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 1 entries in each of the rate and state variable arrays.
% There are a total of 18 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 (second)');
    LEGEND_CONSTANTS(:,1) = strpad('L_1 in component contraction (mm)');
    LEGEND_CONSTANTS(:,2) = strpad('L_2 in component contraction (mm)');
    LEGEND_CONSTANTS(:,3) = strpad('L_3 in component contraction (mm)');
    LEGEND_CONSTANTS(:,4) = strpad('L_4 in component contraction (mm)');
    LEGEND_CONSTANTS(:,5) = strpad('f_c in component contraction (newton)');
    LEGEND_CONSTANTS(:,6) = strpad('v_max in component contraction (mm_per_second)');
    LEGEND_CONSTANTS(:,7) = strpad('curv in component contraction (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('k_1 in component contraction (newton)');
    LEGEND_CONSTANTS(:,9) = strpad('k_2 in component contraction (per_mm)');
    LEGEND_CONSTANTS(:,10) = strpad('F_1 in component contraction (newton)');
    LEGEND_CONSTANTS(:,11) = strpad('d_LSEC1 in component contraction (mm)');
    LEGEND_CONSTANTS(:,12) = strpad('k_sh in component contraction (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('L_m in component contraction (mm)');
    LEGEND_CONSTANTS(:,14) = strpad('F_im in component contraction (newton)');
    LEGEND_CONSTANTS(:,15) = strpad('tau in component contraction (second)');
    LEGEND_ALGEBRAIC(:,5) = strpad('v_cc in component contraction (mm_per_second)');
    LEGEND_ALGEBRAIC(:,6) = strpad('f_v in component contraction (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('f_L in component contraction (newton)');
    LEGEND_ALGEBRAIC(:,4) = strpad('f_sec in component contraction (newton)');
    LEGEND_ALGEBRAIC(:,3) = strpad('delta_L_sec in component contraction (mm)');
    LEGEND_CONSTANTS(:,16) = strpad('delta_L_sec1 in component contraction (mm)');
    LEGEND_CONSTANTS(:,17) = strpad('k in component contraction (newton_per_mm)');
    LEGEND_STATES(:,1) = strpad('L_cc in component contraction (mm)');
    LEGEND_ALGEBRAIC(:,2) = strpad('L_mtc in component contraction (mm)');
    LEGEND_CONSTANTS(:,18) = strpad('A in component contraction (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt L_cc in component contraction (mm)');
    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) = -24;
    CONSTANTS(:,2) = -14;
    CONSTANTS(:,3) = 4;
    CONSTANTS(:,4) = 14;
    CONSTANTS(:,5) = 0.51;
    CONSTANTS(:,6) = -152;
    CONSTANTS(:,7) = 9.5;
    CONSTANTS(:,8) = 0.0064;
    CONSTANTS(:,9) = 0.414;
    CONSTANTS(:,10) = 8.9;
    CONSTANTS(:,11) = 2.9;
    CONSTANTS(:,12) = 2.5;
    CONSTANTS(:,13) = 2.6;
    CONSTANTS(:,14) = 20.6;
    CONSTANTS(:,15) = 0.065;
    CONSTANTS(:,16) = 4.1;
    CONSTANTS(:,17) = 8.2;
    STATES(:,1) = 0.2;
    CONSTANTS(:,18) = 1;
    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(:,1) = piecewise({STATES(:,1)>=CONSTANTS(:,1)&STATES(:,1)<=CONSTANTS(:,2),  (CONSTANTS(:,5)./(CONSTANTS(:,2) - CONSTANTS(:,1))).*(STATES(:,1) - CONSTANTS(:,1)) , STATES(:,1)>CONSTANTS(:,2)&STATES(:,1)<=0.00000,  ((1.00000 - CONSTANTS(:,5))./ - CONSTANTS(:,2)).*(STATES(:,1) - CONSTANTS(:,2)) , STATES(:,1)>0.00000&STATES(:,1)<=CONSTANTS(:,3), 1.00000 , STATES(:,1)>CONSTANTS(:,3)&STATES(:,1)<=CONSTANTS(:,4),  ( - 1.00000./(CONSTANTS(:,4) - CONSTANTS(:,3))).*(STATES(:,1) - CONSTANTS(:,3)) }, NaN);
    ALGEBRAIC(:,2) = piecewise({VOI<=1.00000, 0.290000 , VOI>1.00000&VOI<5.00000, 0.220000 }, 0.190000);
    ALGEBRAIC(:,3) = (ALGEBRAIC(:,2) - STATES(:,1)) - CONSTANTS(:,13);
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)>0.00000&ALGEBRAIC(:,3)<CONSTANTS(:,16),  (CONSTANTS(:,10)./(exp(CONSTANTS(:,12)) - 1.00000)).*(exp(( CONSTANTS(:,12).*ALGEBRAIC(:,3))./CONSTANTS(:,16)) - 1.00000) , ALGEBRAIC(:,3)<=CONSTANTS(:,16), CONSTANTS(:,10)+ CONSTANTS(:,17).*(ALGEBRAIC(:,3) - CONSTANTS(:,16)) }, NaN);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    RATES(:,1) = ALGEBRAIC(:,5);
   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(:,1)>=CONSTANTS(:,1)&STATES(:,1)<=CONSTANTS(:,2),  (CONSTANTS(:,5)./(CONSTANTS(:,2) - CONSTANTS(:,1))).*(STATES(:,1) - CONSTANTS(:,1)) , STATES(:,1)>CONSTANTS(:,2)&STATES(:,1)<=0.00000,  ((1.00000 - CONSTANTS(:,5))./ - CONSTANTS(:,2)).*(STATES(:,1) - CONSTANTS(:,2)) , STATES(:,1)>0.00000&STATES(:,1)<=CONSTANTS(:,3), 1.00000 , STATES(:,1)>CONSTANTS(:,3)&STATES(:,1)<=CONSTANTS(:,4),  ( - 1.00000./(CONSTANTS(:,4) - CONSTANTS(:,3))).*(STATES(:,1) - CONSTANTS(:,3)) }, NaN);
    ALGEBRAIC(:,2) = piecewise({VOI<=1.00000, 0.290000 , VOI>1.00000&VOI<5.00000, 0.220000 }, 0.190000);
    ALGEBRAIC(:,3) = (ALGEBRAIC(:,2) - STATES(:,1)) - CONSTANTS(:,13);
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)>0.00000&ALGEBRAIC(:,3)<CONSTANTS(:,16),  (CONSTANTS(:,10)./(exp(CONSTANTS(:,12)) - 1.00000)).*(exp(( CONSTANTS(:,12).*ALGEBRAIC(:,3))./CONSTANTS(:,16)) - 1.00000) , ALGEBRAIC(:,3)<=CONSTANTS(:,16), CONSTANTS(:,10)+ CONSTANTS(:,17).*(ALGEBRAIC(:,3) - CONSTANTS(:,16)) }, NaN);
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(:,5) = soln(1);
        ALGEBRAIC(:,6) = soln(2);
    else
        SET_ALGEBRAIC(:,5) = logical(1);
        SET_ALGEBRAIC(:,6) = 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(:,5) = soln(1);
            TEMP_ALGEBRAIC(:,6) = soln(2);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    ALGEBRAIC(:,5) = algebraicCandidate(1);
    ALGEBRAIC(:,6) = algebraicCandidate(2);
    resid(1) = ALGEBRAIC(:,5) -  (1.00000./ALGEBRAIC(:,6)).*(ALGEBRAIC(:,4)./( CONSTANTS(:,18).*ALGEBRAIC(:,1).*CONSTANTS(:,14)));
    resid(2) = ALGEBRAIC(:,6) - (CONSTANTS(:,6) - ALGEBRAIC(:,5))./(CONSTANTS(:,6)+ ALGEBRAIC(:,5).*CONSTANTS(:,7));
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