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 =6;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 22 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 (minute)');
    LEGEND_STATES(:,1) = strpad('m in component m (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('kM_plus in component m (fourth_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('kM_minus in component m (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('CaMtotal in component m (micromolar)');
    LEGEND_STATES(:,2) = strpad('x in component x (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('dmdt in component m (flux)');
    LEGEND_STATES(:,3) = strpad('z in component z (micromolar)');
    LEGEND_CONSTANTS(:,4) = strpad('kN_plus in component z (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('kN_minus in component z (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('CaNtotal in component z (micromolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('dzdt in component z (flux)');
    LEGEND_STATES(:,4) = strpad('h in component h (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('d in component h (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('f in component h (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('phi in component phi (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('lamda in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('L0 in component model_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('y in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('N in component model_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('psi in component psi (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('Vx in component x (flux)');
    LEGEND_CONSTANTS(:,12) = strpad('Kx in component x (micromolar)');
    LEGEND_CONSTANTS(:,13) = strpad('V1 in component x (flux)');
    LEGEND_CONSTANTS(:,14) = strpad('K1 in component x (micromolar)');
    LEGEND_CONSTANTS(:,15) = strpad('V2 in component x (flux)');
    LEGEND_CONSTANTS(:,16) = strpad('K2 in component x (micromolar)');
    LEGEND_CONSTANTS(:,17) = strpad('V3 in component x (flux)');
    LEGEND_CONSTANTS(:,18) = strpad('K3 in component x (micromolar)');
    LEGEND_CONSTANTS(:,19) = strpad('kc in component x (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('alpha in component x (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('Caex in component x (micromolar)');
    LEGEND_ALGEBRAIC(:,6) = strpad('dxdt in component x (flux)');
    LEGEND_RATES(:,1) = strpad('d/dt m in component m (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt z in component z (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt h in component h (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt x in component x (micromolar)');
    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) = 0.0;
    CONSTANTS(:,1) = 500.0;
    CONSTANTS(:,2) = 100.0;
    CONSTANTS(:,3) = 25.0;
    STATES(:,2) = 0.0;
    STATES(:,3) = 1.0E-8;
    CONSTANTS(:,4) = 5.0;
    CONSTANTS(:,5) = 5.0;
    CONSTANTS(:,6) = 25.0;
    STATES(:,4) = 0.0;
    CONSTANTS(:,7) = 0.4;
    CONSTANTS(:,8) = 0.1;
    CONSTANTS(:,9) = 5.0;
    CONSTANTS(:,10) = 13.0;
    CONSTANTS(:,11) = 1000.0;
    CONSTANTS(:,12) = 500.0;
    CONSTANTS(:,13) = 30000.0;
    CONSTANTS(:,14) = 4.3;
    CONSTANTS(:,15) = 100.0;
    CONSTANTS(:,16) = 0.1;
    CONSTANTS(:,17) = 10000.0;
    CONSTANTS(:,18) = 100.0;
    CONSTANTS(:,19) = 10.0;
    CONSTANTS(:,20) = 0.006;
    CONSTANTS(:,21) = 1.0;
    CONSTANTS(:,22) = power(10.0000,  - (CONSTANTS(:,10)./2.00000));
    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) =  CONSTANTS(:,1).*(CONSTANTS(:,3) - STATES(:,1)).*power(STATES(:,2), 3.00000) -  CONSTANTS(:,2).*STATES(:,1);
    RATES(:,3) =  CONSTANTS(:,4).*(CONSTANTS(:,6) - STATES(:,3)).*STATES(:,1) -  CONSTANTS(:,5).*STATES(:,3);
    ALGEBRAIC(:,3) = 1.00000./STATES(:,3);
    ALGEBRAIC(:,4) = 1.00000./(1.00000+( CONSTANTS(:,22).*(power( CONSTANTS(:,9).*ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000))./( ( CONSTANTS(:,9).*ALGEBRAIC(:,3) - 1.00000).*((ALGEBRAIC(:,3) - 1.00000)./(power(ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000))));
    RATES(:,4) =  CONSTANTS(:,7).*ALGEBRAIC(:,4).*(1.00000./STATES(:,3)).*(1.00000 - STATES(:,4)) -  CONSTANTS(:,8).*(1.00000 -  ALGEBRAIC(:,4).*(1.00000./STATES(:,3))).*STATES(:,4);
    ALGEBRAIC(:,5) = (1.00000+CONSTANTS(:,22))./((power(ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000)./(ALGEBRAIC(:,3) - 1.00000)+ CONSTANTS(:,22).*((power( CONSTANTS(:,9).*ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000)./( CONSTANTS(:,9).*ALGEBRAIC(:,3) - 1.00000)));
    RATES(:,2) = ( CONSTANTS(:,11).*CONSTANTS(:,21))./(CONSTANTS(:,12)+CONSTANTS(:,21)) - ( STATES(:,4).*ALGEBRAIC(:,5).*(1.00000./STATES(:,3)).*(( CONSTANTS(:,13).*STATES(:,2))./(CONSTANTS(:,14)+STATES(:,2)))+ STATES(:,4).*ALGEBRAIC(:,5).*(1.00000./STATES(:,3)).*(( CONSTANTS(:,15).*STATES(:,2))./(CONSTANTS(:,16)+STATES(:,2)))+ (1.00000./(1.00000+ CONSTANTS(:,19).*STATES(:,3))).*(( CONSTANTS(:,17).*STATES(:,2))./(CONSTANTS(:,18)+STATES(:,2)))+ CONSTANTS(:,20).*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
    ALGEBRAIC(:,3) = 1.00000./STATES(:,3);
    ALGEBRAIC(:,4) = 1.00000./(1.00000+( CONSTANTS(:,22).*(power( CONSTANTS(:,9).*ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000))./( ( CONSTANTS(:,9).*ALGEBRAIC(:,3) - 1.00000).*((ALGEBRAIC(:,3) - 1.00000)./(power(ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000))));
    ALGEBRAIC(:,5) = (1.00000+CONSTANTS(:,22))./((power(ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000)./(ALGEBRAIC(:,3) - 1.00000)+ CONSTANTS(:,22).*((power( CONSTANTS(:,9).*ALGEBRAIC(:,3), CONSTANTS(:,10)+1.00000) - 1.00000)./( CONSTANTS(:,9).*ALGEBRAIC(:,3) - 1.00000)));
    ALGEBRAIC(:,1) =  CONSTANTS(:,1).*(CONSTANTS(:,3) - STATES(:,1)).*power(STATES(:,2), 3.00000) -  CONSTANTS(:,2).*STATES(:,1);
    ALGEBRAIC(:,2) =  CONSTANTS(:,4).*(CONSTANTS(:,6) - STATES(:,3)).*STATES(:,1) -  CONSTANTS(:,5).*STATES(:,3);
    ALGEBRAIC(:,6) = ( CONSTANTS(:,11).*CONSTANTS(:,21))./(CONSTANTS(:,12)+CONSTANTS(:,21)) - ( STATES(:,4).*ALGEBRAIC(:,5).*(1.00000./STATES(:,3)).*(( CONSTANTS(:,13).*STATES(:,2))./(CONSTANTS(:,14)+STATES(:,2)))+ STATES(:,4).*ALGEBRAIC(:,5).*(1.00000./STATES(:,3)).*(( CONSTANTS(:,15).*STATES(:,2))./(CONSTANTS(:,16)+STATES(:,2)))+ (1.00000./(1.00000+ CONSTANTS(:,19).*STATES(:,3))).*(( CONSTANTS(:,17).*STATES(:,2))./(CONSTANTS(:,18)+STATES(:,2)))+ CONSTANTS(:,20).*STATES(:,2));
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