], 1e-16, 1e-16)
# checking active par setting
model.setActiveParameter([0, 1, 2, 3, 5])
ott.assert_almost_equal(model.getParameter(), [
6, 7, 8, 2, extraParameter[-1]], 1e-16, 1e-16)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
covarianceModel = ot.ProductCovarianceModel()
if covarianceModel.getSpatialDimension() == 1:
scale = covarianceModel.getScale()[0]
if covarianceModel.isStationary():
def f(x):
return [covarianceModel(x)[0, 0]]
func = ot.PythonFunction(1,1,f)
func.setDescription(['$tau$', '$cov$'])
cov_graph = func.draw(-3.0 * scale, 3.0 * scale, 129)
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(covarianceModel))
cov_axis = fig.add_subplot(111)
View(cov_graph, figure=fig, axes=[cov_axis], add_legend=False)
else:
def f(x):
return [covarianceModel([x[0]], [x[1]])[0, 0]]
func = ot.PythonFunction(2,1,f)
func.setDescription(['$s$', '$t$', '$cov$'])
cov_graph = func.draw([-3.0 * scale]*2, [3.0 * scale]*2, [129]*2)
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(covarianceModel))
cov_axis = fig.add_subplot(111)
View(cov_graph, figure=fig, axes=[cov_axis], add_legend=False)
myDefautModel = ot.DiracCovarianceModel()
print('myDefautModel = ', myDefautModel)
test_model(myDefautModel)
amplitude = [1.5 + 2.0 * k for k in range(2)]
dimension = 2
spatialCorrelation = ot.CorrelationMatrix(dimension)
for j in range(dimension):
for i in range(j + 1, dimension):
spatialCorrelation[i,
j] = (i + 1.0) / dimension - (j + 1.0) / dimension
myModel = ot.DiracCovarianceModel(inputDimension, amplitude,
spatialCorrelation)
test_model(myModel, x1=[0.5, 0.0], x2=[0.5, 0.0])
myDefautModel = ot.ProductCovarianceModel()
print('myDefautModel = ', myDefautModel)
test_model(myDefautModel)
cov1 = ot.AbsoluteExponential([2.0], [3.0])
cov2 = ot.SquaredExponential([2.0], [3.0])
myModel = ot.ProductCovarianceModel([cov1, cov2])
test_model(myModel)
# Collection ==> add covariance models
# Add AbsoluteExponentialModel to the collection
myAbsoluteExponential = ot.AbsoluteExponential([2.0] * inputDimension, [3.0])
mySquaredExponential = ot.SquaredExponential([2.0] * inputDimension, [3.0])
# Add exponentialModel to the collection
amplitude = [4.0, 2.0]
scale = [1.0] * inputDimension
XX_input = ot.Sample([[0.1, 0], [0.32, 0], [0.6, 0], [0.9, 0], [
0.07, 1], [0.1, 1], [0.4, 1], [0.5, 1], [0.85, 1]])
y_output = ot.Sample(len(XX_input), 1)
for i in range(len(XX_input)):
y_output[i, 0] = fun_mixte(XX_input[i])
def C(s, t):
return m.exp(-4.0 * abs(s - t) / (1 + (s * s + t * t)))
N = 32
a = 4.0
myMesh = ot.IntervalMesher([N]).build(ot.Interval(-a, a))
myCovariance = ot.CovarianceMatrix(myMesh.getVerticesNumber())
for k in range(myMesh.getVerticesNumber()):
t = myMesh.getVertices()[k]
for l in range(k + 1):
s = myMesh.getVertices()[l]
myCovariance[k, l] = C(s[0], t[0])
covModel_discrete = ot.UserDefinedCovarianceModel(myMesh, myCovariance)
f_ = ot.SymbolicFunction(["tau", "theta", "sigma"], [
"(tau!=0) * exp(-1/theta) * sigma * sigma + (tau==0) * exp(0) * sigma * sigma"])
rho = ot.ParametricFunction(f_, [1, 2], [0.2, 0.3])
covModel_discrete = ot.StationaryFunctionalCovarianceModel([1.0], [
1.0], rho)
covModel_continuous = ot.SquaredExponential([1.0], [1.0])
covarianceModel = ot.ProductCovarianceModel(
[covModel_continuous, covModel_discrete])
covarianceModel.discretize(XX_input)
ot.RandomGenerator.SetSeed(0)
ot.RandomGenerator.SetState(ot.RandomGeneratorState(ot.Indices([0] * 768), 0))
POD2 = otpod.KrigingPOD(inputSample,
signals,
detection,
noiseThres,
saturationThres,
boxCox=False)
if ot.__version__ == '1.6':
covColl = ot.CovarianceModelCollection(4)
scale = [5.03148, 13.9442, 20, 20]
for i in range(4):
c = ot.SquaredExponential(1, scale[i])
c.setAmplitude([15.1697])
covColl[i] = c
covarianceModel = ot.ProductCovarianceModel(covColl)
elif ot.__version__ > '1.6':
covarianceModel = ot.SquaredExponential([5.03148, 13.9442, 20, 20],
[15.1697])
POD2.setCovarianceModel(covarianceModel)
POD2.setInitialStartSize(0)
POD2.setSamplingSize(100)
POD2.setSimulationSize(100)
POD2.run()
detectionSize2 = POD2.computeDetectionSize(0.6, 0.95)
def test_2_a90():
np.testing.assert_almost_equal(detectionSize2[0],
4.423224253595858,
decimal=4)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.ProductCovarianceModel().__class__.__name__ == 'ExponentialModel':
covarianceModel = ot.ExponentialModel([0.5], [5.0])
elif ot.ProductCovarianceModel(
).__class__.__name__ == 'GeneralizedExponential':
covarianceModel = ot.GeneralizedExponential([2.0], [3.0], 1.5)
elif ot.ProductCovarianceModel(
).__class__.__name__ == 'ProductCovarianceModel':
amplitude = [1.0]
scale1 = [4.0]
scale2 = [4.0]
cov1 = ot.ExponentialModel(scale1, amplitude)
cov2 = ot.ExponentialModel(scale2, amplitude)
covarianceModel = ot.ProductCovarianceModel([cov1, cov2])
elif ot.ProductCovarianceModel().__class__.__name__ == 'RankMCovarianceModel':
variance = [1.0, 2.0]
basis = ot.LinearBasisFactory().build()
covarianceModel = ot.RankMCovarianceModel(variance, basis)
else:
covarianceModel = ot.ProductCovarianceModel()
title = str(covarianceModel)[:100]
if covarianceModel.getInputDimension() == 1:
scale = covarianceModel.getScale()[0]
if covarianceModel.isStationary():
def f(x):
return [covarianceModel(x)[0, 0]]
func = ot.PythonFunction(1, 1, f)
myDefautModel = ot.AbsoluteExponential()
print("myDefautModel = ", myDefautModel)
myModel = ot.AbsoluteExponential(spatialDimension)
test_model(myModel)
myDefautModel = ot.MaternModel()
print("myDefautModel = ", myDefautModel)
myModel = ot.MaternModel(spatialDimension, 8.0, 2.0)
test_model(myModel)
myDefautModel = ot.ProductCovarianceModel()
print("myDefautModel = ", myDefautModel)
coll = ot.CovarianceModelCollection()
coll.add(ot.AbsoluteExponential(1, 3.0))
coll.add(ot.SquaredExponential(1, 2.0))
myModel = ot.ProductCovarianceModel(coll)
test_model(myModel)
collection = ot.CovarianceModelCollection()
# Collection ==> add covariance models
# Add AbsoluteExponentialModel to the collection
myAbsoluteExponential = ot.AbsoluteExponential(spatialDimension, 3.0)
collection.add(myAbsoluteExponential)
# Add SquaredExponentialModel to the collection
mySquaredExponential = ot.SquaredExponential(spatialDimension, 2.0)
