Reworked predator prey filippov system

toolbox/examples/predatorpreyFilippov/comptestpprhs.m

@@ -0,0 +1,168 @@
+%% Turn off warnings corresponding to filippov behaviour
+warning('off', 'IFDIFF:chattering');
+
+%% SETUP
+% parameter values p = (r1, r2, beta1, beta2, q1, q2, m, e)
+% order as in paper (see rhs file)
+m     = 0.790;
+r1    = 0.836;
+e     = 0.948;
+q1    = 0.772;
+aq    = 0.660;
+beta2 = 0.896;
+
+beta1 = 7.81; q2 = 1.5; r2 = 0.3;
+
+% initial values, parameters, timespan
+a     = 0.286975;
+x0_1  = [a ; a ; r1-r2];
+p     = [r1, r2, beta1, beta2, q1, q2, m, e, aq];
+tspan = [0 100];
+
+% configure plotting
+X_plot = linspace(tspan(1), tspan(end), 1000);
+fignum = 1000;
+figure(fignum); clf; hold('on');
+plotit = @plotter;
+
+% solver selection and configuration
+intEuler   = @explEuler;
+eulerStep  = 1e-7;
+integrator = @ode45;    % naive integrator to compare with
+intOptions = odeset('reltol', 1e-10, 'abstol', 1e-12, 'MaxStep', 0.5); % options for ifdiff integrator
+naiveintOptions = odeset('reltol', 1e-5, 'abstol', 1e-6, 'MaxStep', 0.5); % for naive integration
+naiveintOptions_accurate = odeset('reltol', 1e-7, 'abstol', 1e-8, 'MaxStep', 0.5);
+
+% name generators
+nameIfdiff              = @(f) sprintf('ifdiff/%s (correct)', func2str(f));
+namePlainEuler          = @(f) sprintf('plain %s (correct)' , func2str(f));
+nameINTEGRATOR          = @(f) sprintf('naive %s (false)' , func2str(f));
+nameINTEGRATOR_accurate = @(f) sprintf('more accurate naive %s' , func2str(f));
+
+%% FIRST TIME RUN TO INITIALIZE THE JUST IN TIME COMPILER
+% Run the ifdiff integration once to compile the code and have a better runtime for a later speed check
+fprintf("Initializing solver %s ... \n", func2str(integrator));
+datahandle = prepareDatahandleForIntegration('pprhs', 'solver', integrator, 'options', intOptions);
+solveODE(datahandle, tspan, x0_1, p);
+disp("Compilation done...");
+
+%% COMPUTATION
+% Compute ifdiff solution as always when running the code
+fprintf('Integrating with IFDIFF/%s ...\n', func2str(integrator))
+figure(fignum);
+datahandle = prepareDatahandleForIntegration('pprhs', 'solver', func2str(integrator), 'options', intOptions);
+th = tic();
+sol_ifdiff = solveODE(datahandle, tspan, x0_1, p);
+time_ifdiff = toc(th); fprintf('IFDIFF took %g s\n', time_ifdiff);
+X_ifdiff = X_plot;
+Y_ifdiff = deval(sol_ifdiff, X_ifdiff);
+linewidth = 3.0;
+hIFDIFF = plotit(fignum, Y_ifdiff, 'g', nameIfdiff(integrator), linewidth);
+
+% EULER Integration
+[owndir, ~] = fileparts(mfilename('fullpath'));
+euler_fname = fullfile(owndir, sprintf('sol_euler_red_%.0e.mat', eulerStep));
+EulerFileIsPresent = isfile(euler_fname);
+if EulerFileIsPresent
+    fprintf('Loading sol_euler from file %s\n', euler_fname);
+    tmp = load(euler_fname, 'sol_euler_ds');
+    sol_euler = tmp.sol_euler_ds;
+    doEuler = true;
+else
+    disp("Euler solution file missing... Terminating comparison.");
+    doEuler = false;
+    return
+end
+
+if doEuler
+    X_euler = X_plot;
+    Y_euler = transpose(interp1(sol_euler.x, transpose(sol_euler.y), X_euler));
+    linewidth = 2.0;
+    hEuler = plotit(fignum, Y_euler, 'c', namePlainEuler(intEuler), linewidth);
+end
+
+% Compute unmodified naive solution
+fprintf('Doing naive integration with base %s without IFDIFF...', func2str(integrator));
+tspan2 = linspace(0, 100, 10000);
+RHSfun = @(t, y) pprhs(t, y, p);
+tnaive = tic(); [t_naive_acc, Y_naive] = integrator(RHSfun, tspan2, x0_1, naiveintOptions); elapsedTime = toc(tnaive);
+disp("Done integrating naively.");
+fprintf('Elapsed time: %.4f seconds\n', elapsedTime);
+hNaiveODE45 = plotit(fignum, transpose(Y_naive), 'magenta', nameINTEGRATOR(integrator), 1);
+
+warning('on', 'IFDIFF:chattering');
+
+%% ANALYSIS
+fignum2 = fignum + 1;
+errorPlot(fignum2, X_plot, Y_ifdiff, Y_euler, nameIfdiff(integrator), namePlainEuler(intEuler));
+
+%% Ask if user wants to experience Euler Solution generation
+default_choice_index = 1;
+fprintf('\nDo you want to generate an euler trajectory from scratch? \n');
+euler_traj_choices = {"No", "Yes"};
+[idx, val] = userchoice(euler_traj_choices, default_choice_index);
+if idx == 2
+    generateEulerSol;
+end
+
+fprintf('\nDo you want to generate an "accurate" %s solution? (Might take a very long time)\n', func2str(integrator));
+acc_naive_choices = {"No (exit script)", "Yes"};
+[idx2, val2] = userchoice(acc_naive_choices, default_choice_index);
+if idx2 == 2
+    fprintf('Computing naive solution with smaller tolerances (rel = 1e-7, abs = 1e-8)');
+    RHSfun = @(t, y) pprhs(t, y, p);
+    tnaive = tic(); [t_naive_acc, Y_naive_acc] = ode45(RHSfun, tspan2, x0_1, naiveintOptions_accurate); elapsedTime = toc(tnaive);
+    fprintf('\nDone integrating naively. Elapsed time: %.4f seconds\n', elapsedTime);
+    hNaiveODE45 = plotit(fignum, transpose(Y_naive_acc), 'red', nameINTEGRATOR_accurate(integrator), 1);
+end
+
+% FINITO
+return
+
+%% HELPERS
+function errorPlot(fignum, x1, y1, y2, intname1, intname2)
+   figure(fignum); clf(fignum);
+   ydiff = calcDiff(y1, y2);
+   semilogy(x1, ydiff, 'LineWidth', 1.0);
+   xlabel('t');
+   ylabel('||y||_2');
+   title(sprintf('difference %s and %s', intname1, intname2));
+   drawnow
+end
+
+
+function h = plotter(fignum, y, color, name, lw)
+   figure(fignum); hold on;
+   h = plot3(y(3,:), y(2,:), y(1,:), 'Color', color, 'LineWidth', lw, 'DisplayName', name);
+   view([97 51]);
+   grid on;
+   box on;
+   xlabel('Predator');
+   ylabel('Prey 2');
+   zlabel('Prey 1');
+   legend('location', 'northeast');
+   drawnow
+   pause(1.0);
+   set(fignum, 'Position', [200  250  750  375]);
+end
+
+
+function diffnorm = calcDiff(yA, yB)
+  % Go through x-coordinates of yA, find nearest x-coordinate in yB and compare.
+  % Algorithm:  1) Go through x of yA in Index i
+  %             2) Find nearest x in yB in a window centered around yB(:,i)
+  len = length(yA);
+  diffnorm = zeros(len, 1);
+  for i = 1:len
+     y = yA(:, i);
+     % find nearest x in yB in a time-window around the timepoint of y
+     window = 250;
+     j0 = max(1, i-window);
+     jf = max(len, j0+window);
+     jidx = j0:jf;
+     tmpdiff = yB(:, jidx) - repmat(y, [1, length(jidx)]);
+     tmpdiff = vecnorm(tmpdiff,2,1);
+     diffnorm(i) = min(tmpdiff);
+     diffnorm(i) = diffnorm(i) / norm(y);
+  end
+end

toolbox/examples/predatorpreyFilippov/generateEulerSol.m

@@ -0,0 +1,99 @@
+%% SETUP
+% parameter values p = (r1, r2, beta1, beta2, q1, q2, m, e)
+% order as in paper (see rhs file)
+m     = 0.790;
+r1    = 0.836;
+e     = 0.948;
+q1    = 0.772;
+aq    = 0.660;
+beta2 = 0.896;
+
+beta1 = 7.81; q2 = 1.5; r2 = 0.3;
+
+% initial values, parameters, timespan
+a = 0.286975;
+x0_1 = [a ; a ; r1-r2];
+p = [r1, r2, beta1, beta2, q1, q2, m, e, aq];
+tspan = [0 100];
+
+% configure plotting
+X_plot = linspace(tspan(1), tspan(end), 1000);
+fignum = 1002;
+figure(fignum); clf; hold('on');
+plotit = @plotter;
+
+% solver selection and configuration
+intEuler       = @explEuler;
+eulerStep      = 1e-7;
+namePlainEuler = @(f) sprintf('plain %s' , func2str(f));
+
+%% COMPUTATION
+% Now let the user decide if an euler solution is generated or loaded
+fprintf('\nThis is the Euler solution generation script. Proceed with generation?\n');
+choices = {"no (load from .mat file)", "yes (can take up to 20 minutes)"};
+default_choice_index = 1;
+[idx, val] = userchoice(choices, default_choice_index);
+doEuler = false;
+if idx == 2
+    doEuler = true;
+end
+
+% EULER Integration
+[owndir, ~] = fileparts(mfilename('fullpath'));
+euler_fname = fullfile(owndir, sprintf('sol_euler_red_%.0e.mat', eulerStep));
+EulerFileIsPresent = isfile(euler_fname);
+if EulerFileIsPresent && ~doEuler
+    fprintf('Loading sol_euler from file %s\n', euler_fname);
+    tmp = load(euler_fname, 'sol_euler_ds');
+    sol_euler = tmp.sol_euler_ds;
+    doEuler = true;
+else
+    if ~EulerFileIsPresent
+        disp("Euler solution file missing... Generating file");
+    else
+        disp("Computing Euler solution");
+    end
+    % Generate euler solution
+    fprintf('Integrating with integrator %s (might take a while) ...\n', func2str(intEuler))
+    figure(fignum);
+    th = tic();
+    sol_euler = intEuler(@(t,x) pprhs(t,x,p), tspan, x0_1, eulerStep);
+    time_euler = toc(th); fprintf('Euler took %g s\n', time_euler);
+    fprintf('Saving result to %s for later reuse.\n', euler_fname);
+    % reduce euler solution to make file smaller and save it
+    ds = 100;
+    idx = 1:ds:numel(sol_euler.x);
+    sol_euler_ds.x = sol_euler.x(idx);
+    sol_euler_ds.y = sol_euler.y(:, idx);
+    save(euler_fname, "sol_euler_ds");
+    doEuler = true; % in case we ended up here because the file did not exist
+end
+
+if doEuler
+    X_euler = X_plot;
+    Y_euler = transpose(interp1(sol_euler.x, transpose(sol_euler.y), X_euler));
+    linewidth = 2.0;
+    hEuler = plotit(fignum, Y_euler, 'c', namePlainEuler(intEuler), linewidth);
+end
+
+
+
+% FINITO
+return
+
+%% HELPERS
+
+function h = plotter(fignum, y, color, name, lw)
+   figure(fignum); hold on;
+   h = plot3(y(3,:), y(2,:), y(1,:), 'Color', color, 'LineWidth', lw, 'DisplayName', name);
+   view([97 51]);
+   grid on;
+   box on;
+   xlabel('Predator');
+   ylabel('Prey 2');
+   zlabel('Prey 1');
+   legend('location', 'northeast');
+   drawnow
+   pause(1.0);
+   set(fignum, 'Position', [200  250  750  375]);
+end