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#! /usr/bin/env python
import openturns as ot
from openturns.experimental import GaussianProcessRegression, GaussianProcessFitter
import openturns.testing as ott
# Test 1
def test_one_input_one_output():
sampleSize = 6
dimension = 1
f = ot.SymbolicFunction(["x0"], ["x0 * sin(x0)"])
X = ot.Sample(sampleSize, dimension)
for i in range(sampleSize):
X[i, 0] = 3.0 + i
X[0, 0] = 1.0
X[1, 0] = 3.0
Y = f(X)
# create covariance model
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential()
# create algorithm
fit_algo = GaussianProcessFitter(X, Y, covarianceModel, basis)
# set sensible optimization bounds and estimate hyper parameters
fit_algo.setOptimizationBounds(ot.Interval(X.getMin(), X.getMax()))
fit_algo.setOptimizationAlgorithm(ot.NLopt("LN_NELDERMEAD"))
fit_algo.run()
# perform an evaluation
fit_result = fit_algo.getResult()
algo = GaussianProcessRegression(fit_result)
algo.run()
result = algo.getResult()
ott.assert_almost_equal(result.getMetaModel()(X), Y)
ott.assert_almost_equal(result.getResiduals(), [1.32804e-07], 1e-3, 1e-3)
ott.assert_almost_equal(result.getRelativeErrors(), [5.20873e-21])
# Prediction accuracy
ott.assert_almost_equal(result.getMetaModel()([7.5]), f([7.5]), 0.3, 0.0)
# Test 2
def test_two_inputs_one_output():
inputDimension = 2
# Learning data
levels = [8, 5]
box = ot.Box(levels)
inputSample = box.generate()
# Scale each direction
inputSample *= 10.0
model = ot.SymbolicFunction(["x", "y"], ["cos(0.5*x) + sin(y)"])
outputSample = model(inputSample)
# Validation
sampleSize = 10
inputValidSample = ot.JointDistribution(2 * [ot.Uniform(0, 10.0)]).getSample(
sampleSize
)
outputValidSample = model(inputValidSample)
# 2) Definition of exponential model
# The parameters have been calibrated using TNC optimization
# and AbsoluteExponential models
scale = [5.33532, 2.61534]
amplitude = [1.61536]
covarianceModel = ot.SquaredExponential(scale, amplitude)
# 3) Basis definition
basis = ot.ConstantBasisFactory(inputDimension).build()
# 4) GPF algorithm
fit_algo = GaussianProcessFitter(inputSample, outputSample, covarianceModel, basis)
# set sensible optimization bounds and estimate hyper parameters
fit_algo.setOptimizationBounds(
ot.Interval(inputSample.getMin(), inputSample.getMax())
)
fit_algo.setOptimizationAlgorithm(ot.NLopt("LN_NELDERMEAD"))
fit_algo.run()
# perform an evaluation
fit_result = fit_algo.getResult()
# Regression algorithm
algo = GaussianProcessRegression(fit_result)
algo.run()
result = algo.getResult()
# Get meta model
metaModel = result.getMetaModel()
outData = metaModel(inputValidSample)
# 5) Errors
# Interpolation
ott.assert_almost_equal(outputSample, metaModel(inputSample), 3.0e-5, 3.0e-5)
# Prediction
ott.assert_almost_equal(outputValidSample, outData, 1.0e-1, 1e-1)
def test_two_outputs():
f = ot.SymbolicFunction(["x"], ["x * sin(x)", "x * cos(x)"])
sampleX = ot.Sample([[1.0], [2.0], [3.0], [4.0], [5.0], [6.0], [7.0], [8.0]])
sampleY = f(sampleX)
# Build a basis phi from R --> R^2
# phi_{0,0} = phi_{0,1} = x
# phi_{1,0} = phi_{1,1} = x^2
phi0 = ot.AggregatedFunction(
[ot.SymbolicFunction(["x"], ["x"]), ot.SymbolicFunction(["x"], ["x"])]
)
phi1 = ot.AggregatedFunction(
[ot.SymbolicFunction(["x"], ["x^2"]), ot.SymbolicFunction(["x"], ["x^2"])]
)
basis = ot.Basis([phi0, phi1])
covarianceModel = ot.SquaredExponential([1.0])
covarianceModel.setActiveParameter([])
covarianceModel = ot.TensorizedCovarianceModel([covarianceModel] * 2)
fit_algo = GaussianProcessFitter(sampleX, sampleY, covarianceModel, basis)
# set sensible optimization bounds and estimate hyper parameters
fit_algo.setOptimizationAlgorithm(ot.NLopt("LN_NELDERMEAD"))
fit_algo.run()
# perform an evaluation
fit_result = fit_algo.getResult()
algo = GaussianProcessRegression(fit_result)
algo.run()
result = algo.getResult()
mm = result.getMetaModel()
assert mm.getOutputDimension() == 2, "wrong output dim"
ott.assert_almost_equal(mm([5.5]), [-3.88363, 3.90286])
def test_stationary_fun():
# fix https://github.com/openturns/openturns/issues/1861
ot.RandomGenerator.SetSeed(0)
rho = ot.SymbolicFunction("tau", "exp(-abs(tau))*cos(2*pi_*abs(tau))")
model = ot.StationaryFunctionalCovarianceModel([1], [1], rho)
x = ot.Normal().getSample(20)
x.setDescription(["J0"])
y = x + ot.Normal(0, 0.1).getSample(20)
y.setDescription(["G0"])
fit_algo = GaussianProcessFitter(x, y, model, ot.LinearBasisFactory().build())
# set sensible optimization bounds and estimate hyper parameters
fit_algo.setOptimizationAlgorithm(ot.NLopt("LN_NELDERMEAD"))
fit_algo.run()
# perform an evaluation
fit_result = fit_algo.getResult()
algo = GaussianProcessRegression(fit_result)
algo.run()
result = algo.getResult()
mm = result.getMetaModel()
ott.assert_almost_equal(mm([5.5]), [5.58838])
if __name__ == "__main__":
test_one_input_one_output()
test_two_inputs_one_output()
test_two_outputs()
test_stationary_fun()
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