# and iteratively compute the approximations with Riley's algorithms
# (as in (2) on slide 42 on https://drna.padovauniversitypress.it/system/files/papers/Fasshauer-2008-Lecture3.pdf)
# AUTHOR: NK, kraemer(at)ins.uni-bonn.de
import numpy as np
import sys
sys.path.insert(0, '../modules/')
from ptSetFcts import getPtsHalton
from kernelMtrcs import buildKernelMtrx, buildKernelMtrxCond
from kernelFcts import gaussKernel, tpsKernel, maternKernel, expKernel
import scipy.special
np.set_printoptions(precision=1)
dim = 2
numReps = 7
def matKernel(pt1, pt2):
return maternKernel(pt1, pt2, 0.5)
print("\nGaussian:")
for i in range(numReps):
numPts = 2**(i + 3)
ptSet = getPtsHalton(numPts, dim)
kernelMtrx = buildKernelMtrx(ptSet, ptSet, gaussKernel, 0.0)
print("(", numPts, ",", np.abs(np.min(np.linalg.eigvals(kernelMtrx))), ")")
def gaussMixMdlSym(pt, mean=2, variance=0.5):
leftModel = np.exp(-(pt + mean)**2 /
(2 * variance)) / (np.sqrt(2 * np.pi * variance))
rightModel = np.exp(-(pt - mean)**2 /
(2 * variance)) / (np.sqrt(2 * np.pi * variance))
return leftModel + rightModel
def evaluatePotentialGaussianPrior(pt, nOrmConst=1., data=observation):
return evaluatePotential(pt) * gaussMixMdlSym(pt)
numPtsQmc = 10000
ptSet = 20 * getPtsHalton(numPtsQmc, 1) - 10
normConst = compQuadQMC(evaluatePotentialGaussianPrior, ptSet)
plotPts = np.linspace(-10, 10, 500)
likelihood = evaluatePotential(plotPts, normConst)
priorVals = gaussMixMdlSym(plotPts)
posteriorVals = priorVals * likelihood
def postDens(pt):
return evaluatePotential(pt, normConst) * gaussMixMdlSym(pt)
def postDensCM(pt):
return pt * evaluatePotential(pt, normConst) * gaussMixMdlSym(pt)