# Create an event based on a process¶

This example gives elements to create an event based on a multivariate stochastic process. Let be a stochastic process of dimension , where is discretized on the mesh . We suppose that contains vertices.

We define the event as:

where is a domain of .

A particular domain is the cartesian product of type:

In that case, the library defines by its both extreme points : and .

In the general case, is a Domain object that is able to check if it contains a given point in .

The library creates an Event object from the process and the domain . Then, it is possible to get a realization of the event , which is scalar if is a realization of on .

[1]:

from __future__ import print_function
import openturns as ot

[2]:

# Define a 2-d mesh
indices = ot.Indices([40, 20])
mesher = ot.IntervalMesher(indices)
lowerBound = [0., 0.]
upperBound = [2., 1.]
interval = ot.Interval(lowerBound, upperBound)
mesh = mesher.build(interval)

[4]:

# Create the covariance model
amplitude = [1.0, 2.0, 3.0]
scale = [4.0, 5.0]
spatialCorrelation = ot.CorrelationMatrix(3)
spatialCorrelation[0, 1] = 0.8
spatialCorrelation[0, 2] = 0.6
spatialCorrelation[1, 2] = 0.1
covmodel = ot.ExponentialModel(scale, amplitude, spatialCorrelation)

# Create a normal process
process = ot.GaussianProcess(covmodel, mesh)

[5]:

# Create a domain A in R^3: [0.8; 1.2]*[1.5; 1.6]*[0.5; 0.7]
lowerBound = [0.8, 1.5, 0.5]
upperBound = [1.2, 1.6, 0.7]
domain = ot.Interval(lowerBound, upperBound)

# Create the event
event = ot.ProcessEvent(process, domain)