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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Test 1
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)
Y2 = f(X2)
# create covariance model
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential()
# create algorithm
algo = ot.KrigingAlgorithm(X, Y, covarianceModel, basis)
# set sensible optimization bounds and estimate hyperparameters
algo.setOptimizationBounds(ot.Interval(X.getMin(), X.getMax()))
algo.run()
# perform an evaluation
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])
# Kriging variance is 0 on learning points
covariance = result.getConditionalCovariance(X)
nullMatrix = ot.Matrix(sampleSize, sampleSize)
ott.assert_almost_equal(covariance, nullMatrix, 0.0, 1e-13)
# Kriging variance is non-null on validation points
validCovariance = result.getConditionalCovariance(X2)
values = ot.Matrix(
[
[0.81942182, -0.35599947, -0.17488593, 0.04622401, -0.03143555, 0.04054783],
[-0.35599947, 0.20874735, 0.10943841, -0.03236419, 0.02397483, -0.03269184],
[-0.17488593, 0.10943841, 0.05832917, -0.01779918, 0.01355719, -0.01891618],
[0.04622401, -0.03236419, -0.01779918, 0.00578327, -0.00467674, 0.00688697],
[-0.03143555, 0.02397483, 0.01355719, -0.00467674, 0.0040267, -0.00631173],
[0.04054783, -0.03269184, -0.01891618, 0.00688697, -0.00631173, 0.01059488],
]
)
ott.assert_almost_equal(validCovariance - values, nullMatrix, 0.0, 1e-7)
# 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, 1e-14, 1e-13)
# Variance per marginal
var = result.getConditionalMarginalVariance(X)
ott.assert_almost_equal(var, ot.Sample(sampleSize, 1), 1e-14, 1e-13)
# Prediction accuracy
ott.assert_almost_equal(Y2, result.getMetaModel()(X2), 0.3, 0.0)
# 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
scales = [5.33532, 2.61534]
amplitude = [1.61536]
covarianceModel = ot.SquaredExponential(scales, amplitude)
# 3) Basis definition
basis = ot.ConstantBasisFactory(inputDimension).build()
# 4) Kriging algorithm
algo = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
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)
# 6) Kriging variance is 0 on learning points
covariance = result.getConditionalCovariance(inputSample)
ott.assert_almost_equal(covariance, ot.SquareMatrix(len(inputSample)), 7e-7, 7e-7)
# 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-13)
# Variance per marginal
var = result.getConditionalMarginalVariance(inputSample)
ott.assert_almost_equal(var, ot.Sample(inputSample.getSize(), 1), 0.0, 1e-13)
# Estimation
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 = [[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)
algo = ot.KrigingAlgorithm(sampleX, sampleY, covarianceModel, basis)
algo.run()
result = algo.getResult()
mm = result.getMetaModel()
assert mm.getOutputDimension() == 2, "wrong output dim"
ott.assert_almost_equal(mm(sampleX), sampleY)
# Check the conditional covariance
reference_covariance = ot.Matrix(
[
[4.4527, 0.0, 8.34404, 0.0],
[0.0, 2.8883, 0.0, 5.41246],
[8.34404, 0.0, 15.7824, 0.0],
[0.0, 5.41246, 0.0, 10.2375],
]
)
ott.assert_almost_equal(
result([[9.5], [10.0]]).getCovariance() - reference_covariance,
ot.Matrix(4, 4),
0.0,
2e-2,
)
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"])
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), 1e-16, 1e-16)
assert (
algo.getResult().getMetaModel().getOutputDescription() == y.getDescription()
), "wrong output description"
def test_stationary_no_basis():
# fix https://github.com/openturns/openturns/issues/2403
ot.RandomGenerator.SetSeed(0)
model = ot.AbsoluteExponential()
size = 15
x = ot.Normal().getSample(size)
y = x + ot.Normal(0, 0.01).getSample(size)
algo = ot.KrigingAlgorithm(x, y, model)
algo.run()
result = algo.getResult()
variance = result.getConditionalMarginalVariance(x)
ott.assert_almost_equal(variance, ot.Sample(len(x), 1), 1e-15, 1e-15)
if __name__ == "__main__":
test_one_input_one_output()
test_two_inputs_one_output()
test_two_outputs()
test_stationary_fun()
test_stationary_no_basis()
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