RandomFields

Random Fields

Python package to generate random fields in 2D or 3D on unstructured grids.

Background information

The random fields are generated using gstools.

Currently, the following covariance models are available:

• Gaussian
• Exponential
• Matern
• Linear

Installation

To install the package, run the following command in the terminal:

pip install git+https://github.com/StemVibrations/RandomFields

Tutorial

Example in 2D

In this example we generate a random field on a 2D regular grid.

First you need to import the packages:

import numpy as np
from random_fields.generate_field import RandomFields, ModelName
from random_fields.utils import plot2D

Then you need to define the grid:

x = np.linspace(0, 100, 50)
y = np.linspace(0, 50, 50)

x, y = np.meshgrid(x, y)

In this example we create a mesh of 50x50 points between 0 and 100 in x and 0 and 50 in y direction.

Then we define the random field properties:

nb_dimensions = 2
mean = 10
variance = 2
vertical_scale_fluctuation = 10
anisotropy = [1]
angle = [0]
model_rf = ModelName.Gaussian

In this example we use a Gaussian covariance model.

Then we create the random field:

rf = RandomFields(model_rf, nb_dimensions, mean, variance, vertical_scale_fluctuation, anisotropy, angle, seed=14)
rf.generate(np.array([x.ravel(), y.ravel()]).T)

To visualise the results you can run:

plot2D([np.array([x.ravel(), y.ravel()]).T], [rf.random_field], title="Random Field", output_folder="./", output_name="random_field.png")

The result is the following random field:

Example in 3D

In this example we generate a random field on a 3D regular grid.

First you need to import the packages:

import numpy as np
from random_fields.generate_field import RandomFields, ModelName
from random_fields.utils import plot3D

Then you need to define the grid:

x = np.linspace(0, 100, 50)
y = np.linspace(0, 50, 50)
z = np.linspace(0, 25, 25)

x, y, z = np.meshgrid(x, y, z)

In this example we create a mesh of 50x50x25 points between 0 and 100 in x, 0 and 50 in y direction and 0 and 25 in z direction.

Then we define the random field properties:

nb_dimensions = 3
mean = 10
variance = 2
vertical_scale_fluctuation = 10
anisotropy = [5, 5]
angle = [0, 0]
model_rf = ModelName.Gaussian

Then we create the random field:

rf = RandomFields(model_rf, nb_dimensions, mean, variance, vertical_scale_fluctuation, anisotropy, angle, seed=14)
rf.generate(np.array([x.ravel(), y.ravel(), z.ravel()]).T)

To visualise the results you can run:

plot3D([np.array([x.ravel(), y.ravel(), z.ravel()]).T], [rf.random_field], title="Random Field", output_folder="./", output_name="random_field_3D.png")

The result is the following random field: