Questions tagged [memoization]
For questions related to user defined caching mechanisms, memoization, in particular.
0
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4answers
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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
58 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
69 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
votes
1answer
99 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
votes
1answer
110 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
votes
1answer
70 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 ...
16
votes
1answer
266 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 ...
0
votes
2answers
118 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 ...
3
votes
0answers
119 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
62 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
votes
1answer
100 views
Debugging and decision support tools for Dynamic Programming (cached definitions) in Mathematica
I'm using the Quantum Computing library with this example:
...
0
votes
0answers
71 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
votes
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
100 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
vote
1answer
81 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
votes
4answers
444 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
vote
1answer
127 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 ...
2
votes
1answer
131 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, ...
1
vote
1answer
201 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 ...
0
votes
0answers
66 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 ...
4
votes
1answer
134 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
votes
0answers
294 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 ...
6
votes
2answers
1k 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
137 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
63 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
81 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
93 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
171 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
670 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:
...
13
votes
1answer
221 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 ...
45
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
170 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
142 views
2
votes
0answers
1k views
SystemException[MemoryAllocationFailure] with Memoized function [closed]
Version 10.1 Win7x64 Enterprise.
This is more of a report than a question but others may have seen the same / have insights.
I have some code (that I can't really post as it's too big) with a large ...
8
votes
1answer
217 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. ...
3
votes
0answers
69 views
Parallelization and memoization? [duplicate]
I have an expensive function on discrete values,
f[n_] := f[n] = n^2 (* Expensive calculation *)
Since f[n] is an expensive ...
9
votes
2answers
256 views
using memoization with conditional statement
I would like some advice about the use of memoization in conjunction with conditional statements. Let me try to explain my problem:
I am constructing a function depending on a number of parameters. ...
7
votes
2answers
312 views
Correct way to use memoization for recurrence relation having an Integral
I am trying to construct a way to make a function for the following recurrence relation.
$$ Q(N,L) = \int_{0}^{L-(N-1)a} Q(N-1, L-a-z) dz $$,
with the initial condition $Q(2,L) = \frac{1}{2} (a-L)...
5
votes
0answers
211 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
3answers
340 views
have a function redefine itself as it maps through a list
I have a list which contains sublists, e.g.
list = {{a,b}, {a,b,c}, {a,b,a,a}, {b,c}, ...}
I then map a function through each sublist. This function should ...
2
votes
3answers
154 views
Extract memoized results in the form of a rule
Lets say I define a function f with memoization. Is there some way to extract the memoized values?
For example,
...
15
votes
1answer
1k 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, ...
4
votes
4answers
440 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 ...
0
votes
1answer
101 views
Optimizing repeated function calls
Easiest way to keep my library nice, is to naively call some functions many times with same parameters. Doing so prevents from zoo of (library-)global variables and complicated initialisation ...
7
votes
1answer
243 views
Garbage collection for memoized functions on subkernels
I have a top-level function which operates on some data:
findBestIntegers[data_]:=ParallelMap[optimize,data]
which makes parallelized calls to an optimization ...
1
vote
2answers
84 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.
...
4
votes
2answers
251 views
Is it possible to `Protect` a dynamic programming process?
I wrote a function using dynamic programming to speed up the evaluation. For safety, I also want to protect this function. Take factorial for example:
...
11
votes
2answers
1k 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 ...
5
votes
2answers
234 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
...
19
votes
3answers
728 views
