# Create a gaussian process from a cov. model using HMatrix¶

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

[1]:

from __future__ import print_function
import openturns as ot


Define the covariance model :

[2]:

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 :

[3]:

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


Finally define the gaussian process :

[4]:

# create the process
process = ot.GaussianProcess(covarianceModel, timeGrid)
print(process)

GaussianProcess(trend=[x0]->[0.0], covariance=AbsoluteExponential(scale=[10], amplitude=[1]))


We set the sampling method to HMAT

[5]:

process.setSamplingMethod(1)


We sample the process :

[6]:

# draw a sample
sample = process.getSample(6)
sample.drawMarginal(0)

[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.