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# 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.

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

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:

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:

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