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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
def cleanSymmetricTensor(inSymmetricTensor):
rowDim = inSymmetricTensor.getNbRows()
colDim = inSymmetricTensor.getNbColumns()
sheetDim = inSymmetricTensor.getNbSheets()
for i in range(rowDim):
for j in range(colDim):
for k in range(sheetDim):
inSymmetricTensor[i, j, k] = 1.0e-4 * round(
1.0e4 * inSymmetricTensor[i, j, k]
)
if abs(inSymmetricTensor[i, j, k]) < 1.0e-6:
inSymmetricTensor[i, j, k] = 0.0
return inSymmetricTensor
meanPoint = ot.Point(1)
sigma = ot.Point(1)
R = ot.CorrelationMatrix(1)
# Create a collection of distribution
aCollection = ot.DistributionCollection()
aCollection.add(ot.Uniform(-1.0, 2.0))
aCollection.add(ot.Gamma(2.0, 2.0, 0.0))
dim = aCollection.getSize()
# Instantiate one distribution object
distribution = ot.JointDistribution(aCollection, ot.IndependentCopula(dim))
# Test for sampling
size = 10000
sample = distribution.getSample(size)
print("sample first=", repr(sample[0]), " last=", repr(sample[size - 1]))
print("sample mean=", repr(sample.computeMean()))
print("sample covariance=", repr(sample.computeCovariance()))
transform = distribution.getIsoProbabilisticTransformation()
print("isoprobabilistic transformation=", repr(transform))
transformedSample = transform(sample)
print(
"transformed sample first=",
repr(transformedSample[0]),
" last=",
repr(transformedSample[size - 1]),
)
print("transformed sample mean=", repr(transformedSample.computeMean()))
print("transformed sample covariance=", repr(transformedSample.computeCovariance()))
# Test for evaluation
inverseTransform = distribution.getInverseIsoProbabilisticTransformation()
print("inverse isoprobabilistic transformation=", repr(inverseTransform))
transformedBackSample = inverseTransform(transformedSample)
print(
"transformed back sample first=",
repr(transformedBackSample[0]),
" last=",
repr(transformedBackSample[size - 1]),
)
print("transformed back sample mean=", repr(transformedBackSample.computeMean()))
print(
"transformed back sample covariance=",
repr(transformedBackSample.computeCovariance()),
)
point = ot.Point(dim, 1.0)
print("point=", repr(point))
transformedPoint = transform(point)
print("transform value at point =", repr(transformedPoint))
print("transform gradient at point =", repr(transform.gradient(point)))
print(
"transform gradient at point (FD)=",
repr(
ot.CenteredFiniteDifferenceGradient(1.0e-5, transform.getEvaluation()).gradient(
point
)
),
)
print(
"transform hessian at point =",
repr(cleanSymmetricTensor(transform.hessian(point))),
)
print(
"transform hessian at point (FD) =",
repr(
cleanSymmetricTensor(
ot.CenteredFiniteDifferenceHessian(
1.0e-4, transform.getEvaluation()
).hessian(point)
)
),
)
print(
"inverse transform value at transformed point =",
repr(inverseTransform(transformedPoint)),
)
print(
"inverse transform gradient at transformed point =",
repr(inverseTransform.gradient(transformedPoint)),
)
print(
"inverse transform gradient at transformed point (FD)=",
repr(
ot.CenteredFiniteDifferenceGradient(
1.0e-5, inverseTransform.getEvaluation()
).gradient(transformedPoint)
),
)
print(
"inverse transform hessian at transformed point =",
repr(cleanSymmetricTensor(inverseTransform.hessian(transformedPoint))),
)
print(
"inverse transform hessian at transformed point (FD) =",
repr(
cleanSymmetricTensor(
ot.CenteredFiniteDifferenceHessian(
1.0e-4, inverseTransform.getEvaluation()
).hessian(transformedPoint)
)
),
)
# Test for parameters
print("parameters gradient at point=", repr(transform.parameterGradient(point)))
# Validation using finite difference
eps = 1e-5
factor = 1.0 / (2.0 * eps)
gradient = ot.Matrix(5, 2)
# dT/dp0
coll = ot.DistributionCollection(dim)
coll[0] = ot.Uniform(-1.0 + eps, 2.0)
coll[1] = aCollection[1]
left = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
coll[0] = ot.Uniform(-1.0 - eps, 2.0)
right = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[0, 0] = dTdp[0]
gradient[0, 1] = dTdp[1]
# dT/dp1
coll = ot.DistributionCollection(dim)
coll[0] = ot.Uniform(-1.0, 2.0 + eps)
coll[1] = aCollection[1]
left = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
coll[0] = ot.Uniform(-1.0, 2.0 - eps)
right = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[1, 0] = dTdp[0]
gradient[1, 1] = dTdp[1]
# dT/dp2
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0 + eps, 2.0, 0.0)
left = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0 - eps, 2.0, 0.0)
right = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[2, 0] = dTdp[0]
gradient[2, 1] = dTdp[1]
# dT/dp3
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0, 2.0 + eps, 0.0)
left = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0, 2.0 - eps, 0.0)
right = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[3, 0] = dTdp[0]
gradient[3, 1] = dTdp[1]
# dT/dp4
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0, 2.0, 0.0 + eps)
left = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0, 2.0, 0.0 - eps)
right = ot.JointDistribution(coll).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[4, 0] = dTdp[0]
gradient[4, 1] = dTdp[1]
print("parameters gradient (FD) =", repr(gradient))
# Test for parameters
print(
"(inverse) parameters gradient at point=",
repr(inverseTransform.parameterGradient(point)),
)
# dT/dp0
coll = ot.DistributionCollection(dim)
coll[0] = ot.Uniform(-1.0 + eps, 2.0)
coll[1] = aCollection[1]
left = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
coll[0] = ot.Uniform(-1.0 - eps, 2.0)
right = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[0, 0] = dTdp[0]
gradient[0, 1] = dTdp[1]
# dT/dp1
coll = ot.DistributionCollection(dim)
coll[0] = ot.Uniform(-1.0, 2.0 + eps)
coll[1] = aCollection[1]
left = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
coll[0] = ot.Uniform(-1.0, 2.0 - eps)
right = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[1, 0] = dTdp[0]
gradient[1, 1] = dTdp[1]
# dT/dp2
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0 + eps, 2.0, 0.0)
left = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0 - eps, 2.0, 0.0)
right = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[2, 0] = dTdp[0]
gradient[2, 1] = dTdp[1]
# dT/dp3
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0, 2.0 + eps, 0.0)
left = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0, 2.0 - eps, 0.0)
right = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[3, 0] = dTdp[0]
gradient[3, 1] = dTdp[1]
# dT/dp4
coll = ot.DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = ot.Gamma(2.0, 2.0, 0.0 + eps)
left = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
coll[1] = ot.Gamma(2.0, 2.0, 0.0 - eps)
right = ot.JointDistribution(coll).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[4, 0] = dTdp[0]
gradient[4, 1] = dTdp[1]
print("(inverse) parameters gradient (FD) =", repr(gradient))
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