Anonymous Function with changing array size

Question

I have the following code to solve some ordinary differential equation(ODE). In order to relieve myself of the burden of typing a long expression in each iteration of the for loop I decided to define an anonymous function. When I defined the anonymous function before initializing x vector it turned out an error since it used the elements of the vector x in calculations. The anonymous function is as follows:

fnc = @(i) (-100 * (x(i) - cos(h * t(i))) - sin(h * t(i)));

In order to resolve the problem I initialized all elements of x to be zeros beforehand to avoid it complaining as follows:

Undefined function 'x' for input
arguments of type 'double'.

However, it turned out to mess up with solution depending on where I put the anonymous function. What may be the reason for this behaviour? My code can be found below, you can see the commented out regions to see where I tried to implement the anonymous function.

close all;
clear all;
clc;
t_s = 0; % Starting time 
t_f = 1; % Finishing time
h = 0.2; % Time step 
t = t_s:h:t_f;
N = (t_f - t_s) / h; % Number of time steps (excluding initial points)
% x = zeros(1, N + 1);
fnc = @(i) (-100 * (x(i) - cos(h * t(i))) - sin(h * t(i)));
x(1) = 1; % Initial condition given in the problem
x(2) = x(1) + h * fnc(1);
for in = 3:N+1
%    fnc = @(i) (-100 * (x(i) - cos(h * t(i))) - sin(h * t(i)));
   x(in) =  x(in - 1) + (3 / 2) * h * fnc(in - 1) + (-1 / 2) * h * fnc(in - 2); 
end

Luis Mendo · Accepted Answer · 2014-12-31 02:58:54Z

1

The value of x is "hardwired" into the anonymous function when you create it. The function internally stores the value that x has at that time, and will always use that. Subsequent changes to x have no effect on the function. See this example from the documentation:

For example, create a function handle to an anonymous function that requires coefficients a, b, and c.

a = 1.3;
b = .2;
c = 30;
parabola = @(x) a*x.^2 + b*x + c;

Because a, b, and c are available at the time you create parabola, the function handle includes those values. The values persist within the function handle even if you clear the variables:

clear a b c
x = 1;
y = parabola(x)
y =
31.5000

You can check which values are stored by the function using functions. For example:

>> x = [1 2 3 4];
>> fnc = @(i) (-100 * (x(i) - cos(h * t(i))) - sin(h * t(i)));
>> f = functions(fnc)
f = 
     function: '@(i)(-100*(x(i)-cos(h*t(i)))-sin(h*t(i)))'
         type: 'anonymous'
         file: ''
    workspace: {[1x1 struct]}
>> f.workspace{1}
ans = 
    x: [1 2 3 4]

If you need the function to depend on x, put x as an additional input (and call the function with the desired x each time):

fnc = @(i,x) (-100 * (x(i) - cos(h * t(i))) - sin(h * t(i)));

edited Dec 31, 2014 at 2:58

answered Dec 31, 2014 at 2:39

Luis Mendo

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3 Comments

Vesnog Over a year ago

Well thanks that was very explanatory can I define this function before defining or initializing x by the way?

Luis Mendo Over a year ago

@Vesnog No, unless x is declared as an input: fnc = @(i,x)... All variables that are not inputs to the function need to be defined, and their values are fixed regarding the function

Vesnog Over a year ago

Okay I understood now thanks for your effort, I appreciate it.

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