Example Rework

toolbox/examples/canonicalExample/canonicalExample_naive.m → toolbox/examples/canonicalExample/naiveCanonicalExample.m

@@ -13,11 +13,11 @@
 % integrate
 fprintf('Integrating ...')
 tic
-sol = integrator(@(t,x) canonicalExampleRHS(t,x,p), tspan, y0, options);
+sol = integrator(@(t,x) rhsCanonicalExample(t,x,p), tspan, y0, options);
 toc
 fprintf('Integrating with limited step size...')
 tic
-soltrue = integrator(@(t,x) canonicalExampleRHS(t,x,p), tspan, y0, optionsExact);
+soltrue = integrator(@(t,x) rhsCanonicalExample(t,x,p), tspan, y0, optionsExact);
 toc
 
 % evaluate solution

toolbox/examples/canonicalExample/canonicalExampleAnalyticSolution.m → toolbox/examples/canonicalExample/rhsAnalyticSolution.m

@@ -1,4 +1,4 @@
-function [funcSolPiecewise, tSwitch, switchingFunc, varargout] = canonicalExampleAnalyticSolution()
+function [funcSolPiecewise, tSwitch, switchingFunc, varargout] = rhsAnalyticSolution()
 %[funcSolPiecewise, tSwitch, switchingFunc, varargout] = CANONICALEXAMPLEANALYTICSOLUTION()
 %[funcSolPiecewise, tSwitch, switchingFunc, t0, y0, p] = CANONICALEXAMPLEANALYTICSOLUTION()
 %

toolbox/examples/canonicalExample/canonicalExampleRHS.m → toolbox/examples/canonicalExample/rhsCanonicalExample.m

@@ -1,4 +1,4 @@
-function dx = canonicalExampleRHS(t,x,p)
+function dx = rhsCanonicalExample(t,x,p)
 
 dx = zeros(2,1);
 dx(1) = 0.01 * t.^2  +  x(2).^3;

toolbox/examples/canonicalExample/analyticalSolution.m → toolbox/examples/canonicalExample/runAnalyticalSolution.m

@@ -3,7 +3,7 @@
 tPlotStep = 0.01;
 
 %% Analytical solution
-[solTrue, switches, switchingFunctions, t0, y0, p] = canonicalExampleAnalyticSolution;
+[solTrue, switches, switchingFunctions, t0, y0, p] = rhsAnalyticSolution;
 tspan = [t0, tf];
 tPlot = t0:tPlotStep:tf;
 
@@ -26,7 +26,7 @@
 %% Solution ifdiff
 integrator = @ode45;
 odeoptionsrhs_test = odeset( 'AbsTol', 1e-14,'RelTol', 1e-12);
-datahandle    = prepareDatahandleForIntegration('canonicalExampleRHS', 'integrator', func2str(integrator), 'options', odeoptionsrhs_test);
+datahandle    = prepareDatahandleForIntegration('rhsCanonicalExample', 'integrator', integrator, 'options', odeoptionsrhs_test);
 sol           = solveODE(datahandle, tspan, y0, p);
 
 %% Plot analytical solution vs. ifdiff
@@ -44,7 +44,7 @@
 %set(gca,'XTick',0:5:20);
 
 %% Plot analytical solution vs ode45
-canonicalExampleRHS_ode45 = @(t,y) canonicalExampleRHS(t,y,p);
+canonicalExampleRHS_ode45 = @(t,y) rhsCanonicalExample(t,y,p);
 sol_ode45 = ode45(canonicalExampleRHS_ode45, tspan, y0);
 
 figure

toolbox/examples/canonicalExample/canonicalExampleRHS_test.m → toolbox/examples/canonicalExample/runCanonicalExample.m

@@ -4,13 +4,19 @@
 timeinterval = [t0,tf];
 initstates   = [1  0 ];
 p            = 5.437;
+odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-12, 'MaxStep', 1000);
+
+%%
+fprintf('Integration with %s...\n  ', func2str(integrator));
+th = tic();
+sol_matlab = integrator(@(t,x) rhsCanonicalExample(t,x,p), timeinterval, initstates, odeoptions);
+time_matlab = toc(th); fprintf('Took %g seconds\n', time_matlab);
 
 %%
 fprintf('Preprocessing...\n  ');
-odeoptions = odeset( 'AbsTol', 1e-20, 'RelTol', 1e-12);
-filename = 'canonicalExampleRHS';
+filename = 'rhsCanonicalExample';
 th = tic();
-dhandle = prepareDatahandleForIntegration(filename, 'integrator', func2str(integrator), 'options', odeoptions);
+dhandle = prepareDatahandleForIntegration(filename, 'integrator', integrator, 'options', odeoptions);
 time_prepare = toc(th); fprintf('Took %g seconds\n', time_prepare);
 
 %%
@@ -19,13 +25,6 @@
 sol_ifdiff = solveODE(dhandle, timeinterval, initstates, p);
 time_ifdiff = toc(th); fprintf('Took %g seconds\n', time_ifdiff);
 
-%% 
-fprintf('Integration with %s...\n  ', func2str(integrator));
-th = tic();
-sol_matlab = integrator(@(t,x) canonicalExampleRHS(t,x,p), timeinterval, initstates, odeoptions);
-time_matlab = toc(th); fprintf('Took %g seconds\n', time_matlab);
-
-
 %%
 % do explicit euler integration
 fprintf('AccurateEuler integration...\n  ');
@@ -38,7 +37,7 @@
 dt = (tf-t0) / N_euler;  % time increment
 for k = 1:N_euler
    T(k+1)   = t0 + k*dt;
-   X(:,k+1) = X(:,k) + dt * canonicalExampleRHS(T(k), X(:,k), p);
+   X(:,k+1) = X(:,k) + dt * rhsCanonicalExample(T(k), X(:,k), p);
 end
 time_euler = toc(th); fprintf('Took %g seconds\n', time_euler);
 skipper = floor(N_euler/1000);

toolbox/examples/canonicalExample/sensitivities_CanonicalExample.m → toolbox/examples/canonicalExample/sensCanonicalExample.m

@@ -2,7 +2,7 @@
 
 integrator = @ode45;
 odeoptionsrhs_test = odeset( 'AbsTol', 1e-14,'RelTol', 1e-12);
-datahandle    = prepareDatahandleForIntegration('canonicalExampleRHS', 'integrator', func2str(integrator), 'options', odeoptionsrhs_test);
+datahandle    = prepareDatahandleForIntegration('rhsCanonicalExample', 'integrator', integrator, 'options', odeoptionsrhs_test);
 
 tspan         = [0 20];
 initialvalues = [1;0];
@@ -40,7 +40,7 @@
 
 t_plot = 0:0.01:20;
 %sensitivities_END_plot = sensitivities_function_ENDpiecewise(t_plot);
-sensitivities_END_plot = sensitivities_function_VDE(t_plot);
+sensitivities_END_plot = sensitivities_function_VDE(t_plot); %correct?
 
 sensdata_y11 = arrayfun( @(x) x.Gy(1,1), sensitivities_END_plot);
 sensdata_y12 = arrayfun( @(x) x.Gy(1,2), sensitivities_END_plot);

toolbox/examples/coulomb/coulomb_rhs.m → toolbox/examples/coulomb/rhsCoulomb.m

@@ -1,4 +1,4 @@
-function dx = coulomb_rhs(t,x,U)
+function dx = rhsCoulomb(t,x,U)
 % INPUT:   t - time
 %          x - state
 %          U - function handle of one variable (time) [voltage]

toolbox/examples/coulomb/coulomb_test.m → toolbox/examples/coulomb/runCoulomb.m

@@ -32,7 +32,7 @@
 dt = (times.tf - times.t0) / Neuler;    % time increment
 for k = 1:Neuler
    T(k+1)   = times.t0 + k*dt;
-   X(:,k+1) = X(:,k) + dt * coulomb_rhs(T(k), X(:,k), Ufun);
+   X(:,k+1) = X(:,k) + dt * rhsCoulomb(T(k), X(:,k), Ufun);
    %if k > 10; break; end
 end
 fprintf('Euler integration took %g seconds.\n', toc());
@@ -43,7 +43,7 @@
 % try with ode-solver
 odesolver = @ode15s;
 tic
-sol = odesolver(@(t,x) coulomb_rhs(t,x,@U_umax3), [times.t0, times.tf], x0);
+sol = odesolver(@(t,x) rhsCoulomb(t,x,@U_umax3), [times.t0, times.tf], x0);
 fprintf('%s integration took %g seconds.\n', func2str(odesolver), toc());
 Tode = Teuler;
 Xode = deval(sol, Tode);

toolbox/examples/daeExample/daeExample_README.md → toolbox/examples/daeExamples/acadamicDaeExample/README_DaeExample.md

@@ -123,12 +123,12 @@ legend([Plain_plot_1(1), IFDIFF_plot_1(1), Switch_plot]);
 hold off
 ```
 
-![](plots_daeExample/plot1.png)
+![](plotsDaeExample/plot1.png)
 
 We notice that the integrator strategy results in small steps here for the plain solver as well as IFDIFF. This is standard behavior for `ode15s` which is a multi-step method; it is not a defect caused by improper treatment of switching events.
 However, if we take a closer look, we see that the integration with IFDIFF is accurate around the switching point. 
 
-![](plots_daeExample/plot1_close.png)
+![](plotsDaeExample/plot1_close.png)
 
 ## Additional Content
 

toolbox/examples/daeExample/daeExampleRHS.m → toolbox/examples/daeExamples/acadamicDaeExample/rhsDaeExample.m

@@ -1,13 +1,16 @@
-function f = daeExampleRHS(~, x, p)
-
+function f = rhsDaeExample(~, x, p)
+    %
     f = zeros(2,1);
+
     % algebraic constraint
-    z = x(1) + x(2);
+    z = x(1) + x(2) + x(2)^3 - p; 
     f(2) = z;
-    % differential variables
+
+    % differential equation
     if x(2) < p
         f(1) = x(2);
     else
         f(1) = 0;
     end
-end
+
+end