Questions tagged [memoization]
For questions related to user defined caching mechanisms, memoization, in particular.
71
questions
1
vote
0answers
38 views
RegionPlot3D incorrectly plots regions defined by memoized functions
RegionPlot3D incorrectly plots regions defined by memoized functions.
A memoizer:
...
3
votes
1answer
78 views
Memoization of functions with optional arguments
Consider the following function that generates a sparse diagonal matrix:
...
1
vote
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
votes
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 ...
0
votes
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
votes
0answers
33 views
Optimising tensor operations under memory constraints
Let riem is a free variable with riem ∈ Arrays[{4, 4, 4, 4} as assumption. Let:
...
2
votes
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
votes
1answer
129 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
vote
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 ...
0
votes
4answers
107 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
68 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
votes
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
votes
1answer
253 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
157 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
315 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
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 ...
4
votes
0answers
146 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
votes
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
votes
0answers
89 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
111 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
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
votes
4answers
586 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
145 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
141 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
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 ...
0
votes
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
200 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
407 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
230 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:
...
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 ...
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
220 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
2
votes
0answers
2k 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 ...
11
votes
2answers
275 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. ...
4
votes
0answers
97 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
308 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. ...
8
votes
2answers
362 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
232 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
351 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
164 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,
...
