Questions tagged [memoization]
For questions related to user defined caching mechanisms, memoization, in particular.
74
questions
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answer
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How to remember evaluation across sessions?
I am performing a very time-consuming symbolic calculation.
When I reopen a saved Mathematica notebook, it takes quite a long time to evaluate.
Is there an option to tell Mathematica to remember the ...
- 61
0
votes
2
answers
78
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Memoization and recursions
My question is bolded within the text below.
Memoization speeds up a recursion that needs to recall a prior rule other than the last one calculated. For instance, on my machine, the following take 0....
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4
votes
1
answer
178
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Why is a function of two functions that use memoization still slow?
I have two functions that I both use memoization for. My goal is to plot the ratio of these two functions. Since I already plot the functions by themselves, and I use memoization, it would seem to me ...
1
vote
0
answers
39
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RegionPlot3D incorrectly plots regions defined by memoized functions
RegionPlot3D incorrectly plots regions defined by memoized functions.
A memoizer:
...
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3
votes
1
answer
120
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Memoization of functions with optional arguments
Consider the following function that generates a sparse diagonal matrix:
...
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1
vote
0
answers
36
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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 ...
- 703
0
votes
1
answer
66
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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 ...
- 501
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0
answers
18
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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 ...
- 2,037
2
votes
0
answers
40
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Optimising tensor operations under memory constraints
Let riem is a free variable with riem ∈ Arrays[{4, 4, 4, 4} as assumption. Let:
...
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2
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0
answers
114
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Why does this memoized function cause the kernel to quit? [closed]
The following memoized recursive function causes the kernel to beep and quit.
...
- 311
3
votes
1
answer
149
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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.
...
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1
vote
2
answers
136
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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 ...
- 279
0
votes
4
answers
122
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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 ...
- 187
0
votes
1
answer
71
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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:
$$
\...
- 522
2
votes
1
answer
125
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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 ...
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votes
1
answer
148
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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 ...
- 2,292
6
votes
1
answer
325
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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 ...
- 2,037
0
votes
1
answer
197
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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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votes
1
answer
341
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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 ...
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0
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2
answers
155
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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 ...
- 545
4
votes
0
answers
156
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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:
...
- 967
2
votes
1
answer
96
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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 ...
- 2,207
2
votes
1
answer
116
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Debugging and decision support tools for Dynamic Programming (cached definitions) in Mathematica
I'm using the Quantum Computing library with this example:
...
- 261
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0
answers
93
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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
...
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25
votes
4
answers
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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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2
votes
2
answers
120
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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
...
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1
vote
1
answer
91
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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 ~ ...
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4
votes
4
answers
652
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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 ...
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1
vote
1
answer
169
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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
1
answer
152
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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
1
answer
226
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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 ...
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votes
0
answers
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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 ...
- 2,292
5
votes
1
answer
219
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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:
...
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votes
0
answers
469
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 ...
- 2,292
7
votes
2
answers
2k
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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 ...
- 199
4
votes
2
answers
190
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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-...
- 1,375
3
votes
0
answers
64
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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 ...
- 2,292
1
vote
0
answers
87
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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.
...
- 1,548
7
votes
0
answers
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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 ...
- 2,195
10
votes
1
answer
261
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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 ...
- 21.5k
9
votes
1
answer
688
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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:
...
user1722
13
votes
1
answer
248
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 ...
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48
votes
2
answers
3k
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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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3
votes
1
answer
249
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 ...
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2
answers
154
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2
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0
answers
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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 ...
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11
votes
2
answers
292
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. ...
- 2,439
4
votes
0
answers
98
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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 ...
- 10.7k
9
votes
2
answers
342
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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. ...
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votes
2
answers
393
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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)...
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