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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
coll1 = ot.DistributionCollection(0)
coll1.add(ot.Normal(1.0, 2.5))
coll1.add(ot.Gamma(1.5, 3.0, 0.0))
pointLow = ot.Point(0)
pointLow.add(coll1[0].computeQuantile(0.25)[0])
pointLow.add(coll1[1].computeQuantile(0.25)[0])
pointHigh = ot.Point(0)
pointHigh.add(coll1[0].computeQuantile(0.75)[0])
pointHigh.add(coll1[1].computeQuantile(0.75)[0])
coll2 = ot.DistributionCollection(0)
coll2.add(ot.Gamma(2.5, 2.0, 0.0))
coll2.add(ot.Normal(3.0, 1.5))
# First, check the old constructor
transformation = ot.MarginalTransformationEvaluation(coll1)
print("transformation=", repr(transformation))
print("transformation(", pointLow, ")=", repr(transformation(pointLow)))
print("transformation(", pointHigh, ")=", repr(transformation(pointHigh)))
# Validation using finite difference
eps = 1e-5
factor = 1.0 / (2.0 * eps)
gradientLow = ot.Matrix(5, 2)
gradientHigh = ot.Matrix(5, 2)
# dT/dp0
coll = ot.DistributionCollection(2)
coll[0] = ot.Normal(1.0 + eps, 2.5)
coll[1] = coll1[1]
left = ot.MarginalTransformationEvaluation(coll)
coll[0] = ot.Normal(1.0 - eps, 2.5)
right = ot.MarginalTransformationEvaluation(coll)
dTdp = (left(pointLow) - right(pointLow)) * factor
gradientLow[0, 0] = dTdp[0]
gradientLow[0, 1] = dTdp[1]
dTdp = (left(pointHigh) - right(pointHigh)) * factor
gradientHigh[0, 0] = dTdp[0]
gradientHigh[0, 1] = dTdp[1]
# dT/dp1
coll = ot.DistributionCollection(2)
coll[0] = ot.Normal(1.0, 2.5 + eps)
coll[1] = coll1[1]
left = ot.MarginalTransformationEvaluation(coll)
coll[0] = ot.Normal(1.0, 2.5 - eps)
right = ot.MarginalTransformationEvaluation(coll)
dTdp = (left(pointLow) - right(pointLow)) * factor
gradientLow[1, 0] = dTdp[0]
gradientLow[1, 1] = dTdp[1]
dTdp = (left(pointHigh) - right(pointHigh)) * factor
gradientHigh[1, 0] = dTdp[0]
gradientHigh[1, 1] = dTdp[1]
# dT/dp2
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5 + eps, 3.0, 0.0)
left = ot.MarginalTransformationEvaluation(coll)
coll[1] = ot.Gamma(1.5 - eps, 3.0, 0.0)
right = ot.MarginalTransformationEvaluation(coll)
dTdp = (left(pointLow) - right(pointLow)) * factor
gradientLow[2, 0] = dTdp[0]
gradientLow[2, 1] = dTdp[1]
dTdp = (left(pointHigh) - right(pointHigh)) * factor
gradientHigh[2, 0] = dTdp[0]
gradientHigh[2, 1] = dTdp[1]
# dT/dp3
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5, 3.0 + eps, 0.0)
left = ot.MarginalTransformationEvaluation(coll)
coll[1] = ot.Gamma(1.5, 3.0 - eps, 0.0)
right = ot.MarginalTransformationEvaluation(coll)
dTdp = (left(pointLow) - right(pointLow)) * factor
gradientLow[3, 0] = dTdp[0]
gradientLow[3, 1] = dTdp[1]
dTdp = (left(pointHigh) - right(pointHigh)) * factor
gradientHigh[3, 0] = dTdp[0]
gradientHigh[3, 1] = dTdp[1]
# dT/dp4
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5, 3.0, 0.0 + eps)
left = ot.MarginalTransformationEvaluation(coll)
coll[1] = ot.Gamma(1.5, 3.0, 0.0 - eps)
right = ot.MarginalTransformationEvaluation(coll)
dTdp = (left(pointLow) - right(pointLow)) * factor
gradientLow[4, 0] = dTdp[0]
gradientLow[4, 1] = dTdp[1]
dTdp = (left(pointHigh) - right(pointHigh)) * factor
gradientHigh[4, 0] = dTdp[0]
gradientHigh[4, 1] = dTdp[1]
print(
"transformation parameters gradient=",
repr(transformation.parameterGradient(pointLow)),
)
print("finite difference parameters gradient=", repr(gradientLow))
print(
"transformation parameters gradient=",
repr(transformation.parameterGradient(pointHigh)),
)
print("finite difference parameters gradient=", repr(gradientHigh))
print("input dimension=", transformation.getInputDimension())
print("output dimension=", transformation.getOutputDimension())
# Second, check the constructor for old inverse transformation
transformation = ot.MarginalTransformationEvaluation(
coll1, ot.MarginalTransformationEvaluation.TO
)
print("transformation=", repr(transformation))
uLow = ot.Point(coll1.getSize(), 0.25)
uHigh = ot.Point(coll1.getSize(), 0.75)
print("transformation(", uLow, ")=", repr(transformation(uLow)))
print("transformation(", uHigh, ")=", repr(transformation(uHigh)))
# Validation using finite difference
# dT/dp0
coll = ot.DistributionCollection(2)
coll[0] = ot.Normal(1.0 + eps, 2.5)
coll[1] = coll1[1]
left = ot.MarginalTransformationEvaluation(coll, ot.MarginalTransformationEvaluation.TO)
coll[0] = ot.Normal(1.0 - eps, 2.5)
right = ot.MarginalTransformationEvaluation(
coll, ot.MarginalTransformationEvaluation.TO
)
dTdp = (left(uLow) - right(uLow)) * factor
gradientLow[0, 0] = dTdp[0]
gradientLow[0, 1] = dTdp[1]
dTdp = (left(uHigh) - right(uHigh)) * factor
gradientHigh[0, 0] = dTdp[0]
gradientHigh[0, 1] = dTdp[1]
# dT/dp1
coll = ot.DistributionCollection(2)
coll[0] = ot.Normal(1.0, 2.5 + eps)
coll[1] = coll1[1]
left = ot.MarginalTransformationEvaluation(coll, ot.MarginalTransformationEvaluation.TO)
coll[0] = ot.Normal(1.0, 2.5 - eps)
right = ot.MarginalTransformationEvaluation(
coll, ot.MarginalTransformationEvaluation.TO
)
dTdp = (left(uLow) - right(uLow)) * factor
gradientLow[1, 0] = dTdp[0]
gradientLow[1, 1] = dTdp[1]
dTdp = (left(uHigh) - right(uHigh)) * factor
gradientHigh[1, 0] = dTdp[0]
gradientHigh[1, 1] = dTdp[1]
# dT/dp2
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5 + eps, 3.0, 0.0)
left = ot.MarginalTransformationEvaluation(coll, ot.MarginalTransformationEvaluation.TO)
coll[1] = ot.Gamma(1.5 - eps, 3.0, 0.0)
right = ot.MarginalTransformationEvaluation(
coll, ot.MarginalTransformationEvaluation.TO
)
dTdp = (left(uLow) - right(uLow)) * factor
gradientLow[2, 0] = dTdp[0]
gradientLow[2, 1] = dTdp[1]
dTdp = (left(uHigh) - right(uHigh)) * factor
gradientHigh[2, 0] = dTdp[0]
gradientHigh[2, 1] = dTdp[1]
# dT/dp3
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5, 3.0 + eps, 0.0)
left = ot.MarginalTransformationEvaluation(coll, ot.MarginalTransformationEvaluation.TO)
coll[1] = ot.Gamma(1.5, 3.0 - eps, 0.0)
right = ot.MarginalTransformationEvaluation(
coll, ot.MarginalTransformationEvaluation.TO
)
dTdp = (left(uLow) - right(uLow)) * factor
gradientLow[3, 0] = dTdp[0]
gradientLow[3, 1] = dTdp[1]
dTdp = (left(uHigh) - right(uHigh)) * factor
gradientHigh[3, 0] = dTdp[0]
gradientHigh[3, 1] = dTdp[1]
# dT/dp4
coll = ot.DistributionCollection(2)
coll[0] = coll1[0]
coll[1] = ot.Gamma(1.5, 3.0, 0.0 + eps)
left = ot.MarginalTransformationEvaluation(coll, ot.MarginalTransformationEvaluation.TO)
coll[1] = ot.Gamma(1.5, 3.0, 0.0 - eps)
right = ot.MarginalTransformationEvaluation(
coll, ot.MarginalTransformationEvaluation.TO
)
dTdp = (left(uLow) - right(uLow)) * factor
gradientLow[4, 0] = dTdp[0]
gradientLow[4, 1] = dTdp[1]
dTdp = (left(uHigh) - right(uHigh)) * factor
gradientHigh[4, 0] = dTdp[0]
gradientHigh[4, 1] = dTdp[1]
print(
"transformation parameters gradient=",
repr(transformation.parameterGradient(uLow)),
)
print("finite difference parameters gradient=", repr(gradientLow))
print(
"transformation parameters gradient=",
repr(transformation.parameterGradient(uHigh)),
)
print("finite difference parameters gradient=", repr(gradientHigh))
print("input dimension=", transformation.getInputDimension())
print("output dimension=", transformation.getOutputDimension())
# Third, check the constructor for the new transformation
transformation = ot.MarginalTransformationEvaluation(coll1, coll2)
print("transformation=", repr(transformation))
print("transformation(", pointLow, ")=", repr(transformation(pointLow)))
print("transformation(", pointHigh, ")=", repr(transformation(pointHigh)))
print("input dimension=", transformation.getInputDimension())
print("output dimension=", transformation.getOutputDimension())
T1 = ot.MarginalTransformationEvaluation([ot.Exponential(2.0)], [ot.Exponential(1.0)])
print("T1=", T1)
T2 = ot.MarginalTransformationEvaluation([ot.Exponential(1.0)], [ot.Exponential(2.0)])
print("T2=", T2)
T3 = ot.MarginalTransformationEvaluation(
[ot.Exponential(3.0, 4.0)], [ot.Exponential(3.0, 5.0)]
)
print("T3=", T3)
|
