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Gaussian_process_2D_squared_exp.png (648 × 325 pixels, file size: 69 KB, MIME type: image/png)

Summary

Description
English: Random sample from 2D gaussian process with squared exponetial radial covariance function.
Date
Source Own work
Author Physikinger
PNG development
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This plot was created with Matplotlib.
Source code
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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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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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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22 August 2017

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Date/TimeThumbnailDimensionsUserComment
current22:21, 22 August 2017Thumbnail for version as of 22:21, 22 August 2017648 × 325 (69 KB)Physikingerfont size
21:58, 22 August 2017Thumbnail for version as of 21:58, 22 August 2017820 × 408 (82 KB)PhysikingerUser created page with UploadWizard

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