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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7
votes
1answer
428 views

Very fast way to do a coordinate frame transform

I need a function that rotates and translates a huge amount of line segments. For example, I have a set of line segments in the form {{x0,y0,z0},{x1,y1,z1}} ...
6
votes
0answers
438 views

Optimizing NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
2
votes
1answer
1k views

Methods to speed up numerical NDSolve, NIntegrate,

I am not very used to do numerical simulations on Mathematica. Do you have any ideas how to improve i.e. speed up my code? ...
9
votes
3answers
756 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 ...
18
votes
1answer
509 views

How can I effectively performance-profile Dynamics?

How to optimize performance-wise a complex dynamic expression (like a GUI) with lots of dynamically updated components, which require different update-frequencies? I was hesitant to ask this question ...
10
votes
5answers
2k views

Best way to create symmetric matrices

From time to time I need to generate symmetric matrices with relatively expensive cost of element evaluation. Most frequently these are Gram matrices where elements are $L_2$ dot products. Here are ...
45
votes
1answer
1k views

Profiling from Mathematica

I've always wished I could do some profiling like you get in Wolfram Workbench, but directly from Mathematica, without using or having Workbench. If it is possible, how can I do it?
8
votes
3answers
298 views

Faster Alternatives to DateDifference

I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following: Input: A time/date specified by ...
9
votes
1answer
651 views

How to tell mathematica not to resolve stiffness issues

Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
32
votes
9answers
1k views

Happy 2K prime question

This being the Q number 2K in the site, and this being the day we got the confirmation of mathematica.se graduating soon, I think a celebration question is in order. So... What is the fastest way to ...
23
votes
6answers
1k views

Faster alternatives for DayOfWeek

It has been noticed on several occasions that DayOfWeek function is rather slow when applied to a large list of dates, e.g. in this recent question. What faster ...
5
votes
1answer
376 views

Tridiagonal symmetric matrix eigenvalue using bisection

I know that Eigenvalues is already quite well implemented in Mathematica, nor am I foolishly trying to improve on it. In order to improve my programming skills, I ...
12
votes
3answers
674 views

What compilers are “suitable” for CompilationTarget->“C”?

The documentation for CompilationTarget says, "if you do not have a suitable C compiler then you will not be able to set CompilationTarget to C". Well at this time, I don't have a compiler installed ...
6
votes
2answers
503 views

Trying to extract information from an MDB file. Import is too slow

I am running a Linux box and as usual the documentation for this type of box is not great. I am trying to open up and extract and possibly include later on information from a "mdb" file. The file ...
1
vote
1answer
145 views

Interprocedural optimization

Lets say I want to build a list of the first 1000000 primes. This is simple enough, I can just do: AbsoluteTiming[plist = Table[Prime[i], {i, 1000000}];] and it ...
11
votes
1answer
490 views

Space-efficient null space of sparse array

I have a roughly 100,000 × 3,000 matrix (as a SparseArray) that I'd like to find the kernel (null space) of. It has about 500,000 nonzero entries, all -1 or 1. ...
9
votes
1answer
290 views

Memory Leak in RowReduce?

Recently I tried to do what I thought was a fairly small (relative to the 6 GB of RAM that I have on my machine) row reduction calculation on a matrix representing an undetermined linear system and ...
34
votes
2answers
1k views

Performance tuning for game solving (peg solitaire | senku)

There's a game I saw at a friend's yesterday, that I often see at people's homes, but never for enough time to think on it too hard. It's called peg solitaire (thanks @R.M). So I came home and I ...
8
votes
4answers
386 views

Plotting the components of a function that returns a list in different colors without redundant evaluations of the function

I have a function f which takes a number as input, and returns a list of numbers (the length of the list is constant). f is hard ...
23
votes
1answer
3k views

Finding long strings of identical digits in transcendental numbers

Introduction Describing the three main streams of present-day mathematical philosophy (formalism, Platonism and intuitionism) in a well-known book, The Emperor's New Mind, R. Penrose says: ...it ...
11
votes
1answer
589 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
300 views

Memory leak in FE?

A very abridged example of what was originally a major leak ...
8
votes
1answer
182 views

Reducing the memory footprint of lists of machine numbers

I have a large 1D dataset of double precision numbers that are stored in many external database files. In order to load the whole dataset into Mathematica 8 I iterate over the files ...
4
votes
1answer
128 views

How to speed up mouse events?

Grids of dynamic objects responding to mouseovers seem to be quite slow in general, for instance: ...
9
votes
3answers
561 views

Improve speed for calculating a recursive sequence

I want to calculate following recursive sequence: $\alpha_{0}=0,\\ \cos(\alpha_{i})=\cos(\alpha_{i-1})\cdot\cos(\beta_{i})+\sin(\alpha_{i-1})\cdot\sin(\beta_{i})\cdot\cos(\gamma_{i}).$ In ...
8
votes
2answers
782 views

Rapidly binning 3D data

I have a set of data (about 20 million datapoints for my real data) of the form {x, y, z, m}. There are 3 spatial coordinates x, ...
4
votes
1answer
259 views

Noticeable slowdown in graphical performance when using manipulate

I have been making these mathematica 3D objects that involve a molecule with some sort of surface displayed above them. This is done fairly easily by: ...
6
votes
2answers
171 views

Control which variables get embedded inside Manipulate

While trying to analyse several different datasets I got what I thought was a good idea: define a "function" that returns a Manipulate object. But this has some ...
8
votes
1answer
310 views

Speed up DensityHistogram rendering (display)

When I tried to present some pre-calculated density histograms inside Manipulate I noticed that the display of DensityHistogram is extremely slow. Here is a simple ...
5
votes
1answer
227 views

Can we know the background code associated with basic mathematica functions

I wanted to know how computers calculate basic functions like Sqrt so first I checked how humans do it I found that they use something called "Newton's method" that ...
13
votes
2answers
778 views

Speeding up random walk for many particles

I am trying to speed up this code for many particles to take a random walk. I'm not sure why it is so slow for such a simple task. I got a few hints from colleagues to reduce the precision of the ...
42
votes
2answers
9k views

How can I use Mathematica's graph functions to cheat at Boggle?

This question is inspired by a Stack Overflow question that I decided to solve using Mathematica. In addition to Mathematica, I thought I'd use some of the new version's graph-related functionality, ...
27
votes
3answers
604 views

Are there guidelines for avoiding the unpacking of a packed array?

Packed arrays are very useful because they save memory and generally allow speedier and more efficient calculation times. If a list of data currently stored as a packed array is unpacked, it can slow ...
24
votes
3answers
2k views

How to read data file quickly?

I have a tab separated value file with 10 million rows each of which has three tab separated values. The first value is a string, the second an integer, and the third another string. How to read ...
5
votes
2answers
643 views

Speeding up mathematica by subsitituting numerical values

According to this Wolfram Blog post, one can speed up Mathematica code by substituting numerical values as soon as possible. How does one substitute before the main expression is evaluated? The ...
7
votes
1answer
186 views

Why do images in a PopupMenu sometimes make a program load sluggishly?

In a demonstration, I would like to display a PopupMenu with a list of small PDF images, each weighing in at approximately 50k. The code of interest is below: ...
12
votes
4answers
539 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
7
votes
2answers
188 views

Speed up Fourier for Booleans

I'm calculating a bit of the power spectrum of a two color cellular automaton using: ...
18
votes
4answers
2k views

Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. I wrote the following ...
56
votes
2answers
4k views

Shaving the last 50 ms off NMinimize

The epilogue: A paper where the below answer is used was published. The answer below is cited among the references:) The background: I have to fit an objective function for ~10 000 datasets in near ...
18
votes
3answers
429 views

Is there a faster way to create a matrix of indices from ragged data?

I have data that is given as a list of ordered pairs mixed with scalars. The pairs can contain infinite bounds. My goal is to convert the data into an index used in future computations. ...
18
votes
3answers
2k views

Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...
16
votes
2answers
790 views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
9
votes
1answer
451 views

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

The functions GeoDirection and GeoDistance have memory leaks. To see this, run the example functions below and watch as the Physical Memory Available in the Windows Task Manager, Performance tab, ...
16
votes
4answers
450 views

Getting lengths of sublists that sum to more than one

I have a long list of numbers, and I'm interested in finding the length of each sublist that totals to more than 1, so for the list ...
7
votes
4answers
553 views

Loop optimization

I wrote this to generate a 6D distribution of particles. ...
43
votes
2answers
2k views

What is a Mathematica packed array?

A simple sounding question with a few sub questions: What is the difference between unpacked vs packed array? Are packed arrays more space efficent, how much so? Are packed arrays more time ...
12
votes
2answers
279 views

Parallelization of distinct array write access from subkernels

I'm working on an implementation of a multivariate FFT, which is (or at least should be) highly parallelizable due to the row-column-algorithm. However, i can't figure out how to implement that. The ...
60
votes
8answers
12k views

How to make an inkblot?

How to effectively create a polygon that looks like a realistic inkblot? So far, I could come up with this (borrowing from Ed Pegg Jr.'s Rorschach demonstration): ...
6
votes
1answer
146 views

Efficient conditional division

I was curious about the following little problem. Suppose $n \in \mathbb{N}$ is some large number and $p$ is a (possibly large) prime, and I want to update $n$ according to $$n := \begin{cases} n/p, ...