"""
Create a random walk process
============================
"""
# %%
# This example details first how to create and manipulate a random walk.
#
# A random walk :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` is a process
# where :math:`\mathcal{D}=\mathbb{R}` discretized on the time grid :math:`(t_i)_{i \geq 0}` such
# that:
#
# .. math::
# \begin{aligned}
# X_{t_0} & = & \underline{x}_{t_0} \\
# \forall n>0,\: X_{t_n} & = & X_{t_{n-1}} + \varepsilon_{t_n}
# \end{aligned}
#
# where :math:`\underline{x}_0 \in \mathbb{R}^d` and :math:`\varepsilon` is a white noise of
# dimension :math:`d`.
#
# 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.
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
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([[-1.0, -2.0], [1.0, 3.0]], [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()