Tutorial · Intermediate · 8 min

Writing your own functions

Short one-liners with @(x), longer functions with function … end, and how to pass them to integral, fzero and friends.

1. One-line functions

   @(x) … makes a function you can store in a variable and call like any other.

   f = @(x) x.^2 .* exp(-x);
   f(2)
   fplot(f, [0 10])
   title('f(x) = x² e^(−x)')

   Try it ↗

2. Functions in your script

   Longer functions use function output = name(inputs) … end. They can sit anywhere in the script and have their own variables.

   function a = ring_area(r_outer, r_inner)
     a = pi * (r_outer.^2 - r_inner.^2);
   end
   
   r = linspace(1, 3, 50);
   plot(r, ring_area(r, 1))
   xlabel('outer radius'), ylabel('area')

   Try it ↗

3. Several outputs

   List outputs in square brackets, and ask for them the same way.

   function [m, s] = summary(x)
     m = mean(x);
     s = std(x);
   end
   
   [m, s] = summary([2 4 4 4 5 5 7 9])

   Try it ↗

   m = 5
   s = 2.1381

4. Functions as inputs

   Numerical tools take functions: integral integrates, fzero finds roots, fminbnd finds a minimum.

   f = @(x) x.^2 .* exp(-x);
   area = integral(f, 0, Inf)
   peak = fminbnd(@(x) -f(x), 0, 10)
   cross = fzero(@(x) f(x) - 0.2, 0.5)

   Try it ↗

   area = 2
   peak = 2
   cross = 0.60527