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start.m
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clc
clearvars
%--------------------------------------------------------------------------
% The solver provides the solution of the linear system of equations with
% Gaussian noise using belief propagation (BP) algorithm applied over the
% factor graph.
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% Input data: data.mat file with variables:
% data.A - coefficient matrix m x n (m>n);
% data.b - observation values column vector dimension of m x 1;
% data.v - observation variances column vector dimension of m x 1;
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% User Options:
%
% Post-Processing Options:
% user.save - write data to a text file;
% user.radius - compute spectral radius for synchronous and randomized
% damping scheduling, if spectral radius is less than 1
% the BP algorithm converges;
% user.error - compute mean absolute error, root mean square error
% and weighted residual sum of squares for solution;
%
% Design of Iteration Scheme:
% user.stop - the BP algorithm in the iteration loop is running until
% the criterion is reached, where the criterion is applied
% on the vector of mean-value messages from factor nodes to
% variable nodes in two consecutive iterations;
% user.maxi - the upper limit on BP iterations;
%
% Convergence Parameters:
% user.prob - a Bernoulli random variable with probability "prob"
% independently sampled for each mean value message from
% indirect factor node to a variable node, with values
% between 0 and 1;
% user.alph - the damped message is evaluated as a linear combination of
% the message from the previous and the current iteration,
% with weights "alph" and 1 - "alph", where "alph" is
% between 0 and 1;
% Note: We use an improved BP algorithm that applies synchronous scheduling
% with randomized damping. The randomized damping parameter pairs lead to
% a trade-off between the number of non-converging simulations and the rate
% of convergence. In general, for the selection of "prob" and "alph" for
% which only a small fraction of messages are combined with their values in
% a previous iteration, and that is a case for "prob" close to 0 or "alph"
% close to 1, we observe a large number of non-converging simulations.
%
% Virtual Factor Nodes
% user.mean - the mean value of virtual factor nodes;
% user.vari - the variance value of the virtual factor nodes;
% Note: The virtual factor node is a singly-connected factor node used
% if the variable node x is not directly observed. In a usual scenario,
% without prior knowledge, the variance of virtual factor nodes tend to
% infinity.
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% More information:
% - M. Cosovic and D. Vukobratovic, "Distributed Gauss-Newton Method for
% State Estimation Using Belief Propagation," in IEEE Transactions on
% Power Systems, vol. 34, no. 1, pp. 648-658, Jan. 2019.
% - M. Cosovic, "Design and Analysis of Distributed State Estimation
% Algorithms Based on Belief Propagation and Applications in Smart
% Grids." arXiv preprint arXiv:1811.08355 (2018).
%--------------------------------------------------------------------------
%--------------------------------Load Data---------------------------------
addpath(genpath(pwd))
load('data33_14.mat')
%--------------------------------------------------------------------------
%-------------------------Post-processing Options--------------------------
user.save = 0;
user.radius = 0;
user.error = 1;
%--------------------------------------------------------------------------
%-----------------------Design of Iteration Scheme-------------------------
user.stop = 10^-6;
user.maxi = 200;
%--------------------------------------------------------------------------
%-------------------------Convergence Parameters---------------------------
user.prob = 0.7;
user.alph = 0.5;
%--------------------------------------------------------------------------
%--------------------------Virtual Factor Nodes----------------------------
user.mean = 0;
user.vari = 10^60;
%--------------------------------------------------------------------------
%-----------------------------Main Functions-------------------------------
[bp, wls] = a1_preprocessing(data, user);
[bp] = b1_belief_propagation(bp, user);
[wls, bp] = c1_postprocessing(data, wls, bp, user);
%--------------------------------------------------------------------------