MATLAB

Anonymous Functions

This example shows how to define functions at the command line with anonymous functions.

Integrating a Function

Consider the function 10*x.

$$h(x)= 10x$$

If we want to allow any multiplier of x, not just 10, we might create a variable g (where g is initially set to 10), and create a new function

$$h(x)= g * x$$

Let's do this in MATLAB® by creating a function handle h.

g=10;
h=@(x) g*x;

You can integrate the function by passing its handle to the INTEGRAL function.

integral(h,1,10)
ans =

  495.0000

Consider another function:

$$f(x)= sin(\alpha x)$$

Create a function handle to this function where alpha = 0.9.

alpha=0.9;
f=@(x) sin(alpha*x);

Plot the function and shade the area under it.

x=0:pi/100:pi;
area(x,f(x)); % You can evaluate f without feval
title('f(x)= sin(\alpha x), \alpha =.9');

We can use the INTEGRAL function to calculate the area under the function between a range of values.

integral(f,0,pi)
ans =

    2.1678

Minimizing a Function

Consider the function:

$$f(x)=a x^2 + bx + c$$

where a=1, b=-2, and c=1

Create a function handle for it.

a=1;b=-2;c=1;
f=@(x)(a*x.^2+b*x+c);
ezplot(f); % Plot the function
title('f(x)=ax^2+bx+c, a=1,b=-2,c=1');
hold on;

% Find and plot the minimum
minimum=fminbnd(f,-2,2);       % We can pass the function handle directly
                               % to the minimization routine
plot(minimum,f(minimum),'d');  % We can evaluate the function without
                               % using feval
grid;
hold off;

2D Functions

We can create handles to functions of many variables

a=pi;b=15;
f=@(x,y) (a*x+b*y);
ezsurf(f);
title('f(x,y)=ax+by, a=\pi, b=15');

Function Composition

We can also create handles to functions of functions

f=@(x) x.^2;
g=@(x) 3*x;
h=@(x) g(f(x));
h(3)
ans =

    27