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import openturns as ot
import openturns.experimental as otexp
import openturns.testing as ott
from openturns.usecases.fire_satellite import FireSatelliteModel
ot.TESTPREAMBLE()
def use_case_1(X, Y):
"""
optim problem (scale)
Dirac model
"""
ot.ResourceMap.Reload()
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getOptimizeParameters()
assert algo.getKeepCholeskyFactor()
algo.setKeepCholeskyFactor(False)
algo.run()
cov_amplitude = [0.19575]
trend_coefficients = [-0.1109, 1.0149]
result = algo.getResult()
ott.assert_almost_equal(
result.getCovarianceModel().getAmplitude(), cov_amplitude, 1e-4, 1e-4
)
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_2(X, Y):
"""
No optim with Dirac model
"""
ot.ResourceMap.Reload()
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getKeepCholeskyFactor()
algo.setKeepCholeskyFactor(False)
algo.setOptimizeParameters(False)
algo.run()
cov_amplitude = [1]
trend_coefficients = [-0.1109, 1.01498]
result = algo.getResult()
ott.assert_almost_equal(
result.getCovarianceModel().getAmplitude(), cov_amplitude, 1e-4, 1e-4
)
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_3(X, Y):
"""
full optim problem (scale)
analytical variance estimate
"""
ot.ResourceMap.Reload()
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.AbsoluteExponential(inputDimension)
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getOptimizeParameters()
algo.setKeepCholeskyFactor(False)
algo.run()
cov_param = [0.0078, 1]
trend_coefficients = [-0.110943, 1.01498]
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
print(result.getCovarianceModel().getParameter())
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
print(result.getTrendCoefficients())
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_4(X, Y):
"""
optim problem (scale)
Biased variance estimate
"""
ot.ResourceMap.Reload()
ot.ResourceMap.SetAsBool("GeneralLinearModelAlgorithm-UnbiasedVariance", False)
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.AbsoluteExponential(inputDimension)
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getKeepCholeskyFactor()
assert algo.getOptimizeParameters()
algo.setKeepCholeskyFactor(False)
algo.run()
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
print(result.getCovarianceModel().getParameter())
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), [0.0078, 1], 1e-4, 1e-4
)
print(result.getTrendCoefficients())
ott.assert_almost_equal(
result.getTrendCoefficients(), [-0.110943, 1.01498], 1e-4, 1e-4
)
def use_case_5(X, Y):
"""
full optim problem (scale, amplitude)
"""
ot.ResourceMap.Reload()
ot.ResourceMap.SetAsBool("GaussianProcessFitter-UnbiasedVariance", False)
ot.ResourceMap.SetAsBool(
"GaussianProcessFitter-UseAnalyticalAmplitudeEstimate", False
)
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.AbsoluteExponential(inputDimension)
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getKeepCholeskyFactor()
assert algo.getOptimizeParameters()
algo.setKeepCholeskyFactor(False)
bounds = ot.Interval([1e-2] * 2, [100] * 2)
algo.setOptimizationBounds(bounds)
algo.run()
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
print(result.getCovarianceModel().getParameter())
cov_param = [8.499, 0.9998]
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-3, 1e-3
)
print(result.getTrendCoefficients())
trend_coefficients = [0.09867, 0.995]
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_6(X, Y):
ot.RandomGenerator.SetSeed(0)
ot.ResourceMap.Reload()
ot.ResourceMap.SetAsBool(
"GaussianProcessFitter-UseAnalyticalAmplitudeEstimate", False
)
covarianceModel = ot.AbsoluteExponential()
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel)
assert algo.getKeepCholeskyFactor()
algo.setKeepCholeskyFactor(False)
assert algo.getOptimizeParameters()
algo.run()
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
print(result.getCovarianceModel().getParameter())
cov_param = [2.55922, 1]
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
ott.assert_almost_equal(result.getTrendCoefficients(), [])
def use_case_7(X, Y):
ot.RandomGenerator.SetSeed(0)
ot.ResourceMap.Reload()
ot.ResourceMap.SetAsScalar("GaussianProcessFitter-OptimizationLowerBoundScaleFactor", 0.0)
covarianceModel = ot.AbsoluteExponential()
with ott.assert_raises(TypeError):
algo = otexp.GaussianProcessFitter(X, Y, covarianceModel)
algo.run()
def bugfix_optim_no_feasible():
ot.RandomGenerator.SetSeed(0)
ot.ResourceMap.Reload()
m = FireSatelliteModel()
model = m.model
inputDistribution = m.distribution
experiment = ot.LHSExperiment(inputDistribution, 10 * m.dim)
inputTrainingSet = experiment.generate()
outputTrainingSet = model(inputTrainingSet)
linear_basis = ot.LinearBasisFactory(m.dim).build()
basis = ot.Basis(
[
ot.AggregatedFunction([linear_basis.build(k)] * 3)
for k in range(linear_basis.getSize())
]
)
myCov1 = ot.MaternModel([1.0] * m.dim, 2.5)
myCov2 = ot.SquaredExponential([1.0] * m.dim)
myCov3 = ot.MaternModel([1.0] * m.dim, 2.5)
# optimal we should get after the optimization process
optimal_cov_parameter = [7.874e+06, 1513, 1413, 43.96, 5.509, 4.625,
5.159, 0.6612, 3.245, 4.945, 8.074, 5.419]
covarianceModel = ot.TensorizedCovarianceModel([myCov1, myCov2, myCov3])
scaleOptimizationBounds = ot.Interval(
[1.0e6, 1.0e3, 1.0e3, 1.0, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1],
[2.0e7, 2.0e3, 2.0e3, 1e2, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0],
)
algo = otexp.GaussianProcessFitter(
inputTrainingSet, outputTrainingSet, covarianceModel, basis
)
algo.setOptimizationBounds(scaleOptimizationBounds)
algo.setOptimizeParameters(True)
algo.run()
# Get result & residual
result = algo.getResult()
residual = result.getMetaModel()(inputTrainingSet) - outputTrainingSet
# Define multivariate square function
sqr_func = ot.SymbolicFunction(["x", "y", "z"], ["x*x", "y*y", "z*z"])
# Squared residual
squared_epsilon = sqr_func(residual).computeMean()
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), optimal_cov_parameter, 1e-1, 1e-3
)
ott.assert_almost_equal(squared_epsilon, [7.248e-06, 298.4, 0.9051], 5e-1, 1e-3)
if __name__ == "__main__":
ot.RandomGenerator.SetSeed(0)
sampleSize = 40
inputDimension = 1
# Create the function to estimate
model = ot.SymbolicFunction(["x0"], ["x0"])
X = ot.Sample(sampleSize, inputDimension)
for i in range(sampleSize):
X[i, 0] = 3.0 + (8.0 * i) / sampleSize
Y = model(X)
# Add a small noise to data
Y += (
ot.GaussianProcess(ot.AbsoluteExponential([0.1], [0.2]), ot.Mesh(X))
.getRealization()
.getValues()
)
use_case_1(X, Y)
use_case_2(X, Y)
use_case_3(X, Y)
use_case_4(X, Y)
use_case_5(X, Y)
use_case_6(X, Y)
use_case_7(X, Y)
# fix https://github.com/openturns/openturns/issues/2953
bugfix_optim_no_feasible()
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