def updateStatistics(self):
for curLevel in range(len(self.space4Level)):
samples = self.y4Level[curLevel]
self.variance4level[curLevel] = np.var(samples, 0)
compCost = self.space4Level[curLevel].dim() ** 2 / 1000.
# Simple for uniform meshes
# optSamples = self.constCompCost * np.sqrt(
# np.sqrt(np.sqrt(np.mean(np.abs(self.variance4level[curLevel]))) / compCost))
# Same but for general meshes
space = self.space4Level[curLevel]
domainArea = assemble(interpolate(Constant(1), space) * dx)
varianceMean = Function(space)
varianceMean.vector().set_local(np.abs(self.variance4level[curLevel]))
varianceIntMean = np.sqrt(assemble(varianceMean * dx) / domainArea)
optSamples = self.constCompCost * np.sqrt(np.sqrt(
varianceIntMean / compCost))
# Alernate from ???
# l = curLevel + 2
# maxL = len(self.space4Level) + 1
# epsOptSamples = 0.1
# optSamples = l ** (2 + 2 * epsOptSamples) * 2 ** (2 * (maxL - l))
self.optNumSamples4Level[curLevel] = np.rint(optSamples).astype(int)
self.compCost4lvl[-1] = sum(list(len(samples) * (space.dim() ** 2)
for (space, samples) in zip(self.space4Level, self.y4Level)))
def runCycle(self):
# initial sampling
print("Level {level}".format(level = 0))
self.sampleSolutions()
self.updateStatistics()
self.sampleSolutions()
meanFunction = Function(self.space4Level[0])
meanFunction.vector().set_local(np.mean(self.y4Level[0], 0))
self.mean4level[0] = meanFunction
for level in range(1, self.maxLevels):
print("Level {level}".format(level = level))
self.addLevel()
self.sampleSolutions()
self.updateStatistics()
self.sampleSolutions()
levelFunction = Function(self.space4Level[level])
levelFunction.vector().set_local(np.mean(self.y4Level[level], 0))
self.mean4level.append(levelFunction)
for curLevel in range(level):
tempFunction = Function(self.space4Level[curLevel])
tempFunction.vector().set_local(np.mean(self.y4Level[curLevel], 0))
self.mean4level[level] += tempFunction
