class WeightedL2BFRanking(Ranking):
def __init__(self):
super(self.__class__, self).__init__()
self._estimationStrategy = AnalyticEstimationStrategy()
self.initialized = False
def update(self, grid, v, gpi, params, *args, **kws):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} |v_i| \sqrt{E[\varphi_i^2]}
@param grid: Grid grid
@param v: numpy array coefficients
"""
# update the quadrature operations
if not self.initialized:
self._estimationStrategy.initQuadratureStrategy(grid)
U = params.getIndependentJointDistribution()
T = params.getJointTransformation()
self.vol, self.W, self.D = self._estimationStrategy._extractPDFforMomentEstimation(U, T)
self.initialized = True
# get maximum coefficient of ancestors
vi = 0.0
gs = grid.getStorage()
for _, gpp in parents(grid, gpi):
if gs.isContaining(gpp):
ix = gs.getSequenceNumber(gpp)
vi = max(vi, np.abs(v[ix]))
# prepare data
basisi = getBasis(grid)
# compute the second moment for the current grid point
secondMoment, _ = self._estimationStrategy.computeSystemMatrixForVarianceList(gs,
[gpi], basisi,
[gpi], basisi,
self.W, self.D)
secondMoment = max(0.0, self.vol * secondMoment[0])
# update the ranking
return np.abs(vi * np.sqrt(secondMoment))
class ExpectationValueOptRanking(Ranking):
def __init__(self):
super(self.__class__, self).__init__()
self._estimationStrategy = AnalyticEstimationStrategy()
self.initialized = False
self._linearForm = LinearGaussQuadratureStrategy()
def compute_mean_phii(self, gs, gpi, basisi):
mean_phii, _ = self._estimationStrategy.computeSystemMatrixForMeanList(
gs, [gpi], basisi, self.W, self.D)
return mean_phii[0]
def update(self, grid, v, gpi, params, *args, **kws):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | |v_i| E(\varphi_i)
@param grid: Grid grid
@param v: numpy array coefficients
@param admissibleSet: AdmissibleSet
"""
# update the quadrature operations
if not self.initialized:
self._estimationStrategy.initQuadratureStrategy(grid)
U = params.getIndependentJointDistribution()
T = params.getJointTransformation()
self.vol, self.W, self.D = self._estimationStrategy._extractPDFforMomentEstimation(
U, T)
self.initialized = True
# prepare data
gs = grid.getStorage()
# compute stiffness matrix for next run
basis = getBasis(grid)
ix = gs.getSequenceNumber(gpi)
mean_phii = self.compute_mean_phii(gs, gpi, basis)
return np.abs(v[ix]) * mean_phii
class VarianceOptRanking(Ranking):
def __init__(self):
super(self.__class__, self).__init__()
self._estimationStrategy = AnalyticEstimationStrategy()
self.initialized = False
def compute_mean_uwi_phii(self, gs, gpswi, w, gpi, basis):
A, _ = self._estimationStrategy.computeSystemMatrixForVarianceList(
gs, gpswi, basis, [gpi], basis, self.W, self.D)
return np.dot(w, A)
def compute_mean_uwi(self, gs, gpswi, w, basis):
b, _ = self._estimationStrategy.computeSystemMatrixForMeanList(
gs, gpswi, basis, self.W, self.D)
return np.dot(w, b)
def compute_mean_phii(self, gs, gpi, basisi):
mean_phii, _ = self._estimationStrategy.computeSystemMatrixForMeanList(
gs, [gpi], basisi, self.W, self.D)
return mean_phii[0]
def compute_var_phii(self, gs, gpi, basisi, mean_phii):
A_var, _ = self._estimationStrategy.computeSystemMatrixForVarianceList(
gs, [gpi], basisi, [gpi], basisi, self.W, self.D)
return A_var[0, 0] - mean_phii**2
def update(self, grid, v, gpi, params, *args, **kws):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | -v_i^2 V(\varphi_i) - 2 v_i Cov(u_indwli \varphi_i)|
@param grid: Grid grid
@param v: numpy array coefficients
@param admissibleSet: AdmissibleSet
"""
# update the quadrature operations
if not self.initialized:
self._estimationStrategy.initQuadratureStrategy(grid)
U = params.getIndependentJointDistribution()
T = params.getJointTransformation()
self.vol, self.W, self.D = self._estimationStrategy._extractPDFforMomentEstimation(
U, T)
self.initialized = True
# prepare data
gs = grid.getStorage()
basis = getBasis(grid)
# load coefficients and vectors and matrices for variance and mean
# estimation
w = np.ndarray(gs.getSize() - 1)
ix = gs.getSequenceNumber(gpi)
# prepare list of grid points
gpswi = []
jx = 0
for j in range(gs.getSize()):
gpj = gs.getPoint(j)
if gpi.getHash() != gpj.getHash():
gpswi.append(gpj)
w[jx] = v[j]
jx += 1
# compute the covariance
mean_uwi_phii = self.compute_mean_uwi_phii(gs, gpswi, w, gpi, basis)
mean_phii = self.compute_mean_phii(gs, gpi, basis)
mean_uwi = self.compute_mean_uwi(gs, gpswi, w, basis)
cov_uwi_phii = mean_uwi_phii - mean_phii * mean_uwi
# compute the variance of phi_i
var_phii = self.compute_var_phii(gs, gpi, basis, mean_phii)
# update the ranking
return np.abs(-v[ix]**2 * var_phii - 2 * v[ix] * cov_uwi_phii)