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 =13;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 19 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_CONSTANTS(:,17) = strpad('F in component main (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('R_T in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('R_off in component main (dimensionless)');
    LEGEND_STATES(:,1) = strpad('D in component main (dimensionless)');
    LEGEND_STATES(:,2) = strpad('A_1 in component main (dimensionless)');
    LEGEND_STATES(:,3) = strpad('A_2 in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('lambda_off in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('lambda_on in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('lambda_D in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('lambda_A_1 in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('lambda_A_2 in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('lambda_A2_cyc in component main (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('Ca in component main (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('Ca_50 in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('k_on in component XB_RU_interaction (per_second)');
    LEGEND_ALGEBRAIC(:,13) = strpad('k_off in component XB_RU_interaction (per_second)');
    LEGEND_CONSTANTS(:,2) = strpad('k_0_on in component main (per_second)');
    LEGEND_CONSTANTS(:,3) = strpad('k_0_off in component main (per_second)');
    LEGEND_CONSTANTS(:,4) = strpad('k_Ca_on in component main (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('k_Ca_off in component main (per_second)');
    LEGEND_ALGEBRAIC(:,10) = strpad('f in component XB_XB_interaction (per_second)');
    LEGEND_ALGEBRAIC(:,11) = strpad('f_prime in component XB_XB_interaction (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('f_0 in component main (per_second)');
    LEGEND_CONSTANTS(:,7) = strpad('f_prime_0 in component main (per_second)');
    LEGEND_CONSTANTS(:,8) = strpad('h in component main (per_second)');
    LEGEND_CONSTANTS(:,9) = strpad('h_prime in component main (per_second)');
    LEGEND_CONSTANTS(:,10) = strpad('g in component main (per_second)');
    LEGEND_CONSTANTS(:,11) = strpad('n_H in component main (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('u in component main (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('w in component main (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('v in component main (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('k_u_on in component RU_rate_constant (per_second)');
    LEGEND_CONSTANTS(:,19) = strpad('k_u_off in component RU_rate_constant (per_second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('k_w_on in component RU_RU_interaction (per_second)');
    LEGEND_ALGEBRAIC(:,9) = strpad('k_w_off in component RU_RU_interaction (per_second)');
    LEGEND_RATES(:,1) = strpad('d/dt D in component main (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt A_1 in component main (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt A_2 in component main (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 = [];
    CONSTANTS(:,1) = 1;
    STATES(:,1) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    CONSTANTS(:,2) = 0;
    CONSTANTS(:,3) = 100;
    CONSTANTS(:,4) = 120;
    CONSTANTS(:,5) = 50;
    CONSTANTS(:,6) = 50;
    CONSTANTS(:,7) = 400;
    CONSTANTS(:,8) = 8;
    CONSTANTS(:,9) = 6;
    CONSTANTS(:,10) = 4;
    CONSTANTS(:,11) = 1;
    CONSTANTS(:,12) = 1;
    CONSTANTS(:,13) = 1;
    CONSTANTS(:,14) = 1;
    CONSTANTS(:,15) = CONSTANTS(:,5)./CONSTANTS(:,4);
    CONSTANTS(:,16) =  CONSTANTS(:,15).*100.000;
    CONSTANTS(:,17) = 1.00000./(1.00000+power(CONSTANTS(:,16)./CONSTANTS(:,15),  - CONSTANTS(:,11)));
    CONSTANTS(:,18) = CONSTANTS(:,2)+( (CONSTANTS(:,4) - CONSTANTS(:,2)).*CONSTANTS(:,16))./(CONSTANTS(:,15)+CONSTANTS(:,16));
    CONSTANTS(:,19) = CONSTANTS(:,3)+( (CONSTANTS(:,5) - CONSTANTS(:,3)).*CONSTANTS(:,16))./(CONSTANTS(:,15)+CONSTANTS(:,16));
    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(:,3) =  CONSTANTS(:,8).*STATES(:,2) -  (CONSTANTS(:,9)+CONSTANTS(:,10)).*STATES(:,3);
    ALGEBRAIC(:,7) = STATES(:,3)./CONSTANTS(:,1);
    ALGEBRAIC(:,10) =  CONSTANTS(:,6).*power(1.00000+ ALGEBRAIC(:,7).*(exp(CONSTANTS(:,14) - 1.00000) - 1.00000), 2.00000);
    ALGEBRAIC(:,11) =  CONSTANTS(:,7).*power(1.00000+ ALGEBRAIC(:,7).*(exp( - (CONSTANTS(:,14) - 1.00000)) - 1.00000), 2.00000);
    RATES(:,2) = ( ALGEBRAIC(:,10).*STATES(:,1)+ CONSTANTS(:,9).*STATES(:,3)) -  (ALGEBRAIC(:,11)+CONSTANTS(:,8)).*STATES(:,2);
    ALGEBRAIC(:,1) = CONSTANTS(:,1) - (STATES(:,1)+STATES(:,2)+STATES(:,3));
    ALGEBRAIC(:,6) = (STATES(:,1)+STATES(:,2)+STATES(:,3))./CONSTANTS(:,1);
    ALGEBRAIC(:,8) =  CONSTANTS(:,18).*power(1.00000+ ALGEBRAIC(:,6).*(CONSTANTS(:,12) - 1.00000), 2.00000);
    ALGEBRAIC(:,12) =  ALGEBRAIC(:,8).*power(1.00000+ ALGEBRAIC(:,7).*(exp(CONSTANTS(:,13) - 1.00000) - 1.00000), 2.00000);
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*power(CONSTANTS(:,12) -  ALGEBRAIC(:,6).*(CONSTANTS(:,12) - 1.00000), 2.00000);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,9).*power(1.00000+ ALGEBRAIC(:,7).*(exp( - (CONSTANTS(:,13) - 1.00000)) - 1.00000), 2.00000);
    RATES(:,1) = ( ALGEBRAIC(:,12).*ALGEBRAIC(:,1)+ ALGEBRAIC(:,11).*STATES(:,2)+ CONSTANTS(:,10).*STATES(:,3)) -  (ALGEBRAIC(:,13)+ALGEBRAIC(:,10)).*STATES(:,1);
   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
    ALGEBRAIC(:,7) = STATES(:,3)./CONSTANTS(:,1);
    ALGEBRAIC(:,10) =  CONSTANTS(:,6).*power(1.00000+ ALGEBRAIC(:,7).*(exp(CONSTANTS(:,14) - 1.00000) - 1.00000), 2.00000);
    ALGEBRAIC(:,11) =  CONSTANTS(:,7).*power(1.00000+ ALGEBRAIC(:,7).*(exp( - (CONSTANTS(:,14) - 1.00000)) - 1.00000), 2.00000);
    ALGEBRAIC(:,1) = CONSTANTS(:,1) - (STATES(:,1)+STATES(:,2)+STATES(:,3));
    ALGEBRAIC(:,6) = (STATES(:,1)+STATES(:,2)+STATES(:,3))./CONSTANTS(:,1);
    ALGEBRAIC(:,8) =  CONSTANTS(:,18).*power(1.00000+ ALGEBRAIC(:,6).*(CONSTANTS(:,12) - 1.00000), 2.00000);
    ALGEBRAIC(:,12) =  ALGEBRAIC(:,8).*power(1.00000+ ALGEBRAIC(:,7).*(exp(CONSTANTS(:,13) - 1.00000) - 1.00000), 2.00000);
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*power(CONSTANTS(:,12) -  ALGEBRAIC(:,6).*(CONSTANTS(:,12) - 1.00000), 2.00000);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,9).*power(1.00000+ ALGEBRAIC(:,7).*(exp( - (CONSTANTS(:,13) - 1.00000)) - 1.00000), 2.00000);
    ALGEBRAIC(:,2) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = STATES(:,2)./CONSTANTS(:,1);
    ALGEBRAIC(:,4) = STATES(:,3)./(STATES(:,1)+STATES(:,2)+STATES(:,3));
    ALGEBRAIC(:,5) = ALGEBRAIC(:,1)./CONSTANTS(:,1);
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