# Questions tagged [memoization]

For questions related to user defined caching mechanisms, memoization, in particular.

20 questions
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### What does the construct f[x_] := f[x] = … mean?

This question mentions "x := x = trickery". What does defining a function as f[x_] := f[x] = ... do and what is it good for?
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### How can I implement dynamic programming for a function with more than one argument?

Dynamic programming is a technique for avoiding the repeated computation of the same values in a recursive program. Each value computed is immediately stored. If the value is needed again, it is not ...
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### Get polynomial interpolation formula

I'm attempting to get a polynomial interpolation formula out of Mathematica but I am absolutely lost. I stared out using ...
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### How to clear parts of a memoized function?

I have a function of two variables, e.g.: f[a_, b_] := f[a, b] = something f[a - 1, b - 1] etc With the above code I used the concept of memoization to speed up ...
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### Parallelize evaluation of function with memoization

I have a complicated function that I need multiple times, so I want to memoize it and have the first evaluation done in parallel. Unlike in my example below it's not a continuous function, so ...
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### Memoization of Rounded inputs

Memoization is a technique for improving performance by having a function remember its previous arguments. For example, f[x_]:=f[x]=mySlowFunction[x] will be ...
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### Using Memoization with a Mutable Object

In looking for a solution to this question, I ran across some old binary tree code by Daniel Lichtblau, reproduced below: ...
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### How to memoize a function with Options?

Consider the following modified fibonacci function: ...
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### Memoization with pure functions?

Is this possible? If I have a simple function, say: f=If[#>0,1,2]& then for each value of # this will re-evaluate f right? Is it possible to define a ...
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### Dynamic Programming with delayed evaluation

By using dynamical programming, we can save intermediate steps for recursive relations, as in f[n_]:= f[n] = f[n-1] + f[n-2] However, this only stores ...
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### Saving memoization to disk

I like using memoization (i.e. the construct myFunction[x_]:=myFunction[x]=...) when I have a heavy function that I need to re-evaluate on the same arguments. ...
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### Throwaway memoization makes built-ins faster?

Yesterday I got into an argument with @UnchartedWorks over in the comment thread here. At first glance, he posted a duplicate of Marius' answer, but with some unnecessary memoization: ...
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### How to do memoization together with evaluation of a complicated function

UPDATE 2: much shorter version Given a list of paired indices {i, j}={{1,2}, {3,4}, …}, I need to first evaluate a rather complicated function test[i,j,x] (because ...
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### Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
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### Create recursive sequence of functions with memoization

I am trying to create a sequence of functions and have it properly memoize the results. The recursive operation is simply convolution, so it possible there is a better way to do this (obviously, if I ...
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### Dropbox datastore

Dropbox seems to have a feature where it can be used as a database. This would be really cool to use for memoized functions, that can be restored on several computers and sessions. I have a function ...
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### Clever caching of a recursively defined function

I've got a function of the form f[n,s] where n is a natural number and s is a finite ...
Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...