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#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
ot.PlatformInfo.SetNumericalPrecision(5)
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):
if abs(inSymmetricTensor[i, j, k]) < 1.0e-6:
inSymmetricTensor[i, j, k] = 0.0
return inSymmetricTensor
# Instantiate one distribution object
dim = 3
meanPoint = ot.Point(dim, 1.0)
meanPoint[0] = 0.5
meanPoint[1] = -0.5
sigma = ot.Point(dim, 1.0)
sigma[0] = 2.0
sigma[1] = 3.0
R = ot.CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.5
distribution = ot.Normal(meanPoint, sigma, R)
# 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 (FD)=",
repr(inverseTransform.gradient(transformedPoint)),
)
print(
"inverse transform gradient at transformed point =",
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)))
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