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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8
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1answer
199 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 ...
8
votes
4answers
129 views

ImageApply Performance Difference

How come the timing difference between these calls is so big? (0.2 and 39 seconds on my computer) ImageApply[q3, img] ImageApply[q3[#] &, img] Where ...
8
votes
2answers
748 views

Why is Mathematica's expansion of expressions with square roots so slow?

Mathematica expansion of expressions with symbols isn't slow, but with square roots it is very slow. In Maple or Mupad both are fast: with square roots they both take less than a second. Here is an ...
8
votes
1answer
196 views

Why is `Block` significantly faster than `ReplaceAll` for inputting variable values

Given that the documentation for FindMinimum uses ReplaceAll for its various examples of what to do with the found solution to ...
8
votes
1answer
210 views

Why is building a table of function values so much slower than just plotting the function?

Here is a function that take some time to evaluate: n = 1000; coeffs = RandomVariate[NormalDistribution[], n]; f[x_] := Sum[coeffs[[k]] Sin[k x]/k, {k, 1, n}]; ...
8
votes
2answers
893 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, ...
8
votes
2answers
744 views

Mathematica rule substitution memory

First I present the specific programming question, and then I provide further background details. Given an expression in Mathematica, say f=3x+7y, there are two ...
8
votes
2answers
178 views

Bad performance from SubsetQ?

Can I say this is a bad performance from the new V10 function SubsetQ? Here are some tests comparing it to ...
8
votes
2answers
130 views

vectorized operations is not efficient?

Consider the following example: ...
8
votes
1answer
276 views

Optimizing the performance of an algorithm

First - a bit of an introduction. If you're only interested in the code, you can skip this section. The following question is drawn from Dennis E. Shasha's Puzzling Adventures, and is listed under ...
8
votes
2answers
351 views

Finding all sets of elements with two common elements in a large dataset

I have a very large network of atoms ($\approx 10^6$ atoms) with fixed positions that resemble a cellular structure: I have two files including: fixed locations of each atom set of points which ...
8
votes
1answer
827 views

Integration strategies for oscillatory multidimensional function

I am seeking to integrate a highly oscillatory, multidimensional function. I am currently using NIntegrate's QuasiMonteCarlo approach. However, this is time-consuming and, given my current resources, ...
8
votes
1answer
333 views

Elementwise, compilable min function

I am trying to implement efficiently a transfer-matrix like algorithm. On each iteration, I have two vectors $x=\{x_1,\dots,x_n\}$, $y=\{y_1,\dots,y_n\}$ with real numbers and I need to compute the ...
8
votes
1answer
335 views

Compiled version of (Norm/@coordinates)

Here I define (NormCoordinates). ...
8
votes
0answers
105 views

Efficient image stacking

I have a list of lists of images that I would like to stack and create mean images for each list of images. Images are .jpg files 2592x1944 pixels large. Each list ...
8
votes
0answers
98 views

How to make Graphics3D with multiple lighting sources being rendered faster

I have a very "precise"(through setting "SpherePoints") Sphere illuminated by hundreds of random color lighting sources. The ...
8
votes
0answers
198 views

Improving the performance of a package for working with rational functions

As Mathematica gets slow for large symbolic calculations, the cost of putting terms over a common denominator (Together), in particular, gets too high. It occurred ...
8
votes
0answers
326 views

Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
8
votes
0answers
254 views

Using Compile to speed up Function with PermutationProduct

I have the following fairly simple routine dot involving PermutationProduct that I wish to speed up using ...
7
votes
4answers
609 views

Loop optimization

I wrote this to generate a 6D distribution of particles. ...
7
votes
3answers
480 views

Speed up ContourPlot3D

I have two issues with the following code. (1) It executes too slowly. If I use "Speed" instead of "Quality" for PerformanceGoal, I get the speed but an undesirable delay in proper rendering of the ...
7
votes
5answers
2k 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 ...
7
votes
3answers
364 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 ...
7
votes
3answers
2k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
7
votes
4answers
230 views

Why does array packing in Table behave like this?

Consider the following example, which generate two identical arrays. Why sometimes the array is packed and sometimes it doesn't? And why they perform differently? Here the arrays are packed: ...
7
votes
5answers
323 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 ...
7
votes
2answers
310 views

Compiling a spatial predator-prey model and optimising it for speed

I just made a spatial predator-prey model but it runs a little slow and I am seeking some advice on how to compile it to optimise it for speed. I first define matrix with 0 for an empty site, 1 for a ...
7
votes
2answers
248 views

How can this AbsoluteTime call be made faster?

I need to convert tons of date strings into absolute times. This generates an example data set of 10,000 strings: ...
7
votes
2answers
200 views

Speed up Fourier for Booleans

I'm calculating a bit of the power spectrum of a two color cellular automaton using: ...
7
votes
2answers
719 views

Working with large data, pass-by-reference, compiled functions

I think I know the answer to this, but after two days of Googling, this is my last effort before going down an unwanted path... I have a function that takes lots of large data as arguments as well as ...
7
votes
4answers
249 views

Position of Subsets in a List

I have a particular list of integers and a matrix whose entries are lists. Say I know that my particular list is a subset of at least some of the elements in the matrix. I want to find an efficient ...
7
votes
2answers
319 views

Solving variant of the knapsack/money-changing problem

I'm trying to solve a variant of the knapsack/changing money problem where I have a set of a few numbers and I'm trying to find the linear (integer) combinations of them which are close to a given ...
7
votes
2answers
306 views

Using a given colour table with Image?

Context I would like to represent large images with a given colour table. Now, if I use Image ...
7
votes
1answer
284 views

Compiling Map over expression that yields a ragged array

I'm trying to speed up a function that looks in the neighborhood of each 3D point in a large dataset and finds all the points within 1 unit in each direction, x, y, z. I've started by using ...
7
votes
1answer
634 views

Speeding up numerical Fourier Transform

I wrote this function NFourierTransform, which takes a function $f(k)$ and numerically calculates the fourier transform integral for discrete values of $k \in ...
7
votes
3answers
204 views

How to speed up auxilary DoolittleDecomposite function?

The Doolittle Decomposition algorithm as below: $$A=LU$$ where $A= \begin{bmatrix} a_{11} & a_{12} & \cdots a_{1n}\\ a_{21} & a_{22} & \cdots a_{2n}\\ \vdots & \vdots & \vdots ...
7
votes
3answers
231 views

Issue with very large lists in Mathematica

I have a need to work with very large arrays of data in Mathematica. The length of the list is not known upfront. The typical size is a few hundred thousands elements and could easily go beyond a ...
7
votes
1answer
213 views

Is there a faster way to Map an Association?

Consider mapping an existing Association in a manner such as this: ...
7
votes
4answers
560 views

Suppress connection to Wolfram|Alpha when making unit conversions

I want to speed up calculations with unit conversions. I suspect primarily that some units evaluate from Wolfram|Alpha. Any way to prevent this automatically, so that Mathematica throws ...
7
votes
2answers
273 views

Complement on pre-sorted lists

Is there any way to instruct Complement to skip the sorting part? If the answer is no (likely), the next question would be: how can I remove from a sorted list ...
7
votes
1answer
194 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: ...
7
votes
1answer
268 views

Why do Tooltips slow down Dynamic so much? Is there a faster alternative?

I'm working on a Dynamic ListPlot with a few thousand plots, and it seems that wrapping the points with Tooltip slows the Dynamic responsiveness substantially. With the simple example below, dragging ...
7
votes
1answer
511 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}} ...
7
votes
1answer
157 views

Simpler code evaluating Dickman's function?

I've read here that Mathematica 10 can Obtain symbolic solutions to delay differential equations. Would that help in numericaly evaluating Dickman's function $\rho(u)$ ? It is a delay differential ...
7
votes
1answer
836 views

Exporting a sequence of graphs as video efficiently

I have a sequence of graphs that are being created within Mathematica which I'm exporting to create an animated plot of the graph, as follows. ...
7
votes
1answer
309 views

1D Random Walk with Excluded Sites and Variable Time-Step

Here is the physical problem I would like to simulate: Consider the following variations to the 1d random walk: allow for certain, random sites to be excluded with probability 1/2. allow for the ...
7
votes
1answer
195 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
7
votes
1answer
137 views

Compiled function crashes kernel when trying to list over different length arguments

I'm trying to speed up a tally/binning operation that I have to run many times. I have many lists of between 1 and 10 numbers from the range [1,5] and I want to ...
7
votes
2answers
971 views

Elegant way to handle columns operations

Inspired by this question from @sjdh and by my recurrent use of columns operations in database sets, I was looking for one way to make columns operations more symetric, so I can handle with matrix and ...
7
votes
1answer
243 views

how can I avoid CPU waste (by master kernel) using WaitNext?

I'm using WaitNext in Mathematica for parallel processing on Mac OS X. I have 4 processors on my MacBook and LaunchKernels[] ...