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 7 entries in each of the rate and state variable arrays.
% There are a total of 41 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 (millisecond)');
    LEGEND_CONSTANTS(:,41) = strpad('F_SE in component F_SE (newton)');
    LEGEND_CONSTANTS(:,1) = strpad('cT in component F_SE (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('kT in component F_SE (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('LT_r in component F_SE (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('LT in component user_defined_constants (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('F_max in component user_defined_constants (newton)');
    LEGEND_ALGEBRAIC(:,2) = strpad('F_PE1 in component F_PE1 (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('c1 in component F_PE1 (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('k1 in component F_PE1 (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('L_r1 in component F_PE1 (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('eta in component F_PE1 (millisecond)');
    LEGEND_STATES(:,1) = strpad('L in component L (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('L_max in component user_defined_constants (dimensionless)');
    LEGEND_STATES(:,2) = strpad('V in component V (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,5) = strpad('F_PE2 in component F_PE2 (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('c2 in component F_PE2 (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('k2 in component F_PE2 (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('L_r2 in component F_PE2 (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('FL in component FL (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('beta in component FL (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('omega in component FL (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('rho in component FL (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('FV in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('av0 in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('av1 in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('av2 in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('cv0 in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('cv1 in component FV (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('bv in component FV (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,23) = strpad('V_max in component FV (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Af in component Af (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('af in component Af (dimensionless)');
    LEGEND_CONSTANTS(:,25) = strpad('nf0 in component Af (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('nf1 in component Af (dimensionless)');
    LEGEND_CONSTANTS(:,27) = strpad('nf in component Af (dimensionless)');
    LEGEND_STATES(:,3) = strpad('Y in component Y (dimensionless)');
    LEGEND_STATES(:,4) = strpad('S in component S (dimensionless)');
    LEGEND_STATES(:,5) = strpad('f_eff in component rise_and_fall_time (dimensionless)');
    LEGEND_STATES(:,6) = strpad('L_eff in component L_eff (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('F0 in component F0 (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('F_CE in component F_CE (newton)');
    LEGEND_ALGEBRAIC(:,13) = strpad('F_total in component F_total (newton)');
    LEGEND_CONSTANTS(:,28) = strpad('T_L in component L_eff (millisecond)');
    LEGEND_CONSTANTS(:,29) = strpad('T_s in component S (millisecond)');
    LEGEND_CONSTANTS(:,30) = strpad('as1 in component S (dimensionless)');
    LEGEND_CONSTANTS(:,31) = strpad('as2 in component S (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('as_ in component S (dimensionless)');
    LEGEND_CONSTANTS(:,32) = strpad('c_Y in component Y (dimensionless)');
    LEGEND_CONSTANTS(:,33) = strpad('V_Y in component Y (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,34) = strpad('T_Y in component Y (millisecond)');
    LEGEND_STATES(:,7) = strpad('f_int in component rise_and_fall_time (dimensionless)');
    LEGEND_ALGEBRAIC(:,10) = strpad('df_eff_dt in component rise_and_fall_time (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,11) = strpad('T_f in component rise_and_fall_time (millisecond)');
    LEGEND_CONSTANTS(:,35) = strpad('T_f1 in component rise_and_fall_time (millisecond)');
    LEGEND_CONSTANTS(:,36) = strpad('T_f2 in component rise_and_fall_time (millisecond)');
    LEGEND_CONSTANTS(:,37) = strpad('T_f3 in component rise_and_fall_time (millisecond)');
    LEGEND_CONSTANTS(:,38) = strpad('T_f4 in component rise_and_fall_time (millisecond)');
    LEGEND_CONSTANTS(:,39) = strpad('f_env in component user_defined_constants (dimensionless)');
    LEGEND_CONSTANTS(:,40) = strpad('mass in component V (kilogram)');
    LEGEND_ALGEBRAIC(:,3) = strpad('V0 in component V0 (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('L0 in component L0 (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt L_eff in component L_eff (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt S in component S (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Y in component Y (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt f_int in component rise_and_fall_time (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt f_eff in component rise_and_fall_time (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt V in component V (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt L in component L (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 = [];
    CONSTANTS(:,1) = 27.8;
    CONSTANTS(:,2) = 0.0047;
    CONSTANTS(:,3) = 0.964;
    CONSTANTS(:,4) = 0.02;
    CONSTANTS(:,5) = 23;
    CONSTANTS(:,6) = 23;
    CONSTANTS(:,7) = 0.046;
    CONSTANTS(:,8) = 1.17;
    CONSTANTS(:,9) = 0.001;
    STATES(:,1) = 0.15;
    CONSTANTS(:,10) = 0.13;
    STATES(:,2) = 0.09314;
    CONSTANTS(:,11) = 23;
    CONSTANTS(:,12) = 0.046;
    CONSTANTS(:,13) = 1.17;
    CONSTANTS(:,14) = 1.55;
    CONSTANTS(:,15) = 0.75;
    CONSTANTS(:,16) = 2.12;
    CONSTANTS(:,17) = -1.53;
    CONSTANTS(:,18) = 0;
    CONSTANTS(:,19) = 0;
    CONSTANTS(:,20) = -5.7;
    CONSTANTS(:,21) = 9.18;
    CONSTANTS(:,22) = 0.69;
    CONSTANTS(:,23) = -9.15;
    CONSTANTS(:,24) = 0.56;
    CONSTANTS(:,25) = 2.1;
    CONSTANTS(:,26) = 3.3;
    CONSTANTS(:,27) = 1;
    STATES(:,3) = 1;
    STATES(:,4) = 1;
    STATES(:,5) = 0;
    STATES(:,6) = 0.1497;
    CONSTANTS(:,28) = 0.088;
    CONSTANTS(:,29) = 43;
    CONSTANTS(:,30) = 1.76;
    CONSTANTS(:,31) = 0.96;
    CONSTANTS(:,32) = 0.35;
    CONSTANTS(:,33) = 0.1;
    CONSTANTS(:,34) = 200;
    STATES(:,7) = 0;
    CONSTANTS(:,35) = 0.35;
    CONSTANTS(:,36) = 0.1;
    CONSTANTS(:,37) = 200;
    CONSTANTS(:,38) = 200;
    CONSTANTS(:,39) = 1;
    CONSTANTS(:,40) = 0.005;
    CONSTANTS(:,41) =  CONSTANTS(:,1).*CONSTANTS(:,5).*CONSTANTS(:,2).*log(exp((CONSTANTS(:,4) - CONSTANTS(:,3))./CONSTANTS(:,2))+1.00000);
    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) = (1.00000 - ( CONSTANTS(:,32).*(1.00000 - exp( - abs(STATES(:,2))./CONSTANTS(:,33)))+STATES(:,3)))./CONSTANTS(:,34);
    RATES(:,1) = STATES(:,2);
    ALGEBRAIC(:,1) = piecewise({STATES(:,5)<0.100000, CONSTANTS(:,30) }, CONSTANTS(:,31));
    RATES(:,4) = (ALGEBRAIC(:,1) - STATES(:,4))./CONSTANTS(:,29);
    ALGEBRAIC(:,8) = 1.00000 - exp( - power(( STATES(:,3).*STATES(:,4).*STATES(:,5))./( CONSTANTS(:,24).*CONSTANTS(:,27)), CONSTANTS(:,27)));
    RATES(:,6) = power(STATES(:,1) - STATES(:,6), 3.00000)./( CONSTANTS(:,28).*(1.00000 - ALGEBRAIC(:,8)));
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,7) = (CONSTANTS(:,39) - STATES(:,7))./ALGEBRAIC(:,11);
    RATES(:,5) = ALGEBRAIC(:,10);
    ALGEBRAIC(:,2) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log(exp((STATES(:,1)./CONSTANTS(:,10) - CONSTANTS(:,8))./CONSTANTS(:,7))+1.00000)+ CONSTANTS(:,9).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,11).*(exp( CONSTANTS(:,12).*(STATES(:,1) - CONSTANTS(:,13))) - 1.00000);
    ALGEBRAIC(:,6) = exp( - power(abs((power(STATES(:,1), CONSTANTS(:,14)) - 1.00000)./CONSTANTS(:,15)), CONSTANTS(:,16)));
    ALGEBRAIC(:,7) = piecewise({STATES(:,2)<=0.00000, (CONSTANTS(:,23) - STATES(:,2))./(CONSTANTS(:,23)+ (CONSTANTS(:,20)+ CONSTANTS(:,21).*STATES(:,1)).*STATES(:,2)) }, (CONSTANTS(:,22) -  (CONSTANTS(:,17)+ CONSTANTS(:,18).*STATES(:,1)+ CONSTANTS(:,19).*power(STATES(:,1), 2.00000)).*STATES(:,2))./(CONSTANTS(:,22)+STATES(:,2)));
    ALGEBRAIC(:,9) =  ALGEBRAIC(:,8).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,5))+ALGEBRAIC(:,2);
    ALGEBRAIC(:,12) =  ALGEBRAIC(:,9).*CONSTANTS(:,5);
    ALGEBRAIC(:,13) = CONSTANTS(:,41) - ALGEBRAIC(:,12);
    RATES(:,2) = ALGEBRAIC(:,13)./( 1.00000.*CONSTANTS(:,40));
   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({STATES(:,5)<0.100000, CONSTANTS(:,30) }, CONSTANTS(:,31));
    ALGEBRAIC(:,8) = 1.00000 - exp( - power(( STATES(:,3).*STATES(:,4).*STATES(:,5))./( CONSTANTS(:,24).*CONSTANTS(:,27)), CONSTANTS(:,27)));
    ALGEBRAIC(:,2) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log(exp((STATES(:,1)./CONSTANTS(:,10) - CONSTANTS(:,8))./CONSTANTS(:,7))+1.00000)+ CONSTANTS(:,9).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,11).*(exp( CONSTANTS(:,12).*(STATES(:,1) - CONSTANTS(:,13))) - 1.00000);
    ALGEBRAIC(:,6) = exp( - power(abs((power(STATES(:,1), CONSTANTS(:,14)) - 1.00000)./CONSTANTS(:,15)), CONSTANTS(:,16)));
    ALGEBRAIC(:,7) = piecewise({STATES(:,2)<=0.00000, (CONSTANTS(:,23) - STATES(:,2))./(CONSTANTS(:,23)+ (CONSTANTS(:,20)+ CONSTANTS(:,21).*STATES(:,1)).*STATES(:,2)) }, (CONSTANTS(:,22) -  (CONSTANTS(:,17)+ CONSTANTS(:,18).*STATES(:,1)+ CONSTANTS(:,19).*power(STATES(:,1), 2.00000)).*STATES(:,2))./(CONSTANTS(:,22)+STATES(:,2)));
    ALGEBRAIC(:,9) =  ALGEBRAIC(:,8).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,5))+ALGEBRAIC(:,2);
    ALGEBRAIC(:,12) =  ALGEBRAIC(:,9).*CONSTANTS(:,5);
    ALGEBRAIC(:,13) = CONSTANTS(:,41) - ALGEBRAIC(:,12);
    ALGEBRAIC(:,3) = STATES(:,2)./CONSTANTS(:,10);
    ALGEBRAIC(:,4) = STATES(:,1)./CONSTANTS(:,10);
end

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_0;
    if (length(initialGuess_0) ~= 2), initialGuess_0 = [0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_0, options);
        initialGuess_0 = soln;
        ALGEBRAIC(:,10) = soln(1);
        ALGEBRAIC(:,11) = soln(2);
    else
        SET_ALGEBRAIC(:,10) = logical(1);
        SET_ALGEBRAIC(:,11) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_0, options);
            initialGuess_0 = soln;
            TEMP_ALGEBRAIC(:,10) = soln(1);
            TEMP_ALGEBRAIC(:,11) = soln(2);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,10) = algebraicCandidate(1);
    ALGEBRAIC(:,11) = algebraicCandidate(2);
    resid(1) = ALGEBRAIC(:,10) - (STATES(:,7) - STATES(:,5))./ALGEBRAIC(:,11);
    resid(2) = ALGEBRAIC(:,11) - piecewise({ALGEBRAIC(:,10)>=0.00000,  CONSTANTS(:,35).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,36).*CONSTANTS(:,39) }, (CONSTANTS(:,37)+ CONSTANTS(:,38).*ALGEBRAIC(:,8))./STATES(:,1));
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