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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2answers
160 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
8
votes
3answers
488 views

Fast Sieve Implementation

I'm going to write a code to compete in performance with NewPGen. The goal is to sieve numbers that have small factors. Mine is very slow in compare with NewPGen. Here's my code: ...
8
votes
3answers
296 views

Faster Alternatives to DateDifference

I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following: Input: A time/date specified by ...
8
votes
3answers
152 views

How can I use the overhang argument to Partition to avoid using PadLeft and PadRight here?

Say I have a list of values v = {v1, v2, v3, ... }. I need to partition these values to perform operations with a sliding window (think ...
8
votes
2answers
603 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
178 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
1answer
161 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
745 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
647 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
126 views

vectorized operations is not efficient?

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

How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
8
votes
1answer
240 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 ...
8
votes
1answer
263 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
250 views

Correct way to generate large data sets (i.e.forward yield curve )

I would like to generate a set of forward yield curve matrix of size 1000 x 100. First I defined my SparseArray of 1000 x100: ...
8
votes
1answer
467 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
241 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
308 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 ...
8
votes
1answer
328 views

Compiled version of (Norm/@coordinates)

Here I define (NormCoordinates). ...
7
votes
4answers
545 views

Loop optimization

I wrote this to generate a 6D distribution of particles. ...
7
votes
3answers
322 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
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 ...
7
votes
3answers
314 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
4answers
210 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
2answers
1k views

Easier program for period of Fibonacci sequence modulo p

For a little project I need to calculate the period of a Fibonacci sequence modulo p, for which p is a prime number. For example, the Fibonacci sequence modulo 19 would be: $$0, 1, 1, 2, 3, 5, 8, 13, ...
7
votes
5answers
316 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
259 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
6answers
229 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 ...
7
votes
2answers
186 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
630 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
2answers
250 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
1answer
250 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
480 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
402 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
1answer
185 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
410 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
451 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
266 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
227 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[] ...
7
votes
0answers
162 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 ...
7
votes
0answers
235 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 ...
7
votes
0answers
238 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 ...
6
votes
3answers
1k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
6
votes
2answers
236 views

Fastest way to test if a numerical array has complex elements

I am looking for the fastest way to test whether an n-dimensional numerical (NumericQ) array (in the ArrayQ sense) is complex or ...
6
votes
4answers
355 views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
6
votes
2answers
188 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: ...
6
votes
2answers
494 views

Web scraping and multi-threading in Mathematica

I'm working in some web scraping using Mathematica, and today, to speed-up the process, I used bash commands (xargs with parallel options with curl and wget) using ...
6
votes
4answers
208 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 ...
6
votes
3answers
230 views

Riffle and Partition

At some point I noticed that I was using Riffle and Partition together a lot. I would do things like ...
6
votes
2answers
302 views

Memory management and speed for Fast GCD

Let's say that we have some $300\,\text{K}$ digits (arbitrary function) and want to trial factor with $100{,}000{,}000$ first prime numbers. ...
6
votes
2answers
113 views

Integrate perfomance

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral in the new version of Mathematica. Here's the ...