BYOM function call_deri.m (calculates the model output)

Syntax: [Xout TE] = call_deri(t,par,X0v)

This function calls the ODE solver to solve the system of differential equations specified in derivatives.m, or the explicit function(s) in simplefun.m. As input, it gets:

The output Xout provides a matrix with time in rows, and states in columns. This function calls derivatives.m. The optional output TE is the time at which an event takes place (specified using the events function). The events function is set up to catch discontinuities. It should be specified according to the problem you are simulating. If you want to use parameters that are (or influence) initial states, they have to be included in this function.

Contents

Start

function [Xout TE] = call_deri(t,par,X0v)
global glo          % allow for global parameters in structure glo
global zvd   % global structure for zero-variate data

% NOTE: this file is modified so that data and output can be as body length
% whereas the state variable remains body weight. Also, there is a
% calculation to prevent shrinking in physical length (as shells, for
% example, do not shrink).

Initial settings

This part extracts optional settings for the ODE solver that can be set in the main script (defaults are set in prelim_checks). The useode option decides whether to calculate the model results using the ODEs in derivatives.m, or the analytical solution in simplefun.m. Using eventson=1 turns on the events handling. Also modify the sub-function at the bottom of this function! Further in this section, initial values can be determined by a parameter (overwrite parts of X0), and zero-variate data can be calculated. See the example BYOM files for more information.

useode   = glo.useode; % calculate model using ODE solver (1) or analytical solution (0)
eventson = glo.eventson; % events function on (1) or off (0)
stiff    = glo.stiff; % set to 1 to use a stiff solver instead of the standard one

% Unpack the vector X0v, which is X0mat for one scenario
X0 = X0v(2:end); % these are the intitial states for a scenario

% % if needed, extract parameters from par that influence initial states in X0
% % start from specified initial size
% Lw0 = par.Lw0(1);  % initial body length (mm)
% X0(1) = glo.dV*((Lw0*glo.delM)^3); % recalculate to dwt, and put this parameter in the correct location of the initial vector

% start from the value provided in X0mat
if glo.len ~= 0 % only if the switch is set to 1 or 2!
    % Assume that X0mat includes initial length; if it includes mass, no correction is needed here
    % The model is set up in masses, so we need to translate the initial length
    % (in mm body length) to body mass using delM. Assume that size is first state.
    X0(1) = glo.dV*((X0(1) * glo.delM)^3); % initial length to initial dwt
end

% % start at hatching, so calculate initial length from egg weight
% WB0   = par.WB0(1);     % initial dry weight of egg
% yVA   = par.yVA(1);     % yield of structure on assimilates (growth)
% kap   = par.kap(1);     % allocation fraction to soma
% WVb   = WB0 *yVA * kap; % dry body mass at birth
% X0(1) = WVb;            % put this estimate in the correct location of the initial vector

% % if needed, calculate model values for zero-variate data from parameter set
% if ~isempty(zvd)
%     zvd.ku(3) = par.Piw(1) * par.ke(1); % add model prediction as third value
% end

Calculations

This part calls the ODE solver (or the explicit model in simplefun.m) to calculate the output (the value of the state variables over time). There is generally no need to modify this part. The solver ode45 generally works well. For stiff problems, the solver might become very slow; you can try ode15s instead.

c  = X0v(1);     % the concentration (or scenario number)
t  = t(:);       % force t to be a row vector (needed when useode=0)

% specify options for the ODE solver
options = odeset; % start with default options
if eventson == 1
    options = odeset(options, 'Events',@eventsfun); % add an events function
end
options = odeset(options, 'RelTol',1e-4,'AbsTol',1e-7); % specify tightened tolerances
% options = odeset(options,'InitialStep',max(t)/1000,'MaxStep',max(t)/100); % specify smaller stepsize

TE = 0; % dummy for time of events

if useode == 1 % use the ODE solver to calculate the solution
    % call the ODE solver (use ode15s for stiff problems, escpecially for pulses)
    if isempty(options.Events) % if no events function is specified ...
        switch stiff
            case 0
                [~,Xout] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout] = ode15s(@derivatives,t,X0,options,par,c);
        end
    else % with an events functions ... additional output arguments for events:
        % TE catches the time of an event, YE the states at the event, and IE the number of the event
        switch stiff
            case 0
                [~,Xout,TE,YE,IE] = ode45(@derivatives,t,X0,options,par,c);
            case 1
                [~,Xout,TE,YE,IE] = ode113(@derivatives,t,X0,options,par,c);
            case 2
                [~,Xout,TE,YE,IE] = ode15s(@derivatives,t,X0,options,par,c);
        end
    end
else % alternatively, use an explicit function provided in simplefun!
    Xout = simplefun(t,X0,par,c);
end

if isempty(TE) || all(TE == 0) % if there is no event caught
    TE = +inf; % return infinity
end

Output mapping

Xout contains a row for each state variable. It can be mapped to the data. If you need to transform the model values to match the data, do it here.

% This is the new part to avoid shrinking on length
if glo.len ~= 0 % only if the switch is set to 1 or 2!
    % Here, I translate the model output in body mass to estimated shell length
    W = Xout(:,1); % Assume that body weight is the first state
    L = (W/glo.dV).^(1/3)/glo.delM; % estimated shell length
    if glo.len == 2 % when animal cannot shrink in length (but does on volume!)
        maxL = 0;%zeros(size(L)); % remember max size achieved
        for i = 1:length(L) % run through length data
            maxL = max([maxL;L(i)]); % new max is max of old max and previous size
            L(i) = maxL; % replace value in output vector
        end
    end
    Xout(:,1) = L; % replace body weight by length
end

% % To obtain the output of the derivatives at each time point. The values in
% % dXout might be used to replace values in Xout, if the data to be fitted
% % are the changes (rates) instead of the state variable itself.
% % dXout = zeros(size(Xout)); % initialise with zeros
% for i = 1:length(t) % run through all time points
%     dXout(i,:) = derivatives(t(i),Xout(i,:),par,c);
%     % derivatives for each stage at each time
% end

Events function

Modify this part of the code if eventson=1. This subfunction catches the 'events': in this case, it looks for birth and the point where size exceeds the threshold for puberty. This function should be adapted to the problem you are modelling.

Note that the eventsfun has the same inputs, in the same sequence, as derivatives.m.

function [value,isterminal,direction] = eventsfun(t,X,par,c)

global glo

Lwp      = par.Lwp(1); % shell length at puberty
if glo.len ~= 0 % only if the switch is set to 1 or 2!
    % Translate shell length at puberty to body weight
    WVp = glo.dV*(Lwp * glo.delM).^3; % initial length to initial dwt
end

nevents  = 1;          % number of events that we try to catch

value       = zeros(nevents,1); % initialise with zeros
value(1)    = X(1) - WVp;       % thing to follow is body mass (state 1) minus threshold

isterminal  = zeros(nevents,1); % do NOT stop the solver at an event
direction   = zeros(nevents,1); % catch ALL zero crossing when function is increasing or decreasing