function [y] = environ(xx, s, t) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ENVIRONMENTAL MODEL FUNCTION % % Authors: Sonja Surjanovic, Simon Fraser University % Derek Bingham, Simon Fraser University % Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca. % % Copyright 2013. Derek Bingham, Simon Fraser University. % % THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY % FOR THE USE OF THIS SOFTWARE. If software is modified to produce % derivative works, such modified software should be clearly marked. % Additionally, this program is free software; you can redistribute it % and/or modify it under the terms of the GNU General Public License as % published by the Free Software Foundation; version 2.0 of the License. % Accordingly, this program is distributed in the hope that it will be % useful, but WITHOUT ANY WARRANTY; without even the implied warranty % of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % For function details and reference information, see: % http://www.sfu.ca/~ssurjano/ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % OUTPUT AND INPUTS: % % y = row vector of scaled concentrations of the pollutant at the % space-time vectors (s, t) % Its structure is: % y(s_1, t_1), y(s_1, t_2), ..., y(s_1, t_dt), y(s_2, t_1), ..., % y(s_2,t_dt), ..., y(s_ds, t_1), ..., y(s_ds, t_dt) % xx = [M, D, L, tau] % s = vector of locations (optional), with default value % [0.5, 1, 1.5, 2, 2.5] % t = vector of times (optional), with default value % [0.3, 0.6, ..., 50.7, 60] % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M = xx(1); D = xx(2); L = xx(3); tau = xx(4); if (nargin < 3) t = [0.3:0.3:60]; end if (nargin < 2) s = [0.5, 1, 1.5, 2, 2.5]; end ds = length(s); dt = length(t); dY = ds * dt; Y = zeros(ds, dt); % Create matrix Y, where each row corresponds to si and each column % corresponds to tj. for (ii = 1:ds) si = s(ii); for (jj = 1:dt) tj = t(jj); term1a = M / sqrt(4*pi*D*tj); term1b = exp(-si^2 / (4*D*tj)); term1 = term1a * term1b; term2 = 0; if (tau < tj) term2a = M / sqrt(4*pi*D*(tj-tau)); term2b = exp(-(si-L)^2 / (4*D*(tj-tau))); term2 = term2a * term2b; end C = term1 + term2; Y(ii, jj) = sqrt(4*pi) * C; end end % Convert the matrix into a vector (by rows). Yrow = Y'; y = Yrow(:)'; end