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 =17;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 25 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(:,2) = strpad('Ca_i in component intracellular_ion_concentrations (mM)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Ca_b in component intracellular_ion_concentrations (mM)');
    LEGEND_STATES(:,1) = strpad('TRPN in component intracellular_ion_concentrations (mM)');
    LEGEND_CONSTANTS(:,1) = strpad('Ca_TRPN_Max in component troponin (mM)');
    LEGEND_ALGEBRAIC(:,17) = strpad('J_TRPN in component troponin (mM_per_ms)');
    LEGEND_STATES(:,2) = strpad('z in component tropomyosin (dimensionless)');
    LEGEND_ALGEBRAIC(:,10) = strpad('z_max in component tropomyosin (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('k_on in component troponin (per_mM_per_ms)');
    LEGEND_CONSTANTS(:,3) = strpad('k_Ref_off in component troponin (per_ms)');
    LEGEND_CONSTANTS(:,4) = strpad('gamma_trpn in component troponin (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('alpha_0 in component tropomyosin (per_ms)');
    LEGEND_CONSTANTS(:,6) = strpad('alpha_r1 in component tropomyosin (per_ms)');
    LEGEND_CONSTANTS(:,7) = strpad('alpha_r2 in component tropomyosin (per_ms)');
    LEGEND_CONSTANTS(:,8) = strpad('n_Rel in component tropomyosin (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('K_z in component tropomyosin (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('n_Hill in component tropomyosin (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('Ca_50ref in component tropomyosin (mM)');
    LEGEND_CONSTANTS(:,12) = strpad('z_p in component tropomyosin (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('beta_1 in component tropomyosin (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Ca_50 in component tropomyosin (mM)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Ca_TRPN_50 in component tropomyosin (mM)');
    LEGEND_CONSTANTS(:,23) = strpad('K_2 in component tropomyosin (per_ms)');
    LEGEND_CONSTANTS(:,25) = strpad('K_1 in component tropomyosin (per_ms)');
    LEGEND_ALGEBRAIC(:,9) = strpad('alpha_Tm in component tropomyosin (per_ms)');
    LEGEND_ALGEBRAIC(:,3) = strpad('beta_Tm in component tropomyosin (per_ms)');
    LEGEND_CONSTANTS(:,14) = strpad('beta_0 in component filament_overlap (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('lambda in component Myofilaments (dimensionless)');
    LEGEND_ALGEBRAIC(:,16) = strpad('k_off in component troponin (per_ms)');
    LEGEND_ALGEBRAIC(:,15) = strpad('Tension in component Cross_Bridges (N_per_mm2)');
    LEGEND_CONSTANTS(:,15) = strpad('T_ref in component length_independent_tension (N_per_mm2)');
    LEGEND_ALGEBRAIC(:,4) = strpad('ExtensionRatio in component Myofilaments (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('dExtensionRatiodt in component Myofilaments (per_ms)');
    LEGEND_ALGEBRAIC(:,6) = strpad('lambda_prev in component Myofilaments (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('overlap in component filament_overlap (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('T_Base in component length_independent_tension (N_per_mm2)');
    LEGEND_ALGEBRAIC(:,13) = strpad('T_0 in component isometric_tension (N_per_mm2)');
    LEGEND_ALGEBRAIC(:,14) = strpad('Q in component Cross_Bridges (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('a in component Cross_Bridges (dimensionless)');
    LEGEND_STATES(:,3) = strpad('Q_1 in component Cross_Bridges (dimensionless)');
    LEGEND_STATES(:,4) = strpad('Q_2 in component Cross_Bridges (dimensionless)');
    LEGEND_STATES(:,5) = strpad('Q_3 in component Cross_Bridges (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('A_1 in component Cross_Bridges (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('A_2 in component Cross_Bridges (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('A_3 in component Cross_Bridges (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('alpha_1 in component Cross_Bridges (per_ms)');
    LEGEND_CONSTANTS(:,21) = strpad('alpha_2 in component Cross_Bridges (per_ms)');
    LEGEND_CONSTANTS(:,22) = strpad('alpha_3 in component Cross_Bridges (per_ms)');
    LEGEND_RATES(:,1) = strpad('d/dt TRPN in component intracellular_ion_concentrations (mM)');
    LEGEND_RATES(:,2) = strpad('d/dt z in component tropomyosin (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Q_1 in component Cross_Bridges (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt Q_2 in component Cross_Bridges (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt Q_3 in component Cross_Bridges (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) = 0.067593139865;
    CONSTANTS(:,1) = 70e-3;
    STATES(:,2) = 0.014417937837;
    CONSTANTS(:,2) = 100;
    CONSTANTS(:,3) = 0.2;
    CONSTANTS(:,4) = 2;
    CONSTANTS(:,5) = 8e-3;
    CONSTANTS(:,6) = 2e-3;
    CONSTANTS(:,7) = 1.75e-3;
    CONSTANTS(:,8) = 3;
    CONSTANTS(:,9) = 0.15;
    CONSTANTS(:,10) = 3;
    CONSTANTS(:,11) = 1.05e-3;
    CONSTANTS(:,12) = 0.85;
    CONSTANTS(:,13) = -4;
    CONSTANTS(:,14) = 4.9;
    CONSTANTS(:,15) = 56.2;
    CONSTANTS(:,16) = 0.35;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    CONSTANTS(:,17) = -29;
    CONSTANTS(:,18) = 138;
    CONSTANTS(:,19) = 129;
    CONSTANTS(:,20) = 0.03;
    CONSTANTS(:,21) = 0.13;
    CONSTANTS(:,22) = 0.625;
    CONSTANTS(:,23) =  (( CONSTANTS(:,7).*power(CONSTANTS(:,12), CONSTANTS(:,8)))./(power(CONSTANTS(:,12), CONSTANTS(:,8))+power(CONSTANTS(:,9), CONSTANTS(:,8)))).*(1.00000 - ( CONSTANTS(:,8).*power(CONSTANTS(:,9), CONSTANTS(:,8)))./(power(CONSTANTS(:,12), CONSTANTS(:,8))+power(CONSTANTS(:,9), CONSTANTS(:,8))));
    CONSTANTS(:,24) = 0.00000;
    CONSTANTS(:,25) = ( CONSTANTS(:,7).*power(CONSTANTS(:,12), CONSTANTS(:,8) - 1.00000).*CONSTANTS(:,8).*power(CONSTANTS(:,9), CONSTANTS(:,8)))./power(power(CONSTANTS(:,12), CONSTANTS(:,8))+power(CONSTANTS(:,9), CONSTANTS(:,8)), 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(:,3) =  CONSTANTS(:,17).*CONSTANTS(:,24) -  CONSTANTS(:,20).*STATES(:,3);
    RATES(:,4) =  CONSTANTS(:,18).*CONSTANTS(:,24) -  CONSTANTS(:,21).*STATES(:,4);
    RATES(:,5) =  CONSTANTS(:,19).*CONSTANTS(:,24) -  CONSTANTS(:,22).*STATES(:,5);
    ALGEBRAIC(:,1) = CONSTANTS(:,1) - STATES(:,1);
    ALGEBRAIC(:,4) = piecewise({VOI>1000.00, 1.00000 }, 1.00000);
    ALGEBRAIC(:,5) = piecewise({ALGEBRAIC(:,4)>0.800000&ALGEBRAIC(:,4)<=1.15000, ALGEBRAIC(:,4) , ALGEBRAIC(:,4)>1.15000, 1.15000 }, 0.800000);
    ALGEBRAIC(:,7) =  CONSTANTS(:,11).*(1.00000+ CONSTANTS(:,13).*(ALGEBRAIC(:,5) - 1.00000));
    ALGEBRAIC(:,8) = ( ALGEBRAIC(:,7).*CONSTANTS(:,1))./(ALGEBRAIC(:,7)+ (CONSTANTS(:,3)./CONSTANTS(:,2)).*(1.00000 - ( (1.00000+ CONSTANTS(:,14).*(ALGEBRAIC(:,5) - 1.00000)).*0.500000)./CONSTANTS(:,4)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,5).*power(ALGEBRAIC(:,1)./ALGEBRAIC(:,8), CONSTANTS(:,10));
    ALGEBRAIC(:,3) = CONSTANTS(:,6)+( CONSTANTS(:,7).*power(STATES(:,2), CONSTANTS(:,8) - 1.00000))./(power(STATES(:,2), CONSTANTS(:,8))+power(CONSTANTS(:,9), CONSTANTS(:,8)));
    RATES(:,2) =  ALGEBRAIC(:,9).*(1.00000 - STATES(:,2)) -  ALGEBRAIC(:,3).*STATES(:,2);
    ALGEBRAIC(:,2) = piecewise({VOI<1.00000,  1000.00.*1.84330e-07 , VOI>=10.0000&VOI<15.0000,  1000.00.*((( 1.05500.*power(VOI./1000.00, 3.00000) -  0.0350700.*power(VOI./1000.00, 2.00000))+( 0.000399200.*VOI)./1000.00) - 1.35600e-06) , VOI>=15.0000&VOI<55.0000,  1000.00.*((( 0.0140000.*power(VOI./1000.00, 3.00000) -  0.00255500.*power(VOI./1000.00, 2.00000))+( 0.000149400.*VOI)./1000.00) - 1.42800e-06) , VOI>=55.0000&VOI<250.000,  1000.00.*((( 1.73900e-05.*power(VOI./1000.00, 3.00000) -  3.20900e-06.*power(VOI./1000.00, 2.00000)) - ( 5.68900e-06.*VOI)./1000.00)+1.71900e-06) , VOI>=250.000&VOI<490.000,  1000.00.*(((( 0.000132100.*power(VOI./1000.00, 4.00000) -  0.000219700.*power(VOI./1000.00, 3.00000))+ 0.000137400.*power(VOI./1000.00, 2.00000)) - ( 3.89500e-05.*VOI)./1000.00)+4.44100e-06) },  1000.00.*1.21480e-07);
    ALGEBRAIC(:,11) = 1.00000+ CONSTANTS(:,14).*(ALGEBRAIC(:,5) - 1.00000);
    ALGEBRAIC(:,10) = (CONSTANTS(:,5)./power(ALGEBRAIC(:,8)./CONSTANTS(:,1), CONSTANTS(:,10)) - CONSTANTS(:,23))./(CONSTANTS(:,6)+CONSTANTS(:,25)+CONSTANTS(:,5)./power(ALGEBRAIC(:,8)./CONSTANTS(:,1), CONSTANTS(:,10)));
    ALGEBRAIC(:,12) = ( CONSTANTS(:,15).*STATES(:,2))./ALGEBRAIC(:,10);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,12).*ALGEBRAIC(:,11);
    ALGEBRAIC(:,14) = STATES(:,3)+STATES(:,4)+STATES(:,5);
    ALGEBRAIC(:,15) = piecewise({ALGEBRAIC(:,14)<0.00000, ( ALGEBRAIC(:,13).*( CONSTANTS(:,16).*ALGEBRAIC(:,14)+1.00000))./(1.00000 - ALGEBRAIC(:,14)) }, ( ALGEBRAIC(:,13).*(1.00000+ (CONSTANTS(:,16)+2.00000).*ALGEBRAIC(:,14)))./(1.00000+ALGEBRAIC(:,14)));
    ALGEBRAIC(:,16) = piecewise({1.00000 - ALGEBRAIC(:,15)./( CONSTANTS(:,4).*CONSTANTS(:,15))>0.100000,  CONSTANTS(:,3).*(1.00000 - ALGEBRAIC(:,15)./( CONSTANTS(:,4).*CONSTANTS(:,15))) },  CONSTANTS(:,3).*0.100000);
    ALGEBRAIC(:,17) =  (CONSTANTS(:,1) - STATES(:,1)).*ALGEBRAIC(:,16) -  ALGEBRAIC(:,2).*STATES(:,1).*CONSTANTS(:,2);
    RATES(:,1) = ALGEBRAIC(:,17);
   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) = CONSTANTS(:,1) - STATES(:,1);
    ALGEBRAIC(:,4) = piecewise({VOI>1000.00, 1.00000 }, 1.00000);
    ALGEBRAIC(:,5) = piecewise({ALGEBRAIC(:,4)>0.800000&ALGEBRAIC(:,4)<=1.15000, ALGEBRAIC(:,4) , ALGEBRAIC(:,4)>1.15000, 1.15000 }, 0.800000);
    ALGEBRAIC(:,7) =  CONSTANTS(:,11).*(1.00000+ CONSTANTS(:,13).*(ALGEBRAIC(:,5) - 1.00000));
    ALGEBRAIC(:,8) = ( ALGEBRAIC(:,7).*CONSTANTS(:,1))./(ALGEBRAIC(:,7)+ (CONSTANTS(:,3)./CONSTANTS(:,2)).*(1.00000 - ( (1.00000+ CONSTANTS(:,14).*(ALGEBRAIC(:,5) - 1.00000)).*0.500000)./CONSTANTS(:,4)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,5).*power(ALGEBRAIC(:,1)./ALGEBRAIC(:,8), CONSTANTS(:,10));
    ALGEBRAIC(:,3) = CONSTANTS(:,6)+( CONSTANTS(:,7).*power(STATES(:,2), CONSTANTS(:,8) - 1.00000))./(power(STATES(:,2), CONSTANTS(:,8))+power(CONSTANTS(:,9), CONSTANTS(:,8)));
    ALGEBRAIC(:,2) = piecewise({VOI<1.00000,  1000.00.*1.84330e-07 , VOI>=10.0000&VOI<15.0000,  1000.00.*((( 1.05500.*power(VOI./1000.00, 3.00000) -  0.0350700.*power(VOI./1000.00, 2.00000))+( 0.000399200.*VOI)./1000.00) - 1.35600e-06) , VOI>=15.0000&VOI<55.0000,  1000.00.*((( 0.0140000.*power(VOI./1000.00, 3.00000) -  0.00255500.*power(VOI./1000.00, 2.00000))+( 0.000149400.*VOI)./1000.00) - 1.42800e-06) , VOI>=55.0000&VOI<250.000,  1000.00.*((( 1.73900e-05.*power(VOI./1000.00, 3.00000) -  3.20900e-06.*power(VOI./1000.00, 2.00000)) - ( 5.68900e-06.*VOI)./1000.00)+1.71900e-06) , VOI>=250.000&VOI<490.000,  1000.00.*(((( 0.000132100.*power(VOI./1000.00, 4.00000) -  0.000219700.*power(VOI./1000.00, 3.00000))+ 0.000137400.*power(VOI./1000.00, 2.00000)) - ( 3.89500e-05.*VOI)./1000.00)+4.44100e-06) },  1000.00.*1.21480e-07);
    ALGEBRAIC(:,11) = 1.00000+ CONSTANTS(:,14).*(ALGEBRAIC(:,5) - 1.00000);
    ALGEBRAIC(:,10) = (CONSTANTS(:,5)./power(ALGEBRAIC(:,8)./CONSTANTS(:,1), CONSTANTS(:,10)) - CONSTANTS(:,23))./(CONSTANTS(:,6)+CONSTANTS(:,25)+CONSTANTS(:,5)./power(ALGEBRAIC(:,8)./CONSTANTS(:,1), CONSTANTS(:,10)));
    ALGEBRAIC(:,12) = ( CONSTANTS(:,15).*STATES(:,2))./ALGEBRAIC(:,10);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,12).*ALGEBRAIC(:,11);
    ALGEBRAIC(:,14) = STATES(:,3)+STATES(:,4)+STATES(:,5);
    ALGEBRAIC(:,15) = piecewise({ALGEBRAIC(:,14)<0.00000, ( ALGEBRAIC(:,13).*( CONSTANTS(:,16).*ALGEBRAIC(:,14)+1.00000))./(1.00000 - ALGEBRAIC(:,14)) }, ( ALGEBRAIC(:,13).*(1.00000+ (CONSTANTS(:,16)+2.00000).*ALGEBRAIC(:,14)))./(1.00000+ALGEBRAIC(:,14)));
    ALGEBRAIC(:,16) = piecewise({1.00000 - ALGEBRAIC(:,15)./( CONSTANTS(:,4).*CONSTANTS(:,15))>0.100000,  CONSTANTS(:,3).*(1.00000 - ALGEBRAIC(:,15)./( CONSTANTS(:,4).*CONSTANTS(:,15))) },  CONSTANTS(:,3).*0.100000);
    ALGEBRAIC(:,17) =  (CONSTANTS(:,1) - STATES(:,1)).*ALGEBRAIC(:,16) -  ALGEBRAIC(:,2).*STATES(:,1).*CONSTANTS(:,2);
    ALGEBRAIC(:,6) = ALGEBRAIC(:,4);
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