def discretizeFromJoint(fullDistribution, ticks):
fullDimension = fullDistribution.getDimension()
conditioningDistribution = fullDistribution.getMarginal(
[i for i in range(fullDimension - 1)])
# Add the range bounds to the given ticks
lower = fullDistribution.getRange().getLowerBound()
upper = fullDistribution.getRange().getUpperBound()
expandedTicks = [0] * len(ticks)
for i in range(fullDimension):
expandedTicks[i] = [lower[i]] + ticks[i] + [upper[i]]
# Now perform the full discretization
lengths = [(len(t) - 1) for t in expandedTicks]
tuples = ot.Tuples(lengths).generate()
probabilities = ot.Point(len(tuples))
for i in range(len(tuples)):
tuple = tuples[i]
aFull = [expandedTicks[j][tuple[j]] for j in range(fullDimension)]
bFull = [expandedTicks[j][tuple[j] + 1] for j in range(fullDimension)]
aConditioning = [
expandedTicks[j][tuple[j]] for j in range(fullDimension - 1)
]
bConditioning = [
expandedTicks[j][tuple[j] + 1] for j in range(fullDimension - 1)
]
den = conditioningDistribution.computeProbability(
ot.Interval(aConditioning, bConditioning))
if den > 0.0:
num = fullDistribution.computeProbability(ot.Interval(
aFull, bFull))
probabilities[i] = num / den
return probabilities
def discretizeBernoulliFromConditionalProbability(conditionalProbability,
conditioningDistribution,
ticks,
useSlowIntegration=True,
nodesNumber=32):
conditioningDimension = conditioningDistribution.getDimension()
if useSlowIntegration:
# Accurate but slow
integrator = ot.IteratedQuadrature()
else:
# Less accurate for non-smooth integrand but fast
ot.ResourceMap.SetAsUnsignedInteger(
"GaussLegendre-DefaultMarginalIntegrationPointsNumber",
nodesNumber)
integrator = ot.GaussLegendre(conditioningDimension)
# Add the range bounds to the given ticks
lower = list(conditioningDistribution.getRange().getLowerBound())
upper = list(conditioningDistribution.getRange().getUpperBound())
# Add the range bounds to the given ticks
lower = conditioningDistribution.getRange().getLowerBound()
upper = conditioningDistribution.getRange().getUpperBound()
expandedTicks = [0] * len(ticks)
for i in range(conditioningDimension):
expandedTicks[i] = [lower[i]] + ticks[i] + [upper[i]]
# Now perform the full discretization
lengths = [(len(t) - 1) for t in expandedTicks]
tuples = ot.Tuples(lengths).generate()
probabilitiesTrue = [0] * len(tuples)
def kernel(x):
x = np.array(x)
return conditionalProbability(x) * np.array(
conditioningDistribution.computePDF(x[:, 0:conditioningDimension]))
for i in range(len(tuples)):
tuple = tuples[i]
aConditioning = [
expandedTicks[j][tuple[j]] for j in range(conditioningDimension)
]
bConditioning = [
expandedTicks[j][tuple[j] + 1]
for j in range(conditioningDimension)
]
den = conditioningDistribution.computeProbability(
ot.Interval(aConditioning, bConditioning))
if den > 0.0:
num = integrator.integrate(
ot.PythonFunction(conditioningDimension, 1,
func_sample=kernel),
ot.Interval(aConditioning, bConditioning))[0]
probabilitiesTrue[i] = min(1.0, num / den)
probabilities = ot.Point([1.0 - p for p in probabilitiesTrue] +
probabilitiesTrue)
return probabilities
def discretizeFromConditionalDensity(conditionalDensity,
conditioningDistribution,
ticks,
useSlowIntegration=True,
nodesNumber=32):
fullDimension = conditioningDistribution.getDimension() + 1
if useSlowIntegration:
# Accurate but slow
integrator = ot.IteratedQuadrature()
else:
# Less accurate for non-smooth integrand but fast
ot.ResourceMap.SetAsUnsignedInteger(
"GaussLegendre-DefaultMarginalIntegrationPointsNumber",
nodesNumber)
integrator = ot.GaussLegendre(fullDimension)
# Add the range bounds to the given ticks
lower = list(conditioningDistribution.getRange().getLowerBound())
upper = list(conditioningDistribution.getRange().getUpperBound())
# For the conditioned variable it has to be estimated. We assume that the given
# tick range is a correct margin to get the lower and upper bounds
conditionedMin = min(ticks[fullDimension - 1])
conditionedMax = max(ticks[fullDimension - 1])
delta = conditionedMax - conditionedMin
lower = lower + [conditionedMin - delta]
upper = upper + [conditionedMax + delta]
expandedTicks = [0] * fullDimension
for i in range(fullDimension):
expandedTicks[i] = [lower[i]] + ticks[i] + [upper[i]]
# Now perform the full discretization
lengths = [(len(t) - 1) for t in expandedTicks]
tuples = ot.Tuples(lengths).generate()
probabilities = ot.Point(len(tuples))
def kernel(x):
x = np.array(x)
return conditionalDensity(x) * np.array(
conditioningDistribution.computePDF(x[:, 0:fullDimension - 1]))
for i in range(len(tuples)):
tuple = tuples[i]
aFull = [expandedTicks[j][tuple[j]] for j in range(fullDimension)]
bFull = [expandedTicks[j][tuple[j] + 1] for j in range(fullDimension)]
num = integrator.integrate(
ot.PythonFunction(fullDimension, 1, func_sample=kernel),
ot.Interval(aFull, bFull))[0]
probabilities[i] = num
return probabilities
import openturns as ot
from openturns.viewer import View
# Tuples
d = ot.Tuples([3, 4, 5])
s = ot.Sample(d.generate())
s.setDescription(["X1", "X2", "X3"])
g = ot.Graph()
g.setTitle("Tuples generator")
g.setGridColor("black")
p = ot.Pairs(s)
g.add(p)
View(g)
' + 17*x1^3 - 10*x2^3 + 7*x4^3']) Y = myLinearModel(X) + R print(Y) ################################################################################################ # Build a model Y~(X1+X2+X3+X4)^3+I(Xi)^2+I(Xi)^3 dim = X.getDimension() enumerateFunction = ot.EnumerateFunction(dim) factory = ot.OrthogonalProductPolynomialFactory([ot.MonomialFactory()]*dim, enumerateFunction) # Build 'interactions' as a list of list [a1,a2,a3,a4], and we will generate tensorized # polynomials x1^a1*x2^a2*x3^a3*x4^a4. # Y ~ (X1+X2+X3+X4)^4 interactions = [x for x in ot.Tuples([2]*dim).generate()] # Remove X1*X2*X3*X4 to obtain Y ~ (X1+X2+X3+X4)^3 interactions.pop(interactions.index([1]*dim)) for i in xrange(dim): indices = [0]*dim indices[i] = 2 # Y ~ I(Xi)^2 interactions.append(indices[:]) # Y ~ I(Xi)^3 indices[i] = 3 interactions.append(indices[:]) basis = ot.Basis([factory.build(enumerateFunction.inverse(indices)) for indices in interactions]) ################################################################################################ i_min = [interactions.index([0,0,0,0])]
#
# - The Combinations generator, which allows one to generate all the subsets of size :math:`k` of :math:`\{0,\dots,n-1\}`
#
# The total number of generated points is :math:`N=\dfrac{n!}{k!(n-k)!}`.
#
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)
# %%
# Tuples
# ------
experiment = ot.Tuples([2, 3, 5])
print(experiment.generate())
# %%
# K-permutations
# --------------
experiment = ot.KPermutations(3, 4)
print(experiment.generate())
# %%
# Combinations
# ------------
experiment = ot.Combinations(4, 6)
print(experiment.generate())
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
generators = [
ot.Tuples([4, 6, 9]),
ot.KPermutations(4, 6),
ot.Combinations(4, 6)
]
for generator in generators:
print('generator:', generator)
subsets = generator.generate()
print('subset:', subsets)
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
generators = [
ot.Tuples([4, 6, 9]), ot.KPermutations(4, 6), ot.Combinations(4, 6)]
for generator in generators:
print('generator:', generator)
subsets = generator.generate()
print('subset:', subsets)
