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 matplotlib import pyplot as plt
from openturns.viewer import View
f = ot.SymbolicFunction(['x'], ['sin(x)'])
a = -2.5
b = 4.5
algo = ot.GaussLegendre([20])
value, nodes = algo.integrateWithNodes(f, ot.Interval(a, b))
g = f.draw(a, b, 512)
lower = ot.Cloud(nodes, ot.Sample(nodes.getSize(), 1))
lower.setColor("magenta")
lower.setPointStyle('circle')
g.add(lower)
fig = plt.figure(figsize=(8, 4))
plt.suptitle(
r"GaussLegendre example: $\int_{-5/2}^{9/2}\sin(t)\,dt=$" + str(value[0]))
axis = fig.add_subplot(111)
axis.set_xlim(auto=True)
View(g, figure=fig, axes=[axis], add_legend=False)