def __init__(self, simulateur, annee, S, D):
"""
Crée un modèle de pension probabiliste.
Paramètres :
simulateur : un SimulateurRetraite
annee : un flottant, l'année de calcul de P
S : un flottant, le solde financier en part de PIB
D : un flottant positif, le montant des dépenses de retraites
en part de PIB
Description :
Crée un modèle de pension probabiliste pour le
ratio (pension moyenne) / (salaire moyen).
Les entrées du modèle sont "As", "F", "TauC"
et la sortie est "P".
Les paramètres S et D sont fixés par le constructeur
de la classe au moment de la création de l'objet.
* S : le solde financier du système de retraites (% PIB)
* D : le montant des dépenses (% PIB)
* As : l'âge moyen de départ à la retraite défini par l'utilisateur
* F : facteur d'élasticité de report de l'âge de départ
(par exemple F=0.5)
* TauC : le taux de chômage (par exemple TauC = 4.5)
Les distributions des variables sont ot.Uniform
et indépendantes.
Exemple :
S = 0.0
D = 0.14
annee = 2050
modele = ModelePensionProbabiliste(simulateur, annee, S, D)
fonction = modele.getFonction()
inputDistribution = modele.getInputDistribution()
"""
# Crée le modèle de pension complet : entrées = (S, D, As, F, TauC)
modelePension = ot.Function(FonctionPension(simulateur, annee))
# Crée le modèle réduit à partir du modèle complet : entrées = (As, F, TauC)
indices = ot.Indices([0, 1])
referencePoint = ot.Point([S, D])
self.fonction = ot.ParametricFunction(modelePension, indices, referencePoint)
# Distribution
As = ot.Uniform(62.0, 66.0)
F = ot.Uniform(0.25, 0.75)
TauC = ot.Uniform(4.5, 10.0)
self.inputDistribution = ot.ComposedDistribution([As, F, TauC])
self.inputDistribution.setDescription(["As", "F", "TauC"])
return
=================== """ # %% # In this example we are going to concatenate several processes that share the same mesh. # %% from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # Create processes to aggregate myMesher = ot.IntervalMesher(ot.Indices([100, 10])) lowerbound = [0.0, 0.0] upperBound = [2.0, 4.0] myInterval = ot.Interval(lowerbound, upperBound) myMesh = myMesher.build(myInterval) myProcess1 = ot.WhiteNoise(ot.Normal(), myMesh) myProcess2 = ot.WhiteNoise(ot.Triangular(), myMesh) # %% # Draw values of a realization of the 2nd process marginal = ot.HistogramFactory().build(myProcess1.getRealization().getValues()) graph = marginal.drawPDF() view = viewer.View(graph) # %% # Create an aggregated process
gibbs = ot.Gibbs([rwmh_beta, rwmh_alpha])
sample = gibbs.getSample(1000)
print('mu=', sample.computeMean())
print('sigma=', sample.computeStandardDeviation())
# check recompute indices, update bug
initial_state = [0.0, 0.0, 20.0]
target = ot.Normal(3)
weird_target = ot.ComposedDistribution(
[ot.Normal(), ot.Normal(), ot.Dirac(20.0)])
normal0_rwmh = ot.RandomWalkMetropolisHastings(target, initial_state,
ot.Uniform(-10, 10),
[0]) # samples from Normal(0,1)
normal1_rwmh = ot.RandomWalkMetropolisHastings(target, initial_state,
ot.Uniform(-10, 10),
[1]) # samples from Normal(0,1)
dirac_rwmh = ot.RandomWalkMetropolisHastings(weird_target, initial_state,
ot.Normal(),
[2]) # samples from Dirac(20)
# samples from Normal(0,1) x Normal(0,1) x Dirac(20)
gibbs = ot.Gibbs([normal0_rwmh, normal1_rwmh, dirac_rwmh])
sample = gibbs.getSample(1000)
recompute = gibbs.getRecomputeLogPosterior()
print(recompute)
assert recompute == ot.Indices([1, 0, 1]), "wrong recompute indices"
mean = sample.computeMean()
stddev = sample.computeStandardDeviation()
print(mean, stddev)
ott.assert_almost_equal(mean, [-0.015835, 0.169951, 20])
ott.assert_almost_equal(stddev, [0.956516, 1.05469, 0])
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print("sequential conditional quantile(", resCDF, ")=",
distribution.computeSequentialConditionalQuantile(resCDF))
# Extract the marginals
for i in range(dim):
margin = distribution.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF([0.5]))
print("margin CDF=%.6f" % margin.computeCDF([0.5]))
print("margin quantile=", repr(margin.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
if (dim >= 2):
# Extract a 2-D marginal
indices = ot.Indices(2, 0)
indices[0] = 1
indices[1] = 0
print("indices=", repr(indices))
margins = distribution.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF([0.5] * 2))
print("margins CDF=%.6f" % margins.computeCDF([0.5] * 2))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", repr(quantile))
print("margins CDF(qantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
chol = distribution.getCholesky()
invChol = distribution.getInverseCholesky()
print("chol=", repr(chol.clean(1e-6)))
ot.LinearModelTest.LinearModelResidualMean(sampleY, sampleZ).getPValue())
# Durbin Watson
ot.RandomGenerator.SetSeed(5415)
eps = ot.Normal(0, 20)
f = ot.SymbolicFunction('x', '5+2*x+x^2-0.1*x^3')
N = 15
x = ot.Sample([[0], [1.42857], [2.85714], [4.28571], [5.71429], [7.14286],
[8.57143], [10], [11.4286], [12.8571], [14.2857], [15.7143],
[17.1429], [18.5714], [20]])
y = f(x) + eps.getSample(N)
linmodel = ot.LinearModelAlgorithm(x, y).getResult().getCoefficients()
dwTest = ot.LinearModelTest.LinearModelDurbinWatson(x, y)
print('Durbin Watson = ', dwTest)
selection = ot.Indices(5)
selection.fill()
selection2 = ot.Indices(1, 0)
sampleX0 = sampleX.getMarginal(0)
# Regression test between 2 samples : firstSample of dimension n and
# secondSample of dimension 1. If firstSample[i] is the numerical sample
# extracted from firstSample (ith coordinate of each point of the
# numerical sample), PartialRegression performs the Regression test
# simultaneously on all firstSample[i] and secondSample, for i in the
# selection. The Regression test tests ifthe regression model between two
# scalar numerical samples is significant. It is based on the deviation
# analysis of the regression. The t-test is used.
# The two tests must be equal
ot.Normal(0.1, 0.0161812),
ot.LogNormal(7.71, 1.0056),
ot.Uniform(63070.0, 115600.0),
ot.Uniform(990.0, 1110.0),
ot.Uniform(63.1, 116.0),
ot.Uniform(700.0, 820.0),
ot.Uniform(1120.0, 1680.0),
ot.Uniform(9855.0, 12045.0)
]
distribution = ot.ComposedDistribution(coll)
distribution.setDescription(input_names)
# %%
# Freeze r, Tu, Tl from model to go faster
selection = [1, 2, 4]
complement = ot.Indices(selection).complement(dimension)
distribution = distribution.getMarginal(complement)
model = ot.ParametricFunction(model, selection,
distribution.getMarginal(selection).getMean())
input_names_copy = list(input_names)
input_names = itemgetter(*complement)(input_names)
dimension = len(complement)
# %%
# design of experiment
size = 1000
X = distribution.getSample(size)
Y = model(X)
# %%
# create a functional chaos model
#!/usr/bin/env python
from __future__ import print_function
import openturns as ot
import otmorris
# Define model
ot.RandomGenerator.SetSeed(0)
# Number of trajectories
r = 5
# Define experiments in [0,1]^2
print("Use Case #1 : generate trajectories from regular grid")
levels = ot.Indices(2)
levels.fill(5, 0)
morris_experiment = otmorris.MorrisExperimentGrid(levels, r)
grid_bound = morris_experiment.getBounds()
sample1 = morris_experiment.generate()
print("Morris experiment generated from grid = ", sample1)
print("Use Case #2 : generate trajectories from initial lhs design")
size = 20
# Generate an LHS design
dist = ot.ComposedDistribution(2 * [ot.Uniform(0, 1)])
experiment = ot.LHSExperiment(dist, size, True, False)
lhsDesign = experiment.generate()
print("Initial LHS design = ", lhsDesign)
# Generate designs
morris_experiment_lhs = otmorris.MorrisExperimentLHS(lhsDesign, r)
lhs_bound = morris_experiment_lhs.getBounds()
sample2 = morris_experiment.generate()
print("Morris experiment generated from LHS = ", sample2)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
ot.RandomGenerator.SetSeed(0)
# Generate sample with the given plane
distribution = ot.ComposedDistribution(
ot.DistributionCollection(
[ot.Exponential(), ot.Triangular(-1.0, -0.5, 1.0)]))
marginalDegrees = ot.Indices([3, 6])
myPlane = ot.GaussProductExperiment(ot.Distribution(distribution),
marginalDegrees)
sample = myPlane.generate()
# Create an empty graph
graph = ot.Graph("", "x1", "x2", True, "")
# Create the cloud
cloud = ot.Cloud(sample, "blue", "fsquare", "")
# Then, draw it
graph.add(cloud)
fig = plt.figure(figsize=(4, 4))
plt.suptitle("Gauss product experiment")
axis = fig.add_subplot(111)
axis.set_xlim(auto=True)
View(graph, figure=fig, axes=[axis], add_legend=False)
# Check 2-d array which nested dim is size=1 / Function
# interoperability
def aFunc2(x):
return [2.0 * x[0]]
PYNMF = ot.PythonFunction(1, 1, aFunc2)
a0 = np.array(([1.]))
print("Point", PYNMF(a0), "= PYNMF( array", a0, ")")
a1 = np.array(([1.], [2.], [3.]))
print("Sample", PYNMF(a1), "= PYNMF( array", a1, ")")
# Check tuple / Indices conversion
t0 = (1, 2)
i0 = ot.Indices(t0)
print("tuple", t0, "=> Indices", i0)
t1 = tuple(i0)
print("Indices", i0, "=> tuple", tuple([int(x) for x in t0]))
# Check list / Indices conversion
l0 = [3, 4, 5]
i0 = ot.Indices(l0)
print("list", l0, "=> Indices", i0)
l1 = list(i0)
print("Indices", i0, "=> list", [int(x) for x in l1])
# check Indices typemap
sample = ot.Normal(3).getSample(10)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
ot.RandomGenerator.SetSeed(0)
# Generate sample with the given plane
distribution = ot.ComposedDistribution(
[ot.Exponential(), ot.Triangular(-1.0, -0.5, 1.0)])
marginalSizes = ot.Indices([3, 6])
experiment = ot.GaussProductExperiment(
ot.Distribution(distribution), marginalSizes)
sample = experiment.generate()
# Create an empty graph
graph = ot.Graph("Gauss product experiment", "x1", "x2", True, "")
# Create the cloud
cloud = ot.Cloud(sample, "blue", "fsquare", "")
# Then, draw it
graph.add(cloud)
fig = plt.figure(figsize=(4, 4))
axis = fig.add_subplot(111)
axis.set_xlim(auto=True)
View(graph, figure=fig, axes=[axis], add_legend=False)
marginRef = copulaRef.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF =%.6f" %
margin.computePDF(ot.Point(1, 0.25)))
print("margin PDF (ref)=%.6f" %
marginRef.computePDF(ot.Point(1, 0.25)))
print("margin CDF =%.6f" %
margin.computeCDF(ot.Point(1, 0.25)))
print("margin CDF (ref)=%.6f" %
marginRef.computeCDF(ot.Point(1, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = ot.Indices([1, 0])
print("indices=", repr(indices))
margin = copula.getMarginal(indices)
marginRef = copulaRef.getMarginal(indices)
print("margin=", repr(margin))
print("margin PDF =%.6f" % margin.computePDF(ot.Point(2, 0.25)))
print("margin PDF (ref)=%.6f" %
marginRef.computePDF(ot.Point(2, 0.25)))
print("margin CDF =%.6f" % margin.computeCDF(ot.Point(2, 0.25)))
print("margin CDF (ref)=%.6f" %
marginRef.computeCDF(ot.Point(2, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# tbb nested parallelism issue
def _compute_coefficients_legendre(self,
sample_paths,
legendre_quadrature_order=None):
dimension = self._lower_bound.size
truncation_order = self._truncation_order
if legendre_quadrature_order is None:
legendre_quadrature_order = self._legendre_quadrature_order
elif type(legendre_quadrature_order) is not int \
or legendre_quadrature_order <= 0:
raise ValueError('legendre_quadrature_order must be a positive ' +
'integer.')
n_sample_paths = len(sample_paths)
# Gauss-Legendre quadrature nodes and weights
polyColl = ot.PolynomialFamilyCollection([ot.LegendreFactory()] *
dimension)
polynoms = ot.OrthogonalProductPolynomialFactory(polyColl)
U, W = polynoms.getNodesAndWeights(
ot.Indices([legendre_quadrature_order] * dimension))
W = np.ravel(W)
U = np.array(U)
scale = (self._upper_bound - self._lower_bound) / 2.
shift = (self._upper_bound + self._lower_bound) / 2.
X = scale * U + shift
# Compute coefficients
try:
available_memory = int(.9 * get_available_memory())
except:
if self.verbose:
print('WRN: Available memory estimation failed! '
'Assuming 1Gb is available (first guess).')
available_memory = 1024**3
max_size = int(available_memory / 8 / truncation_order /
n_sample_paths)
batch_size = min(W.size, max_size)
if self.verbose and batch_size < W.size:
print('RAM: %d Mb available' % (available_memory / 1024**2))
print('RAM: %d allocable terms / %d total terms' %
(max_size, W.size))
print('RAM: %d loops required' % np.ceil(float(W.size) / max_size))
while True:
coefficients = np.zeros((n_sample_paths, truncation_order))
try:
n_done = 0
while n_done < W.size:
sample_paths_values = np.vstack([
np.ravel(sample_paths[i](X[n_done:(n_done +
batch_size)]))
for i in range(n_sample_paths)
])
mean_values = np.ravel(
self._mean(X[n_done:(n_done +
batch_size)]))[np.newaxis, :]
centered_sample_paths_values = \
sample_paths_values - mean_values
del sample_paths_values, mean_values
eigenelements_values = np.vstack([
self._eigenfunctions[k](
X[n_done:(n_done + batch_size)]) /
np.sqrt(self._eigenvalues[k])
for k in range(truncation_order)
])
coefficients += np.sum(
W[np.newaxis, np.newaxis, n_done:(n_done + batch_size)]
* centered_sample_paths_values[:, np.newaxis, :] *
eigenelements_values[np.newaxis, :, :],
axis=-1)
del centered_sample_paths_values, eigenelements_values
n_done += batch_size
break
except MemoryError:
batch_size /= 2
coefficients *= np.prod(self._upper_bound - self._lower_bound)
return coefficients
def _legendre_galerkin_scheme(self,
legendre_galerkin_order=10,
legendre_quadrature_order=None):
# Input checks
if legendre_galerkin_order <= 0:
raise ValueError('legendre_galerkin_order must be a positive ' +
'integer!')
if legendre_quadrature_order is not None:
if legendre_quadrature_order <= 0:
raise ValueError('legendre_quadrature_order must be a ' +
'positive integer!')
# Settings
dimension = self._lower_bound.size
truncation_order = self._truncation_order
galerkin_size = ot.EnumerateFunction(
dimension).getStrataCumulatedCardinal(legendre_galerkin_order)
if legendre_quadrature_order is None:
legendre_quadrature_order = 2 * legendre_galerkin_order + 1
# Check if the current settings are compatible
if truncation_order > galerkin_size:
raise ValueError(
'The truncation order must be less than or ' +
'equal to the size of the functional basis in the chosen ' +
'Legendre Galerkin scheme. Current size of the galerkin basis '
+ 'only allows to get %d terms in the KL expansion.' %
galerkin_size)
# Construction of the Galerkin basis: tensorized Legendre polynomials
tensorized_legendre_polynomial_factory = \
ot.PolynomialFamilyCollection([ot.LegendreFactory()] * dimension)
tensorized_legendre_polynomial_factory = \
ot.OrthogonalProductPolynomialFactory(
tensorized_legendre_polynomial_factory)
tensorized_legendre_polynomials = \
[tensorized_legendre_polynomial_factory.build(i)
for i in range(galerkin_size)]
# Compute matrix C coefficients using Gauss-Legendre quadrature
polyColl = ot.PolynomialFamilyCollection([ot.LegendreFactory()] *
dimension * 2)
polynoms = ot.OrthogonalProductPolynomialFactory(polyColl)
U, W = polynoms.getNodesAndWeights(
ot.Indices([legendre_quadrature_order] * dimension * 2))
W = np.ravel(W)
scale = (self._upper_bound - self._lower_bound) / 2.
shift = (self._upper_bound + self._lower_bound) / 2.
U = np.array(U)
X = np.repeat(scale, 2) * U + np.repeat(shift, 2)
if self.verbose:
print('Computing matrix C...')
try:
available_memory = int(.9 * get_available_memory())
except:
if self.verbose:
print('WRN: Available memory estimation failed! '
'Assuming 1Gb is available (first guess).')
available_memory = 1024**3
max_size = int(available_memory / 8 / galerkin_size**2)
batch_size = min(W.size, max_size)
if self.verbose and batch_size < W.size:
print('RAM: %d Mb available' % (available_memory / 1024**2))
print('RAM: %d allocable terms / %d total terms' %
(max_size, W.size))
print('RAM: %d loops required' % np.ceil(float(W.size) / max_size))
while True:
C = np.zeros((galerkin_size, galerkin_size))
try:
n_done = 0
while n_done < W.size:
covariance_at_X = self._covariance(X[n_done:(n_done +
batch_size)])
H1 = np.vstack([
np.ravel(tensorized_legendre_polynomials[i](
U[n_done:(n_done + batch_size), :dimension]))
for i in range(galerkin_size)
])
H2 = np.vstack([
np.ravel(tensorized_legendre_polynomials[i](
U[n_done:(n_done + batch_size), dimension:]))
for i in range(galerkin_size)
])
C += np.sum(W[np.newaxis, np.newaxis,
n_done:(n_done + batch_size)] *
covariance_at_X[np.newaxis, np.newaxis, :] *
H1[np.newaxis, :, :] * H2[:, np.newaxis, :],
axis=-1)
del covariance_at_X, H1, H2
n_done += batch_size
break
except MemoryError:
batch_size /= 2
C *= np.prod(self._upper_bound - self._lower_bound)**2.
# Matrix B is orthonormal up to some constant
B = np.diag(
np.repeat(np.prod(self._upper_bound - self._lower_bound),
galerkin_size))
# Solve the generalized eigenvalue problem C D = L B D in L, D
if self.verbose:
print('Solving generalized eigenvalue problem...')
eigenvalues, eigenvectors = linalg.eigh(C, b=B, lower=True)
eigenvalues, eigenvectors = eigenvalues.real, eigenvectors.real
# Sort the eigensolutions in the descending order of eigenvalues
order = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[order]
eigenvectors = eigenvectors[:, order]
# Truncate the expansion
eigenvalues = eigenvalues[:truncation_order]
eigenvectors = eigenvectors[:, :truncation_order]
# Eliminate unsignificant negative eigenvalues
if eigenvalues.min() <= 0.:
if eigenvalues.min() > .01 * eigenvalues.max():
raise Exception(
'The smallest significant eigenvalue seems ' +
'to be negative... Check the positive definiteness of the '
+ 'covariance function.')
else:
truncation_order = np.nonzero(eigenvalues <= 0)[0][0]
eigenvalues = eigenvalues[:truncation_order]
eigenvectors = eigenvectors[:, :truncation_order]
self._truncation_order = truncation_order
print('WRN: truncation_order was too large.')
print('It has been reset to: %d' % truncation_order)
# Define eigenfunctions
class LegendrePolynomialsBasedEigenFunction():
def __init__(self, vector):
self._vector = vector
def __call__(self, x):
x = np.asanyarray(x)
if x.ndim <= 1:
x = np.atleast_2d(x).T
u = (x - shift) / scale
return np.sum([
np.ravel(tensorized_legendre_polynomials[i](u)) *
self._vector[i] for i in range(truncation_order)
],
axis=0)
# Set attributes
self._eigenvalues = eigenvalues
self._eigenfunctions = [
LegendrePolynomialsBasedEigenFunction(vector)
for vector in eigenvectors.T
]
self._legendre_galerkin_order = legendre_galerkin_order
self._legendre_quadrature_order = legendre_quadrature_order
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
try:
mesh = ot.IntervalMesher(ot.Indices(1, 9)).build(ot.Interval(-1.0, 1.0))
factory = ot.KarhunenLoeveP1Factory(mesh, 0.0)
eigenValues = ot.NumericalPoint()
KLModes = factory.buildAsProcessSample(ot.AbsoluteExponential([1.0]),
eigenValues)
print("KL modes=", KLModes)
print("KL eigenvalues=", eigenValues)
cov1D = ot.AbsoluteExponential([1.0])
KLFunctions = factory.build(cov1D, eigenValues)
print("KL functions=", KLFunctions)
print("KL eigenvalues=", eigenValues)
R = ot.CorrelationMatrix(2, [1.0, 0.5, 0.5, 1.0])
scale = [1.0]
amplitude = [1.0, 2.0]
cov2D = ot.ExponentialModel(scale, amplitude, R)
KLFunctions = factory.build(cov2D, eigenValues)
print("KL functions=", KLFunctions)
print("KL eigenvalues=", eigenValues)
except:
import sys
print("t_KarhunenLoeveP1Factory_std.py",
sys.exc_info()[0],
sys.exc_info()[1])
#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
size = 4
indices = ot.Indices(size, 0)
indices.fill()
print("indices=", repr(indices))
print("are indices valid with bound=", size, "? ", indices.check(size))
print("are indices valid with bound=", size // 2, "? ",
indices.check(size // 2))
indices[0] = indices[size - 1]
print("indices after transformation=", repr(indices))
print("are indices valid with bound=", size, "? ", indices.check(size))
print("complement wrt 7=", indices.complement(7))
print("empty complement=", ot.Indices().complement(7))
# slicing
indices2 = ot.Indices((1, 2, 3, 4, 5))
print('indices2[2] = ', indices2[2])
print('indices2[1:3] = ', indices2[1:3])
print('indices2[:] = ', indices2[:])
indices2[1:3] = (88, 99)
print('indices2 = ', indices2)
index = indices2.find(88)
assert index < indices2.getSize(), "wrong index"
assert indices2[index] == 88, "wrong index"
# simulate the true physical model
basis = ot.ConstantBasisFactory(4).build()
covarianceModel = ot.SquaredExponential([5.03148, 13.9442, 20, 20], [15.1697])
krigingModel = ot.KrigingAlgorithm(inputSample, signals, covarianceModel,
basis)
ot.RandomGenerator.SetSeed(0)
np.random.seed(0)
krigingModel.run()
physicalModel = krigingModel.getResult().getMetaModel()
####### Test on the POD models ###################
# Test hitmiss without Box Cox with rf classifier
np.random.seed(0)
ot.RandomGenerator.SetSeed(0)
ot.RandomGenerator.SetState(ot.RandomGeneratorState(ot.Indices([0] * 768), 0))
POD1 = otpod.AdaptiveHitMissPOD(inputDOE, outputDOE, physicalModel, 20,
detection)
POD1.run()
detectionSize1 = POD1.computeDetectionSize(0.9, 0.95)
def test_1_a90():
np.testing.assert_almost_equal(detectionSize1[0],
4.71811745363573,
decimal=5)
def test_1_a95():
np.testing.assert_almost_equal(detectionSize1[1],
5.35497504836619,
#!/usr/bin/env python
# coding: utf-8
from __future__ import print_function
import openturns as ot
import persalys
# mesh model
meshModel0 = persalys.GridMeshModel()
print(meshModel0)
# mesh model
meshModel1 = persalys.GridMeshModel([persalys.Variable('x', 'aDescription')],
ot.Interval(0., 12.), ot.Indices(1, 20))
print(meshModel1)
filename = 'mesh.csv'
mesh = ot.IntervalMesher(ot.Indices(1, 20)).build(ot.Interval(0., 12.))
mesh.getVertices().exportToCSVFile(filename)
# mesh model
meshModel2 = persalys.ImportedMeshModel()
print(meshModel2)
# mesh model
meshModel3 = persalys.ImportedMeshModel(
[persalys.Variable('z', 'aDescription')], 'mesh.csv', ot.Indices(1, 0))
# Then g acts on processes X: Omega * R^nSpat --> R^2 # # Create a trend function fTrend: R^n --> R^q # for example for myXtProcess of dimension 2 # defined on a bidimensional mesh # fTrend : R^2 --> R^2 # (t1, t2) --> (1+2t1, 1+3t2) fTrend = ot.SymbolicFunction(['t1', 't2'], ['1+2*t1', '1+3*t2']) # # Create a Gaussian process of dimension 2 # which mesh is of box of dimension 2 myIndices = ot.Indices([80, 40]) myMesher = ot.IntervalMesher(myIndices) lowerBound = [0., 0.] upperBound = [2., 1.] myInterval = ot.Interval(lowerBound, upperBound) myMesh = myMesher.build(myInterval) # Define a bidimensional temporal Gaussian process on the mesh # with independent components amplitude = [1.0, 1.0] scale = [0.2, 0.3] myCovModel = ot.ExponentialModel(scale, amplitude) myXtProcess_temp = ot.GaussianProcess(myCovModel, myMesh) # Non linear transformation of myXtProcess
E = ot.ParametrizedDistribution(ot.LogNormalMuSigmaOverMu(3e4, 0.12))
F = ot.ParametrizedDistribution(ot.LogNormalMuSigmaOverMu(0.1, 0.20))
list_marginals = [L, b, h, E, F]
distribution = ot.ComposedDistribution(list_marginals)
distribution.setDescription(('L', 'b', 'h', 'E', 'F'))
dim = distribution.getDimension()
level_number = 4
trajectories = 10
jump_step = int(level_number / 2)
levels = [level_number] * dim
# set the bounds of the grid experiment
bound = ot.Interval(
[marginal.computeQuantile(0.01)[0] for marginal in list_marginals],
[marginal.computeQuantile(0.99)[0] for marginal in list_marginals])
experiment = otmorris.MorrisExperimentGrid(levels, bound, trajectories)
experiment.setJumpStep(ot.Indices([jump_step] * dim))
# create and compute the design of experiments
input_sample = experiment.generate()
print("Morris experiment generated from grid = ")
print(input_sample)
output_sample = poutre(input_sample)
# run the Morris analysis
morris = otmorris.Morris(input_sample, output_sample, bound)
print("E(|EE|) = ", morris.getMeanAbsoluteElementaryEffects())
print("E(EE) = ", morris.getMeanElementaryEffects())
print("V(|EE|)^{1/2} = ", morris.getStandardDeviationElementaryEffects())
# # thanks to the method *getInverse()* which produces an object of type # *InverseBoxCoxTransform* that can be evaluated on a field. # The new field based shares the same mesh than the initial field. # # %% from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # Define a process myIndices = ot.Indices([10, 5]) myMesher = ot.IntervalMesher(myIndices) myInterval = ot.Interval([0.0, 0.0], [2.0, 1.0]) myMesh = myMesher.build(myInterval) amplitude = [1.0] scale = [0.2, 0.2] myCovModel = ot.ExponentialModel(scale, amplitude) myXproc = ot.GaussianProcess(myCovModel, myMesh) g = ot.SymbolicFunction(['x1'], ['exp(x1)']) myDynTransform = ot.ValueFunction(g, myMesh) myXtProcess = ot.CompositeProcess(myDynTransform, myXproc) # %% # Draw a field field = myXtProcess.getRealization() graph = field.drawMarginal(0)
#! /usr/bin/env python
import openturns as ot
import pickle
from io import BytesIO
obj_list = []
obj_list.append(ot.Point([1.6, -8.7]))
obj_list.append(ot.Sample([[4.6, -3.7], [8.4, 6.3]]))
obj_list.append(ot.Description(['x', 'y', 'z']))
obj_list.append(ot.Indices([1, 2, 4]))
obj_list.append(ot.Matrix([[1, 2], [3, 4]]))
obj_list.append(ot.SymbolicFunction(['x1', 'x2'], ['y1=x1+x2']))
src = BytesIO()
for obj in obj_list:
pickle.dump(obj, src)
src.seek(0)
for obj in obj_list:
obj2 = pickle.load(src)
print(('object: ' + str(obj)))
print(('same: ' + str(obj2 == obj) + '\n'))
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
# Default constructor
flat1 = ot.IndicesCollection()
print('flat1=', flat1)
# Constructor with Collection<Indices>
coll2 = []
ind1 = ot.Indices(1)
ind4 = ot.Indices(4)
ind4.fill(8)
ind3 = ot.Indices(3)
ind3.fill(3)
coll2.append(ind1)
coll2.append(ind4)
coll2.append(ind3)
flat2 = ot.IndicesCollection(coll2)
print('flat2=', flat2)
# Copy constructor
flat3 = ot.IndicesCollection(flat2)
print('flat3=', flat3)
# Strided
coll4 = []
coll4.append(ind4)
coll4.append(ind4)
coll4.append(ind4)
# Get 95% quantile
quantile = distribution.computeQuantile(0.95)
print("Quantile=", repr(quantile))
print("entropy=%.6f" % distribution.computeEntropy())
for i in range(6):
print("standard moment n=", i, " value=",
distribution.getStandardMoment(i))
print("Standard representative=", distribution.getStandardRepresentative())
print("parameter=", distribution.getParameter())
print("parameterDescription=", distribution.getParameterDescription())
parameter = distribution.getParameter()
parameter[-1] = 0.3
distribution.setParameter(parameter)
print("parameter=", distribution.getParameter())
# To prevent automatic compaction
ot.ResourceMap.SetAsUnsignedInteger("UserDefined-SmallSize", 5)
sample = ot.Sample(40, 3)
for i in range(4):
for j in range(3):
sample[i, j] = 10 * (i // 3 + 1) + 0.1 * (j + 1)
multivariateUserDefined = ot.UserDefined(sample)
print("Multivariate UserDefined=", multivariateUserDefined)
print("Marginal 0=", multivariateUserDefined.getMarginal(0))
indices = ot.Indices(2)
indices[0] = 2
indices[1] = 0
print("Marginal (2, 0)=", multivariateUserDefined.getMarginal(indices))
# With the model, we want to compare values
# We compare values computed with theoritical values
plotSample = ot.Sample(frequencyGrid.getN(), 3)
# Loop of comparison ==> data are saved in plotSample
for k in range(frequencyGrid.getN()):
freq = frequencyGrid.getStart() + k * frequencyGrid.getStep()
plotSample[k, 0] = freq
plotSample[k, 1] = abs(myEstimatedModel_PS(freq)[0, 0])
plotSample[k, 2] = abs(model(freq)[0, 0])
# Graph section
# We build 2 curves
# each one is function of frequency values
ind = ot.Indices(2)
ind.fill()
# Some cosmetics : labels, legend position, ...
graph = ot.Graph("Spectral model estimation", "Frequency",
"Spectral density function", True, "topright", 1.0, ot.GraphImplementation.LOGY)
# The first curve is the estimate density as function of frequency
curve1 = ot.Curve(plotSample.getMarginal(ind))
curve1.setColor('blue')
curve1.setLegend('estimate model')
# The second curve is the theoritical density as function of frequency
ind[1] = 2
curve2 = ot.Curve(plotSample.getMarginal(ind))
curve2.setColor('red')
val1 = ref_point2[0]
val2 = ref_point2[1]
print("point2[0] = %.6f" % val1)
print("point2[1] = %.6f" % val2)
# Copy constructor
point3 = ot.Point(ref_point1)
ref_point3 = point3
val1 = ref_point3[0]
val2 = ref_point3[1]
print("point3[0] = %.6f" % val1)
print("point3[1] = %.6f" % val2)
# Constructor from indices
indices = ot.Indices(5)
indices.fill()
point = ot.Point(indices)
print("point=", point)
# Constructor from python sequence
point4 = ot.Point((1000., 1001.))
i = 0
for coord in point4:
print("point4[%d] = %.6f" % (i, coord))
i += 1
# Comparison operator
if ref_point2 != ref_point2:
print(
"OT::Base::Type::Point.operator == does NOT return the correct value. Says that point2 and point2 are DIFFERENT though they are equal.")
import openturns as ot from matplotlib import pyplot as plt from openturns.viewer import View # Create a process X: R^2 --> R^2 # Define a bi dimensional mesh as a box myIndices = ot.Indices([40, 20]) myMesher = ot.IntervalMesher(myIndices) lowerBound = [0.0, 0.0] upperBound = [2.0, 1.0] myInterval = ot.Interval(lowerBound, upperBound) myMesh = myMesher.build(myInterval) # Define a scalar temporal Gaussian process on the mesh # this process is stationary # myXproc R^2 --> R amplitude = [1.0] scale = [0.2, 0.2] myCovModel = ot.ExponentialModel(scale, amplitude) myXproc = ot.GaussianProcess(myCovModel, myMesh) # Transform myXproc to make its variance depend on the vertex (s,t) # and to get a positive process # thanks to the spatial function g # myXtProcess R --> R g = ot.SymbolicFunction(['x1'], ['exp(x1)']) myDynTransform = ot.ValueFunction(g, 2) myXtProcess = ot.CompositeProcess(myDynTransform, myXproc) myField = myXtProcess.getRealization()
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
size = 4
indices = ot.Indices(size, 0)
indices.fill()
print("indices=", repr(indices))
print("are indices valid with bound=", size, "? ", indices.check(size))
print("are indices valid with bound=", size // 2, "? ",
indices.check(size // 2))
indices[0] = indices[size - 1]
print("indices after transformation=", repr(indices))
print("are indices valid with bound=", size, "? ", indices.check(size))
print("complement wrt 7=", indices.complement(7))
# slicing
indices2 = ot.Indices((1, 2, 3, 4, 5))
print('indices2[2] = ', indices2[2])
print('indices2[1:3] = ', indices2[1:3])
print('indices2[:] = ', indices2[:])
indices2[1:3] = (88, 99)
print('indices2 = ', indices2)
index = indices2.find(88)
assert index < indices2.getSize(), "wrong index"
assert indices2[index] == 88, "wrong index"