File:Gaussianprocess gapUncertainty.gif
Gaussianprocess_gapUncertainty.gif (400 × 200 pixels, file size: 156 KB, MIME type: image/gif, looped, 50 frames, 5.0 s)
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editDescriptionGaussianprocess gapUncertainty.gif |
English: Gaußprozess-Regression: Unsicherheit der Interpolation einer Lücke, dargestellt durch Zufallsfluktiononen gemäß der a-posteriori-Kovarianzfunktion. |
Date | |
Source | Own work |
Author | Physikinger |
GIF development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python code# This source code is public domain
# Author: Christian Schirm
import numpy, scipy.spatial
import matplotlib.pyplot as plt
import imageio
def covMat(x1, x2, covFunc, noise=0): # Covariance matrix
cov = covFunc(scipy.spatial.distance_matrix(numpy.atleast_2d(x1).T, numpy.atleast_2d(x2).T))
if noise: cov += numpy.diag(numpy.ones(len(cov))*noise)
return cov
numpy.random.seed(107)
covFunc1 = lambda d: 2*numpy.exp(-numpy.abs(numpy.sin(1.55*numpy.pi*d))**1.9/3 - d**2/7.)
covFunc2 = lambda d: 1*numpy.exp( - d**2/6.)
covFunc = lambda d: 1.5*numpy.exp(-numpy.abs(numpy.sin(1.55*numpy.pi*d))**1.9/3 - d**2/10.)
n=60
x = numpy.linspace(0, 10, 300)
y1 = numpy.random.multivariate_normal(x.ravel()*0, covMat(x, x, covFunc1, noise=0.00))
y2 = numpy.random.multivariate_normal(x.ravel()*0, covMat(x, x, covFunc2, noise=0.00))
x_known = numpy.concatenate([x[:n+1], x[-n:]])
y_known = numpy.concatenate([y1[:n+1], y2[-n:]])
x_unknown = x[n:-n+1]
Ckk = covMat(x_known, x_known, covFunc, noise=0.000001)
Cuu = covMat(x_unknown, x_unknown, covFunc, noise=0.00)
CkkInv = numpy.linalg.inv(Ckk)
Cuk = covMat(x_unknown, x_known, covFunc, noise=0.0)
m = 0 #numpy.mean(y)
covPost = Cuu - numpy.dot(numpy.dot(Cuk,CkkInv),Cuk.T)
y_unknown = numpy.dot(numpy.dot(Cuk,CkkInv),y_known)
fig = plt.figure(figsize=(4.0,2))
sigma = numpy.sqrt(numpy.diag(covPost))
plt.plot(x_unknown, y_unknown, label=u'Prediction')
plt.fill_between(x_unknown.ravel(), y_unknown - sigma, y_unknown + sigma, color = '0.85')
plt.plot(x[:n+1], y1[:n+1],'k-')
plt.plot(x[-n:], y2[-n:],'k-')
plt.vlines([x[n], x[-n]],-3,3,colors='r', linestyles='--', alpha=0.5)
plt.axis([0,10,-3,3])
plt.savefig('Gaussianprocess_gapMean.svg')
fig = plt.figure(figsize=(4.0,2))
for c in 'C1 C4 C2'.split():
y_random = numpy.random.multivariate_normal(x_unknown.ravel()*0, covPost)
plt.plot(x_unknown, y_unknown + y_random, c, label=u'Prediction')
sigma = numpy.sqrt(numpy.diag(covPost))
plt.plot(x[:n+1], y1[:n+1],'k-')
plt.plot(x[-n:], y2[-n:],'k-')
plt.vlines([x[n], x[-n]],-3,3,colors='r', linestyles='--', alpha=0.5)
plt.axis([0,10,-3,3])
plt.savefig('Gaussianprocess_gap.svg')
# Uncertainty animation
numpy.random.seed(1)
t = numpy.arange(0, 1, 0.02)
covFunc = lambda d: numpy.exp(-(3*numpy.sin(d*numpy.pi))**2) # Covariance function
chol = numpy.linalg.cholesky(covMat(t, t, covFunc, noise=1E-5))
r = chol.dot(numpy.random.randn(len(t), len(covPost)))
cov = covPost+1E-5*numpy.identity(len(covPost))
rSmooth = numpy.linalg.cholesky(cov).dot(r.T)
images = []
fig = plt.figure(figsize=(4.0,2))
for ti in [0]+list(range(len(t))):
plt.plot(x_unknown, y_unknown + rSmooth[:,ti], label=u'Prediction',alpha=1)
#plt.fill_between(x_unknown.ravel(), y_unknown - sigma, y_unknown + sigma, color = '0.85')
plt.plot(x[:n+1], y1[:n+1],'k-')
plt.plot(x[-n:], y2[-n:],'k-')
plt.vlines([x[n], x[-n]],-3,3,colors='r', linestyles='--', alpha=0.5)
plt.axis([0,10,-3,3])
plt.xlabel('t')
#plt.tight_layout()
fig.canvas.draw()
s, (width, height) = fig.canvas.print_to_buffer()
images.append(numpy.fromstring(s, numpy.uint8).reshape((height, width, 4)))
fig.clf()
# Save GIF animation
fileOut = 'Gaussianprocess_gapUncertainty.gif'
imageio.mimsave(fileOut, images[1:])
# Optimize GIF size
from pygifsicle import optimize
optimize(fileOut, colors=16)
|
Licensing
editI, the copyright holder of this work, hereby publish it under the following license:
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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 20:37, 8 September 2021 | 400 × 200 (156 KB) | Physikinger (talk | contribs) | Smaller file size | |
17:26, 1 December 2019 | 400 × 200 (234 KB) | Physikinger (talk | contribs) | Smaller file size | ||
17:16, 1 December 2019 | 400 × 200 (236 KB) | Physikinger (talk | contribs) | Smaller file size | ||
12:24, 1 December 2019 | 400 × 200 (936 KB) | Physikinger (talk | contribs) | Correct aspect | ||
12:23, 1 December 2019 | 400 × 200 (859 KB) | Physikinger (talk | contribs) | Correct aspect | ||
12:11, 1 December 2019 | 420 × 300 (1.36 MB) | Physikinger (talk | contribs) | User created page with UploadWizard |
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