def __init__(self, p1, p2, size):
self.size = size
self.KF1 = openturns.KrawtchoukFactory(size[0] - 1, p1)
self.KF2 = openturns.KrawtchoukFactory(size[1] - 1, p2)
steps = []
for i in xrange(5):
for j in xrange(5):
steps.append((i, j))
self.Q = [(self.KF1.build(n), self.KF2.build(m)) for n, m in steps]
def __init__(self, p1, p2, size):
self.size = size
self.KF1 = openturns.KrawtchoukFactory(size[0] - 1, p1)
self.KF2 = openturns.KrawtchoukFactory(size[1] - 1, p2)
steps = []
for i in xrange(5):
for j in xrange(5):
steps.append((i, j))
self.Qf = [(self.KF1.build(n), self.KF2.build(m)) for n, m in steps]
self.q = []
N, M = self.size
for qf in self.Qf:
K1, K2 = qf
arr = numpy.zeros(self.size)
for x in xrange(N):
for y in xrange(M):
arr[x, y] = K1(x) * K2(y)
self.q.append(arr)
# %%
# STEP 1: Construction of the multivariate orthonormal basis
# ----------------------------------------------------------
# %%
# Create the univariate polynomial family collection which regroups the polynomial families for each direction.
# %%
polyColl = ot.PolynomialFamilyCollection(inputDimension)
# %%
# We could use the Krawtchouk and Charlier families (for discrete distributions).
# %%
polyColl[0] = ot.KrawtchoukFactory()
polyColl[1] = ot.CharlierFactory()
# %%
# We could also use the automatic selection of the polynomial which corresponds to the distribution: this is done with the `StandardDistributionPolynomialFactory` class.
# %%
for i in range(inputDimension):
marginal = distribution.getMarginal(i)
polyColl[i] = ot.StandardDistributionPolynomialFactory(marginal)
# %%
# In our specific case, we use specific polynomial factories.
# %%
polyColl[0] = ot.HermiteFactory()
import openturns as ot
import numpy as np
from matplotlib import pyplot as plt
n_functions = 8
function_factory = ot.KrawtchoukFactory()
if function_factory.getClassName() == 'KrawtchoukFactory':
function_factory = ot.KrawtchoukFactory(n_functions, .5)
functions = [function_factory.build(i) for i in range(n_functions)]
measure = function_factory.getMeasure()
if hasattr(measure, 'getA') and hasattr(measure, 'getB'):
x_min = measure.getA()
x_max = measure.getB()
else:
x_min = measure.computeQuantile(1e-3)[0]
x_max = measure.computeQuantile(1. - 1e-3)[0]
n_points = 200
meshed_support = np.linspace(x_min, x_max, n_points)
fig = plt.figure()
ax = fig.add_subplot(111)
for i in range(n_functions):
plt.plot(meshed_support,
[functions[i](x) for x in meshed_support], lw=1.5,
label='$\phi_{' + str(i) + '}(x)$')
plt.xlabel('$x$')
plt.ylabel('$\phi_i(x)$')
plt.xlim(x_min, x_max)
plt.grid()
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width, box.height * 0.9])
plt.legend(loc='upper center', bbox_to_anchor=(.5, 1.25), ncol=4)