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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Set hmat
ot.ResourceMap.SetAsString("KrigingAlgorithm-LinearAlgebra", "HMAT")
def test_one_input_one_output():
sampleSize = 6
dimension = 1
f = ot.SymbolicFunction(["x0"], ["x0 * sin(x0)"])
X = ot.Sample(sampleSize, dimension)
X2 = ot.Sample(sampleSize, dimension)
for i in range(sampleSize):
X[i, 0] = 3.0 + i
X2[i, 0] = 2.5 + i
X[0, 0] = 1.0
X[1, 0] = 3.0
X2[0, 0] = 2.0
X2[1, 0] = 4.0
Y = f(X)
f(X2)
# create algorithm
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential([1e-02], [4.50736])
algo = ot.KrigingAlgorithm(X, Y, covarianceModel, basis)
algo.run()
# perform an evaluation
result = algo.getResult()
ott.assert_almost_equal(result.getMetaModel()(X), Y, 1e-2)
ott.assert_almost_equal(result.getResiduals(), [0.0], 0.0, 1e-2)
ott.assert_almost_equal(result.getRelativeErrors(), [0.0], 0.0, 1e-5)
# Kriging variance is 0 on learning points
covariance = result.getConditionalCovariance(X)
ot.Point(covariance.getImplementation())
ot.Point(sampleSize * sampleSize)
ott.assert_almost_equal(covariance, ot.Matrix(sampleSize, sampleSize), 0.0, 1e-1)
# Covariance per marginal & extract variance component
coll = result.getConditionalMarginalCovariance(X)
var = [mat[0, 0] for mat in coll]
ott.assert_almost_equal(var, [0] * sampleSize, 0.0, 1e-1)
# Variance per marginal
var = result.getConditionalMarginalVariance(X)
ott.assert_almost_equal(var, ot.Sample(sampleSize, 1), 0.0, 1e-1)
# Test 2
def test_two_inputs_one_output():
# Kriging use case
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
covarianceModel = ot.SquaredExponential([5.33532, 2.61534], [1.61536])
# 3) Basis definition
basis = ot.ConstantBasisFactory(inputDimension).build()
# Kriging algorithm
algo = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
algo.run()
result = algo.getResult()
# Get meta model
metaModel = result.getMetaModel()
metaModel(inputValidSample)
# 4) Errors
# Interpolation
ott.assert_almost_equal(outputSample, metaModel(inputSample), 1, 3.0e-5)
# 5) Kriging variance is 0 on learning points
covariance = result.getConditionalCovariance(inputSample)
ott.assert_almost_equal(covariance, ot.SquareMatrix(len(inputSample)), 0.0, 1e-3)
# Covariance per marginal & extract variance component
coll = result.getConditionalMarginalCovariance(inputSample)
var = [mat[0, 0] for mat in coll]
ott.assert_almost_equal(var, [0] * len(var), 0.0, 1e-3)
# Variance per marginal
var = result.getConditionalMarginalVariance(inputSample)
ott.assert_almost_equal(var, ot.Sample(inputSample.getSize(), 1), 0.0, 1e-3)
# Estimation
ott.assert_almost_equal(
outputValidSample, metaModel(inputValidSample), 1.0e-1, 1e-1
)
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)
y = x + ot.Normal(0, 0.1).getSample(20)
algo = ot.KrigingAlgorithm(x, y, model, ot.LinearBasisFactory().build())
algo.run()
result = algo.getResult()
variance = result.getConditionalMarginalVariance(x)
ott.assert_almost_equal(variance, ot.Sample(len(x), 1), 2e-6, 2e-6)
if __name__ == "__main__":
test_one_input_one_output()
test_two_inputs_one_output()
test_stationary_fun()
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