def meshHeart(ntheta, nr):
# First, build the nodes
nodes = ot.Sample(0, 2)
nodes.add([0.0, 0.0])
for j in range(ntheta):
theta = (m.pi * j) / ntheta
if (abs(theta - 0.5 * m.pi) < 1e-10):
rho = 2.0
elif (abs(theta) < 1e-10) or (abs(theta - m.pi) < 1e-10):
rho = 0.0
else:
absTanTheta = abs(m.tan(theta))
rho = absTanTheta**(1.0 / absTanTheta) + m.sin(theta)
cosTheta = m.cos(theta)
sinTheta = m.sin(theta)
for k in range(nr):
tau = (k + 1.0) / nr
r = rho * tau
nodes.add([r * cosTheta, r * sinTheta - tau])
# Second, build the triangles
triangles = []
## First heart
for j in range(ntheta):
triangles.append([0, 1 + j * nr, 1 + ((j + 1) % ntheta) * nr])
# Other hearts
for j in range(ntheta):
for k in range(nr - 1):
i0 = k + 1 + j * nr
i1 = k + 2 + j * nr
i2 = k + 2 + ((j + 1) % ntheta) * nr
i3 = k + 1 + ((j + 1) % ntheta) * nr
triangles.append([i0, i1, i2 % (nr * ntheta)])
triangles.append([i0, i2, i3 % (nr * ntheta)])
return ot.Mesh(nodes, triangles)
def liftAsProcessSample(self, coefficients):
'''Function to lift a sample of coefficients into a collections of
process samples and points.
Parameters
----------
coefficients : ot.Sample
sample of values, follwing a centered normal law in general
Returns
-------
processes : list
ordered list of samples of scalars (ot.Sample) and field samples (ot.ProcessSample)
'''
assert isinstance(coefficients, (ot.Sample, ot.SampleImplementation))
print('Lifting as process sample')
jumpDim = 0
processes = []
for i in range(self.__field_distribution_count__):
if self.__isProcess__[i] :
if not self.__liftWithMean__:
processes.append(self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]]))
else :
processSample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
addConstant2Iterable(processSample, self.__means__[i])
processes.append(processSample)
else :
if not self.__liftWithMean__:
processSample = ot.ProcessSample(ot.Mesh(), 0, 1)
val_sample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
for j, value in enumerate(val_sample):
field = ot.Field(ot.Mesh(),1)
field.setValueAtIndex(0,value)
processSample.add(field)
processes.append(processSample)
else :
processSample = ot.ProcessSample(ot.Mesh(), 0, 1)
val_sample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
mean = self.__means__[i]
for j, value in enumerate(val_sample):
field = ot.Field(ot.Mesh(),1)
field.setValueAtIndex(0,[value[0]+mean]) # adding mean
processSample.add(field)
processes.append(processSample)
jumpDim += self.__mode_count__[i]
return processes
def simulate(self, value_input=None, reset=True, **kwargs):
"""Simulate the fmu.
Parameters
----------
value_input : Vector of input values.
reset : Boolean, toggle resetting the FMU prior to simulation. True by
default.
time : Sequence of floats, time vector (optional).
timestep : Float, time step in seconds (optional).
Additional keyword arguments are passed on to the 'simulate' method of
the underlying PyFMI model object.
"""
kwargs.setdefault("initialization_script", self.initialization_script)
kwargs_simulate = fmi.parse_kwargs_simulate(
value_input, name_input=self.getFMUInputDescription(),
name_output=self.getFMUOutputDescription(),
model=self.model, **kwargs)
if "final_time" in kwargs.keys():
raise Warning("final_time must be set in the constructor.")
if "start_time" in kwargs.keys():
raise Warning("start_time must be set in the constructor.")
simulation = fmi.simulate(self.model,
reset=reset,
start_time=self.start_time,
final_time=self.final_time,
**kwargs_simulate)
time, values = fmi.strip_simulation(simulation,
name_output=self.getOutputDescription(),
final="trajectory")
local_mesh = ot.Mesh([[t] for t in time], [[i, i + 1] for i in range(len(time) - 1)])
interpolation = ot.P1LagrangeInterpolation(local_mesh, self.getOutputMesh(), self.getOutputDimension())
return interpolation(values)
# Test realization
print('One realization= ')
print(myCompositeProcess.getRealization())
# future
print('future=', myCompositeProcess.getFuture(5))
#
# Create a spatial dynamical function
# Create the function g : R^2 --> R^2
# (x1,x2) --> (x1^2, x1+x2)
g = ot.SymbolicFunction(['x1', 'x2'], ['x1^2', 'x1+x2'])
# Convert g : R --> R into a spatial fucntion
myDynFunc = ot.ValueFunction(g, ot.Mesh(2))
# 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
class AggregatedKarhunenLoeveResults(object):
'''Class allowing us to aggregated scalar distributions and stochastic processes.
Thanks to the Karhunen-Loève expansion we can consider a process with a given
covariance model as a vector of random variables following a centered normal law.
By stacking the scalar distributions and the vectors representative of the fields we
obtain a unique vector representation of our aggregate.
It is a link between a non homogenous ensemble of fields and scalars to a unique vector
of scalars.
'''
def __init__(self, composedKLResultsAndDistributions):
'''Initializes the aggregation
Parameters
----------
composedKLResultsAndDistributions : list
list of ordered ot.Distribution and ot.KarhunenLoeveResult objects
'''
self.__KLResultsAndDistributions__ = atLeastList(composedKLResultsAndDistributions) #KLRL : Karhunen Loeve Result List
assert len(self.__KLResultsAndDistributions__)>0
self.__field_distribution_count__ = len(self.__KLResultsAndDistributions__)
self.__name__ = 'Unnamed'
self.__KL_lifting__ = []
self.__KL_projecting__ = []
#Flags
self.__isProcess__ = [False]*self.__field_distribution_count__
self.__has_distributions__ = False
self.__unified_dimension__ = False
self.__unified_mesh__ = False
self.__isAggregated__ = False
self.__means__ = [.0]*self.__field_distribution_count__
self.__liftWithMean__ = False
# checking the nature of eachelement of the input list
for i in range(self.__field_distribution_count__):
# If element is a Karhunen Loeve decomposition
if isinstance(self.__KLResultsAndDistributions__[i], ot.KarhunenLoeveResult):
# initializing lifting and projecting objects.
self.__KL_lifting__.append(ot.KarhunenLoeveLifting(self.__KLResultsAndDistributions__[i]))
self.__KL_projecting__.append(ot.KarhunenLoeveProjection(self.__KLResultsAndDistributions__[i]))
self.__isProcess__[i] = True
# If element is a distribution
elif isinstance(self.__KLResultsAndDistributions__[i], (ot.Distribution, ot.DistributionImplementation)):
self.__has_distributions__ = True
if self.__KLResultsAndDistributions__[i].getMean()[0] != 0 :
print('The mean value of distribution {} at index {} of type {} is not 0.'.format(str('"'+self.__KLResultsAndDistributions__[i].getName()+'"'), str(i), self.__KLResultsAndDistributions__[i].getClassName()))
name_distr = self.__KLResultsAndDistributions__[i].getName()
self.__means__[i] = self.__KLResultsAndDistributions__[i].getMean()[0]
self.__KLResultsAndDistributions__[i] -= self.__means__[i]
self.__KLResultsAndDistributions__[i].setName(name_distr)
print('Distribution recentered and mean added to list of means')
print('Set the "liftWithMean" flag to true if you want to include the mean.')
# We can say that the inverse iso probabilistic transformation is analoguous to lifting
self.__KL_lifting__.append(self.__KLResultsAndDistributions__[i].getInverseIsoProbabilisticTransformation())
# We can say that the iso probabilistic transformation is analoguous to projecting
self.__KL_projecting__.append(self.__KLResultsAndDistributions__[i].getIsoProbabilisticTransformation())
# If the function has distributions it cant be homogenous
if not self.__has_distributions__ :
self.__unified_mesh__ = all_same([self.__KLResultsAndDistributions__[i].getMesh() for i in range(self.__field_distribution_count__)])
self.__unified_dimension__ = ( all_same([self.__KLResultsAndDistributions__[i].getCovarianceModel().getOutputDimension() for i in range(self.__field_distribution_count__)])\
and all_same([self.__KLResultsAndDistributions__[i].getCovarianceModel().getInputDimension() for i in range(self.__field_distribution_count__)]))
# If only one object is passed it has to be an decomposed aggregated process
if self.__field_distribution_count__ == 1 :
if hasattr(self.__KLResultsAndDistributions__[0], 'getCovarianceModel') and hasattr(self.__KLResultsAndDistributions__[0], 'getMesh'):
#Cause when aggregated there is usage of multvariate covariance functions
self.__isAggregated__ = self.__KLResultsAndDistributions__[0].getCovarianceModel().getOutputDimension() > self.__KLResultsAndDistributions__[0].getMesh().getDimension()
print('Process seems to be aggregated. ')
else :
print('There is no point in passing only one process that is not aggregated')
raise TypeError
self.threshold = max([self.__KLResultsAndDistributions__[i].getThreshold() if hasattr(self.__KLResultsAndDistributions__[i], 'getThreshold') else 1e-3 for i in range(self.__field_distribution_count__)])
#Now we gonna get the data we will usually need
self.__process_distribution_description__ = [self.__KLResultsAndDistributions__[i].getName() for i in range(self.__field_distribution_count__)]
self._checkSubNames()
self.__mode_count__ = [self.__KLResultsAndDistributions__[i].getEigenValues().getSize() if hasattr(self.__KLResultsAndDistributions__[i], 'getEigenValues') else 1 for i in range(self.__field_distribution_count__)]
self.__mode_description__ = self._getModeDescription()
def __repr__(self):
'''Visual representation of the object
'''
covarianceList = self.getCovarianceModel()
eigValList = self.getEigenValues()
meshList = self.getMesh()
reprStr = '| '.join(['class = ComposedKarhunenLoeveResultsAndDistributions',
'name = {}'.format(self.getName()),
'Aggregation Order = {}'.format(str(self.__field_distribution_count__)),
'Threshold = {}'.format(str(self.threshold)),
*['Covariance Model {} = '.format(str(i))+covarianceList[i].__repr__() for i in range(self.__field_distribution_count__)],
*['Eigen Value {} = '.format(str(i))+eigValList[i].__repr__() for i in range(self.__field_distribution_count__)],
*['Mesh {} = '.format(str(i))+meshList[i].__repr__().partition('data=')[0] for i in range(self.__field_distribution_count__)]])
return reprStr
def _checkSubNames(self):
"""Check's the names of the objects passed to see if they are all unique
or if default ones have to be assigned"""
if len(set(self.__process_distribution_description__)) != len(self.__process_distribution_description__) :
print('The process names are not unique.')
print('Using generic name. ')
for i, process in enumerate(self.__KLResultsAndDistributions__):
oldName = process.getName()
newName = 'X_'+str(i)
print('Old name was {}, new one is {}'.format(oldName, newName))
process.setName(newName)
self.__process_distribution_description__ = [self.__KLResultsAndDistributions__[i].getName() for i in range(self.__field_distribution_count__)]
def _getModeDescription(self):
"""Returns the description of each element of the input vector.
(The vector obtained once the processes expanded and stacked with the distribution)
"""
modeDescription = list()
for i, nMode in enumerate(self.__mode_count__):
for j in range(nMode):
modeDescription.append(self.__process_distribution_description__[i]+'_'+str(j))
return modeDescription
def _checkCoefficients(self, coefficients):
'''Function to check if the vector passed has the right number of
elements'''
nModes = sum(self.__mode_count__)
if (isinstance(coefficients, ot.Point), len(coefficients) == nModes):
return True
elif (isinstance(coefficients, (ot.Sample, ot.SampleImplementation)) and len(coefficients[0]) == nModes):
return True
else :
print('The vector passed has not the right number of elements.')
print('n° elems: {} != {}'.format(str(len(coefficients)), str(nModes)))
return False
# new method
def getMean(self, i = None):
'''Get the mean value of the stochastic processes and the scalar distributions
Parameters
----------
i : int
index of distribution or process
'''
if i is not None:
return self.__means__[i]
else :
return self.__means__
# new method
def setMean(self, i, val ):
'''Sets the mean of the variable at the index i to a value
Parameters
----------
i : int
index of distribution or process
val : float, int
value to which we set the mean
'''
self.__means__[i] = val
# new method
def setLiftWithMean(self, theBool):
'''Flag to say if we add the mean to the generated values of fields or scalars
If not, all the events are centered
Parameters
----------
theBool : bool
if to lift the distributions and processes to their non homogenous
original space with their mean value or centereds
'''
self.__liftWithMean__ = theBool
def getClassName(self):
'''Returns a list of the class each process/distribution belongs to.
'''
classNames=[self.__KLResultsAndDistributions__[i].__class__.__name__ for i in range(self.__field_distribution_count__) ]
return list(set(classNames))
def getCovarianceModel(self):
'''Returns a list of covariance models for each process.
'''
return [self.__KLResultsAndDistributions__[i].getCovarianceModel() if hasattr(self.__KLResultsAndDistributions__[i], 'getCovarianceModel') else None for i in range(self.__field_distribution_count__) ]
def getEigenValues(self):
'''Returns a list of the eigen values for each process.
'''
return [self.__KLResultsAndDistributions__[i].getEigenValues() if hasattr(self.__KLResultsAndDistributions__[i], 'getEigenValues') else None for i in range(self.__field_distribution_count__) ]
def getId(self):
'''Returns a list containing the ID of each process/distribution.
'''
return [self.__KLResultsAndDistributions__[i].getId() for i in range(self.__field_distribution_count__) ]
def getImplementation(self):
'''Returns a list containing the implementation of each process/distribution, else None.
'''
return [self.__KLResultsAndDistributions__[i].getImplementation() if hasattr(self.__KLResultsAndDistributions__[i], 'getImplementation') else None for i in range(self.__field_distribution_count__) ]
def getMesh(self):
'''Returns a list containing the mesh of each process or None if it's a distribution.
'''
return [self.__KLResultsAndDistributions__[i].getMesh() if hasattr(self.__KLResultsAndDistributions__[i], 'getMesh') else None for i in range(self.__field_distribution_count__) ]
def getModes(self):
'''Returns a list containing the modes of each process, None if distribution
'''
return [self.__KLResultsAndDistributions__[i].getModes() if hasattr(self.__KLResultsAndDistributions__[i], 'getModes') else None for i in range(self.__field_distribution_count__) ]
def getModesAsProcessSample(self):
'''Returns a list containing the modes as a pcess sample for each process in the aggregation.
'''
return [self.__KLResultsAndDistributions__[i].getModesAsProcessSample() if hasattr(self.__KLResultsAndDistributions__[i], 'getModesAsProcessSample') else None for i in range(self.__field_distribution_count__) ]
def getName(self):
'''Returns the name of the aggregation object.
'''
return self.__name__
def getProjectionMatrix(self):
'''Returns the projection matrix for each Karhunen-Loeve decomposition,
None if it's a distribution.
'''
return [self.__KLResultsAndDistributions__[i].getProjectionMatrix() if hasattr(self.__KLResultsAndDistributions__[i], 'getProjectionMatrix') else None for i in range(self.__field_distribution_count__) ]
def getScaledModes(self):
'''Returns the scaled modes for each Karhunen-Loeve decomposition,
None if it's a distribution.
'''
return [self.__KLResultsAndDistributions__[i].getScaledModes() if hasattr(self.__KLResultsAndDistributions__[i], 'getScaledModes') else None for i in range(self.__field_distribution_count__) ]
def getScaledModesAsProcessSample(self):
'''Returns the scaled modes as a proess sample for each Karhunen-Loeve decomposition,
None if it's a distribution.
'''
return [self.__KLResultsAndDistributions__[i].getScaledModesAsProcessSample() if hasattr(self.__KLResultsAndDistributions__[i], 'getScaledModes') else None for i in range(self.__field_distribution_count__) ]
def getThreshold(self):
'''Gets the global threshold for the Karhunen-Loeve expansions approximation.
'''
return self.threshold
def setName(self,name):
'''Sets the name of the aggregation object.
'''
self.__name__ = name
def liftAsProcessSample(self, coefficients):
'''Function to lift a sample of coefficients into a collections of
process samples and points.
Parameters
----------
coefficients : ot.Sample
sample of values, follwing a centered normal law in general
Returns
-------
processes : list
ordered list of samples of scalars (ot.Sample) and field samples (ot.ProcessSample)
'''
assert isinstance(coefficients, (ot.Sample, ot.SampleImplementation))
print('Lifting as process sample')
jumpDim = 0
processes = []
for i in range(self.__field_distribution_count__):
if self.__isProcess__[i] :
if not self.__liftWithMean__:
processes.append(self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]]))
else :
processSample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
addConstant2Iterable(processSample, self.__means__[i])
processes.append(processSample)
else :
if not self.__liftWithMean__:
processSample = ot.ProcessSample(ot.Mesh(), 0, 1)
val_sample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
for j, value in enumerate(val_sample):
field = ot.Field(ot.Mesh(),1)
field.setValueAtIndex(0,value)
processSample.add(field)
processes.append(processSample)
else :
processSample = ot.ProcessSample(ot.Mesh(), 0, 1)
val_sample = self.__KL_lifting__[i](coefficients[:, jumpDim : jumpDim + self.__mode_count__[i]])
mean = self.__means__[i]
for j, value in enumerate(val_sample):
field = ot.Field(ot.Mesh(),1)
field.setValueAtIndex(0,[value[0]+mean]) # adding mean
processSample.add(field)
processes.append(processSample)
jumpDim += self.__mode_count__[i]
return processes
def liftAsField(self, coefficients):
'''Function to lift a vector of coefficients into a list of
process samples and points.
Parameters
----------
coefficients : ot.Point
one vector values, follwing a centered normal law in general
Returns
-------
to return : list
ordered list of scalars (ot.Point) and fields (ot.Field)
'''
assert isinstance(coefficients, (ot.Point)), 'function only lifts points'
valid = self._checkCoefficients(coefficients)
print('Lifting as field')
if valid :
to_return = []
jumpDim = 0
for i in range(self.__field_distribution_count__):
if self.__isProcess__[i] :
field = self.__KLResultsAndDistributions__[i].liftAsField(coefficients[jumpDim : jumpDim + self.__mode_count__[i]])
jumpDim += self.__mode_count__[i]
if not self.__liftWithMean__:
to_return.append(field)
else :
vals = field.getValues()
vals += self.__means__[i]
field.setValues(vals)
to_return.append(field)
else :
value = self.__KL_lifting__[i](coefficients[jumpDim : jumpDim + self.__mode_count__[i]])
jumpDim += self.__mode_count__[i]
if not self.__liftWithMean__:
#print('field value is',value)
field = ot.Field(ot.Mesh(),1)
field.setValueAtIndex(0,value)
to_return.append(field)
else :
#print('field value is',value)
field = ot.Field(ot.Mesh(),1)
value[0] += self.__means__[i]
field.setValueAtIndex(0,value)
to_return.append(field)
return to_return
else :
raise Exception('DimensionError : the vector of coefficient has the wrong shape')
algo_kl_process_1D = ot.KarhunenLoeveP1Algorithm(
mesh_1D, process_1D.getCovarianceModel())
algo_kl_process_1D.run()
kl_results_1D = algo_kl_process_1D.getResult()
algo_kl_process_2D = ot.KarhunenLoeveP1Algorithm(
mesh_2D, process_2D.getCovarianceModel())
algo_kl_process_2D.run()
kl_results_2D = algo_kl_process_2D.getResult()
### Now let's compose our Karhunen Loeve Results and our distributions.
composedKLResultsAndDistributions = aklr.AggregatedKarhunenLoeveResults(
[kl_results_2D, kl_results_1D, scalar_distribution])
### Now let's see if we manage to project and lift the realizations we had before.
realizationFields = [field_2D, field_1D, ot.Field(ot.Mesh(), [scalar_0[0]])]
projectedCoeffs = composedKLResultsAndDistributions.project(realizationFields)
print('Projected coefficients are :', projectedCoeffs)
liftedFieldsO = composedKLResultsAndDistributions.liftAsField(projectedCoeffs)
print('Lifted fields are :', liftedFieldsO)
### Now let's use our function wrapper and see if we get the same results!
dummyWrapper = klgfw.KarhunenLoeveGeneralizedFunctionWrapper(
composedKLResultsAndDistributions, dummyFunction2Wrap, None, 1)
print('testing call:')
dummyWrapper(projectedCoeffs)
class TestComposeAndWrap(unittest.TestCase):
def testLiftAndProject(self,
vertices.append([0.0, 0.0, 0.0])
vertices.append([0.0, 0.0, 1.0])
vertices.append([0.0, 1.0, 0.0])
vertices.append([0.0, 1.0, 1.0])
vertices.append([1.0, 0.0, 0.0])
vertices.append([1.0, 0.0, 1.0])
vertices.append([1.0, 1.0, 0.0])
vertices.append([1.0, 1.0, 1.0])
simplicies = []
simplicies.append([0, 1, 2, 4])
simplicies.append([3, 5, 6, 7])
simplicies.append([1, 2, 3, 6])
simplicies.append([1, 2, 4, 6])
simplicies.append([1, 3, 5, 6])
simplicies.append([1, 4, 5, 6])
mesh3D = ot.Mesh(vertices, simplicies)
def myPyFunc(X):
Xs = ot.Sample(X)
Y = Xs * ([2.0] * Xs.getDimension())
Y.setDescription(ot.Description.BuildDefault(values.getDimension(), "Y"))
return Y
in_dim = 3
out_dim = 3
myFunc = ot.PythonFieldFunction(mesh3D, in_dim, mesh3D, out_dim, myPyFunc)
print('myFunc=', myFunc)
# and AbsoluteExponential models
covarianceModel = ot.SquaredExponential([7.63, 2.11], [7.38])
# 3) Basis definition
basis = ot.ConstantBasisFactory(inputDimension).build()
# Kriging algorithm
algo = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
algo.setOptimizeParameters(False) # do not optimize hyper-parameters
algo.run()
result = algo.getResult()
vertices = [[1.0, 0.0], [2.0, 0.0], [2.0, 1.0], [1.0, 1.0], [1.5, 0.5]]
simplicies = [[0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4]]
mesh2D = ot.Mesh(vertices, simplicies)
process = ot.ConditionedGaussianProcess(result, mesh2D)
# Get a realization of the process
realization = process.getRealization()
print("realization = ", repr(realization))
# Get a sample & compare it to expectation
sample = process.getSample(5000)
mean = sample.computeMean()
print("Mean over 5000 realizations = ", repr(mean))
# Check if one can sample the process over a mesh containing conditioning points
# and 100 new points
vertices = ot.Sample(inputSample)
vertices.add(
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
import os
ot.TESTPREAMBLE()
nrVertices = 100
vertices = ot.Normal().getSample(nrVertices).sort()
simplices = [[i, i + 1] for i in range(nrVertices - 1)]
mesh1 = ot.Mesh(vertices, simplices)
vertices *= -1.0
mesh2 = ot.Mesh(vertices, simplices)
for mesh in [mesh1, mesh2]:
lowerBound = mesh.getLowerBound()[0]
upperBound = mesh.getUpperBound()[0]
n = mesh.getSimplicesNumber()
print("mesh=", mesh, "lowerBound=", lowerBound, "upperBound=", upperBound,
n, "simplices")
algo = ot.EnclosingSimplexMonotonic1D(mesh.getVertices())
ot.RandomGenerator.SetSeed(0)
test = ot.Sample(ot.Uniform(-3.0, 3.0).getSample(1000))
vertices = mesh.getVertices()
for vertex in test:
index = algo.query(vertex)
x = vertex[0]
if x < lowerBound or x > upperBound:
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
mesh = ot.RegularGrid(0.0, 1.0, 4)
values = [(x, 2.0 * x, x * x) for x in mesh.getValues()]
outPoint = [2.5]
interpolation = ot.P1LagrangeInterpolation(mesh, ot.Mesh([outPoint]),
len(values[0]))
print("Interpolation=", interpolation)
print("Values at", outPoint, "=", interpolation(values))
print("mesh1D=", mesh1D)
# Manual bounding box
mesh1D = mesher1D.build(levelSet1D, ot.Interval(-10.0, 10.0))
print("mesh1D=", mesh1D)
# The 2D mesher
mesher2D = ot.LevelSetMesher([5] * 2)
print("mesher2D=", mesher2D)
function2D = ot.SymbolicFunction(
["x0", "x1"], ["cos(x0 * x1)/(1 + 0.1 * (x0^2 + x1^2))"])
levelSet2D = ot.LevelSet(function2D, level)
# Automatic bounding box
mesh2D = ot.Mesh(mesher2D.build(levelSet2D))
print("mesh2D=", mesh2D)
# Manual bounding box
mesh2D = mesher2D.build(levelSet2D, ot.Interval([-10.0] * 2, [10.0] * 2))
print("mesh2D=", mesh2D)
# The 3D mesher
mesher3D = ot.LevelSetMesher([3] * 3)
print("mesher3D=", mesher3D)
function3D = ot.SymbolicFunction(
["x0", "x1", "x2"],
["cos(x0 * x1 + x2)/(1 + 0.1*(x0^2 + x1^2 + x2^2))"])
levelSet3D = ot.LevelSet(function3D, level)
import openturns as ot
mesh = ot.Mesh(5)
for v in mesh:
print(v)
print('OK')
mesh.exportToTXT('/tmp/mesh.txt')
# check that hmat library was found
print('7: HMatrix (hmat-oss)'.ljust(width), end=' ')
try:
# This is a little bit tricky because HMat 1.0 fails with 1x1 matrices
ot.ResourceMap.SetAsUnsignedInteger('TemporalNormalProcess-SamplingMethod',
1)
vertices = [[0.0, 0.0, 0.0]]
vertices.append([1.0, 0.0, 0.0])
vertices.append([0.0, 1.0, 0.0])
vertices.append([0.0, 0.0, 1.0])
simplices = [[0, 1, 2, 3]]
# Discard messages from HMat
ot.Log.Show(0)
process = ot.TemporalNormalProcess(ot.ExponentialModel(3),
ot.Mesh(vertices, simplices))
f = process.getRealization()
print('OK')
except:
print('no')
# check that nlopt library was found
print('8: optimization (NLopt)'.ljust(width), end=' ')
try:
problem = ot.OptimizationProblem()
algo = ot.SLSQP()
algo.setProblem(problem)
print('OK')
except:
print('no')
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
import math as m
ot.PlatformInfo.SetNumericalPrecision(6)
# 1D example
mesh1D = ot.Mesh()
print("Default 1D mesh=", mesh1D)
vertices = ot.Sample(0, 1)
vertices.add([0.5])
vertices.add([1.5])
vertices.add([2.1])
vertices.add([2.7])
simplicies = [[]] * 3
simplicies[0] = [0, 1]
simplicies[1] = [1, 2]
simplicies[2] = [2, 3]
mesh1D = ot.Mesh(vertices, simplicies)
mesh1Ddomain = ot.MeshDomain(mesh1D)
tree = ot.KDTree(vertices)
enclosingSimplex = ot.EnclosingSimplexAlgorithm(vertices, simplicies)
print("1D mesh=", mesh1D)
print("Is empty? ", mesh1D.isEmpty())
print("vertices=", mesh1D.getVertices())
print("simplices=", mesh1D.getSimplices())
print("volume=", "%.3f" % mesh1D.getVolume())
print("simplices volume=", mesh1D.computeSimplicesVolume())
p = [1.3]
print("is p=", p, " in mesh? ", mesh1Ddomain.contains(p))
for i, vertex in enumerate(test):
index = bvh.query(vertex)
if index >= nrSimplices:
print(i, "is outside")
else:
found, coordinates = mesh.checkPointInSimplexWithCoordinates(
vertex, index)
if not found:
print("Wrong simplex found for", vertex, "(index=", index,
simplices[index], "barycentric coordinates=",
coordinates)
indices = bvh.query(test)
for i, index in enumerate(indices):
if index >= nrSimplices:
print(i, "is outside")
else:
found, coordinates = mesh.checkPointInSimplexWithCoordinates(
test[i], index)
if not found:
print("Wrong simplex found for", test[i], "(index=", index,
simplices[index], "barycentric coordinates=",
coordinates)
# segfault with 1 simplex
mesh = ot.Mesh([[0.0, 0.0], [1.0, 0.0], [0.5, 1.0]], [[0, 1, 2]])
bvh = ot.BoundingVolumeHierarchy(mesh.getVertices(), mesh.getSimplices())
print(bvh.query([0.125, 0.2]))
print(bvh.query([0.125, 0.3]))
sample.add(point2)
sample.add(point3)
sample.add(point4)
sample.add(point2)
sample.add(point4)
sample.add(point3)
print(sample)
study.add('sample', sample)
mesh = ot.IntervalMesher([50] * 3).build(ot.Interval(3))
study.add('mesh', mesh)
study.save()
study2 = ot.Study()
study2.setStorageManager(ot.XMLH5StorageManager(fileName))
study2.load()
sample2 = ot.Sample()
study2.fillObject('sample', sample2)
print(sample2)
assert sample == sample2, "wrong sample"
mesh2 = ot.Mesh()
study2.fillObject('mesh', mesh2)
assert mesh == mesh2, "wrong mesh"
# cleanup
os.remove(fileName)
os.remove(fileName.replace(".xml.gz", ".h5"))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
# Define the vertices of the mesh
vertices = [[0.0, 0.0], [1.0, 0.0], [1.0, 1.0],
[1.5, 1.0], [2.0, 1.5], [0.5, 1.5]]
# Define the simplices of the mesh
simplices = [[0, 1, 2], [1, 2, 3], [2, 3, 4], [2, 4, 5], [0, 2, 5]]
# Create the Mesh
mesh2D = ot.Mesh(vertices, simplices)
# Create a Graph
graph = ot.Graph('Mesh 2D', '', '', True, 'bottomright')
graph.add(mesh2D.draw())
# Then, draw it
fig = plt.figure(figsize=(4, 4))
axis = fig.add_subplot(111)
View(graph, figure=fig, axes=[axis], add_legend=True)
axis.set_xlim(auto=True)
# Set Numerical precision to 4
ot.PlatformInfo.SetNumericalPrecision(4)
sampleSize = 40
spatialDimension = 1
# Create the function to estimate
model = ot.SymbolicFunction(["x0"], ["x0"])
X = ot.Sample(sampleSize, spatialDimension)
for i in range(sampleSize):
X[i, 0] = 3.0 + (8.0 * i) / sampleSize
Y = model(X)
# Add a small noise to data
Y += ot.GaussianProcess(ot.AbsoluteExponential(
[0.1], [0.2]), ot.Mesh(X)).getRealization().getValues()
basis = ot.LinearBasisFactory(spatialDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(spatialDimension)
print("===================================================\n")
algo = ot.GeneralLinearModelAlgorithm(X, Y, covarianceModel, basis)
algo.run()
result = algo.getResult()
print("\ncovariance (dirac, optimized)=", result.getCovarianceModel())
print("trend (dirac, optimized)=", result.getTrendCoefficients())
print("===================================================\n")
# Now without estimating covariance parameters
basis = ot.LinearBasisFactory(spatialDimension).build()
covarianceModel = ot.DiracCovarianceModel(spatialDimension)
field = ot.Field(mesh, values)
evaluation = ot.P1LagrangeEvaluation(field)
x = [2.3]
y = evaluation(x)
print(y)
ott.assert_almost_equal(y, [0.55])
# Learning sample on meshD
mesher = ot.IntervalMesher([7, 7])
lowerbound = [-1.0, -1.0]
upperBound = [1, 1]
interval = ot.Interval(lowerbound, upperBound)
meshD = mesher.build(interval)
sample = ot.ProcessSample(meshD, 10, 1)
field = ot.Field(meshD, 1)
for k in range(sample.getSize()):
field.setValues(ot.Normal().getSample(64))
sample[k] = field
lagrange = ot.P1LagrangeEvaluation(sample)
# New mesh
mesh = ot.Mesh(
ot.MonteCarloExperiment(ot.ComposedDistribution([ot.Uniform(-1, 1)] * 2),
200).generate())
point = mesh.getVertices()[0]
y = lagrange(point)
print(y)
index = lagrange.getEnclosingSimplexAlgorithm().query(point)
print(index)
assert index == 12, "wrong index"
# ------------------
# %%
# In this paragraph we create a mesh :math:`\mathcal{M}` associated to a domain :math:`\mathcal{D} \in \mathbb{R}^n`.
#
# A mesh is defined from vertices in :math:`\mathbb{R}^n` and a topology that connects the vertices: the simplices. The simplex :math:`Indices([i_1,\dots, i_{n+1}])` relies the vertices of index :math:`(i_1,\dots, i_{n+1})` in :math:`\mathbb{N}^n`. In dimension 1, a simplex is an interval :math:`Indices([i_1,i_2])`; in dimension 2, it is a triangle :math:`Indices([i_1,i_2, i_3])`.
#
# The library enables to easily create a mesh which is a box of dimension :math:`d=1` or :math:`d=2` regularly meshed in all its directions, thanks to the object IntervalMesher.
#
# Consider :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` a multivariate stochastic process of dimension :math:`d`, where :math:`\mathcal{D} \in \mathbb{R}^n`. The mesh :math:`\mathcal{M}` is a discretization of the domain :math:`\mathcal{D}`.
# %%
# A one dimensional mesh is created and represented by :
vertices = [[0.5], [1.5], [2.1], [2.7]]
simplicies = [[0, 1], [1, 2], [2, 3]]
mesh1D = ot.Mesh(vertices, simplicies)
graph1 = mesh1D.draw()
graph1.setTitle('One dimensional mesh')
view = viewer.View(graph1)
# %%
# We define a bidimensional mesh :
vertices = [[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [1.5, 1.0], [2.0, 1.5],
[0.5, 1.5]]
simplicies = [[0, 1, 2], [1, 2, 3], [2, 3, 4], [2, 4, 5], [0, 2, 5]]
mesh2D = ot.Mesh(vertices, simplicies)
graph2 = mesh2D.draw()
graph2.setTitle('Bidimensional mesh')
graph2.setLegendPosition('bottomright')
view = viewer.View(graph2)
print("Checking %s" % (x_train_value))
indices = np.argwhere(x_test == x_train_value)
if len(indices) == 1:
print(" Delete %s" % (x_train_value))
x_test_filtered = np.delete(x_test_filtered, indices[0, 0])
else:
print(" OK")
return x_test_filtered
# %%
vertices_filtered = deleteCommonValues(np.array(x_train.asPoint()),
np.array(vertices.asPoint()))
# %%
evaluationMesh = ot.Mesh(ot.Sample([[vf] for vf in vertices_filtered]))
# %%
process = ot.ConditionedGaussianProcess(krigingResult, evaluationMesh)
# %%
trajectories = process.getSample(10)
type(trajectories)
# %%
# The `getSample` method returns a `ProcessSample`. By comparison, the `getSample` method of a `KrigingRandomVector` would return a `Sample`.
# %%
graph = trajectories.drawMarginal()
graph.add(plot_data_test(x_test, y_test))
graph.add(plot_data_train(x_train, y_train))
# Set Numerical precision to 4
ot.PlatformInfo.SetNumericalPrecision(4)
sampleSize = 40
inputDimension = 1
# Create the function to estimate
model = ot.SymbolicFunction(["x0"], ["x0"])
X = ot.Sample(sampleSize, inputDimension)
for i in range(sampleSize):
X[i, 0] = 3.0 + (8.0 * i) / sampleSize
Y = model(X)
# Add a small noise to data
Y += ot.GaussianProcess(ot.AbsoluteExponential([0.1], [0.2]),
ot.Mesh(X)).getRealization().getValues()
basis = ot.LinearBasisFactory(inputDimension).build()
# Case of a misspecified covariance model
covarianceModel = ot.DiracCovarianceModel(inputDimension)
print("===================================================\n")
algo = ot.GeneralLinearModelAlgorithm(X, Y, covarianceModel, basis)
algo.run()
result = algo.getResult()
print("\ncovariance (dirac, optimized)=", result.getCovarianceModel())
print("trend (dirac, optimized)=", result.getTrendCoefficients())
print("===================================================\n")
# Now without estimating covariance parameters
basis = ot.LinearBasisFactory(inputDimension).build()
def __init__(self):
self.__mesh = ot.Mesh(42)