# Tagged Questions

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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### How to quickly calculate intersections of filled curves?

I am trying to quickly calculate the intersection of polygons with more than 6,000 points. A compiled solution would be preferable. Here is one example of the problem: ...
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### Why is my animation so slow?

I have an animated plot of the kind ...
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### Combining lists with common elements efficiently [duplicate]

Possible Duplicate: Computing the equivalence classes of the symmetric transitive closure of a relation I am required to process sets consisting of 2-element subsets of integers by combining ...
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### 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 ...
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### Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
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### Using Compile to speed up Function with PermutationProduct [closed]

I have the following fairly simple routine dot involving PermutationProduct that I wish to speed up using ...
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### Fast Spherical Linear Interpolation of list of quaternions

An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...
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### Why is LogLogPlot[] slower than Plot[]?

I notice that LogLogPlot runs quite bit more slowly than ordinary Plot. For example, consider the following two blocks of code ...
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### How to improve the performance of solutions to Project Euler (#39)?

This is the problem 39 of Project Euler, which I asked in the chat room two days ago. My original code runs as slowly as snails, and finally I got two answers from JM and Rojo. Unfortunately, both of ...
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### How can I efficiently check if a graph is unit distance?

A unit distance graph is a graph that is embeddable in the plane so that every edge has length 1. ...
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### What is the fastest way to count square-free words?

Background A word is a string of letters in an alphabet. A square-free word has no adjacent repeating substring. For example, (in the ternary alphabet of {0,1,2}) the words 00, 012121, and 0212012021 ...
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### Compiled version of (Norm/@coordinates)

Here I define (NormCoordinates). ...
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### Compiled function error - nontensor object created

I'm trying to optimize code that uses Position MANY times. The following toy code works: ...
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### 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}} ...
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### Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### Faster Alternatives to DateDifference

I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following: Input: A time/date specified by <...
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### 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 NDSolve...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Memory leak in FE?

A very abridged example of what was originally a major leak ...
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### 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 ...
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### How to speed up mouse events?

Grids of dynamic objects responding to mouseovers seem to be quite slow in general, for instance: ...
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### 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 ...
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### 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, ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### How can I use Mathematica's graph functions to cheat at Boggle?

Boggle is a word game played with 16 dice and a 4x4 tray. This question is inspired by a Stack Overflow question about Boggle that I decided to solve using Mathematica. In addition to Mathematica, I ...
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### 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 ...
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### 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 ...
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### 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 ...