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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
dimension = 2
inVar = ot.Description(dimension)
inVar[0] = "x1"
inVar[1] = "x2"
formula = ot.Description(1)
formula[0] = "x1^3+1.5*x2^3-x1*x2"
model = ot.SymbolicFunction(inVar, formula)
coll = []
formula[0] = "x1"
coll.append(ot.SymbolicFunction(inVar, formula))
formula[0] = "x2"
coll.append(ot.SymbolicFunction(inVar, formula))
formula[0] = "x1^2"
coll.append(ot.SymbolicFunction(inVar, formula))
formula[0] = "x2^2"
coll.append(ot.SymbolicFunction(inVar, formula))
basis = ot.Basis(coll)
indices = list(range(len(coll)))
size = 5
inputSample = ot.Sample(size * size, dimension)
weight = ot.Point(inputSample.getSize(), 1)
for i in range(inputSample.getSize()):
inputSample[i] = ot.Point((float(i % size) / size, (1.0 * (i // size)) / size))
weight[i] = (i % size + 1) * ((i // size) + 1)
penalizationFactor = 0.25
# Uniform weight, no penalization
algo = ot.PenalizedLeastSquaresAlgorithm(
inputSample, model(inputSample), ot.Point(inputSample.getSize(), 1.0), coll, indices
)
print("Uniform weight, no penalization")
print("Coefficients=", (algo.getCoefficients()))
print("Residual=%g" % algo.getResidual())
print("RelativeError=%g" % algo.getRelativeError())
# Uniform weight, spherical penalization
algo = ot.PenalizedLeastSquaresAlgorithm(
inputSample,
model(inputSample),
ot.Point(inputSample.getSize(), 1.0),
coll,
indices,
penalizationFactor,
)
print("Uniform weight, spherical penalization")
print("Coefficients=", (algo.getCoefficients()))
print("Residual=%g" % algo.getResidual())
# Non uniform weight, spherical penalization
algo = ot.PenalizedLeastSquaresAlgorithm(
inputSample, model(inputSample), weight, coll, indices
)
print("Non uniform weight, no penalization")
print("Coefficients=", (algo.getCoefficients()))
print("Residual=%g" % algo.getResidual())
algo = ot.PenalizedLeastSquaresAlgorithm(
inputSample, model(inputSample), weight, coll, indices, penalizationFactor
)
print("Non uniform weight, spherical penalization")
print("Coefficients=", (algo.getCoefficients()))
print("Residual=%g" % algo.getResidual())
penalizationMatrix = ot.CovarianceMatrix(4)
for i in range(4):
penalizationMatrix[i, i] = 1.0
for i in range(3):
penalizationMatrix[i, i + 1] = 1.0 / 8.0
algo = ot.PenalizedLeastSquaresAlgorithm(
inputSample,
model(inputSample),
weight,
coll,
indices,
penalizationFactor,
penalizationMatrix,
)
print("Non uniform weight, non spherical penalization")
print("Coefficients=", (algo.getCoefficients()))
print("Residual=%g" % algo.getResidual())
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