How to use memoization in MatLab?

if I have some function substantially more complicated than

function out = y(x)
out = 2*x;
end

but let's just go with this one... is there a way to save the value y(1) for example, so that if I call y(5) and then y(1) again, it's not going to CALCULATE y(1) but pull it from memory? Maybe have a function create a separate variable "y1" and store it? The problem is that I would like to not have to create empty variable BEFORE running the function (because i may not know what names they should have), i want it to create them by itself. Is there a way to do it? I guess one way would be to maybe create an empty array "y" and then store each value in its respective cell? So solution to y(1) would go to cell #1 in the array, and so on... This doesn't feel right tho. And I still don't know how that would prevent the function from doing the same calculation over and over again rather than just doing it once.

Any hints would be appreciated :]

Answer 1

[per isakson]

See Use nested functions to memoize costly functions, search Answer and File Exchange

Answer 2

[Prabhakar]

Memoize was added to MATLAB in R2017a.

The documentation is a good resource to begin with, or if you prefer here is a blog which walks you through it.

[Walter Roberson]

For earlier versions

https://www.mathworks.com/matlabcentral/fileexchange/34565-micro-cache--memoize-cache-function-results

https://www.mathworks.com/matlabcentral/fileexchange/49949-cachedcall

https://blogs.mathworks.com/loren/2006/02/08/use-nested-functions-to-memoize-costly-functions/

See also https://www.mathworks.com/matlabcentral/answers/345464-recurrence-relation-for-any-given-n#comment_467043 in which I present the memoized version of a recursive relationship, and code that emulates memoize() for use with earlier versions.