Note
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Create a random walk processΒΆ
This example details first how to create and manipulate a random walk.
A random walk is a process where discretized on the time grid such that:
where and is a white noise of dimension .
The library proposes to model it through the object RandomWalk defined thanks to the origin, the distribution of the white noise and the time grid.
from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)
Define the origin
origin = [0.0]
Define an 1-d mesh
tgrid = ot.RegularGrid(0.0, 1.0, 500)
1-d random walk and discrete distribution
dist = ot.UserDefined([[-1], [10]], [0.9, 0.1])
process = ot.RandomWalk(origin, dist, tgrid)
sample = process.getSample(5)
graph = sample.drawMarginal(0)
graph.setTitle('1D Random Walk with discrete steps')
view = viewer.View(graph)
1-d random walk and continuous distribution
dist = ot.Normal(0.0, 1.0)
process = ot.RandomWalk(origin, dist, tgrid)
sample = process.getSample(5)
graph = sample.drawMarginal(0)
graph.setTitle('1D Random Walk with continuous steps')
view = viewer.View(graph)
Define the origin
origin = [0.0]*2
color palette
pal = ['red', 'cyan', 'blue', 'yellow', 'green']
2-d random walk and discrete distribution
dist = ot.UserDefined([[-1., -2.], [1., 3.]], [0.5, 0.5])
process = ot.RandomWalk(origin, dist, tgrid)
sample = process.getSample(5)
graph = ot.Graph('2D Random Walk with discrete steps', 'X1', 'X2', True)
for i in range(5):
graph.add(ot.Curve(sample[i], pal[i % len(pal)], 'solid'))
view = viewer.View(graph)
2-d random walk and continuous distribution
dist = ot.Normal(2)
process = ot.RandomWalk(origin, dist, tgrid)
sample = process.getSample(5)
graph = ot.Graph('2D Random Walk with continuous steps', 'X1', 'X2', True)
for i in range(5):
graph.add(ot.Curve(sample[i], pal[i % len(pal)], 'solid'))
view = viewer.View(graph)
plt.show()
Total running time of the script: ( 0 minutes 0.463 seconds)