MATLAB cell array of function handles - How does it work?

Question

I am trying to understand the following commands of a MATLAB script :

global operatorObj
calcEVR_handles = operatorObj.calcEVR_handles;
m = operatorObj.nInputs
E = zeros(m,1);
V = zeros(m,1);
R = zeros(m,m);
for i=1:m
    [E(i), V(i), R(i,i)] = calcEVR_handles{i}(t,x);
end

What can calcEVR_handles be, if t is a float and x is a vector?

Answer 1

calcEVR_handles (to me) looks like a cell array where each element is a handle to a function. Each element in calcEVR_handles is an anonymous function that takes in a single value t and a single vector x. As such, by doing calcEVR_handles{i}, you would access the corresponding function stored at the i^th element in the cell array. Once you have access, you then pass your parameters to this function and it gives you those three outputs.

To show you an example of this working, consider the following cell array that works similarly to calcEVR_handles.

calcCellFunc = {@sin, @cos, @tan};

This is a three element cell array, where each element is a handle to a function. The @ is a special character in MATLAB that denotes that you are creating a handle to a function. It's also used to create anonymous functions, but let's shelve that for this answer. You can read more about it here if you want to delve into more detail regarding this.

Back to our cell array of handles, we will make handles for sin, cos and tan. You can then iterate over your cell array by accessing the function you want by calcCellFunc{idx} where idx is the element you want in the cell array. This will ultimately give you the function stored at index idx. Once you do that, you can then call the function and specify whatever inputs you want (or none if it doesn't take any inputs). Here's a quick example for you. Let's create a random 5 x 5 matrix, and run through each function with this matrix serving as the input. We then take each of these outputs and store them into a corresponding slot in an output cell array. As such:

rng(123); %// Set seed for reproducibility
M = rand(5);
calcCellFunc = {@sin, @cos, @tan};
out = cell(1, numel(calcCellFunc)); %// To store the results for each function
for idx = 1 : numel(calcCellFunc)
    out{idx} = calcCellFunc{idx}(M); %// Get the function, then pass 
                                     %// the matrix M to it
end

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If you want to make things clear, you could split up the out statement to this instead:

func = calcCellFunc{idx}; %// Get access to the function
out{idx} = func(M); %// Pass M to this function

If you're new to handles / anonymous functions, you should probably use the above code first to make it explicitly clear on what MATLAB is doing. You are first getting access to the function you want that is stored in the cell array, and then you pass your arguments to this function.

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If we display the output, we get:

>> celldisp(out)

out{1} =

0.6415    0.4106    0.3365    0.6728    0.5927
0.2823    0.8309    0.6662    0.1815    0.7509
0.2249    0.6325    0.4246    0.1746    0.6627
0.5238    0.4626    0.0596    0.5069    0.5737
0.6590    0.3821    0.3876    0.5071    0.6612



out{2} =

0.7671    0.9118    0.9417    0.7398    0.8054
0.9593    0.5564    0.7458    0.9834    0.6604
0.9744    0.7745    0.9054    0.9846    0.7489
0.8518    0.8866    0.9982    0.8620    0.8191
0.7522    0.9241    0.9218    0.8619    0.7502



out{3} =

0.8363    0.4503    0.3573    0.9094    0.7359
0.2942    1.4934    0.8932    0.1845    1.1370
0.2308    0.8167    0.4690    0.1773    0.8850
0.6149    0.5218    0.0597    0.5880    0.7004
0.8761    0.4135    0.4205    0.5884    0.8814

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The first element of the output cell array has the output when you pass M to sin, the second when you pass M to cos, and the third when you pass M to tan.

So the next question you're asking... why is this useful?

Point #1 - Nix the copying and pasting

This kind of code writing is very useful because if you want to use the same inputs and supply them to many different functions, we would naturally be inclined to do some copying and pasting. Take each of your function names, and create a single line for each. Each line would call the corresponding function you want, followed by the input arguments. This can become quite tedious, and so one smart way to do it would be to place your function name as a handle into a cell array, and to write one for loop that goes over all of the functions dynamically. You could even explore cellfun and escape using the for loop to iterate over all of the function handles too, but I'll leave that for you to read up on. In this way, you have very maintainable code and if you want to remove functions that don't need to be run, just remove the handles from the cell array rather than scrolling down to where the line that invokes this function is located and removing that.

This is actually a very common technique in computer science / software engineering in general. In fact, this is actually quite close to what are known as function pointers. This is MATLAB's cheap way of doing it, but the logic behind this is essentially the same.

Point #2 - Higher Order Functions

Another way this is useful is if you have a function where one (or more than one!) of the inputs is a function, and you also specify inputs into this function as additional parameters to this function. This is what is known as a higher order function. The outputs would be based on using this input function, and the additional inputs you specify to it and the outputs are based on using this input function and the inputs you specify for this function.

One very good example is the fzero function in MATLAB. The goal is to find the root of a non-linear function, and the first parameter is a handle to a function that you specify. The base behaviour behind how fzero works is the same no matter what the function is. All you have to do is specify the function you want to solve and the initial guess of where you think this root is.

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All in all, anonymous functions are very useful.