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 =16;
end
% There are a total of 8 entries in each of the rate and state variable arrays.
% There are a total of 37 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 Environmental (second)');
    LEGEND_CONSTANTS(:,1) = strpad('S in component Parameters (hertz)');
    LEGEND_CONSTANTS(:,2) = strpad('Zeta in component Parameters (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('R0 in component Parameters (mm)');
    LEGEND_CONSTANTS(:,4) = strpad('Cwall in component Parameters (mm_per_mmHg)');
    LEGEND_CONSTANTS(:,5) = strpad('Kne in component Parameters (mmHg_per_mm)');
    LEGEND_CONSTANTS(:,6) = strpad('K1 in component Parameters (mmHg_per_mm)');
    LEGEND_CONSTANTS(:,7) = strpad('K2 in component Parameters (mmHg_per_mm)');
    LEGEND_CONSTANTS(:,8) = strpad('K3 in component Parameters (mmHg_per_mm)');
    LEGEND_CONSTANTS(:,9) = strpad('Bwall in component Parameters (mmHg_s_per_sq_mm)');
    LEGEND_CONSTANTS(:,10) = strpad('B1 in component Parameters (mmHg_s_per_mm)');
    LEGEND_CONSTANTS(:,11) = strpad('B2 in component Parameters (mmHg_s_per_mm)');
    LEGEND_CONSTANTS(:,12) = strpad('B3 in component Parameters (mmHg_s_per_mm)');
    LEGEND_CONSTANTS(:,13) = strpad('Tsmax in component Parameters (AU)');
    LEGEND_CONSTANTS(:,14) = strpad('Tpmax in component Parameters (AU)');
    LEGEND_CONSTANTS(:,15) = strpad('Tsmin in component Parameters (AU)');
    LEGEND_CONSTANTS(:,16) = strpad('Tpmin in component Parameters (AU)');
    LEGEND_CONSTANTS(:,17) = strpad('Gcns in component Parameters (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('Gs in component Parameters (per_Hertz)');
    LEGEND_CONSTANTS(:,19) = strpad('Gp in component Parameters (per_Hertz)');
    LEGEND_CONSTANTS(:,20) = strpad('tau_nor in component Parameters (second)');
    LEGEND_CONSTANTS(:,21) = strpad('tau_ach in component Parameters (second)');
    LEGEND_CONSTANTS(:,22) = strpad('tau_HR_nor in component Parameters (second)');
    LEGEND_CONSTANTS(:,23) = strpad('tau_HR_ach in component Parameters (second)');
    LEGEND_CONSTANTS(:,24) = strpad('HRo in component Parameters (Beats_per_min)');
    LEGEND_CONSTANTS(:,25) = strpad('HRmax in component Parameters (Beats_per_min)');
    LEGEND_CONSTANTS(:,26) = strpad('HRmin in component Parameters (Beats_per_min)');
    LEGEND_CONSTANTS(:,27) = strpad('Beta in component Parameters (dimensionless)');
    LEGEND_CONSTANTS(:,28) = strpad('delta_th in component Parameters (dimensionless)');
    LEGEND_CONSTANTS(:,29) = strpad('q_nor in component Parameters (per_s)');
    LEGEND_CONSTANTS(:,30) = strpad('q_ach in component Parameters (per_s)');
    LEGEND_CONSTANTS(:,31) = strpad('K_nor in component Parameters (AU)');
    LEGEND_CONSTANTS(:,32) = strpad('K_ach in component Parameters (AU)');
    LEGEND_CONSTANTS(:,33) = strpad('Gamma in component Parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('alpha_cns in component Nervous_System (hertz)');
    LEGEND_ALGEBRAIC(:,9) = strpad('n in component Nervous_System (hertz)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Delta in component Coupling_Dynamics (dimensionless)');
    LEGEND_CONSTANTS(:,34) = strpad('alpha_s0 in component Nervous_System (hertz)');
    LEGEND_CONSTANTS(:,35) = strpad('alpha_p0 in component Nervous_System (hertz)');
    LEGEND_STATES(:,1) = strpad('A in component Aortic_Wall (mm_sq)');
    LEGEND_ALGEBRAIC(:,1) = strpad('P in component Aortic_Wall (mmHg)');
    LEGEND_ALGEBRAIC(:,2) = strpad('R in component Aortic_Wall (mm)');
    LEGEND_STATES(:,2) = strpad('Eps_1 in component Coupling_Dynamics (dimensionless)');
    LEGEND_STATES(:,3) = strpad('Eps_2 in component Coupling_Dynamics (dimensionless)');
    LEGEND_STATES(:,4) = strpad('Eps_3 in component Coupling_Dynamics (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('Eps_wall in component Coupling_Dynamics (dimensionless)');
    LEGEND_ALGEBRAIC(:,13) = strpad('Ts in component PNS_tones (AU)');
    LEGEND_ALGEBRAIC(:,14) = strpad('Tp in component PNS_tones (AU)');
    LEGEND_STATES(:,5) = strpad('c_nor in component Norepinephrine (AU)');
    LEGEND_STATES(:,6) = strpad('C_ach in component Acetylcholine (AU)');
    LEGEND_ALGEBRAIC(:,3) = strpad('delta_HR_ss in component Heart_Response_Nor (Beats_per_min)');
    LEGEND_CONSTANTS(:,36) = strpad('delta_HR_smax in component Heart_Response_Nor (Beats_per_min)');
    LEGEND_STATES(:,7) = strpad('delta_HR_s in component Heart_Response_Nor (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,4) = strpad('delta_HR_ps in component HR_ach (Beats_per_min)');
    LEGEND_CONSTANTS(:,37) = strpad('delta_HR_pmax in component HR_ach (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,6) = strpad('delta_HR_pfast in component HR_ach (Beats_per_min)');
    LEGEND_STATES(:,8) = strpad('delta_HR_pslow in component HR_ach (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,8) = strpad('delta_HR_p in component HR_ach (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,15) = strpad('HR in component HR_Combined (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,12) = strpad('HR_p in component HR_Combined (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,10) = strpad('HR_s in component HR_Combined (Beats_per_min)');
    LEGEND_ALGEBRAIC(:,16) = strpad('Period in component HR_Combined (Sec_per_Beat)');
    LEGEND_RATES(:,1) = strpad('d/dt A in component Aortic_Wall (mm_sq)');
    LEGEND_RATES(:,2) = strpad('d/dt Eps_1 in component Coupling_Dynamics (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Eps_2 in component Coupling_Dynamics (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt Eps_3 in component Coupling_Dynamics (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt c_nor in component Norepinephrine (AU)');
    LEGEND_RATES(:,6) = strpad('d/dt C_ach in component Acetylcholine (AU)');
    LEGEND_RATES(:,7) = strpad('d/dt delta_HR_s in component Heart_Response_Nor (Beats_per_min)');
    LEGEND_RATES(:,8) = strpad('d/dt delta_HR_pslow in component HR_ach (Beats_per_min)');
    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) = 480;
    CONSTANTS(:,2) = 1;
    CONSTANTS(:,3) = 1.6;
    CONSTANTS(:,4) = 0.006;
    CONSTANTS(:,5) = 1;
    CONSTANTS(:,6) = 1.5;
    CONSTANTS(:,7) = 3.75;
    CONSTANTS(:,8) = 1.05;
    CONSTANTS(:,9) = 1;
    CONSTANTS(:,10) = 1;
    CONSTANTS(:,11) = 10;
    CONSTANTS(:,12) = 206.973;
    CONSTANTS(:,13) = 4.12;
    CONSTANTS(:,14) = 4.994;
    CONSTANTS(:,15) = 0.5;
    CONSTANTS(:,16) = 1.6;
    CONSTANTS(:,17) = 1;
    CONSTANTS(:,18) = 0.178;
    CONSTANTS(:,19) = 0.492;
    CONSTANTS(:,20) = 9.1;
    CONSTANTS(:,21) = 0.2;
    CONSTANTS(:,22) = 2.1;
    CONSTANTS(:,23) = 2.5;
    CONSTANTS(:,24) = 282.648;
    CONSTANTS(:,25) = 483.218;
    CONSTANTS(:,26) = 226.238;
    CONSTANTS(:,27) = 0.175;
    CONSTANTS(:,28) = 0;
    CONSTANTS(:,29) = 0.1099;
    CONSTANTS(:,30) = 5;
    CONSTANTS(:,31) = 1.12;
    CONSTANTS(:,32) = 0.65;
    CONSTANTS(:,33) = 0.75;
    CONSTANTS(:,34) = 58.6;
    CONSTANTS(:,35) = 76.019;
    STATES(:,1) = 15.20531;
    STATES(:,2) = 0.2042;
    STATES(:,3) = 0.183;
    STATES(:,4) = 0.161;
    STATES(:,5) = 1.441;
    STATES(:,6) = 1.0;
    STATES(:,7) = 0;
    STATES(:,8) = 0;
    CONSTANTS(:,36) = CONSTANTS(:,25) - CONSTANTS(:,24);
    CONSTANTS(:,37) = CONSTANTS(:,24) - CONSTANTS(:,26);
    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) = 100.000+ 10.0000.* sin( 5.00000.*VOI);
    RATES(:,1) = ( - (power((STATES(:,1)./ pi), 1.0 ./ 2) - CONSTANTS(:,3))./CONSTANTS(:,4)+ALGEBRAIC(:,1))./CONSTANTS(:,9);
    ALGEBRAIC(:,3) = ( CONSTANTS(:,36).*power(STATES(:,5), 2.00000))./(power(CONSTANTS(:,31), 2.00000)+power(STATES(:,5), 2.00000));
    RATES(:,7) = ( - STATES(:,7)+ALGEBRAIC(:,3))./CONSTANTS(:,22);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,37).*power(STATES(:,6), 2.00000))./(power(CONSTANTS(:,32), 2.00000)+power(STATES(:,6), 2.00000));
    RATES(:,8) = ( - STATES(:,8)+ (1.00000 - CONSTANTS(:,33)).*ALGEBRAIC(:,4))./CONSTANTS(:,23);
    ALGEBRAIC(:,2) = power(STATES(:,1)./ pi, 0.500000);
    ALGEBRAIC(:,5) = (ALGEBRAIC(:,2) - CONSTANTS(:,3))./CONSTANTS(:,3);
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    ALGEBRAIC(:,7) = ALGEBRAIC(:,5) - STATES(:,2);
    ALGEBRAIC(:,9) =  CONSTANTS(:,1).*(ALGEBRAIC(:,7) -  CONSTANTS(:,2).*CONSTANTS(:,28));
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*ALGEBRAIC(:,9);
    ALGEBRAIC(:,13) = CONSTANTS(:,15)+(CONSTANTS(:,13) - CONSTANTS(:,15))./(exp( CONSTANTS(:,18).*(ALGEBRAIC(:,11) - CONSTANTS(:,34)))+1.00000);
    RATES(:,5) =  - (STATES(:,5)./CONSTANTS(:,20))+ CONSTANTS(:,29).*ALGEBRAIC(:,13);
    ALGEBRAIC(:,14) = CONSTANTS(:,16)+(CONSTANTS(:,14) - CONSTANTS(:,16))./(exp(  - CONSTANTS(:,19).*(ALGEBRAIC(:,11) - CONSTANTS(:,35)))+1.00000);
    RATES(:,6) =  - (STATES(:,6)./CONSTANTS(:,21))+ CONSTANTS(:,30).*ALGEBRAIC(:,14);
   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) = 100.000+ 10.0000.* sin( 5.00000.*VOI);
    ALGEBRAIC(:,3) = ( CONSTANTS(:,36).*power(STATES(:,5), 2.00000))./(power(CONSTANTS(:,31), 2.00000)+power(STATES(:,5), 2.00000));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,37).*power(STATES(:,6), 2.00000))./(power(CONSTANTS(:,32), 2.00000)+power(STATES(:,6), 2.00000));
    ALGEBRAIC(:,2) = power(STATES(:,1)./ pi, 0.500000);
    ALGEBRAIC(:,5) = (ALGEBRAIC(:,2) - CONSTANTS(:,3))./CONSTANTS(:,3);
    ALGEBRAIC(:,7) = ALGEBRAIC(:,5) - STATES(:,2);
    ALGEBRAIC(:,9) =  CONSTANTS(:,1).*(ALGEBRAIC(:,7) -  CONSTANTS(:,2).*CONSTANTS(:,28));
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*ALGEBRAIC(:,9);
    ALGEBRAIC(:,13) = CONSTANTS(:,15)+(CONSTANTS(:,13) - CONSTANTS(:,15))./(exp( CONSTANTS(:,18).*(ALGEBRAIC(:,11) - CONSTANTS(:,34)))+1.00000);
    ALGEBRAIC(:,14) = CONSTANTS(:,16)+(CONSTANTS(:,14) - CONSTANTS(:,16))./(exp(  - CONSTANTS(:,19).*(ALGEBRAIC(:,11) - CONSTANTS(:,35)))+1.00000);
    ALGEBRAIC(:,6) =  CONSTANTS(:,33).*ALGEBRAIC(:,4);
    ALGEBRAIC(:,8) = ALGEBRAIC(:,6)+STATES(:,8);
    ALGEBRAIC(:,10) = CONSTANTS(:,24)+STATES(:,7);
    ALGEBRAIC(:,12) = CONSTANTS(:,24) - ALGEBRAIC(:,8);
    ALGEBRAIC(:,15) = ALGEBRAIC(:,12)+( (ALGEBRAIC(:,10) - CONSTANTS(:,24)).*(ALGEBRAIC(:,12) -  CONSTANTS(:,27).*CONSTANTS(:,26)))./(CONSTANTS(:,24) -  CONSTANTS(:,27).*CONSTANTS(:,26));
    ALGEBRAIC(:,16) = 60.0000./ALGEBRAIC(:,15);
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) ~= 3), initialGuess_0 = [0.1,0.1,0.1];, 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;
        RATES(:,2) = soln(1);
        RATES(:,3) = soln(2);
        RATES(:,4) = soln(3);
    else
        SET_RATES(:,2) = logical(1);
        SET_RATES(:,3) = logical(1);
        SET_RATES(:,4) = 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_RATES(:,2) = soln(1);
            TEMP_RATES(:,3) = soln(2);
            TEMP_RATES(:,4) = soln(3);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    RATES(:,2) = algebraicCandidate(1);
    RATES(:,3) = algebraicCandidate(2);
    RATES(:,4) = algebraicCandidate(3);
    resid(1) = RATES(:,2) - (( CONSTANTS(:,5).*(ALGEBRAIC(:,5) - STATES(:,2)) -  CONSTANTS(:,6).*(STATES(:,2) - STATES(:,3)))./CONSTANTS(:,10)+RATES(:,3));
    resid(2) = RATES(:,3) - (( CONSTANTS(:,6).*(STATES(:,2) - STATES(:,3)) -  CONSTANTS(:,7).*(STATES(:,3) - STATES(:,4)))+ CONSTANTS(:,10).*RATES(:,2)+ CONSTANTS(:,11).*RATES(:,4))./(CONSTANTS(:,10)+CONSTANTS(:,11));
    resid(3) = RATES(:,4) - (( CONSTANTS(:,7).*(STATES(:,3) - STATES(:,4)) -  CONSTANTS(:,8).*STATES(:,4))+ CONSTANTS(:,11).*RATES(:,3))./(CONSTANTS(:,11)+CONSTANTS(:,12));
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