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

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67
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5answers
5k views

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?
45
votes
4answers
2k views

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 ...
9
votes
3answers
5k views

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 ...
21
votes
3answers
1k views

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 ...
12
votes
3answers
339 views

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 ...
33
votes
3answers
869 views

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 ...
39
votes
2answers
2k views

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 ...
12
votes
3answers
492 views

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: ...
11
votes
2answers
795 views

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 ...
15
votes
3answers
451 views

How to memoize a function with Options?

Consider the following modified fibonacci function: ...
1
vote
1answer
149 views

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 ...
9
votes
3answers
919 views

Improve speed for calculating a recursive sequence

I want to calculate following recursive sequence: $\alpha_{0}=0,\\ \cos(\alpha_{i})=\cos(\alpha_{i-1})\cdot\cos(\beta_{i})+\sin(\alpha_{i-1})\cdot\sin(\beta_{i})\cdot\cos(\gamma_{i}).$ In ...
5
votes
0answers
119 views

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 ...
4
votes
4answers
377 views

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 ...
3
votes
0answers
65 views

Change of basis of polynomials

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 ...
2
votes
1answer
114 views

Kernel crashed after $RecursionLimit = Infinity

$RecursionLimit = Infinity; T[n_, k_]:= T[n, k] = If[n == 0 || k == 1, 1, T[n, k-1] + If[n<k, 0, T[n-k, k]]]; Table[T[n!, n], {n, 1, 9}] Without ...
1
vote
2answers
75 views

Unintentional function memoisation via Dynamic

I needed to display edge labels of a graph in a way that allows the edge labels to be moved. ...