Roughly speaking, there are two ways we at MathWorks can speed up MATLAB. We can dive into individual functions to remove overheads, improve algorithms and so on or we can make performance enhancements to the language itself that have the potential to speed-up a range of computations across many domains. Today, I'm going to take a look at an example of the latter where function handles have been made faster as part of the R2023a release.

### What are function handles?

Straight

from the documentation: "A function handle is a MATLAB data type that represents a function. A typical use of function handles is to pass a function to another function. For example, you can use function handles as input arguments to functions that evaluate mathematical expressions over a range of values."

For example, say you have the function

We can create a handle

and use it to call the function to compute the square of four as follows:

This simple looking idea turns out to be extremely useful and you'll find function handles used all over the place in MATLAB code.

### Function handle speed test

Let's use our function handle to compute the square of 100 million numbers without storing the results. A somewhat pointless calculation but it will serve our purposes in demonstrating that the function handle overhead has been significantly reduced.

On my machine, I get the following times

- R2022b: 33 seconds
- R2023a: 0.77 seconds

Just over 40x faster in the new release. The practical upshot is that function handles to path and local functions are now about as fast as direct function calls.

OK, that's great but this is an extremely artificial example. What does this mean in real life when we try to do something more useful?

### Faster function handles means faster ODE solvers.

This example is inspired by the one we ship in the bench command. The vanderpol function is defined at the end of this script and here I call it using the handle @vanderpol. I repeat the computation 5 times and take the best result.

% ODE. van der Pol equation, mu = 1

numRepeats = 5; % Number of times I'll repeat the computation. I'll later only report the best one.

t = zeros(1,numRepeats); % Store the timing results

[s,y] = ode45(@vanderpol,tspan,y0);

fprintf("ode45 best time is %.2f seconds\n",min(t))

ode45 best time is 0.21 seconds

- R2022b: 0.4 seconds
- R2023a: 0.21 seconds

That's almost a 2x speed-up. This is far from the 40x speed-up we saw earlier but this shows that there's a lot more going on in ode45 than just function calls.

### Faster optimisation routines?

Anything that makes use of a function handle many times should see some speed-up. After considering ODEs, the next thing that I thought about was mathematical optimisation. After all, optimisers call their objective function many times! Here's a simple example from Global Optimisation Toolbox using

simulated annealing.

numRepeats = 5; % Number of times I'll repeat the computation. I'll later only report the best one.

t = zeros(1,numRepeats); % Store the timing results

tic;[x,fval,exitFlag,output] = simulannealbnd(@objective,x0);

end

Optimization terminated: change in best function value less than options.FunctionTolerance.
Optimization terminated: change in best function value less than options.FunctionTolerance.
Optimization terminated: change in best function value less than options.FunctionTolerance.
Optimization terminated: change in best function value less than options.FunctionTolerance.
Optimization terminated: change in best function value less than options.FunctionTolerance.

Let's discover the best time out of the 5 runs

fprintf("Simulated annealing best time is %.2f seconds\n",min(t))

Simulated annealing best time is 0.16 seconds

and how many function calls were made.

fprintf("The optimiser made %d function calls\n",output.funccount);

The optimiser made 2971 function calls

- R2022b: 0.19 seconds
- R2023a: 0.16 seconds

This was supposed to be a demonstration of when faster function handles didn't make a noticeable difference. The savings on function handle overhead for ~3000 evaluations is expected to be much less than even 0.01 seconds on my machine but this result for this piece of code seems to be fairly robust (for me at least). Granted, this isn't going to change your life but it's heading in the right direction.

### Over to you

If you have some code that uses function handles a lot and have noticed any speed-up, let me know in the comment section

or on twitter.

function y = computeSquare(x)

%Used to show function handle overheads

function dydt = vanderpol(~,y)

%VANDERPOL Evaluate the van der Pol ODEs for mu = 1

dydt = [y(2); (1-y(1)^2)*y(2)-y(1)];

function y = objective(x)

%used for simulated annealing demo

y = (4-2.1.*x(1).^2+x(1).^4./3).*x(1).^2+x(1).*x(2)+(-4+4.*x(2).^2).*x(2).^2;

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