function [x,y] = sample_lds(F, H, Q, R, init_state, T, models, G, u)% SAMPLE_LDS Simulate a run of a (switching) stochastic linear dynamical system.% [x,y] = switching_lds_draw(F, H, Q, R, init_state, models, G, u)% %   x(t+1) = F*x(t) + G*u(t) + w(t),  w ~ N(0, Q),  x(0) = init_state%   y(t) =   H*x(t) + v(t),  v ~ N(0, R)%% Input:% F(:,:,i) - the transition matrix for the i'th model% H(:,:,i) - the observation matrix for the i'th model% Q(:,:,i) - the transition covariance for the i'th model% R(:,:,i) - the observation covariance for the i'th model% init_state(:,i) - the initial mean for the i'th model% T - the num. time steps to run for%% Optional inputs:% models(t) - which model to use at time t. Default = ones(1,T)% G(:,:,i) - the input matrix for the i'th model. Default = 0.% u(:,t)   - the input vector at time t. Default = zeros(1,T)%% Output:% x(:,t)    - the hidden state vector at time t.% y(:,t)    - the observation vector at time t.if ~iscell(F)  F = num2cell(F, [1 2]);  H = num2cell(H, [1 2]);  Q = num2cell(Q, [1 2]);  R = num2cell(R, [1 2]);endM = length(F);%T = length(models);if nargin < 7,  models = ones(1,T);endif nargin < 8,  G = num2cell(repmat(0, [1 1 M]));  u = zeros(1,T);end[os ss] = size(H{1});state_noise_samples = cell(1,M);obs_noise_samples = cell(1,M);for i=1:M  state_noise_samples{i} = sample_gaussian(zeros(length(Q{i}),1), Q{i}, T)';  obs_noise_samples{i} = sample_gaussian(zeros(length(R{i}),1), R{i}, T)';endx = zeros(ss, T);y = zeros(os, T);m = models(1);x(:,1) = init_state(:,m);y(:,1) = H{m}*x(:,1) + obs_noise_samples{m}(:,1);for t=2:T  m = models(t);  x(:,t) = F{m}*x(:,t-1) + G{m}*u(:,t-1) + state_noise_samples{m}(:,t);  y(:,t) = H{m}*x(:,t)  + obs_noise_samples{m}(:,t);end