Create a gaussian process from a cov. model using HMatrixΒΆ

In this basic example we are going to build a gaussian process from its covariance model and using the HMatrix as sampling method.

from __future__ import print_function
import openturns as ot

Define the covariance model :

dimension = 1
amplitude = [1.0] * dimension
scale = [10] * dimension
covarianceModel = ot.AbsoluteExponential(scale, amplitude)

Define the time grid on which we want to sample the gaussian process :

# define a mesh
tmin = 0.0
step = 0.01
n = 10001
timeGrid = ot.RegularGrid(tmin, step, n)

Finally define the gaussian process :

# create the process
process = ot.GaussianProcess(covarianceModel, timeGrid)
GaussianProcess(trend=[x0]->[0.0], covariance=AbsoluteExponential(scale=[10], amplitude=[1]))

We set the sampling method to HMAT


We sample the process :

# draw a sample
sample = process.getSample(6)

We notice here that we are able to sample the covariance model over a mesh of size 10000, which is usually tricky on laptop. This is mainly due to the compression.