What is the need for a nested function?

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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
  3 Comments
Dyuman Joshi
Dyuman Joshi on 22 Nov 2022
You are correct, Stephen. I didn't read through properly, my bad.

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Accepted Answer

Stephen23
Stephen23 on 22 Nov 2022
Edited: Stephen23 on 22 Nov 2022
"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:
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.
  1 Comment
Avinash Gupta
Avinash Gupta on 22 Nov 2022
Thanks for the quick response. I didn't know about these concepts. I will read through them.
Cheers!!

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