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 =7;
end
% There are a total of 11 entries in each of the rate and state variable arrays.
% There are a total of 57 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 (hour)');
    LEGEND_STATES(:,1) = strpad('Q_Ca_p in component Q_Ca_p (millimole)');
    LEGEND_CONSTANTS(:,1) = strpad('J_bp_Ca in component model_fluxes (millimole_per_hour)');
    LEGEND_ALGEBRAIC(:,1) = strpad('J_pb_Ca in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,2) = strpad('J_pu_Ca in component model_fluxes (millimole_per_hour)');
    LEGEND_ALGEBRAIC(:,4) = strpad('J_ip_Ca in component model_fluxes (millimole_per_hour)');
    LEGEND_STATES(:,2) = strpad('Q_P_p in component Q_P_p (millimole)');
    LEGEND_CONSTANTS(:,39) = strpad('J_bp_P in component model_fluxes (millimole_per_hour)');
    LEGEND_ALGEBRAIC(:,5) = strpad('J_pb_P in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,3) = strpad('J_pu_P in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,49) = strpad('J_ip_P in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,56) = strpad('J_pc_P in component model_fluxes (millimole_per_hour)');
    LEGEND_ALGEBRAIC(:,7) = strpad('J_cp_P in component model_fluxes (millimole_per_hour)');
    LEGEND_STATES(:,3) = strpad('Q_P_c in component Q_P_c (millimole)');
    LEGEND_STATES(:,4) = strpad('Q_PTH_p in component Q_PTH_p (millimole)');
    LEGEND_ALGEBRAIC(:,2) = strpad('S_PTH in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,4) = strpad('C_PTH_p in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,5) = strpad('k_PTH in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,5) = strpad('Q_Ca_b in component Q_Ca_b (millimole)');
    LEGEND_STATES(:,6) = strpad('Q_P_b in component Q_P_b (millimole)');
    LEGEND_STATES(:,7) = strpad('Q_E_k in component Q_E_k (millimole)');
    LEGEND_CONSTANTS(:,6) = strpad('S_E in component model_parameters (millimole_per_hour)');
    LEGEND_CONSTANTS(:,7) = strpad('k_E in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,8) = strpad('Q_D_p in component Q_D_p (millimole)');
    LEGEND_CONSTANTS(:,8) = strpad('k_D in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,9) = strpad('Q_TCa_i in component Q_TCa_i (millimole)');
    LEGEND_CONSTANTS(:,50) = strpad('k1_D in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,51) = strpad('k2_D in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,10) = strpad('Q_C_PT in component Q_C_PT (millimole)');
    LEGEND_CONSTANTS(:,52) = strpad('k3_D in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,53) = strpad('k4_D in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,11) = strpad('Q_TP_k in component Q_TP_k (millimole)');
    LEGEND_CONSTANTS(:,54) = strpad('k1_P in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k2_P in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('J_P_ing in component model_fluxes (millimole_per_hour)');
    LEGEND_CONSTANTS(:,11) = strpad('Stoic_Ca_P in component model_fluxes (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('k_Ca_i in component model_fluxes (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('C_Ca_i in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,14) = strpad('C_Ca_p in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,15) = strpad('C_P_p in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,16) = strpad('k_Ca_b in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('k3_P in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('k4_P in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,40) = strpad('Y_Ca_i_2plus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,41) = strpad('Y_Ca_p_1minus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('C_D_p in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,55) = strpad('Ca_thr in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,57) = strpad('Ca_T in component model_parameters (second_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,3) = strpad('P_thr in component model_parameters (millimole_per_hour)');
    LEGEND_ALGEBRAIC(:,6) = strpad('P_T in component model_parameters (litre_per_hour)');
    LEGEND_CONSTANTS(:,42) = strpad('Y_i_D_p_1plus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,43) = strpad('Y_PT_D_p_1plus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,44) = strpad('Y_k_Jext_1plus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,45) = strpad('Y_PTH_p_2plus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,46) = strpad('Y_PTH_p_2minus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,47) = strpad('Y_i_D_p_1minus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,48) = strpad('Y_PT_D_p_1minus in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,20) = strpad('Y_Ca_i_2plus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('Y_PTH_p_2plus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('Y_PTH_p_2minus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,23) = strpad('Y_Ca_p_1plus_minus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,24) = strpad('Y_i_D_p_1plus_minus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,25) = strpad('Y_PT_D_p_1plus_minus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,26) = strpad('Y_k_Jext_1plus_minus_Max in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,27) = strpad('X_R_PTH_Ca in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,28) = strpad('X_R_i_Ca in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,29) = strpad('X_R_PTH_D in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,30) = strpad('X_R_E_PTH in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,31) = strpad('X_R_i_D in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,32) = strpad('X_R_P_k_PTH in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,33) = strpad('b_PTH_Ca in component model_parameters (litre_per_millimole)');
    LEGEND_CONSTANTS(:,34) = strpad('b_PTH_D in component model_parameters (litre_per_picomole)');
    LEGEND_CONSTANTS(:,35) = strpad('b_E_PTH in component model_parameters (litre_per_picomole)');
    LEGEND_CONSTANTS(:,36) = strpad('b_i_D in component model_parameters (litre_per_picomole)');
    LEGEND_CONSTANTS(:,37) = strpad('a in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,38) = strpad('d in component model_parameters (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt Q_Ca_p in component Q_Ca_p (millimole)');
    LEGEND_RATES(:,2) = strpad('d/dt Q_P_p in component Q_P_p (millimole)');
    LEGEND_RATES(:,3) = strpad('d/dt Q_P_c in component Q_P_c (millimole)');
    LEGEND_RATES(:,4) = strpad('d/dt Q_PTH_p in component Q_PTH_p (millimole)');
    LEGEND_RATES(:,5) = strpad('d/dt Q_Ca_b in component Q_Ca_b (millimole)');
    LEGEND_RATES(:,6) = strpad('d/dt Q_P_b in component Q_P_b (millimole)');
    LEGEND_RATES(:,7) = strpad('d/dt Q_E_k in component Q_E_k (millimole)');
    LEGEND_RATES(:,8) = strpad('d/dt Q_D_p in component Q_D_p (millimole)');
    LEGEND_RATES(:,9) = strpad('d/dt Q_TCa_i in component Q_TCa_i (millimole)');
    LEGEND_RATES(:,10) = strpad('d/dt Q_C_PT in component Q_C_PT (millimole)');
    LEGEND_RATES(:,11) = strpad('d/dt Q_TP_k in component Q_TP_k (millimole)');
    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) = 1.000;
    CONSTANTS(:,1) = 3.3;
    CONSTANTS(:,2) = 0.21;
    STATES(:,2) = 1.000;
    CONSTANTS(:,3) = 1.27;
    STATES(:,3) = 3226.0;
    STATES(:,4) = 1.000;
    CONSTANTS(:,4) = 3.85;
    CONSTANTS(:,5) = 100.0;
    STATES(:,5) = 100.0;
    STATES(:,6) = 1.000;
    STATES(:,7) = 1.000;
    CONSTANTS(:,6) = 1.000;
    CONSTANTS(:,7) = 0.05;
    STATES(:,8) = 1.000;
    CONSTANTS(:,8) = 0.1;
    STATES(:,9) = 1.000;
    STATES(:,10) = 1.000;
    STATES(:,11) = 1.000;
    CONSTANTS(:,9) = 1.000;
    CONSTANTS(:,10) = 1.000;
    CONSTANTS(:,11) = 0.464;
    CONSTANTS(:,12) = 1.000;
    CONSTANTS(:,13) = 1.000;
    CONSTANTS(:,14) = 2.4;
    CONSTANTS(:,15) = 1.2;
    CONSTANTS(:,16) = 1.000;
    CONSTANTS(:,17) = 1.000;
    CONSTANTS(:,18) = 51.8;
    CONSTANTS(:,19) = 90.0;
    CONSTANTS(:,20) = 1.000;
    CONSTANTS(:,21) = 1.000;
    CONSTANTS(:,22) = 1.000;
    CONSTANTS(:,23) = 0.02;
    CONSTANTS(:,24) = 0.02;
    CONSTANTS(:,25) = 0.01;
    CONSTANTS(:,26) = 0.01;
    CONSTANTS(:,27) = 1.0;
    CONSTANTS(:,28) = 1.0;
    CONSTANTS(:,29) = 90.0;
    CONSTANTS(:,30) = 3.85;
    CONSTANTS(:,31) = 90.0;
    CONSTANTS(:,32) = 90.0;
    CONSTANTS(:,33) = 0.05;
    CONSTANTS(:,34) = 0.03;
    CONSTANTS(:,35) = 0.55;
    CONSTANTS(:,36) = 0.03;
    CONSTANTS(:,37) = 0.85;
    CONSTANTS(:,38) = 0.15;
    CONSTANTS(:,39) =  CONSTANTS(:,11).*CONSTANTS(:,1);
    CONSTANTS(:,40) =  CONSTANTS(:,20).*(CONSTANTS(:,13)./(CONSTANTS(:,13)+CONSTANTS(:,28)));
    CONSTANTS(:,41) =  CONSTANTS(:,23).*( CONSTANTS(:,37).*(1.00000 -  tanh( CONSTANTS(:,33).*(CONSTANTS(:,14) - CONSTANTS(:,27))))+CONSTANTS(:,38));
    CONSTANTS(:,42) =  CONSTANTS(:,24).*( CONSTANTS(:,37).*(1.00000+ tanh( CONSTANTS(:,36).*(CONSTANTS(:,19) - CONSTANTS(:,31))))+CONSTANTS(:,38));
    CONSTANTS(:,43) =  CONSTANTS(:,25).*( CONSTANTS(:,37).*(1.00000+ tanh( CONSTANTS(:,34).*(CONSTANTS(:,19) - CONSTANTS(:,29))))+CONSTANTS(:,38));
    CONSTANTS(:,44) =  CONSTANTS(:,26).*( CONSTANTS(:,37).*(1.00000+ tanh( CONSTANTS(:,35).*( 1.00000.*CONSTANTS(:,15) - CONSTANTS(:,30))))+CONSTANTS(:,38));
    CONSTANTS(:,45) =  CONSTANTS(:,21).*(CONSTANTS(:,4)./(CONSTANTS(:,4)+ 1.00000.*CONSTANTS(:,32)));
    CONSTANTS(:,46) =  CONSTANTS(:,22).*(CONSTANTS(:,32)./( 1.00000.*CONSTANTS(:,4)+CONSTANTS(:,32)));
    CONSTANTS(:,47) =  CONSTANTS(:,24).*( CONSTANTS(:,37).*(1.00000 -  tanh( CONSTANTS(:,36).*(CONSTANTS(:,19) - CONSTANTS(:,31))))+CONSTANTS(:,38));
    CONSTANTS(:,48) =  CONSTANTS(:,25).*( CONSTANTS(:,37).*(1.00000 -  tanh( CONSTANTS(:,34).*(CONSTANTS(:,19) - CONSTANTS(:,29))))+CONSTANTS(:,38));
    CONSTANTS(:,49) = CONSTANTS(:,10);
    CONSTANTS(:,50) = CONSTANTS(:,42);
    CONSTANTS(:,51) = CONSTANTS(:,47);
    CONSTANTS(:,52) = CONSTANTS(:,43);
    CONSTANTS(:,53) = CONSTANTS(:,48);
    CONSTANTS(:,54) = CONSTANTS(:,44);
    CONSTANTS(:,55) = 1.95000+CONSTANTS(:,45);
    CONSTANTS(:,56) =  CONSTANTS(:,18).*1.00000.*CONSTANTS(:,15);
    CONSTANTS(:,57) = CONSTANTS(:,55)./CONSTANTS(:,14);
    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(:,7) = CONSTANTS(:,6) -  CONSTANTS(:,7).*STATES(:,7);
    RATES(:,8) =  1.00000.*STATES(:,7) -  CONSTANTS(:,8).*STATES(:,8);
    RATES(:,9) =  (1.00000 - STATES(:,9)).*CONSTANTS(:,50) -  STATES(:,9).*CONSTANTS(:,51);
    RATES(:,10) =  (1.00000 - STATES(:,10)).*CONSTANTS(:,52) -  STATES(:,10).*CONSTANTS(:,53);
    RATES(:,11) =  (1.00000 - STATES(:,11)).*CONSTANTS(:,54) -  STATES(:,11).*CONSTANTS(:,9);
    ALGEBRAIC(:,2) =  1.00000.*CONSTANTS(:,41).*( CONSTANTS(:,52).*(1.00000 - STATES(:,10)) -  CONSTANTS(:,53).*STATES(:,10));
    RATES(:,4) = ALGEBRAIC(:,2) -  CONSTANTS(:,5).*1.00000.*CONSTANTS(:,4);
    ALGEBRAIC(:,1) =  CONSTANTS(:,16).*STATES(:,5);
    RATES(:,5) = ALGEBRAIC(:,1) - CONSTANTS(:,1);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,40).*(1.00000 - STATES(:,9)).*1.00000.*CONSTANTS(:,50)+ CONSTANTS(:,12).*1.00000.*(CONSTANTS(:,13) - CONSTANTS(:,14))) -  STATES(:,9).*CONSTANTS(:,51);
    RATES(:,1) = (CONSTANTS(:,1)+ALGEBRAIC(:,4)) - (ALGEBRAIC(:,1)+CONSTANTS(:,2));
    ALGEBRAIC(:,5) =  CONSTANTS(:,11).*ALGEBRAIC(:,1);
    RATES(:,6) = ALGEBRAIC(:,5) - CONSTANTS(:,39);
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*STATES(:,3);
    RATES(:,2) = (CONSTANTS(:,39)+CONSTANTS(:,49)+ALGEBRAIC(:,7)) - (ALGEBRAIC(:,5)+CONSTANTS(:,3)+CONSTANTS(:,56));
    RATES(:,3) = CONSTANTS(:,56) - ALGEBRAIC(:,7);
   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) =  1.00000.*CONSTANTS(:,41).*( CONSTANTS(:,52).*(1.00000 - STATES(:,10)) -  CONSTANTS(:,53).*STATES(:,10));
    ALGEBRAIC(:,1) =  CONSTANTS(:,16).*STATES(:,5);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,40).*(1.00000 - STATES(:,9)).*1.00000.*CONSTANTS(:,50)+ CONSTANTS(:,12).*1.00000.*(CONSTANTS(:,13) - CONSTANTS(:,14))) -  STATES(:,9).*CONSTANTS(:,51);
    ALGEBRAIC(:,5) =  CONSTANTS(:,11).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*STATES(:,3);
    ALGEBRAIC(:,3) =  CONSTANTS(:,46).*STATES(:,11);
    ALGEBRAIC(:,6) = ALGEBRAIC(:,3)./CONSTANTS(:,15);
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