# Tips and Tricks - Combining Functions Using Anonymous Functions

By Loren Shure, MathWorks

Anonymous functions let you create simple functions as variables without having to store the functions in a file. You can construct complex expressions by combining multiple anonymous functions. Here are some sample combinations.

## Function Composition

In this example we will create a single function by having one function call another.

Suppose we want to compute the standard deviation of the mean of some data—for example, std(mean(x)). We can construct separate anonymous functions to compute the mean and standard deviation and then combine them:

f = @mean;
g = @std;
fCompg = @(x) g(f(x));


To ensure that the function composition works as expected, we evaluate the first function and use its output as input to the second. We then check that this two-step process is equivalent to the one-step evaluation of the result that we obtained from function composition:

x = rand(10,4);
fx = f(x);
gfx = g(fx);
gfx2 = fCompg(x);
gfsEqual = isequal(gfx,gfx2) gfsEqual = 1


We could create a generalized composition operator g(f) and use that instead:

compose = @(g,f)@(x)g(f(x))
fCompg2 = compose(g,f)
gfcx = fCompg2(x);
gfcEqual = isequal(gfx, gfcx) gfcEqual = 1


## Conditional Function Composition

Now let’s look at a more complicated composition. Suppose that we want to compute the expression:
y = sin(x) – mean(x) + 3, but we don’t always want to subtract the mean or add 3. We dynamically build one function to compute y, which subtracts the mean or adds 3 only when we want it to.

Let’s start by building function handles for computing the sine, subtracting the mean, and adding 3:

x = 0:pi/100:pi/2;
myfunc = @sin;
meanValue = @mean;
three = @(x) 3;


While the variable containing each function handle retains its name, the function it describes can change. Note that this example works only when x is a row or column vector. For multidimensional data, the expressions would be more complicated, and we would use bsxfun.

We combine these functions conditionally. For simplicity, let’s say we want to add 3 but don’t want to subtract the mean. In a more realistic example, we would use logical comparisons to determine which functions to apply:

if false
myfunc = @(x) myfunc(x) - meanValue(x);
end
if true
myfunc = @(x) myfunc(x) + three(x);
end


Let’s try this on the data x that we created earlier:

mf3mean = myfunc(x);


Whatever functions we combine with the original function, we always have a function handle to evaluate. We can use it to specify additional information as we build up an appropriate function for our calculation.

## A Versatile Technique

Using anonymous functions is a versatile technique that you might find useful in a wide range of calculations, from the simplest to the most complex. We’ve looked at just two examples. In fact, the number of possibilities is limitless.

Published 2011 - 91953v00