Questions tagged [performance-tuning]

Questions on optimizing Mathematica code for higher performance. This may mean faster execution, lower memory usage or both. Not to be confused with mathematical optimization.

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20
votes
4answers
553 views

Function that caches when it returns unevaluated

How would you go about implementing a function that caches not the result but the fact that it didn't match a pattern? So that it doesn't waste time recomputing a complex time-consuming pattern ...
25
votes
8answers
4k views

Fastest square number test

What is the fastest possible square number test in Mathematica, both for machine size and big integers? I presume starting in version 8 the fastest will be a dedicated C LibraryLink function.
36
votes
3answers
2k views

Can a Trie be implemented efficiently?

What is the most space and time efficient way to implement a Trie in Mathematica? Will it be practically faster than what is natively available in appropriate cases?
36
votes
4answers
3k views

How to collect result continuously (interruptible calculation) when running parallel calculations?

This is the most common pattern to compute a table of results: Table[function[p], {p, parameters}] (regardless of how it's implemented, it could be a ...
15
votes
2answers
324 views

How do you determine the optimal autocompilation length on your system

When you pack lists there is an overhead therefore packing a list with, say, 2 elements is likely to cost more than you get back in efficiency. Mathematica has default list lengths for which functions ...
30
votes
2answers
817 views

How can I ensure that I am constructing patterns in the most efficient way possible?

Inspired by this answer, I am interested to know if there are best practices or rules of thumb for constructing patterns, for example for use in function definitions (...
53
votes
2answers
3k views

Adaptive sampling for slow to compute functions in 2D

EDIT: Although I have posted an answer based on my current progress, this in incomplete. Please see the "open issues" section in the answer. Most plotting functions in Mathematica adjust the ...
24
votes
1answer
768 views

Is there an NDSolve`ProcessEquations analog for NIntegrate?

NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving ...
41
votes
5answers
21k views

What is the most efficient way to add rows and columns to a matrix?

Say I have a matrix m and a vector v. ...
63
votes
4answers
4k views

Speeding up this fractal-generating code

I used the code below (which is a sample from this gist containing more similar code) in my answer to my own question about Mandelbrot-like sets for functions other than the simple quadratic on Math....
42
votes
2answers
6k views

How can I improve the speed of eigenvalue decompositions for large matrices?

I often need to compute the eigenvalues of large matrices, and I invariably resort to MATLAB for these, simply because it is much faster. I'd like to change that, so that I can work entirely inside my ...
14
votes
1answer
261 views

Choosing among different function definitions without sacrificing speed

I'm working on some code that numerically integrates a function, let's call it G, which calls another function, F, that can be ...
119
votes
1answer
7k views

File-backed lists/variables for handling large data

Background Currently I am working with some large data (most of it generated by Mathematica itself). I usually find it a hassle to do this. For example, I just exported a large amount of data to ...
97
votes
4answers
3k views

What best practices or performance considerations are there for choosing between Cases, Position, Pick and Select?

Cases, Select,Pick and Position each have different ...
20
votes
2answers
2k views

Efficient way of finding shortest distance between two sets of points in mathematica

I have two sets of 3D points, say a = RandomReal[1, {10, 3}]; b = RandomReal[1, {10, 3}]; I wanna find the first N pairs that have shortest distance between the ...
194
votes
3answers
46k views

Alternatives to procedural loops and iterating over lists in Mathematica

While there are some cases where a For loop might be reasonable, it's a general mantra – one I subscribe to myself – that "if you are using a ...
176
votes
5answers
16k views

Performance tuning in Mathematica?

What performance tuning tricks do you use to make a Mathematica application faster? MATLAB has an amazing profiler, but from what I can tell, Mathematica has no similar functionality.

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