What is the need for a nested function?

Hello. This is a code for solving van der Pol equation using ode45. Its available on 12000.org. I hope posting it here is not violating any community guidelines.

Problem: I do not quite see the need for the 'function nma_project_511()'. Its neither taking any input nor giving any outpit. However, running the code without it throws an error regarding c and k being unrecognized. Kindly advise.

Website link: https://12000.org/my_notes/vanderpol/using_ODE45_to_solve_vanderpol/index.htm

function nma_project_511()

% This function solves the Van Der Pol nonlinear ode

% numerically using Matlab's ode45.

% % Final project for 511, CSUF, spring 2009. Instructor: Dr Oh, Sang June

% % Written by : Nasser M. Abbasi

% Van Der Pol ode is x''(t) - c (1-x^2(t)) x'(t) + k x(t) = 0

t = 0:0.001:100; % time scale

c = 1; k = 1;

x0 = 10; v0 = 3;

[t,x] = ode45( @rhs, t, [x0,v0]);

subplot(2,1,1);

plot(t,x(:,1));

xlabel('t'); ylabel('x(t)');

title(sprintf('Van Der Pol, position vs, time, c=%3.2f, k=%3.2f',c,k));

subplot(2,1,2);

plot(x(:,1),x(:,2));

xlabel('x(t)'); ylabel('v(t)');

hold on;

plot(x0,v0,'*r','MarkerSize',10);

title(sprintf('Phase portait showing limit cycle. x(0)=%3.2f, v(0)=%3.2f',x0,v0));

axis equal

hold off;

function dxdt=rhs(t,x)

dxdt_1 = x(2);

dxdt_2 = c*(1-x(1)^2)*x(2)-k*x(1);

dxdt = [dxdt_1 ; dxdt_2];

end

end

[Dyuman Joshi]

The function is used to define the ODE and use it as an input to ode45(), as it can be seen in the this command

[t,x] = ode45( @rhs, t, [x0,v0]);  

[Stephen23]

"The function is used to define the ODE and use it as an input to ode45(), as it can be seen in the this command "

No, that is the function RHS(). The OP is asking about the function NMA_PROJECT_511().

[Dyuman Joshi]

You are correct, Stephen. I didn't read through properly, my bad.

Answer 1

[Stephen23]

"I do not quite see the need for the 'function nma_project_511()'"

There are two main ways to pass extra parameters to functions that are provided to ODE or optimization routines:

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

https://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

As you can see, using nested functions is one way of parameterizing a function. The author of that code chose to use a nested function (not required, but a design choice). A nested function requires a parent function. Ergo, the function NMA_PROJECT_511() is required to make the code work, otherwise RHS() would not be a nested function.

PS: If you have a background in some other languages then you might be used to variables magically being accessible in other workspaces based on very broad and generous scoping rules. MATLAB is not other languages: unless you specifically do something to make it happen (e.g. pass arguments or write a nested function) variables are not accessible in other functions' workspaces.

[Avinash Gupta]

Thanks for the quick response. I didn't know about these concepts. I will read through them.

Cheers!!