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 =13;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 43 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 (day)');
    LEGEND_STATES(:,1) = strpad('OB_p in component OB_p (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('D_OB_u in component OB_p (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('K_D1_TGF_beta in component OB_p (pM)');
    LEGEND_CONSTANTS(:,3) = strpad('K_D2_TGF_beta in component model_parameters (pM)');
    LEGEND_CONSTANTS(:,4) = strpad('D_OB_p in component model_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('TGF_beta in component TGF_beta (pM)');
    LEGEND_STATES(:,2) = strpad('OB_a in component OB_a (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('A_OB_a in component OB_a (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('OC_a in component OC_a (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('D_OC_p in component OC_a (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('A_OC_a in component OC_a (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('K_D3_TGF_beta in component OC_a (pM)');
    LEGEND_CONSTANTS(:,8) = strpad('OC_p in component OC_a (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('RANKL in component RANKL (pM)');
    LEGEND_ALGEBRAIC(:,9) = strpad('pi_RANKL_act_OC_p in component RANKL (dimensionless)');
    LEGEND_STATES(:,4) = strpad('BV in component BV (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('OC_a_tilde in component BV (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('OB_a_tilde in component BV (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('OC_a_initial in component BV (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('OB_a_initial in component BV (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('k_form in component BV (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('k_res in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('alpha in component TGF_beta (pM)');
    LEGEND_CONSTANTS(:,14) = strpad('D_TGF_beta_tilde in component TGF_beta (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('S_TGF_beta in component TGF_beta (flux)');
    LEGEND_CONSTANTS(:,37) = strpad('PTH in component PTH (pM)');
    LEGEND_CONSTANTS(:,38) = strpad('pi_PTH_rep_OB_p in component PTH (dimensionless)');
    LEGEND_CONSTANTS(:,39) = strpad('pi_PTH_act_OB_p in component PTH (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('beta_PTH in component PTH (flux)');
    LEGEND_CONSTANTS(:,17) = strpad('D_PTH_tilde in component PTH (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('P_PTH_d in component PTH (flux)');
    LEGEND_CONSTANTS(:,19) = strpad('K_D4_PTH in component PTH (pM)');
    LEGEND_CONSTANTS(:,20) = strpad('K_D5_PTH in component PTH (pM)');
    LEGEND_CONSTANTS(:,21) = strpad('K_D6_PTH in component PTH (pM)');
    LEGEND_CONSTANTS(:,22) = strpad('K_D7_PTH in component PTH (pM)');
    LEGEND_CONSTANTS(:,40) = strpad('pi_PTH_act_OB_a in component PTH (dimensionless)');
    LEGEND_CONSTANTS(:,41) = strpad('pi_PTH_rep_OB_a in component PTH (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('OPG in component OPG (pM)');
    LEGEND_CONSTANTS(:,23) = strpad('beta1_OPG in component OPG (flux)');
    LEGEND_CONSTANTS(:,24) = strpad('beta2_OPG in component OPG (flux)');
    LEGEND_CONSTANTS(:,25) = strpad('OPG_max in component OPG (pM)');
    LEGEND_ALGEBRAIC(:,6) = strpad('P_OPG_e in component OPG (flux)');
    LEGEND_CONSTANTS(:,26) = strpad('P_OPG_d in component OPG (flux)');
    LEGEND_CONSTANTS(:,27) = strpad('D_OPG_tilde in component OPG (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,42) = strpad('pi_PTH_rep_OB in component OPG (dimensionless)');
    LEGEND_CONSTANTS(:,28) = strpad('K_A2_RANKL in component RANKL (per_pM)');
    LEGEND_CONSTANTS(:,29) = strpad('K_A1_RANKL in component RANKL (per_pM)');
    LEGEND_CONSTANTS(:,30) = strpad('RANK in component RANKL (pM)');
    LEGEND_ALGEBRAIC(:,7) = strpad('RANKL_eff in component RANKL (pM)');
    LEGEND_ALGEBRAIC(:,10) = strpad('RANKL_tot in component RANKL (pM)');
    LEGEND_ALGEBRAIC(:,13) = strpad('P_RANKL in component RANKL (flux)');
    LEGEND_ALGEBRAIC(:,11) = strpad('P_RANKL_e in component RANKL (flux)');
    LEGEND_CONSTANTS(:,31) = strpad('P_RANKL_d in component RANKL (flux)');
    LEGEND_CONSTANTS(:,32) = strpad('R1_RANKL in component RANKL (pM)');
    LEGEND_CONSTANTS(:,33) = strpad('R2_RANKL in component RANKL (pM)');
    LEGEND_CONSTANTS(:,34) = strpad('beta_RANKL in component RANKL (flux)');
    LEGEND_ALGEBRAIC(:,12) = strpad('D_RANKL in component RANKL (flux)');
    LEGEND_CONSTANTS(:,35) = strpad('D_RANKL_tilde in component RANKL (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,43) = strpad('pi_PTH_act_OB in component RANKL (dimensionless)');
    LEGEND_CONSTANTS(:,36) = strpad('K_D8_RANKL in component RANKL (pM)');
    LEGEND_RATES(:,1) = strpad('d/dt OB_p in component OB_p (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt OB_a in component OB_a (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt OC_a in component OC_a (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt BV in component BV (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) = 1.0;
    CONSTANTS(:,1) = 7.000e-4;
    CONSTANTS(:,2) = 4.545e-3;
    CONSTANTS(:,3) = 1.416e-3;
    CONSTANTS(:,4) = 5.348e-0;
    STATES(:,2) = 1.0;
    CONSTANTS(:,5) = 1.890e-1;
    STATES(:,3) = 1.0;
    CONSTANTS(:,6) = 7.000e-1;
    CONSTANTS(:,7) = 1.416e-3;
    CONSTANTS(:,8) = 1.0;
    STATES(:,4) = 100.0;
    CONSTANTS(:,9) = 1.0;
    CONSTANTS(:,10) = 1.0;
    CONSTANTS(:,11) = 1.571e0;
    CONSTANTS(:,12) = 1.000e0;
    CONSTANTS(:,13) = 1.000e0;
    CONSTANTS(:,14) = 1.000e0;
    CONSTANTS(:,15) = 0.0;
    CONSTANTS(:,16) = 2.500e2;
    CONSTANTS(:,17) = 8.600e1;
    CONSTANTS(:,18) = 0.0;
    CONSTANTS(:,19) = 1.5e2;
    CONSTANTS(:,20) = 1.5e2;
    CONSTANTS(:,21) = 2.226e-1;
    CONSTANTS(:,22) = 2.226e-1;
    CONSTANTS(:,23) = 1.0;
    CONSTANTS(:,24) = 0.0;
    CONSTANTS(:,25) = 2.000e8;
    CONSTANTS(:,26) = 0.0;
    CONSTANTS(:,27) = 3.500e-1;
    CONSTANTS(:,28) = 3.412e-2;
    CONSTANTS(:,29) = 1.000e-3;
    CONSTANTS(:,30) = 1.000e1;
    CONSTANTS(:,31) = 0.0;
    CONSTANTS(:,32) = 0.0;
    CONSTANTS(:,33) = 1.0;
    CONSTANTS(:,34) = 1.684e4;
    CONSTANTS(:,35) = 1.013e1;
    CONSTANTS(:,36) = 1.306e1;
    CONSTANTS(:,37) = (CONSTANTS(:,16)+CONSTANTS(:,18))./CONSTANTS(:,17);
    CONSTANTS(:,38) = 1.00000./(1.00000+CONSTANTS(:,37)./CONSTANTS(:,21));
    CONSTANTS(:,39) = CONSTANTS(:,37)./(CONSTANTS(:,19)+CONSTANTS(:,37));
    CONSTANTS(:,40) = CONSTANTS(:,37)./(CONSTANTS(:,20)+CONSTANTS(:,37));
    CONSTANTS(:,41) = 1.00000./(1.00000+CONSTANTS(:,37)./CONSTANTS(:,22));
    CONSTANTS(:,42) = CONSTANTS(:,38);
    CONSTANTS(:,43) = CONSTANTS(:,39);
    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
    ALGEBRAIC(:,4) = ( CONSTANTS(:,13).*CONSTANTS(:,12).*STATES(:,3)+CONSTANTS(:,15))./CONSTANTS(:,14);
    RATES(:,1) =  CONSTANTS(:,1).*(ALGEBRAIC(:,4)./(CONSTANTS(:,2)+ALGEBRAIC(:,4))) -  CONSTANTS(:,4).*STATES(:,1).*(1.00000./(1.00000+ALGEBRAIC(:,4)./CONSTANTS(:,3)));
    RATES(:,2) =  CONSTANTS(:,4).*STATES(:,1).*(1.00000./(1.00000+ALGEBRAIC(:,4)./CONSTANTS(:,3))) -  CONSTANTS(:,5).*STATES(:,2);
    ALGEBRAIC(:,1) = STATES(:,3) - CONSTANTS(:,9);
    ALGEBRAIC(:,3) = STATES(:,2) - CONSTANTS(:,10);
    RATES(:,4) =  CONSTANTS(:,11).*ALGEBRAIC(:,3) -  CONSTANTS(:,12).*ALGEBRAIC(:,1);
    ALGEBRAIC(:,2) = piecewise({VOI>0.00000&VOI<=100.000, 0.0210000 }, 0.00210000);
    ALGEBRAIC(:,5) = ( ( CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*STATES(:,2)).*CONSTANTS(:,42)+CONSTANTS(:,26))./(( ( CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*STATES(:,2)).*CONSTANTS(:,42))./CONSTANTS(:,25)+CONSTANTS(:,27));
    ALGEBRAIC(:,7) =  ( CONSTANTS(:,32).*STATES(:,1)+ CONSTANTS(:,33).*STATES(:,2)).*CONSTANTS(:,43);
    ALGEBRAIC(:,8) =  (ALGEBRAIC(:,7)./(1.00000+ CONSTANTS(:,29).*ALGEBRAIC(:,5)+ CONSTANTS(:,28).*CONSTANTS(:,30))).*((CONSTANTS(:,34)+CONSTANTS(:,31))./(CONSTANTS(:,34)+ CONSTANTS(:,35).*ALGEBRAIC(:,7)));
    ALGEBRAIC(:,9) = ALGEBRAIC(:,8)./(CONSTANTS(:,36)+ALGEBRAIC(:,8));
    RATES(:,3) =  ALGEBRAIC(:,2).*CONSTANTS(:,8).*ALGEBRAIC(:,9) -  CONSTANTS(:,6).*STATES(:,3).*(ALGEBRAIC(:,4)./(CONSTANTS(:,7)+ALGEBRAIC(:,4)));
   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(:,4) = ( CONSTANTS(:,13).*CONSTANTS(:,12).*STATES(:,3)+CONSTANTS(:,15))./CONSTANTS(:,14);
    ALGEBRAIC(:,1) = STATES(:,3) - CONSTANTS(:,9);
    ALGEBRAIC(:,3) = STATES(:,2) - CONSTANTS(:,10);
    ALGEBRAIC(:,2) = piecewise({VOI>0.00000&VOI<=100.000, 0.0210000 }, 0.00210000);
    ALGEBRAIC(:,5) = ( ( CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*STATES(:,2)).*CONSTANTS(:,42)+CONSTANTS(:,26))./(( ( CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*STATES(:,2)).*CONSTANTS(:,42))./CONSTANTS(:,25)+CONSTANTS(:,27));
    ALGEBRAIC(:,7) =  ( CONSTANTS(:,32).*STATES(:,1)+ CONSTANTS(:,33).*STATES(:,2)).*CONSTANTS(:,43);
    ALGEBRAIC(:,8) =  (ALGEBRAIC(:,7)./(1.00000+ CONSTANTS(:,29).*ALGEBRAIC(:,5)+ CONSTANTS(:,28).*CONSTANTS(:,30))).*((CONSTANTS(:,34)+CONSTANTS(:,31))./(CONSTANTS(:,34)+ CONSTANTS(:,35).*ALGEBRAIC(:,7)));
    ALGEBRAIC(:,9) = ALGEBRAIC(:,8)./(CONSTANTS(:,36)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,6) =  ( CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*STATES(:,2)).*CONSTANTS(:,42).*(1.00000 - ALGEBRAIC(:,5)./CONSTANTS(:,25));
    ALGEBRAIC(:,10) =  ALGEBRAIC(:,8).*(1.00000+ CONSTANTS(:,29).*ALGEBRAIC(:,5)+ CONSTANTS(:,28).*CONSTANTS(:,30));
    ALGEBRAIC(:,11) =  CONSTANTS(:,34).*(1.00000 - ALGEBRAIC(:,10)./ALGEBRAIC(:,7));
    ALGEBRAIC(:,12) =   - CONSTANTS(:,35).*ALGEBRAIC(:,10);
    ALGEBRAIC(:,13) = ALGEBRAIC(:,11)+CONSTANTS(:,31);
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