Commit 903a891b authored by Theo Steininger's avatar Theo Steininger

Added EnsembleLikelihood

parent cb484534
# -*- coding: utf-8 -*-
from likelihood import Likelihood
from ensemble_likelihood import EnsembleLikelihood
from ensemble_likelihood import EnsembleLikelihood
# -*- coding: utf-8 -*-
import numpy as np
from imagine.likelihoods.likelihood import Likelihood
class EnsembleLikelihood(Likelihood):
def __init__(self, measured_data, data_covariance):
def __init__(self, measured_data, data_covariance_operator):
self.measured_data = measured_data
self.data_covariance = data_covariance
self.data_covariance_operator = data_covariance_operator
def __call__(self, observable):
mean = observable.mean(spaces=0)
# https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula#Generalization
# B = A^{-1} + U U^dagger
# A = data_covariance
# B^{-1} c = (A_inv -
# A_inv U (I_k + U^dagger A_inv U)^{-1} U^dagger A_inv) c
k = observable.shape[0]
A = self.data_covariance_operator
obs_val = observable.val.get_full_data()
obs_mean = observable.mean(spaces=0).val.get_full_data()
u_val = observable.val.get_full_data() - obs_mean
U = observable.copy_empty()
U.val = u_val
a_u = A.inverse_times(U, spaces=1)
# build middle-matrix (kxk)
a_u_val = a_u.val.get_full_data()
middle = (np.eye(k) +
np.einsum(u_val.conjugate(), [0, 1],
a_u_val, [2, 1]))
middle = np.linalg.inv(middle)
result_array = np.zeros(k)
for i in xrange(k):
c = self.measured_data - obs_val[i]
# assuming that A == A^dagger, this can be shortend
# a_c = A.inverse_times(c)
# u_a_c = a_c.dot(U, spaces=1)
# u_a_c = u_a_c.conjugate()
# and: double conjugate shouldn't make a difference
# u_a_c = c.conjugate().dot(a_u, spaces=1).conjugate()
u_a_c = c.dot(a_u, spaces=1)
u_a_c_val = u_a_c.val.get_full_data()
first_summand = A.inverse_times(c)
second_summand_val = np.einsum(middle, [0, 1], u_a_c_val, [1])
second_summand_val = np.einsum(a_u_val, [0, 1],
second_summand_val, [0])
second_summand = first_summand.copy_empty()
second_summand.val = second_summand_val
result = c.dot(first_summand - second_summand)
result_array[i] = result
return -result_array.mean()
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