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import openturns as ot
from openturns.experimental import GaussianProcessFitter
import openturns.testing as ott
ot.PlatformInfo.SetNumericalPrecision(4)
ot.TESTPREAMBLE()
def use_case_1(X, Y):
"""
optim problem (scale)
Dirac model
"""
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
algo = 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
"""
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
algo = 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
"""
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.AbsoluteExponential(inputDimension)
algo = GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getOptimizeParameters()
algo.setKeepCholeskyFactor(False)
algo.run()
cov_param = [0.1327, 0.1956]
trend_coefficients = [-0.1034, 1.0141]
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
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.SetAsBool("GeneralLinearModelAlgorithm-UnbiasedVariance", False)
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.AbsoluteExponential(inputDimension)
algo = GaussianProcessFitter(X, Y, covarianceModel, basis)
assert algo.getKeepCholeskyFactor()
assert algo.getOptimizeParameters()
algo.setKeepCholeskyFactor(False)
algo.run()
cov_param = [0.1327, 0.1956]
trend_coefficients = [-0.1034, 1.0141]
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_5(X, Y):
"""
full optim problem (scale, amplitude)
"""
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 = 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()
cov_param = [0.1327, 0.19068]
trend_coefficients = [-0.1034, 1.0141]
result = algo.getResult()
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
ott.assert_almost_equal(
result.getTrendCoefficients(), trend_coefficients, 1e-4, 1e-4
)
def use_case_6(X, Y):
ot.RandomGenerator.SetSeed(0)
covarianceModel = ot.AbsoluteExponential()
algo = GaussianProcessFitter(X, Y, covarianceModel)
assert algo.getKeepCholeskyFactor()
algo.setKeepCholeskyFactor(False)
assert algo.getOptimizeParameters()
algo.run()
result = algo.getResult()
cov_param = [15.6, 2.3680]
assert (
algo.getOptimizationAlgorithm().getImplementation().getClassName() == "Cobyla"
)
ott.assert_almost_equal(
result.getCovarianceModel().getParameter(), cov_param, 1e-4, 1e-4
)
ott.assert_almost_equal(result.getTrendCoefficients(), [])
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)
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