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 =9;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 13 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('t in component main (second)');
    LEGEND_STATES(:,1) = strpad('omega in component main (per_s)');
    LEGEND_CONSTANTS(:,1) = strpad('omega_ref in component main (per_s)');
    LEGEND_ALGEBRAIC(:,1) = strpad('logOmega in component main (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('E_1 in component main (J_per_C2)');
    LEGEND_CONSTANTS(:,3) = strpad('E_2 in component main (J_per_m2)');
    LEGEND_CONSTANTS(:,4) = strpad('R_1 in component main (Js_per_C2)');
    LEGEND_CONSTANTS(:,5) = strpad('R_2 in component main (Js_per_m2)');
    LEGEND_CONSTANTS(:,6) = strpad('L_1 in component main (Js2_per_C2)');
    LEGEND_CONSTANTS(:,7) = strpad('L_2 in component main (Js2_per_m2)');
    LEGEND_CONSTANTS(:,8) = strpad('Bl in component main (Js_per_C_m)');
    LEGEND_ALGEBRAIC(:,2) = strpad('x_1 in component main (J_per_m2)');
    LEGEND_ALGEBRAIC(:,3) = strpad('x_2 in component main (J2_per_m4)');
    LEGEND_CONSTANTS(:,11) = strpad('omega_3 in component main (per_s)');
    LEGEND_CONSTANTS(:,12) = strpad('logOmega_3 in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('G_real in component main (Js_per_C2)');
    LEGEND_ALGEBRAIC(:,5) = strpad('G_imag in component main (Js_per_C2)');
    LEGEND_ALGEBRAIC(:,6) = strpad('amplitude in component main (Js_per_C2)');
    LEGEND_CONSTANTS(:,9) = strpad('amplitude_ref in component main (Js_per_C2)');
    LEGEND_ALGEBRAIC(:,7) = strpad('phase in component main (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('phase_ref in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('phase_degrees in component main (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('logAmplitude in component main (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt omega in component main (per_s)');
    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) = 0.1;
    CONSTANTS(:,1) = 1;
    CONSTANTS(:,2) = 0;
    CONSTANTS(:,3) = 2000;
    CONSTANTS(:,4) = 3.5;
    CONSTANTS(:,5) = 0.4;
    CONSTANTS(:,6) = 0.15;
    CONSTANTS(:,7) = 0.018;
    CONSTANTS(:,8) = 10;
    CONSTANTS(:,9) = 1;
    CONSTANTS(:,10) = 1;
    CONSTANTS(:,11) = power((CONSTANTS(:,3)./CONSTANTS(:,7)), 1.0 ./ 2);
    CONSTANTS(:,12) = 1.00000;
    CONSTANTS(:,12) = arbitrary_log(CONSTANTS(:,11)./CONSTANTS(:,1), 10);
    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(:,1) = CONSTANTS(:,12);
   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) = arbitrary_log(STATES(:,1)./CONSTANTS(:,1), 10);
    ALGEBRAIC(:,2) = CONSTANTS(:,3) -  power(STATES(:,1), 2.00000).*CONSTANTS(:,7);
    ALGEBRAIC(:,3) = power(ALGEBRAIC(:,2), 2.00000)+power( STATES(:,1).*CONSTANTS(:,5), 2.00000);
    ALGEBRAIC(:,4) = CONSTANTS(:,4)+( CONSTANTS(:,5).*power( STATES(:,1).*CONSTANTS(:,8), 2.00000))./ALGEBRAIC(:,3);
    ALGEBRAIC(:,5) =  STATES(:,1).*(CONSTANTS(:,6)+( power(CONSTANTS(:,8), 2.00000).*ALGEBRAIC(:,2))./ALGEBRAIC(:,3));
    ALGEBRAIC(:,6) = power((power(ALGEBRAIC(:,4), 2.00000)+power(ALGEBRAIC(:,5), 2.00000)), 1.0 ./ 2);
    ALGEBRAIC(:,7) = atan(ALGEBRAIC(:,5)./ALGEBRAIC(:,4));
    ALGEBRAIC(:,8) = ( ALGEBRAIC(:,7).*180.000)./ pi;
    ALGEBRAIC(:,9) = arbitrary_log(ALGEBRAIC(:,6)./CONSTANTS(:,9), 10);
end

% Compute a logarithm to any base" +
function x = arbitrary_log(a, base)
    x = log(a) ./ log(base);
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