function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction() % This is the "main function". In Matlab, things work best if you rename this function to match the filename. [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel(); end function [algebraicVariableCount] = getAlgebraicVariableCount() % Used later when setting a global variable with the number of algebraic variables. % Note: This is not the "main method". algebraicVariableCount =0; end % There are a total of 3 entries in each of the rate and state variable arrays. % There are a total of 12 entries in the constant variable array. % function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel() % Create ALGEBRAIC of correct size global algebraicVariableCount; algebraicVariableCount = getAlgebraicVariableCount(); % Initialise constants and state variables [INIT_STATES, CONSTANTS] = initConsts; % Set timespan to solve over tspan = [0, 10]; % Set numerical accuracy options for ODE solver options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1); % Solve model with ODE solver [VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options); % Compute algebraic variables [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS); ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI); % Plot state variables against variable of integration [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends(); figure(); plot(VOI, STATES); xlabel(LEGEND_VOI); l = legend(LEGEND_STATES); set(l,'Interpreter','none'); end function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends() LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = ''; LEGEND_VOI = strpad('time in component environment (second)'); LEGEND_STATES(:,1) = strpad('x in component x (dimensionless)'); LEGEND_CONSTANTS(:,1) = strpad('r_1 in component x (rate)'); LEGEND_CONSTANTS(:,2) = strpad('r_2 in component x (rate)'); LEGEND_CONSTANTS(:,3) = strpad('c_1 in component x (rate)'); LEGEND_STATES(:,2) = strpad('z in component z (dimensionless)'); LEGEND_STATES(:,3) = strpad('y in component y (dimensionless)'); LEGEND_CONSTANTS(:,4) = strpad('r_3 in component y (rate)'); LEGEND_CONSTANTS(:,5) = strpad('r_4 in component y (rate)'); LEGEND_CONSTANTS(:,6) = strpad('c_2 in component y (rate)'); LEGEND_CONSTANTS(:,7) = strpad('epsilon in component model_constants (dimensionless)'); LEGEND_CONSTANTS(:,8) = strpad('r_5 in component z (rate)'); LEGEND_CONSTANTS(:,9) = strpad('r_6 in component z (rate)'); LEGEND_CONSTANTS(:,10) = strpad('r_7 in component z (rate)'); LEGEND_CONSTANTS(:,11) = strpad('z_hat in component z (dimensionless)'); LEGEND_CONSTANTS(:,12) = strpad('y_hat in component z (dimensionless)'); LEGEND_RATES(:,1) = strpad('d/dt x in component x (dimensionless)'); LEGEND_RATES(:,3) = strpad('d/dt y in component y (dimensionless)'); LEGEND_RATES(:,2) = strpad('d/dt z in component z (dimensionless)'); LEGEND_STATES = LEGEND_STATES'; LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC'; LEGEND_RATES = LEGEND_RATES'; LEGEND_CONSTANTS = LEGEND_CONSTANTS'; end function [STATES, CONSTANTS] = initConsts() VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = []; STATES(:,1) = 4.0; CONSTANTS(:,1) = 0.2; CONSTANTS(:,2) = 0.1; CONSTANTS(:,3) = 0.1; STATES(:,2) = 1.0; STATES(:,3) = 0.0; CONSTANTS(:,4) = 0.1; CONSTANTS(:,5) = 0.1; CONSTANTS(:,6) = 0.1; CONSTANTS(:,7) = 0.1; CONSTANTS(:,8) = 0.1; CONSTANTS(:,9) = 0.1; CONSTANTS(:,10) = 0.05; CONSTANTS(:,11) = 2.0; CONSTANTS(:,12) = 1.24; if (isempty(STATES)), warning('Initial values for states not set');, end end function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS) global algebraicVariableCount; statesSize = size(STATES); statesColumnCount = statesSize(2); if ( statesColumnCount == 1) STATES = STATES'; ALGEBRAIC = zeros(1, algebraicVariableCount); utilOnes = 1; else statesRowCount = statesSize(1); ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount); RATES = zeros(statesRowCount, statesColumnCount); utilOnes = ones(statesRowCount, 1); end RATES(:,1) = STATES(:,2).*( CONSTANTS(:,1).*STATES(:,3)+ - CONSTANTS(:,2).*STATES(:,1)+CONSTANTS(:,3)); RATES(:,3) = CONSTANTS(:,7).*((CONSTANTS(:,4)./STATES(:,2) - CONSTANTS(:,5).*STATES(:,1))+CONSTANTS(:,6)); RATES(:,2) = ( CONSTANTS(:,8).*(STATES(:,3) - CONSTANTS(:,12)).*(CONSTANTS(:,11) - STATES(:,2))+ CONSTANTS(:,9).*STATES(:,2).*(CONSTANTS(:,11) - STATES(:,2))) - CONSTANTS(:,10).*STATES(:,2); RATES = RATES'; end % Calculate algebraic variables function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI) statesSize = size(STATES); statesColumnCount = statesSize(2); if ( statesColumnCount == 1) STATES = STATES'; utilOnes = 1; else statesRowCount = statesSize(1); utilOnes = ones(statesRowCount, 1); end end % Pad out or shorten strings to a set length function strout = strpad(strin) req_length = 160; insize = size(strin,2); if insize > req_length strout = strin(1:req_length); else strout = [strin, blanks(req_length - insize)]; end end