Questions tagged [memoization]
For questions related to user defined caching mechanisms, memoization, in particular.
84
questions
2
votes
2
answers
80
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How can I Save function defintion without its DownValues?
I use functions that memorize their values like this one:
...
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2
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0
answers
72
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Nintegrate memoization [closed]
Is there a way to use memoization for NIntegrate (maybe dependent on the method of integration used) to reduce the number of computations for the same subintervals when computing something like the ...
- 43
1
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0
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31
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Getting DownValues from memoized function - ParallelEvaluate only uses one kernel at a time
I have the following code where I calculate primorial(n) using a memoized function. When I run this function in ParallelDo everything is fine - the calculation runs on 8 kernels.
But I want to use ...
- 747
3
votes
1
answer
213
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Memoize a compiled function
Let f be some function, I know that i can memoize a function so that it does not compute again previously calculated values, I can also compile the function to speed up the calculations. But how can I ...
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4
votes
1
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74
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Efficient primorial memoization?
Thinking on this recent question asking to create an primorial list, led me to think
How could we exploit something similar to memoization for primorial?
Maybe something that stored only the largest ...
- 36.2k
3
votes
1
answer
221
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Recursive function Catalan triangle
I'm trying to learn how to build a recursive function. However, I'm not sure to understand how to set a "limit".
Here is what I'm trying to make.
I want a function that gives me the i,j ...
2
votes
2
answers
66
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Pattern matching in Association fails in `Set` assignment
I want to define a symbolic-valued function using Set to memoize the result. However, I get different results when using an ...
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2
votes
0
answers
71
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Controlling memory consumption by memoized function
To speed up a resource-intensive calculation, I use several functions with storing previously calculated values. For example:
...
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1
vote
1
answer
150
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Dynamic programming and Module
In the following example of the dynamic programming, why does f[n] is written at the end of the Module?
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2
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0
answers
50
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Memorization for Rule + ReplaceRepeated?
Question
When build packages of noncummutative algebras I met the choice:
Rule + ReplaceRepeated
...
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7
votes
1
answer
256
views
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 ...
- 71
0
votes
2
answers
135
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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....
- 3,603
4
votes
1
answer
194
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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
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0
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46
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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
136
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Memoization of functions with optional arguments
Consider the following function that generates a sparse diagonal matrix:
...
- 263
1
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0
answers
37
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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 ...
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0
votes
1
answer
114
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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
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21
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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 ...
- 1,874
2
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0
answers
60
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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
133
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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.
...
- 403
3
votes
1
answer
170
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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
174
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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 ...
- 289
0
votes
4
answers
146
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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 ...
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0
votes
1
answer
75
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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
140
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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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8
votes
1
answer
165
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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 ...
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6
votes
1
answer
444
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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 ...
- 1,874
0
votes
1
answer
241
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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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18
votes
1
answer
352
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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
votes
2
answers
173
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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
162
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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:
...
- 1,017
2
votes
1
answer
113
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 ...
- 2,311
2
votes
1
answer
123
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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:
...
- 271
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0
answers
97
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
...
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25
votes
4
answers
1k
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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
127
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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
93
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 ~ ...
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4
votes
4
answers
739
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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
183
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
1
answer
155
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
1
answer
234
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 ...
- 35
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votes
0
answers
73
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 ...
- 2,449
5
votes
1
answer
242
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:
...
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5
votes
0
answers
554
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 ...
- 2,449
7
votes
2
answers
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 ...
- 199
4
votes
2
answers
210
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-...
- 1,415
3
votes
0
answers
65
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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 ...
- 2,449
1
vote
0
answers
89
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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.
...
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7
votes
0
answers
108
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 ...
- 2,285
10
votes
1
answer
288
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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 ...
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