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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11
votes
4answers
410 views

What's fastest way of defining 10^5 down values?

I want to define isGood[___] = False; isGood[#] = True & /@ list where list is a list of several million integers. ...
11
votes
4answers
574 views

How to write this without For loop

Suppose I have a few lists of numbers and want to exponentiate element-wise, then sum up everything into a polynomial. For example, if I have ...
11
votes
5answers
427 views

Most efficient way of making pair list from a list

I have a bunch of datasets which looks like: 3 7 1 6 5 8 2 4 1 2 8 1 5 2 5 ... and I need to make a list of pairs such that the first element makes a pair with ...
11
votes
3answers
540 views

How to speed up Colorize

I have a list of about 500 images similar to the following: A = Import["http://i.stack.imgur.com/1bV4O.png"] ...
11
votes
3answers
1k views

PolarPlot render oddities

I apologize if this is a obvious question and answer, I don't often use Mathematica to display plots or graphics in general to be honest. So, I was tutoring my cousin yesterday in relation to Polar ...
11
votes
5answers
2k views

What is the fastest way to extract a substring from a huge string?

I develop an algorithm to find the most common substrings of a given length n up to a certain distance l in front of a pattern p in a huge sequence S. E.g. I want to find the most common hexamers (...
11
votes
2answers
733 views

Rendering thousands of points

I am trying to render an image with some 120,000 Points. Technically it's just 10,000 points, plus their reflection, plus 5 rotations of both of those sets, but I'm ...
11
votes
3answers
600 views

Plot on command within DynamicModule?

Suppose I have a DynamicModule with all sorts of controls to set some parameters for a graphics object. ...
11
votes
4answers
183 views

Faster position-based duplicate removal in a ragged array?

Take a ragged 2D array: rArray={{4, 2, 1, 0}, {2, 2}, {0, 0, 3, 3, 3}, {4, 0}, {3, 4}} I need to "deduplicate" this, where a duplicate is any element of a ...
11
votes
3answers
810 views

Efficient implementation of a linear complexity measure of binary sequences

For a implementation of testing the quality of random number generators I implemented the NIST test suite in Mathematica based on the nice workbook by Ilja Gerhardt. However I took up the challenge ...
11
votes
2answers
687 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
11
votes
2answers
2k views

Convolution with interpolated function

I have some problems to calculate in reasonable speed the convolution of an interpolated function with a Gauss function. I have here (ExampleData.txt, alternate Pastebin link) data which I ...
11
votes
3answers
560 views

How can I speed up SQL queries in Mathematica?

I have an application that queries a MySQL database many times for data. At the moment, Mathematica and MySQL are running on the same box and yet it takes over 1.6 seconds for the query to run and ...
11
votes
1answer
962 views

What is the fastest way to find an integer-valued row echelon form for a matrix with integer entries?

Let me begin by saying that this is my first post on StackExchange. I apologize in advance if I unwittingly break any of its unwritten rules of etiquette. Recently, I've been trying to understand an ...
11
votes
2answers
297 views

How to “inform” successive ContourPlot calculations?

I need to draw some contour plots of very non-linear functions. As a simple example, take a Mandelbrot Set divergence contour near $z\approx i$. (Just to be clear, I'm not trying to write a ...
11
votes
2answers
652 views

Why is ParallelMap way slower than Map

I recently tried to use ParallelMap instead of Map and to my surprise encountered that ...
11
votes
1answer
333 views

Slow work of SQLInsert with MS SQL Server in V10

This question is very similar to: Slow work of SQLInsert with SQLite, but for MS SQL Server. Unfortunately the use of SQLBeginTransaction and ...
11
votes
1answer
102 views

Speed up Dynamic for graphical interface

I am trying to create a user interface where I can click on certain points in a set of data and save them into a list that can be used later in my code. The problem is it is currently sluggish. Is ...
11
votes
1answer
248 views

Why does Outer sometimes return a packed array, and sometimes not?

For example In[342]:= test3 = Flatten[Outer[Plus, Range[1000], Range[1000]], 1]; // AbsoluteTiming Out[342]= {0.0198735, Null} returns PackedArray (...
11
votes
2answers
325 views

Choose between `Apply` and `Map`

Even though this might be too general question(or not answerable), I want to get some advice here. I apologize in advance if it is not a relevant question. I frequently have to process large list of ...
11
votes
3answers
274 views

Can I return lists with different dimensions from a compiled function?

Sometimes I'll need several lists with different dimensions to be returned by a compiled function, but compiled function will fail if an irregular list contained: ...
11
votes
1answer
935 views

Is there a simple example using OpenCLLink that shows performance advantages?

OpenCLLink allows Mathematica to use the OpenCL parallel computing language. I have done some tests on simple examples, but so far, the CPU regularly outperforms ...
11
votes
2answers
394 views

Memory leak in FE?

A very abridged example of what was originally a major leak ...
11
votes
1answer
155 views

Why FoldList 5 times faster than Apply for matrix multiplication? [duplicate]

Consider this list of $2\times 2$ matrices: list=RandomReal[{-2,2},{500,2,2}]; Now compare timings of Apply and ...
11
votes
1answer
352 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
11
votes
3answers
1k views

Every second evaluation in notebook front end is slow

I'm having a rather baffling problem that Wolfram was unable to help me diagnose, and I'm hoping one of you geniuses in residence here can figure it out. (I don't get access to the Technical Support ...
11
votes
2answers
264 views

Efficiently generating samples from an urn with maximum per element constraint?

I need to sample from a distribution that is a hybrid of uniform and hypergeometric in the sense that all elements are sampled uniformly until an element reaches some specified maximum observations, ...
11
votes
0answers
177 views

Slow JoinAcross performance

Bug introduced in 10.3 I am using JoinAcross to combine two datasets, where the key is an Integer. ...
10
votes
4answers
202 views

Timing problem with ReplaceRepeated

I have the following data: ...
10
votes
4answers
371 views

Efficient way of identifying the indices of first occurrences

It seems to me like identifying the first occurrence of unique elements should take about the same amount of time as it takes to delete duplicates. My data sets are much larger than this (...
10
votes
8answers
429 views

Fast way to get positions of “boxed” array elements?

Given a 2D array (arbitrary numeric / evaluates to numeric elements, simplified for examples, and can be arbitrary dimensions so long as the operation makes sense, I'm working with 2K X 2K in my ...
10
votes
3answers
414 views

Making sure that Timing[] isn't thrown off by caching

In playing with and comparing the various answers to my question here, I tried applying Timing[] to see how fast things ran, but it seemed that some of the answers (...
10
votes
3answers
459 views

Radial distribution function

I have tried to rewrite my old IDL code to calculate the radial correlation function for a regular 2D crystal structure. The theory behind this function is given here: https://en.wikipedia.org/wiki/...
10
votes
2answers
271 views

What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
10
votes
2answers
585 views

Faster “stuttering” accumulate?

Given some list of arbitrary precision numbers, e.g. (actual lists are 1M+ elements long): test={0, 2, 2, 47839283, 2, 0, 0, 2, 0, 1, 2, 0} I need to accumulate ...
10
votes
4answers
1k views

Passing large list by reference

I have the following problem: I would like to control evaluation of a variable that points to a list. For example, frequently in the code I have functions of the form that are supposed to work on ...
10
votes
3answers
266 views

Efficient way to turn a subset into a permutation

For an input vector $\{a_1,a_2,\ldots,a_n,b_{1},b_2,\ldots,b_{m}\}$ and a list of ordered positions $\{k_1,k_2,\ldots, k_n\}$, such that $1\leqslant k_1 < k_2 < \ldots < k_n \leqslant n+m$, I ...
10
votes
1answer
840 views

Poor performance from Graphics3D

I wrote a game -- 2048,Some codes are from http://blog.wolfram.com/. My codes are in notebook downloads I added code so that the game can play in 3D form, but when I play it, I find that it is too ...
10
votes
1answer
754 views

Modular arithmetic - efficiently calculating the remainders of factorials

When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code. ...
10
votes
2answers
442 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way I'...
10
votes
2answers
203 views

ParallelTable behaves differently when it is run inside a package

I've been butting my head against some very weird behaviour by ParallelTable, and its interaction with packages, over the past few weeks, and making relatively ...
10
votes
2answers
230 views

Primes Race (Mathematica Efficiency)

I am currently working with a paper that deals with this concept of Prime Races. You essentially create a large list of prime numbers and then split that list into two teams. You are assigned to ...
10
votes
1answer
140 views

RandomInteger: speed with long lists

I noticed an interesting effect with RandomInteger when looking at the time to create 10^8 random integers. The following code lines all take about 0.5 seconds on a ...
10
votes
1answer
315 views

Creating a NearestFunction that returns an index

I use Nearest repeatedly for large data sets. For example pts = RandomReal[{-1, 1}, {1000, 3}]; Nearest[pts, {0, 0, 0}] I ...
10
votes
1answer
361 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
10
votes
2answers
229 views
+150

How to boost the performance of my own BSplineFunction

In my CAGD package, I implemented a CAGDBSplineFunction[] like built-in BSplineFunction[]. ...
10
votes
1answer
114 views

What are the main differences between RawArray and PackedArray?

What I know: PackedArray is documented (to some extent) in "Developer Utilities Package", RawArray is just mentioned in ...
10
votes
1answer
347 views

Drop selection of columns from a ragged array

I have an application where I need to drop some arbitrary list of columns from a ragged array (where of course the shortest array rows have at least all the specified columns). E.g., given a ragged ...
10
votes
1answer
507 views

GeoDirection and GeoDistance Memory Leaks: How to Recover the Memory?

Bug introduced in 7.0 and fixed in 9.0.0 The functions GeoDirection and GeoDistance have memory leaks. To see this, run the example functions below and watch as the Physical Memory Available in ...
10
votes
2answers
314 views

Update only one element in a dynamic grid?

I've got a grid of buttons that each display an image from an array. When a button is clicked, its image changes. ...