ensemble_likelihood.py 2.17 KB
 Theo Steininger committed Feb 15, 2017 1 2 ``````# -*- coding: utf-8 -*- `````` Theo Steininger committed Feb 21, 2017 3 4 ``````import numpy as np `````` Theo Steininger committed Feb 15, 2017 5 6 ``````from imagine.likelihoods.likelihood import Likelihood `````` Theo Steininger committed Feb 21, 2017 7 `````` `````` Theo Steininger committed Feb 15, 2017 8 ``````class EnsembleLikelihood(Likelihood): `````` Theo Steininger committed Feb 21, 2017 9 `````` def __init__(self, measured_data, data_covariance_operator): `````` Theo Steininger committed Feb 15, 2017 10 `````` self.measured_data = measured_data `````` Theo Steininger committed Feb 21, 2017 11 `````` self.data_covariance_operator = data_covariance_operator `````` Theo Steininger committed Feb 15, 2017 12 13 `````` def __call__(self, observable): `````` Theo Steininger committed Feb 21, 2017 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 `````` # 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()``````