File:Gaussian process 2D squared exp.png
Summary
| Description |
English: Random sample from 2D gaussian process with squared exponetial radial covariance function. |
| Date | |
| Source | Own work |
| Author | Physikinger |
| PNG development | |
| Source code | Python code# This source code is public domain
# Author: Christian Schirm
import numpy
import matplotlib.pyplot as plt
# To speed up the random generation, a numerical trick
# is used based on the fast fourier transform. See e.g.
# D. P. Kroese et al., "Spatial Process Generation", 2013
# https://arxiv.org/pdf/1308.0399.pdf
n = 2**8
x = numpy.arange(-n/2,n/2)/float(n)
def covFunc(r): return numpy.exp(-r**2)
def cov(deltaX, deltaY): return covFunc(8*(deltaX**2 + deltaY**2)**0.5)
indX,indY = numpy.mgrid[0:n,0:n]
C = cov(x[indX],x[indY])
Gamma = numpy.fft.fft2(numpy.roll(numpy.roll(C,len(C)/2,0),len(C)/2,1))
Z1 = numpy.random.randn(n,n) + 1J*numpy.random.randn(n,n)
X = numpy.fft.fft2(numpy.sqrt(Gamma) *Z1/n).real
fig, (plt2, plt1) = plt.subplots(nrows=1, ncols=2, figsize=(10./1.7, 4.5/1.7), dpi=120)
plt1.imshow(X,cmap='viridis',vmin=-2.5,vmax=2.5,extent=[0,10,0,10])
xCov = numpy.linspace(0,0.825,100)
plt2.plot(8*xCov, covFunc(8*xCov), label='exp(-r$^2$)')
plt2.set_xlabel('r')
plt2.set_ylabel('Covariance')
plt2.axis([0,5,0,1])
plt2.legend()
plt.savefig('Gaussian_process_2D_squared_exp.png')
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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