import openturns as ot
from openturns.viewer import View
f = ot.SymbolicFunction(['x'], ['x + x * sin(x)'])
inputSample = ot.Sample([[1.0], [3.0], [5.0], [6.0], [7.0], [8.0]])
outputSample = f(inputSample)
f1 = ot.SymbolicFunction(['x'], ['sin(x)'])
f2 = ot.SymbolicFunction(['x'], ['x'])
f3 = ot.SymbolicFunction(['x'], ['cos(x)'])
basis = ot.Basis([f1, f2, f3])
covarianceModel = ot.SquaredExponential([1.0])
covarianceModel.setActiveParameter([])
algo = ot.GeneralLinearModelAlgorithm(inputSample, outputSample,
covarianceModel, basis)
algo.run()
result = algo.getResult()
metamodel = result.getMetaModel()
graph = f.draw(0.0, 10.0)
graph.add(metamodel.draw(0.0, 10.0))
graph.add(ot.Cloud(inputSample, outputSample))
graph.setColors(['blue', 'red', 'black'])
graph.setLegends(['model', 'meta model', 'sample'])
graph.setLegendPosition('topleft')
graph.setTitle('y(x)=x + x * sin(x)')
View(graph, figure_kw={'figsize': (8, 4)})
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()
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
print("===================================================\n")
algo = ot.GeneralLinearModelAlgorithm(X, Y, covarianceModel, basis)
algo.run()
result = algo.getResult()
print("\ncovariance (dirac, optimized)=", result.getCovarianceModel())
print("trend (dirac, optimized)=", result.getTrendCoefficients())
print("===================================================\n")
# Now without estimating covariance parameters
basis = ot.LinearBasisFactory(inputDimension).build()
covarianceModel = ot.DiracCovarianceModel(inputDimension)
algo = ot.GeneralLinearModelAlgorithm(X, Y, covarianceModel, basis, True)
algo.setOptimizeParameters(False)
algo.run()
result = algo.getResult()
print("\ncovariance (dirac, not optimized)=", result.getCovarianceModel())
ot.RandomGenerator.SetSeed(0) dimension = 2 input_names = ['x1', 'x2'] formulas = ['cos(x1 + x2)'] model = ot.SymbolicFunction(input_names, formulas) distribution = ot.Normal(dimension) x = distribution.getSample(100) y = model(x) # %% # We create a `GeneralLinearModelAlgorithm` based on a linear basis. The `run` method estimats the coefficients of the trend and the hyperparameters of the covariance model. # %% basis = ot.LinearBasisFactory(dimension).build() covarianceModel = ot.SquaredExponential([1] * dimension, [1.0]) algo = ot.GeneralLinearModelAlgorithm(x, y, covarianceModel, basis) algo.run() result = algo.getResult() # %% # We see that the trend coefficients have been estimated. # %% result.getTrendCoefficients() # %% # The parameters of the covariance models also have been estimated. # %% result.getCovarianceModel()
