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 =2;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 20 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('t in component environment (second)');
    LEGEND_CONSTANTS(:,1) = strpad('D_Ca in component parameters (second)');
    LEGEND_CONSTANTS(:,2) = strpad('k_1 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,3) = strpad('k_2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,4) = strpad('f in component parameters (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('g in component parameters (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('Ca_max in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('Total_Tn in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('Total_CB in component parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Ca_t in component Ca_t (dimensionless)');
    LEGEND_STATES(:,1) = strpad('TnCa in component TnCa (dimensionless)');
    LEGEND_STATES(:,2) = strpad('CB_on in component CB_on (dimensionless)');
    LEGEND_STATES(:,3) = strpad('CumCB_on in component CumCB (dimensionless)');
    LEGEND_STATES(:,4) = strpad('CumCB_off in component CumCB (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('F in component force_development (force)');
    LEGEND_STATES(:,5) = strpad('FTI in component force_development (force_second)');
    LEGEND_CONSTANTS(:,16) = strpad('FLA in component force_development (energy)');
    LEGEND_CONSTANTS(:,9) = strpad('phi in component force_development (force)');
    LEGEND_CONSTANTS(:,10) = strpad('s in component force_development (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('L in component force_development (meter)');
    LEGEND_CONSTANTS(:,12) = strpad('L_0 in component force_development (meter)');
    LEGEND_CONSTANTS(:,13) = strpad('F_max in component force_development (force)');
    LEGEND_CONSTANTS(:,18) = strpad('ATP in component ATP (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('ATP_energy in component ATP (energy)');
    LEGEND_CONSTANTS(:,14) = strpad('epsilon in component ATP (energy)');
    LEGEND_CONSTANTS(:,15) = strpad('CumCB_on_end in component ATP (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('Efficiency in component equations_main (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('Economy in component equations_main (second_per_meter)');
    LEGEND_RATES(:,1) = strpad('d/dt TnCa in component TnCa (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt CB_on in component CB_on (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt CumCB_on in component CumCB (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt CumCB_off in component CumCB (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt FTI in component force_development (force_second)');
    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) = 0.1;
    CONSTANTS(:,2) = 40;
    CONSTANTS(:,3) = 20;
    CONSTANTS(:,4) = 10;
    CONSTANTS(:,5) = 10;
    CONSTANTS(:,6) = 1;
    CONSTANTS(:,7) = 1;
    CONSTANTS(:,8) = 1;
    STATES(:,1) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    CONSTANTS(:,9) = 1;
    CONSTANTS(:,10) = 1;
    CONSTANTS(:,11) = 1;
    CONSTANTS(:,12) = 0;
    CONSTANTS(:,13) = 0.228;
    CONSTANTS(:,14) = 1;
    CONSTANTS(:,15) = 1;
    CONSTANTS(:,16) =  CONSTANTS(:,13).*CONSTANTS(:,10).*(CONSTANTS(:,11) - CONSTANTS(:,12));
    CONSTANTS(:,17) =  (CONSTANTS(:,9)./CONSTANTS(:,14)).*(1.00000./CONSTANTS(:,5));
    CONSTANTS(:,18) = CONSTANTS(:,15);
    CONSTANTS(:,19) =  CONSTANTS(:,18).*CONSTANTS(:,14);
    CONSTANTS(:,20) = CONSTANTS(:,16)./CONSTANTS(:,19);
    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(:,2) =  CONSTANTS(:,4).*STATES(:,1).*(CONSTANTS(:,8) - STATES(:,2)) -  CONSTANTS(:,5).*STATES(:,2);
    RATES(:,3) =  CONSTANTS(:,4).*STATES(:,1).*(CONSTANTS(:,8) - STATES(:,2));
    RATES(:,4) =  CONSTANTS(:,5).*STATES(:,2);
    ALGEBRAIC(:,1) = piecewise({VOI>=0.00000&VOI< 0.300000.*CONSTANTS(:,1), ( CONSTANTS(:,6).*(1.00000+ sin((  pi.*(VOI./CONSTANTS(:,1) - 0.150000))./0.300000)))./2.00000 , VOI>= 0.300000.*CONSTANTS(:,1)&VOI<CONSTANTS(:,1), ( CONSTANTS(:,6).*(1.00000 -  sin((  pi.*(VOI./CONSTANTS(:,1) - 0.650000))./0.700000)))./2.00000 }, 0.00000);
    RATES(:,1) =  CONSTANTS(:,2).*ALGEBRAIC(:,1).*(CONSTANTS(:,7) - STATES(:,1)) -  CONSTANTS(:,3).*STATES(:,1);
    ALGEBRAIC(:,2) =  STATES(:,2).*CONSTANTS(:,9);
    RATES(:,5) = ALGEBRAIC(:,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(:,1) = piecewise({VOI>=0.00000&VOI< 0.300000.*CONSTANTS(:,1), ( CONSTANTS(:,6).*(1.00000+ sin((  pi.*(VOI./CONSTANTS(:,1) - 0.150000))./0.300000)))./2.00000 , VOI>= 0.300000.*CONSTANTS(:,1)&VOI<CONSTANTS(:,1), ( CONSTANTS(:,6).*(1.00000 -  sin((  pi.*(VOI./CONSTANTS(:,1) - 0.650000))./0.700000)))./2.00000 }, 0.00000);
    ALGEBRAIC(:,2) =  STATES(:,2).*CONSTANTS(:,9);
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    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