Map function in MATLAB?

Question

The short answer: the built-in function arrayfun does exactly what your map function does for numeric arrays:

>> y = arrayfun(@(x) x^2, 1:10)
y =

     1     4     9    16    25    36    49    64    81   100

There are two other built-in functions that behave similarly: cellfun (which operates on elements of cell arrays) and structfun (which operates on each field of a structure).

However, these functions are often not necessary if you take advantage of vectorization, specifically using element-wise arithmetic operators. For the example you gave, a vectorized solution would be:

>> x = 1:10;
>> y = x.^2
y =

     1     4     9    16    25    36    49    64    81   100

Some operations will automatically operate across elements (like adding a scalar value to a vector) while others operators have a special syntax for element-wise operation (denoted by a . before the operator). Many built-in functions in MATLAB are designed to operate on vector and matrix arguments using element-wise operations (often applied to a given dimension, such as sum and mean for example), and thus don't require map functions.

To summarize, here are some different ways to square each element in an array:

x = 1:10;       % Sample array
f = @(x) x.^2;  % Anonymous function that squares each element of its input

% Option #1:
y = x.^2;  % Use the element-wise power operator

% Option #2:
y = f(x);  % Pass a vector to f

% Option #3:
y = arrayfun(f, x);  % Pass each element to f separately

Of course, for such a simple operation, option #1 is the most sensible (and efficient) choice.

In addition to vector and element-wise operations, there's also cellfun for mapping functions over cell arrays. For example:

cellfun(@upper, {'a', 'b', 'c'}, 'UniformOutput',false)
ans = 
    'A'    'B'    'C'

If 'UniformOutput' is true (or not provided), it will attempt to concatenate the results according to the dimensions of the cell array, so

cellfun(@upper, {'a', 'b', 'c'})
ans =
ABC

A rather simple solution, using Matlab's vectorization would be:

a = [ 10 20 30 40 50 ]; % the array with the original values
b = [ 10 8 6 4 2 ]; % the mapping array
c = zeros( 1, 10 ); % your target array

Now, typing

c( b ) = a

returns

c = 0    50     0    40     0    30     0    20     0    10

c( b ) is a reference to a vector of size 5 with the elements of c at the indices given by b. Now if you assing values to this reference vector, the original values in c are overwritten, since c( b ) contains references to the values in c and no copies.

It seems that the built-in arrayfun doesn't work if the result needed is an array of function: eg: map(@(x)[x x^2 x^3],1:10)

slight mods below make this work better:

function results = map(f,list)
% why doesn't MATLAB have a Map function?
for k = 1:length(list)
    if (k==1)
        r1=f(list(k));
        results = zeros(length(r1),length(list));
        results(:,k)=r1;
    else
        results(:,k) = f(list(k));

    end;
end;
end