📄 gmm_conditional.m
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function [g, c] = gmm_conditional(g, x, idx)
% ALPHA VERSION
% Deriving the conditional, given the joint, is found by considering a
% perfect observation (ie, constraint) at x.
%
% In order to consider p(gmm|x) as a function of x, not just at x=x0,
% this function returns c, the original cross-correlations of g.
%
% see also: Bar p123
% TODO: A better way is to work this out longhand, and calculate directly,
% but for now its easier to set it up as an observation.
D = size(g.x, 1);
Dc = size(x, 1);
H = zeros(Dc, D);
i = index_table(H, [1:Dc; idx]);
H(i) = 1;
gz.w = 1;
gz.x = x;
gz.P = zeros([Dc, Dc, 1]);
g = gmm_update(g, gz, H);
g = gmm_marginal(g, setdiff(1:D, idx));
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