Questions tagged [memoization]

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

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11
votes
2answers
277 views

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. ...
1
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0answers
38 views

RegionPlot3D incorrectly plots regions defined by memoized functions

RegionPlot3D incorrectly plots regions defined by memoized functions. A memoizer: ...
3
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1answer
81 views

Memoization of functions with optional arguments

Consider the following function that generates a sparse diagonal matrix: ...
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0answers
35 views

Creating a library of saved function values [duplicate]

I have a command of the form J[b,c,n] which outputs a list of complex numbers, obtained by using FindRoot. Some outputs take ...
0
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1answer
48 views

Memoization Involving More than one Variable [duplicate]

Good morning. I would like to know if there is a way to implement memoization if there is more than one variable involved in the memoization; or more accurately, for my problem, have the memoization ...
55
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5answers
5k 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 not ...
0
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0answers
18 views

How to memoize with patterns? [duplicate]

Here is an artificial example to explain what I am up to. Define ClearAll[f] f[x_, y_] := f[x, y] = If[x == 0, g[y], g[f[x - 1, y]]] Then ...
2
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0answers
35 views

Optimising tensor operations under memory constraints

Let riem is a free variable with riem ∈ Arrays[{4, 4, 4, 4} as assumption. Let: ...
2
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0answers
100 views

Why does this memoized function cause the kernel to quit? [closed]

The following memoized recursive function causes the kernel to beep and quit. ...
3
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1answer
131 views

Recursive solution to the extended Josephus problem [duplicate]

The Josephus Problem is described here, with extension of killing every $k$th problem. In the simple case where every other person is killed, we can also use the binary trick. ...
1
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2answers
112 views

Save part of memoized function

I have a function whose performing a series of expansions of a complicated function, which can take a lot of time. To avoid bottlenecks, I use memoization so I need to evaluate it only once. For ...
35
votes
3answers
2k 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 ...
0
votes
4answers
108 views

How to “cache” function values to pass to ListPlot?

I have a function which is very expensive to run. I would like to Plot the function for a certain range, but it is time prohibitive to let Plot simply compute the function for a lot of values as it ...
0
votes
1answer
69 views

Memoization (or otherwise) for a recurrent definition of a (double) sequence of functions

Beside I've found answers to similar questions (e.g. this), I can't adapt them to my case. I am interested in the following sequence of functions $p_{m,n}(t)$, where $m$ and $n$ are integer: $$ \...
2
votes
1answer
117 views

a recursive function using memoization

I have looked at a lot of these cases, e.g. Can one identify the design patterns of Mathematica? and the included ones. My trimmed example, here establishing the 'initial conditions' (where the ...
8
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1answer
139 views

Memoization and packages

I am working in a package on symmetric functions, that sometimes are quite expensive to compute. I use memoization extensively, but what is the correct approach for a package intended for the public ...
6
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1answer
254 views

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 ...
0
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1answer
159 views

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 ...
18
votes
1answer
316 views

When to use Once for memoization?

While watching Stephen Wolfram's twitch stream I saw him use Once for memoization, which surprised me since I thought of Once as ...
5
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2answers
292 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 ...
0
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2answers
140 views

memoization based on function expression?

I want to create a function $f$ which takes as a parameter a function $h$, and calculates its integral between $a$ and $b$. But I want to apply memoization to this, by only calculating the integral ...
13
votes
1answer
243 views

How to write crash-robust code?

When a notebook crashes all the work I was doing is lost - I'd like to ameliorate this situation! Is there a way to decorate a symbol so that it is saved to disk whenever it changes, or after a ...
5
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0answers
233 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
0answers
147 views

Memoization of built in function

What is the best way to let mathematica memoize built-in function like e.g. SphericalHarmonicY[l,m,th,ph] One possibility would be for sure: ...
2
votes
1answer
67 views

Timing of three different strategies for fibonacci numbers

A standard way to speed up the creation of Fibonacci numbers is by memoization Instead of: fib1[0] = 0; fib1[1] = 1; fib1[n_] := fib1[n - 1] + fib1[n - 2]; One ...
2
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1answer
110 views

Debugging and decision support tools for Dynamic Programming (cached definitions) in Mathematica

I'm using the Quantum Computing library with this example: ...
0
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0answers
90 views

How to create a listable, memoized function

Suppose I have a known real constant $a$, and I want to calculate $f(n) = \prod_{k=1}^{n}(a-k)$. I know I could memoize this function ...
25
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4answers
1k views

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: ...
2
votes
2answers
112 views

Memoization and finding already calculated DownValue

The problem of plotting an expensive function discussed in this question caught my attention. As an exercies I tried to solve it using memoization as follows ...
1
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1answer
90 views

Forward iterations of coupled recursion equations

I need to do forward iterations of a system of 16 coupled recursion equations that track the frequency of genotypes over time in a biological model. I find that the iterations run slowly (it takes ~ ...
4
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4answers
591 views

Memoization of a function defined by a recurrence relation [duplicate]

I have a function which is defined by the following recurrence relation $$h_{n}(x)=h_{n-1}(x)+\frac{\mathrm{e}^{-x^2}}{2^n n!}H_{n}(x)H_{n-1}(x)$$ with the initial condition $h_{0}(x)=0$ and where the ...
1
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1answer
148 views

Recurrence Table Differentiation

I would like to generate a table of values by differentiating a function for each entry on the table based off of the previous entry. The purpose is to decrease the number of differentiations as the ...
45
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4answers
2k 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 ...
2
votes
1answer
142 views

Memoization only under certain conditions

I have a function that takes in sequences of values (as a list), and recursively removes the largest element from that sequence as part of its computation. Some of these sequences can be quite large, ...
90
votes
5answers
12k 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?
1
vote
1answer
220 views

Which data tabulation concept is best suited for discrete dynamic programming problems (e.g. for optimum series of account withdrawals)?

A bank account has starting balance, which shall be completely withdrawn in n steps, such that the sum of benefits of withdrawals is maximum. Remaining balance yield interest between steps such that ...
17
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1answer
2k views

Relative performance of the Julia language

I was just reviewing the Mathematica benchmark code linked from the Julia language home page http://julialang.org/. The stated goal of the benchmarks is to test the performance of specific algorithms, ...
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0answers
70 views

Reuse symbolic polynomial

Suppose I have a function that returns a polynomial in x, GetPoly[params_,x_]:=GetPoly[params,x]... but it is quite slow, so ...
5
votes
1answer
203 views

How can I access memoized values from parallel evaluation? [duplicate]

I want to evaluate a table of functions with ParallelTable. Here is the serial code: ...
5
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0answers
409 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 ...
7
votes
2answers
2k views

How does one clear the memory of a recursive function

I want to implement the recursive function v[n_] := v[n] = v[n-1] + f[n-1] + Random[NormalDistribution[0,s]] to get ...
4
votes
2answers
165 views

Assigning function values in a memoized recursive module

I have a complicated recursive module which I have memoized. I realised that certain isomorphs of inputs to this function will give the same output. Therefore I decided to memoize all such input-...
3
votes
0answers
64 views

Memoized function with function parameter [duplicate]

I have some code that takes a function and uses the function to do some complicated computation. Thus, I wish to store this so I don't have to repeat this. Below, it is more simple than my real ...
1
vote
0answers
86 views

Prevent Mathematica using previous result [closed]

How can I prevent mathematica from using the previous computation in new one? How do I make the code below to compute same amount of time without memorizing previous computation. ...
7
votes
0answers
102 views

Time complexity to choose the right overload from the memoized function

If we want to save some outputs of the function, we often use the memoization pattern as follows, f[x_]:=f[x]=x f/@Range[10^5] If I call this function many times ...
10
votes
1answer
232 views

How to speed up the evaluation of a function with a large LeafCount but many repeated sub-functions for use in NIntegrate

General Context Apparently, the memory leak in NIntegrate is unavoidable pre-MMA-10.2. I have some (two-dimensional) numerical integration to do on a complicated ...
9
votes
1answer
680 views

Can I memoize retroactively?

I have a function defined something like this: f[x_] := Module[...]; I can easily write a memoized version of it like this: ...
48
votes
2answers
3k 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 ...
3
votes
1answer
222 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 ...
6
votes
2answers
150 views

Combining memoization and SlotSequence

I found myself writing memoizing code like this: ...