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utilities.py
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utilities.py
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# Copyright (c) 2013-2016, Massachusetts Institute of Technology
# Copyright (c) 2016-2022, Alex Gorodetsky
#
# This file is part of GPEXP:
# Author: Alex Gorodetsky alex@alexgorodetsky
#
# GPEXP is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# GPEXP is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GPEXP. If not, see <http://www.gnu.org/licenses/>.
# Code
import numpy as np
import math
def sampleLHS(numPts):
#1D
segSize = 1.0/float(numPts)
pointVal = np.zeros(numPts)
for ii in range(numPts):
segMin = float(ii) * segSize
point = segMin + (np.random.random() * segSize)
pointVal[ii] = point #(point #* (1 - -1)) + -1
return pointVal
def genSample2DCircle(size, radius):
#2Dcircle centered at 0
#implemented using rejection sampling
numPoints = size[0]
numDims = size[1]
samples = np.zeros(size)
for ii in range(numPoints):
notValid = 1
while notValid:
s = np.random.uniform(-1, 1, numDims)
if np.sqrt(s[0]**2.0 + s[1]**2.0) < radius:
notValid = 0
samples[ii,:] = s
return samples
def genSampleNDCircle(size, radius):
numPoints = size[0]
numDims = size[1]
samples = np.zeros(size)
for ii in range(numPoints):
notValid = 1
while notValid:
s = np.random.uniform(-1,1,numDims)
if np.sqrt(np.sum(s**2.0)) < radius:
notValid = 0
samples[ii,:] = s
return samples
def distribFunc2DCircle(points, radius):
area = np.pi*2.0*radius**2
prob = 1.0/area
out = np.zeros((len(points)))
out[points[:,0]**2.0 + points[:,1]**2.0 < radius**2.0] = prob
return out
def distribFuncNDCircle(points, radius):
nDim = points.shape[1]
area = np.pi**(nDim/2.0)/math.gamma(nDim/2.0 + 1)*radius**nDim
prob = 1.0/area
out = np.zeros((len(points)))
out[points[:,0]**2.0 + points[:,1]**2.0 < radius**2.0] = prob
return out
def genSampleUniform(size):
# uniform on [-1, 1]
return np.random.rand(size[0],size[1])*2.0 - 1.0
def distribFuncUniform(points):
out = np.array(np.fabs(points)<1) / 2.0
return out
def distribFuncUniform2D(points):
out = np.array(np.fabs(points)<1) / 4.0
return out
def distribFunctionUniformND(points, dim):
out = np.array(np.fabs(points)<1) / (2.0**dim)
return out
def genSampleMickey(size):
centersIn = [ (0.5,0), (-0.5,0), (0.0,-0.5) ]
radiusesIn = [ 0.3, 0.3, 0.5 ]
centersOut = [ (0.0,-0.5) , (0.2, -0.3 ) , (-0.2, -0.3 ) ]
radiusesOut = [ 0.05, 0.1, 0.1]
#circles = { (0.5,0) : 0.3, (-0.5,0) : 0.3, (0.0,-0.5) : 0.5, (0.0, -0.5): 0.05 ,
# (0.2, -0.3 ) : 0.1, (-0.2, -0.3 ): 0.1}
ellipseCenters = [ 0, -0.75]
ellipseRad = [ 0.2, 0.1]
nSamples = size[0]
samplesKeep = np.zeros((0,2))
while len(samplesKeep) < nSamples:
samples = np.random.rand(nSamples,2)*2.0-1.0
samplesOk = np.zeros((0,2))
#now need to do rejection sampling
#algorithm will check if its in any of the circles
for center, rad in zip(centersIn, radiusesIn):
rSquared = (samples[:,0]- center[0])**2.0 + (samples[:,1] - center[1])**2.0
#print "rsquared ", np.nonzero(rSquared< rad**2)
if len(rSquared) > 0:
ptsok = samples[rSquared < rad**2]
samplesOk = np.concatenate((samplesOk, ptsok), axis=0)
samples = samples[rSquared > rad**2]
for center, rad in zip(centersOut, radiusesOut):
rSquared = (samplesOk[:,0]- center[0])**2.0 + (samplesOk[:,1] - center[1])**2.0
if len(rSquared) > 0:
samplesIn = samplesOk[rSquared < rad**2.0]
samples = np.concatenate((samples, samplesIn ), axis=0)
samplesOk = samplesOk[rSquared > rad**2]
#check ellipse
checkIn = (samplesOk[:,0] - ellipseCenters[0])**2.0/ellipseRad[0]**2 + \
(samplesOk[:,1] - ellipseCenters[1])**2.0/ellipseRad[1]**2
if len(checkIn) > 0:
samplesIn = samplesOk[checkIn<1]
samplesOk = samplesOk[checkIn>1]
samples = np.concatenate((samples, samplesIn), axis=0)
samplesKeep = np.concatenate((samplesKeep, samplesOk), axis=0)
samplesKeep = samplesKeep[0:nSamples,:]
return samplesKeep
def distribFuncMickey(samplesInAAA):
#really slow but works
area = 1.172
centersIn = [ (0.5,0), (-0.5,0), (0.0,-0.5) ]
radiusesIn = [ 0.3, 0.3, 0.5 ]
centersOut = [ (0.0,-0.5) , (0.2, -0.3 ) , (-0.2, -0.3 ) ]
radiusesOut = [ 0.05, 0.1, 0.1]
#circles = { (0.5,0) : 0.3, (-0.5,0) : 0.3, (0.0,-0.5) : 0.5, (0.0, -0.5): 0.05 ,
# (0.2, -0.3 ) : 0.1, (-0.2, -0.3 ): 0.1}
ellipseCenters = [ 0, -0.75]
ellipseRad = [ 0.2, 0.1]
samplesOk = np.zeros((0,2))
samples = samplesInAAA.copy()
#now need to do rejection sampling
#algorithm will check if its in any of the circles
for center, rad in zip(centersIn, radiusesIn):
rSquared = (samples[:,0]- center[0])**2.0 + (samples[:,1] - center[1])**2.0
if len(rSquared < rad**2) > 0:
ptsok = samples[rSquared < rad**2]
#ptsok = samples(list(np.nonzero(rSquared < rad**2)))
samplesOk = np.concatenate((samplesOk, ptsok), axis=0)
if len(rSquared > rad**2) > 0:
samples = samples[rSquared > rad**2]
for center, rad in zip(centersOut, radiusesOut):
rSquared = (samplesOk[:,0]- center[0])**2.0 + (samplesOk[:,1] - center[1])**2.0
if len(rSquared) > 0:
samplesIn = samplesOk[rSquared < rad**2.0]
samples = np.concatenate((samples, samplesIn ), axis=0)
samplesOk = samplesOk[rSquared > rad**2]
#check ellipse
checkIn = (samplesOk[:,0] - ellipseCenters[0])**2.0/ellipseRad[0]**2 + \
(samplesOk[:,1] - ellipseCenters[1])**2.0/ellipseRad[1]**2
if len(checkIn) > 0:
samplesIn = samplesOk[checkIn<1]
samplesOk = samplesOk[checkIn>1]
samples = np.concatenate((samples, samplesIn), axis=0)
indGood = []
for ii in range(len(samplesInAAA)):
#bad sample
for jj in range(len(samplesOk)):
if np.linalg.norm(samplesInAAA[ii,:]-samplesOk[jj,:]) < 1e-15:
indGood.append(ii)
break
out = np.zeros((len(samplesInAAA)))
out[indGood] = 1.0/area
return out
def genSampleTriangle(size):
#gen samples 2DTriangle with slope y = -x
#size is number of samples
numPoints = size[0]
numDims = size[1]
samples = np.zeros(size)
for ii in range(numPoints):
notValid = 1
while notValid:
s = np.random.uniform(-1, 1, numDims)
if s[0] > -s[1]:
notValid = 0
samples[ii,:] = s
return samples
def genSampleDonut(size, radius):
# size is size of samples
# radius is inner radius
# donut with outer radius = 1
numPoints = size[0]
numDims = size[1]
samples = np.zeros(size)
radius = 0.7;
for ii in range(numPoints):
notValid = 1
while notValid:
s = np.random.uniform(-1, 1, numDims)
if np.sqrt(s[0]**2.0 + s[1]**2.0) > radius:
notValid = 0
samples[ii,:] = s
return samples
def onedGaussDistrib(x):
out = 1.0/(2.0*np.pi)**0.5 * np.exp(-0.5*x**2.0)
return out
def twodGaussDistrib(x):
#isotropic 2d gaussian
out = 1.0/(2.0*np.pi) * np.exp(-0.5*x[:,0]**2.0 -0.5*x[:,1]**2.0)
return out