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 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('time in component environment (ms)');
    LEGEND_ALGEBRAIC(:,4) = strpad('Ca_i in component intracellular_ion_concentrations (uM)');
    LEGEND_ALGEBRAIC(:,1) = strpad('mtime in component intracellular_ion_concentrations (dimensionless)');
    LEGEND_STATES(:,1) = strpad('xb in component crossbridges (dimensionless)');
    LEGEND_STATES(:,2) = strpad('TRPN in component troponin (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('k_xb in component crossbridges (per_ms)');
    LEGEND_CONSTANTS(:,2) = strpad('nperm in component crossbridges (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('perm50 in component crossbridges (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('permtot in component crossbridges (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('Ca_50ref in component troponin (uM)');
    LEGEND_CONSTANTS(:,5) = strpad('beta_1 in component troponin (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('k_off in component troponin (per_ms)');
    LEGEND_CONSTANTS(:,7) = strpad('n_TRPN in component troponin (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('lambda_m in component filament_overlap (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('Ca_50 in component troponin (uM)');
    LEGEND_CONSTANTS(:,15) = strpad('lambda in component Myofilaments (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('dlambdadt in component Myofilaments (per_ms)');
    LEGEND_CONSTANTS(:,20) = strpad('overlap in component filament_overlap (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('beta_0 in component filament_overlap (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('lambda_s in component filament_overlap (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('T_ref in component isometric_tension (kPa)');
    LEGEND_ALGEBRAIC(:,3) = strpad('T_0 in component isometric_tension (kPa)');
    LEGEND_ALGEBRAIC(:,5) = strpad('Q in component dynamic_stiffness (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('a in component dynamic_stiffness (dimensionless)');
    LEGEND_STATES(:,3) = strpad('Q_1 in component dynamic_stiffness (dimensionless)');
    LEGEND_STATES(:,4) = strpad('Q_2 in component dynamic_stiffness (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('A_1 in component dynamic_stiffness (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('A_2 in component dynamic_stiffness (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('alpha_1 in component dynamic_stiffness (per_ms)');
    LEGEND_CONSTANTS(:,14) = strpad('alpha_2 in component dynamic_stiffness (per_ms)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Tension in component dynamic_stiffness (kPa)');
    LEGEND_RATES(:,1) = strpad('d/dt xb in component crossbridges (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt TRPN in component troponin (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Q_1 in component dynamic_stiffness (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt Q_2 in component dynamic_stiffness (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) = 0.00046;
    STATES(:,2) = 0.0752;
    CONSTANTS(:,1) = 0.1;
    CONSTANTS(:,2) = 5;
    CONSTANTS(:,3) = 0.35;
    CONSTANTS(:,4) = 0.8;
    CONSTANTS(:,5) = -1.5;
    CONSTANTS(:,6) = 0.1;
    CONSTANTS(:,7) = 2;
    CONSTANTS(:,8) = 1.65;
    CONSTANTS(:,9) = 120;
    CONSTANTS(:,10) = 0.35;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    CONSTANTS(:,11) = -29;
    CONSTANTS(:,12) = 116;
    CONSTANTS(:,13) = 0.1;
    CONSTANTS(:,14) = 0.5;
    CONSTANTS(:,15) = 1.00000;
    CONSTANTS(:,16) = 0.00000;
    CONSTANTS(:,17) = piecewise({CONSTANTS(:,15)>1.20000, 1.20000 }, CONSTANTS(:,15));
    CONSTANTS(:,18) =  CONSTANTS(:,4).*(1.00000+ CONSTANTS(:,5).*(CONSTANTS(:,17) - 1.00000));
    CONSTANTS(:,19) = piecewise({CONSTANTS(:,17)>=0.870000, 0.870000 }, CONSTANTS(:,17));
    CONSTANTS(:,20) = 1.00000+ CONSTANTS(:,8).*((CONSTANTS(:,17)+CONSTANTS(:,19)) - 1.87000);
    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(:,11).*CONSTANTS(:,16) -  CONSTANTS(:,13).*STATES(:,3);
    RATES(:,4) =  CONSTANTS(:,12).*CONSTANTS(:,16) -  CONSTANTS(:,14).*STATES(:,4);
    ALGEBRAIC(:,2) = power(power(STATES(:,2)./CONSTANTS(:,3), CONSTANTS(:,2)), 1.0 ./ 2);
    RATES(:,1) =  CONSTANTS(:,1).*( ALGEBRAIC(:,2).*(1.00000 - STATES(:,1)) -  (1.00000./ALGEBRAIC(:,2)).*STATES(:,1));
    ALGEBRAIC(:,1) = (VOI -  167.000.*floor(VOI./167.000))./1.00000;
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,1)>=1.17000&ALGEBRAIC(:,1)<30.8400,  1.00000.*1.85358e-05.*power(ALGEBRAIC(:,1), 3.00000)+  - 0.00159034.*power(ALGEBRAIC(:,1), 2.00000)+ 0.0436459.*power(ALGEBRAIC(:,1), 1.00000)+0.167079 , ALGEBRAIC(:,1)>=30.8400, (( 1.00000.* - 5.74585e-08.*power(ALGEBRAIC(:,1), 3.00000)+ 3.11222e-05.*power(ALGEBRAIC(:,1), 2.00000)) -  0.00661849.*power(ALGEBRAIC(:,1), 1.00000))+0.720442 }, 0.216000);
    RATES(:,2) =  CONSTANTS(:,6).*( power(ALGEBRAIC(:,4)./CONSTANTS(:,18), CONSTANTS(:,7)).*(1.00000 - STATES(:,2)) - 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(:,2) = power(power(STATES(:,2)./CONSTANTS(:,3), CONSTANTS(:,2)), 1.0 ./ 2);
    ALGEBRAIC(:,1) = (VOI -  167.000.*floor(VOI./167.000))./1.00000;
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,1)>=1.17000&ALGEBRAIC(:,1)<30.8400,  1.00000.*1.85358e-05.*power(ALGEBRAIC(:,1), 3.00000)+  - 0.00159034.*power(ALGEBRAIC(:,1), 2.00000)+ 0.0436459.*power(ALGEBRAIC(:,1), 1.00000)+0.167079 , ALGEBRAIC(:,1)>=30.8400, (( 1.00000.* - 5.74585e-08.*power(ALGEBRAIC(:,1), 3.00000)+ 3.11222e-05.*power(ALGEBRAIC(:,1), 2.00000)) -  0.00661849.*power(ALGEBRAIC(:,1), 1.00000))+0.720442 }, 0.216000);
    ALGEBRAIC(:,3) =  CONSTANTS(:,9).*STATES(:,1).*CONSTANTS(:,20);
    ALGEBRAIC(:,5) = STATES(:,3)+STATES(:,4);
    ALGEBRAIC(:,6) = piecewise({ALGEBRAIC(:,5)<0.00000, ( ALGEBRAIC(:,3).*( CONSTANTS(:,10).*ALGEBRAIC(:,5)+1.00000))./(1.00000 - ALGEBRAIC(:,5)) }, ( ALGEBRAIC(:,3).*(1.00000+ (CONSTANTS(:,10)+2.00000).*ALGEBRAIC(:,5)))./(1.00000+ALGEBRAIC(:,5)));
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