def _computePValuesPermutation(self):
W_obs = self._computeWeightMatrix(self.Y)
self.PValuesPermutation = ot.Point()
N_permutations = ot.KPermutationsDistribution(
self.n, self.n).getSample(self.PermutationBootstrapSize)
permuted_values = [[int(x) for x in N_permutations[j]]
for j in range(self.PermutationBootstrapSize)]
for dim in range(self.d):
HSIC_obs = self._computeHSICIndex(self.X[:, dim], self.Y,
self.CovX[dim], self.CovY, W_obs)
HSIC_l = []
for perm in permuted_values:
Y_p = self.Y[perm]
W = self._computeWeightMatrix(Y_p)
HSIC_l.append(
self._computeHSICIndex(self.X[:, dim], Y_p, self.CovX[dim],
self.CovY, W))
p = np.count_nonzero(np.array(HSIC_l) > HSIC_obs) / (
self.PermutationBootstrapSize + 1)
self.PValuesPermutation.add(p)
return 0
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.KPermutationsDistribution().__class__.__name__ == 'ComposedDistribution'
):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.KPermutationsDistribution().__class__.__name__ ==
'CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
else:
distribution = ot.KPermutationsDistribution()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
distribution.setDescription(['$x_1$', '$x_2$'])
#backends = ["MuParser"]
ot.ResourceMap.SetAsUnsignedInteger('SymbolicParserExprTk-MaxNodeDepth',
100000)
size = 1000
N = 1000
X = ["x" + str(i) for i in range(N)]
P = 10
nb_factors_generator = ot.Binomial(P - 1, 0.5)
# Create the generators once and for all
indices_generator = list()
for k in range(P):
indices_generator.append(ot.KPermutationsDistribution(k + 1, N))
for j in range(17):
print("#" * 50)
M = 2**j
print("M=", M)
t0 = time()
print("Create formula...")
formula = ''
for i in range(M):
K = int(nb_factors_generator.getRealization()[0])
factor = ''
indices = indices_generator[K].getRealization()
for j in range(K + 1):
factor += X[int(indices[j])]
if j < K:
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.KPermutationsDistribution().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.KPermutationsDistribution().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
elif ot.KPermutationsDistribution().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.KPermutationsDistribution()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
plt.suptitle(str(distribution))
# %%
import openturns as ot
# %%
# In this short example we present a simple way to mix the lines of a sample
# thanks to the :class:`~openturns.KPermutationsDistribution` class.
# %%
# We first define a small sample of size :math:`N` based on a standard unit gaussian distribution.
distribution = ot.Normal()
N = 5
sample = distribution.getSample(N)
# %%
# We print the sample :
print(sample)
# %%
# A new set of randomly mixed indices is a realization of a permutation of N elements amongst N :
#
mixingDistribution = ot.KPermutationsDistribution(N, N)
newIndices = mixingDistribution.getSample(1)[0, :]
# %%
# The new indices will be these ones :
print("New indices : ", newIndices)
# %%
# Eventually the randomized sample is
print(sample[[int(i) for i in newIndices]])
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.KPermutationsDistribution().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.KPermutationsDistribution().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.KPermutationsDistribution(
).__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.KPermutationsDistribution(
).__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(
coll, ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.KPermutationsDistribution().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.KPermutationsDistribution().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.KPermutationsDistribution(
).__class__.__name__ == 'MaximumDistribution':
coll = [
ot.Uniform(2.5, 3.5),
ot.LogUniform(1.0, 1.2),
ot.Triangular(2.0, 3.0, 4.0)
]
