Nested Functions

What Are Nested Functions?

A nested function is a function that is completely contained within a parent function. Any function in a program file can include a nested function.

For example, this function named parent contains a nested function named nestedfx:

function parent
disp('This is the parent function')
nestedfx

   function nestedfx
      disp('This is the nested function')
   end

end

The primary difference between nested functions and other types of functions is that they can access and modify variables that are defined in their parent functions. As a result:

Nested functions can use variables that are not explicitly passed as input arguments.
In a parent function, you can create a handle to a nested function that contains the data necessary to run the nested function.

Requirements for Nested Functions

Typically, functions do not require an end statement. However, to nest any function in a program file, all functions in that file must use an end statement.
You cannot define a nested function inside any of the MATLAB^® program control statements, such as if/elseif/else, switch/case, for, while, or try/catch.
You must call a nested function either directly by name (without using feval), or using a function handle that you created using the @ operator (and not str2func).
All of the variables in nested functions or the functions that contain them must be explicitly defined. That is, you cannot call a function or script that assigns values to variables unless those variables already exist in the function workspace. (For more information, see Resolve Error: Attempt to Add Variable to a Static Workspace..)

Sharing Variables Between Parent and Nested Functions

In general, variables in one function workspace are not available to other functions. However, nested functions can access and modify variables in the workspaces of the functions that contain them.

This means that both a nested function and a function that contains it can modify the same variable without passing that variable as an argument. For example, in each of these functions, main1 and main2, both the main function and the nested function can access variable x:

function main1
x = 5;
nestfun1

   function nestfun1 
     x = x + 1;
   end 

end

function main2
nestfun2

   function nestfun2
      x = 5;
   end 
   
x = x + 1;
end

When parent functions do not use a given variable, the variable remains local to the nested function. For example, in this function named main, the two nested functions have their own versions of x that cannot interact with each other:

function main
   nestedfun1
   nestedfun2

   function nestedfun1
      x = 1;
   end

   function nestedfun2
      x = 2;
   end
end

Functions that return output arguments have variables for the outputs in their workspace. However, parent functions only have variables for the output of nested functions if they explicitly request them. For example, this function parentfun does not have variable y in its workspace:

function parentfun
x = 5;
nestfun;

   function y = nestfun
     y = x + 1;
   end 

end

If you modify the code as follows, variable z is in the workspace of parentfun:

function parentfun
x = 5;
z = nestfun;

   function y = nestfun
     y = x + 1;
   end 

end

Using Handles to Store Function Parameters

Nested functions can use variables from three sources:

Input arguments
Variables defined within the nested function
Variables defined in a parent function, also called externally scoped variables

When you create a function handle for a nested function, that handle stores not only the name of the function, but also the values of variables explicitly referenced by the nested function. Variables in the parent workspace that are referenced by nested functions are cleared once the last nested function handle created by that call to the parent function has been cleared.

For example, create a function in a file named makeParabola.m. This function accepts several polynomial coefficients, and returns a handle to a nested function that calculates the value of that polynomial.

function p = makeParabola(a,b,c)
p = @parabola;

   function y = parabola(x)
   y = a*x.^2 + b*x + c;
   end

end

The makeParabola function returns a handle to the parabola function that includes values for coefficients a, b, and c.

At the command line, call the makeParabola function with coefficient values of 1.3, .2, and 30. Use the returned function handle p to evaluate the polynomial at a particular point:

p = makeParabola(1.3,.2,30);

X = 25;
Y = p(X)

Y =
  847.5000

Many MATLAB functions accept function handle inputs to evaluate functions over a range of values. For example, plot the parabolic equation from -25 to +25:

fplot(p,[-25,25])

You can create multiple handles to the parabola function that each use different polynomial coefficients:

firstp = makeParabola(0.8,1.6,32);
secondp = makeParabola(3,4,50);
range = [-25,25];

figure
hold on
fplot(firstp,range)
fplot(secondp,range,'r:')
hold off

Visibility of Nested Functions

Every function has a certain scope, that is, a set of other functions to which it is visible. A nested function is available:

From the level immediately above it. (In the following code, function A can call B or D, but not C or E.)
From a function nested at the same level within the same parent function. (Function B can call D, and D can call B.)

From a function at any lower level. (Function C can call B or D, but not E.)

function A(x, y)              % Main function
B(x,y)
D(y)

   function B(x,y)            % Nested in A
   C(x)
   D(y)

      function C(x)           % Nested in B
      D(x)
      end
   end

   function D(x)              % Nested in A
   E(x)

      function E(x)           % Nested in D
      disp(x)
      end
   end
end

The easiest way to extend the scope of a nested function is to create a function handle and return it as an output argument, as shown in Using Handles to Store Function Parameters. Only functions that can call a nested function can create a handle to it.