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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4
votes
1answer
416 views

Bresenham's line algorithm

Bresenham's line algorithm is producing discretized line for given two points for purpose of plotting for example. Like that: I have to stress that I'm interested in positions, not a plot. ...
4
votes
4answers
389 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
70
votes
2answers
880 views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least in version 7, the performance of a / b and a - b is not ...
2
votes
1answer
101 views

Performance on Binomial Deviate is slow

I hope I won't get spanked for reposting. This is related to a previous question discussed here: Performance on Multinomial Deviate is slow. but this version is simpler because it is a binomial ...
0
votes
0answers
70 views

Optimization of vector manipulation

I'm trying to implement an upwind scheme for solving transport equation (at first, I work with no right hand side and the simpliest case possible - velocity is constant, initial data is smooth, etc). ...
5
votes
1answer
140 views

How to speed up this TDSE code?

I'm trying to build a 1D time-dependent Schrodinger equation solver, using the Crank-Nicholson method. And I think the code is kind of working now, but the speed is still slow for me. Here is the ...
3
votes
2answers
236 views

DynamicModule/Dynamic CheckboxBar Slow for Large Lists

I am trying to create a dynamic construct that takes a large list of expressions and allows the user to interactively select any number of entries for further manipulation. This is what I have ...
3
votes
0answers
72 views

LibraryLink parallel performance

I'm trying to use a LibraryLink function in parallel. It is an embarrassingly parallel problem, so that no dependency between those parallel tasks. However I can only get the parallel efficiency about ...
4
votes
2answers
121 views

Values (or positions) of array row elements within a specified number of positions from target value

I have the need to collect values from the rows of rectangular arrays of arbitrary precision integers, given a target element value and allowed "distance" (positions +/- within the row from found ...
3
votes
0answers
108 views

“Off-label use” of Mathematica functions for performance

Assisting an acquaintance with a simulation where a very large number of binomial probability calculations are required, I pointed them to a slightly obscure function to dramatically speed up their ...
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 ...
6
votes
3answers
204 views

Enumerate the 1-factors (perfect matchings) of $K_n$

Introduction I would like to enumerate the 1-factors, or (near-)perfect matchings, of the complete graph Kn. The adjacency list representation for Kn is basically { (x, y) | 1 ≤ x < y ≤ n }. For ...
-2
votes
2answers
187 views

How to write efficient code? How to make this example run faster? [closed]

I would like to learn writting more efficiently. I am working on problem of simulating random walks (abnormal diffusion). I believe this is good example of inefficient code. How can I make it faster? ...
1
vote
2answers
82 views

Extract the real components from a very large expression

Suppose I have a very long expression (>500,000 characters) which contains a mixture of real and imaginary terms. e.g ...
1
vote
1answer
127 views

Code Performance Tuning

The following code takes over 4 seconds to run. Any one has suggestions to make the expressions for qf, phi, ...
9
votes
5answers
587 views

Fast way of finding position of Interval containing an Integer

I have a large list (about 2.2 million) of pairs of integers. Each pair defines an Interval[{}]. Given some integer x, I need to ...
1
vote
0answers
51 views

Approximate to the speed of Build-In functions

In Mathematica, there is a function PowerMod[a,b,m], which computes a^b mod m. I will concern only this case: ...
10
votes
1answer
223 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 ...
9
votes
8answers
355 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 ...
0
votes
0answers
46 views

Addition of sparse array objects [duplicate]

I have been having some trouble with the addition of large (but very sparse) matrices using SparseArray. Here is the simplest example to illustrate the issue. First, I will define diagonal matrices ...
0
votes
0answers
60 views

trying to speed up sequential use of NDSolve for large system of ODEs

I don't have a basic example just yet but I'll describe the problem for now. I have a large system (>100) of coupled first order ODEs. Where the output from one solution becomes the ICs for the next ...
4
votes
1answer
136 views

Selecting expressions from a sequence that are not subexpressions of earlier elements

I have a While loop that generates and prints an expression on each iteration (there can be thousands of iterations). UPDATE: Some expressions are generated in ...
5
votes
2answers
140 views

Improving performance in the generation of random (directed acyclic) graphs

I need to generate large (directed, acyclic, transitive) graphs. My code in Mathematica gets very slow for large numbers of vertices. I've tried a number of approaches and I can't find any significant ...
42
votes
2answers
2k views

Internal`Bag inside Compile

Since Internal`Bag, Internal`StuffBag and Internal`BagPart can be compiled down, it is a ...
2
votes
3answers
293 views

Re-arranging / selecting of a data table very slow in For loop [duplicate]

My task is quite simple; I have a table of data like M = {{1,2}, {1,3}, {3,4}, {5,1}, {6,9}, {6,8}, {6,1}}; so the table is sorted with respect to the first ...
4
votes
1answer
101 views

Why does a heavy background slow LocatorPane from updating, even if only the locators are Dynamic?

I'm having some trouble getting a dynamic plot to operate efficiently, and I think I've tracked down at least part of the problem to some pretty weird behaviour on the part of ...
7
votes
5answers
1k views

Something faster than Do loops with AppendTo

I am an "old" programmer used to Fortran and Pascal. I can't get rid of For, Do and While ...
9
votes
2answers
317 views

Why is ParallelMap way slower than Map

I recently tried to use ParallelMap instead of Map and to my surprise encountered that ...
0
votes
0answers
41 views

Using Table[ ] vs using Do[Append [ ] ] [duplicate]

Is it generally better/faster to use the Table function over using Do[Append []]? For example, I have this piece of code: ...
0
votes
1answer
87 views

Why does initialization slow down manipulate in this case?

I'm trying to manipulate a plot of function with some parameters. The function is a long expression, so I tried to put it inside the Initialization options of ...
7
votes
5answers
322 views

LengthWhile until first duplication

I have the need to trim each of a large number of potentially very long lists (10^6+ elements) to the length where the last occurrence of any distinct element happens, or said another way, where the ...
4
votes
1answer
224 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
6
votes
1answer
159 views

Better way to get Fisher Exact?

I want to perform a Pearson's $\chi^2$ test to analyse contingency tables; but because I have small numbers, it is recommended to perform instead what is called a Fisher's Exact Test. This requires ...
44
votes
4answers
2k 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 ...
11
votes
3answers
777 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 ...
2
votes
2answers
99 views

Random Choice: List Format & Minimizing Memory Use

This is a two part question, and for that I apologize.. but they're related! Here's what I'm working with: ...
8
votes
3answers
269 views

Pairwise distances of points and classification using GraphDistanceMatrix

The challenge Given $n$ points in $\mathbf{R}^3$ and a cutoff distance, $d$, I would like to determine all pairs of points that are separated by less than the given cutoff distance, $d$, and all ...
4
votes
4answers
269 views

Using Locators in a non-standard Manipulate code

I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed (see this ...
4
votes
2answers
204 views

About auto-compiling and performance between Do and Fold

I was investigating how Fold could improve performance vs Do. I tested the code ...
22
votes
3answers
1k views

Reading periodic elements from a large file

I have a large binary data file (big endian) with 100+ million "rows" of 11 elements, combination of floats and integers. This is the format: ...
6
votes
0answers
287 views

Poor CUDALink performance, when calling a kernel multiple times

When working on a project of mine I noticed that CUDALink shows very poor performance when calling CUDA kernels multiple times in a loop-construct. To demonstrate this I put together this little ...
7
votes
6answers
233 views

Faster list duplicate 'limiter'

Given some list, e.g., {5, 3, 2, 3, 1, 0, 1, 3, 5, 5, 4, 5, 1, 2, 5, 2, 2, 0, 1, 4}, I need to limit the duplicates, if any, to an arbitrarily chosen number. The ...
5
votes
1answer
113 views

Finer granularity with ParallelDo

ParallelDo only parallelizes by the innermost variable. Is it possible to distribute the calculation over all the points (all the variable) separately? let me ...
21
votes
5answers
590 views

More efficient way of generating list of occurrence counts?

Given a list, e.g., target = {a, b, c, b, c, d, c, d, e, f, a, h, g}, I want to generate a list containing the occurrence count of the corresponding element of the ...
5
votes
1answer
169 views

What is the fastest way to maintain a large set of expressions?

In my algorithm I need to maintain a set (an unordered list of distinct elements) of expressions supporting two operations: Test an expression for membership in the set Adding a new expression to ...
4
votes
0answers
91 views

2X slower with ; — LibraryLink performance problem [duplicate]

This is the continued problem of the LibraryLink memory usage question here and here. In the following code, there is a 2X performance difference with only the change of ";". ...
1
vote
1answer
166 views

Using Manipulate with a control variable for selective recalculation

I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed. I've also read ...
4
votes
1answer
157 views

MapThread and Compile

After discovering that MapIndexed cannot be used with compile (see MapIndexed and Compile) I am now trying do implement similar functionality using a combination of ...
1
vote
1answer
252 views

Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...