#! /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) # 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()