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
votes
3answers
180 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 ...
3
votes
1answer
277 views

Computing closest set of points to each point in large set — running out of memory (arrays unpacking)

I have a large set of points in 3D and I'm trying to identify all the points that lie within a certain distance of each point. Then using this data store the vector between the pairs of points. I ...
4
votes
2answers
491 views

Fast Trial Division

I'm going to write a custom Trial Division primality test. I know that PrimeQ will first try trial division and then switches to ...
4
votes
1answer
260 views

speed up iteration with conditionals plus optimize memory usage

Given list1 and list2 whose elements are vectors of a certain (fixed) dimension, I am interested in the behaviour of a scalar ...
4
votes
3answers
405 views

Extracting Pareto elements from a list

How can I extract the Pareto elements from a list? For example, for that list: ...
5
votes
2answers
519 views

Fast Karatsuba Squaring, how to?

I want to improve timing of squaring for big numbers. So I asked What is the fastest way to split a number into parts and What is the most efficient way to add zeros to end of a number with several ...
23
votes
3answers
2k 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: ...
11
votes
2answers
627 views

FiniteFields package is very slow. Any fast substitute for Mathematica?

I want to compute the inverse of matrix, say with dimensions $100 \times 100$, defined over a large finite field extension such as $GF(2^{120})$. I am using the package FiniteFields, but Mathematica's ...
7
votes
1answer
819 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 ...
1
vote
1answer
164 views

Optimization of correlation calculation

How can I make the following line of code run faster? Is there a way to do this calculation as a matrix vs vector than vector vs vector? In the code below, f is a ...
4
votes
1answer
294 views

Performance of a Do-Loop of variable length

If I'm changing a basis depending on a (non quadratic) matrix $\mathbf{M}\in\mathbb Z^{d\times k}$ and some $\mu\in\mathbb N^k$, i.e. i have an array a of the same ...
8
votes
2answers
346 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 ...
3
votes
1answer
393 views

Why can't Mathematica parallelize this?

The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation." ...
1
vote
3answers
119 views

Timing display of Graphics (Front End timing)

I want to know how much wall-time it takes to display a Graphics For example this one: ...
7
votes
2answers
355 views

Use of Cellular Automaton or Discrete Convolution to calculate Potts Energy of a 2D Matrix

In a project of Monte Carlo Modelling of Grain Growth (Link) one of the most costly subroutines is the calculation of the Potts-Energy of an Monte Carlo Grid cell by comparing the center cell value ...
15
votes
2answers
657 views

Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
13
votes
2answers
352 views

Why is NeighborhoodGraph so slow?

To get neighboring vertices I first tried: gg = GridGraph[{10, 10, 10, 10}]; VertexList[NeighborhoodGraph[gg, 1, 1]] // AbsoluteTiming {5.539308, {1, 2, 11, ...
10
votes
2answers
2k views

Convolution with interpolated function

I have some problems to calculate in reasonable speed the convolution of an interpolated function with a Gauss function. I have here (ExampleData.txt, alternate Pastebin link) data which I ...
5
votes
3answers
677 views

How to make brute force coding more efficient?

Hi guys and guysettes, The little Mathematica I've been using/seen so far, it seems to be all about neat "one-liners" using the underlying functions and working with lists & maps to solve issues, ...
8
votes
0answers
382 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 ...
22
votes
2answers
2k views

Difference between AbsoluteTiming and Timing

I need to evaluate the efficiency of my code. Therefore I would like to evaluate the time the code need for some calculations. Mathematica gives me two possibilities for this kind of evaluation: ...
4
votes
1answer
463 views

using interpolation functions in ParallelMap

Edit I am editing the question to give a simple workable example. It is at the bottom under the heading Example. The original question is now headed withe Background. Background I am trying to ...
14
votes
9answers
692 views

Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
11
votes
4answers
409 views

What's fastest way of defining 10^5 down values?

I want to define isGood[___] = False; isGood[#] = True & /@ list where list is a list of several million integers. ...
9
votes
1answer
874 views

Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
2
votes
1answer
300 views

Speed up iterated manipulations of a graph / table

I am trying to generate a version of Watts' model of cascading shocks to a network following the discussion on p. 20-25 of this article. The basic premise is to use the ...
17
votes
2answers
827 views

How can I speed up the classic GA for graph coloring?

I'm trying to compute the chromatic number of this graph (which is 28): g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col"; My genetic ...
22
votes
6answers
2k views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
7
votes
3answers
1k views

How to solve an eigensystem faster?

I have a module that I need to call 1-10 million times in my program. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help. ...
14
votes
1answer
421 views

Removing calls to MainEvalute when using inlined compiled closures

This question is tightly related to the answer Shaving the last 50 ms off NMinimize. There @OleksandR shows how inlined closures can be used to eliminate calls to ...
26
votes
5answers
5k views

Making fractals with Mathematica

I recently saw this post on math.stackexchange and was curious as to how to generate the image in Mathematica. I tried the following naive approach; however, it is extremely slow. ...
12
votes
1answer
1k 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 ...
12
votes
4answers
2k views

3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me, but it is extremely slow. Does anyone have any suggestions on how I could speed ...
11
votes
2answers
669 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
3
votes
3answers
658 views

How to sum up large number of elements in a table quickly?

I have been using Mathematica for some time now but I have a feeling that I am not using it as efficiently as it could be. I have the following problem which I am unable to figure out and it would be ...
12
votes
2answers
5k views

How to calculate the mode of a probability distribution

I was wondering if there is any command to get the mode of the probability distributions. Calculating manually, the mode is (alpha-1)/(alpha+beta-2) While the mean, median or variance of the beta ...
18
votes
1answer
549 views

Using Evaluate and Evaluated -> True in Plot

A few use cases: (1) This, as expected, returns (almost) immediately: f[x_?NumericQ] := Evaluate[(Pause[1]; x)] Plot[f[x], {x, 0, 1}] (2) This takes ...
4
votes
2answers
114 views

Factor out invariant code from Plot

Given a simple Gaussian kernel UnscaledKernel[a_, b_, sigma_] := Exp[-(((a - b)/sigma).((a - b)/sigma))/2] and un-normalized smoothing function ...
9
votes
3answers
429 views

Why is AstronomicalData so slow?

I'm having trouble getting some pretty simple functions using AstronomicalData to perform at anywhere near the speed I need them to. For example, I have many ...
1
vote
2answers
669 views

Launching remote kernels - will it help RAM needs?

Given the exasperating RAM needs of my Mathematica program, I contemplated launching remote kernels to run my Mathematica script. This is a two part question: Part 1 If I launch a remote kernel(s), ...
7
votes
1answer
2k views

Improving NDSolve speed for heavily stiff problems

Having looked around the intergoogles and Mathematica.SE, I thought I'd pose a question with a minimum working example. Here is the situation I am trying to improve: I am solving a 4th order non ...
3
votes
4answers
554 views

Faster code for specific problem

Sorry, but I need the following code much faster and I'm running out of ideas. I do appreciate any help. I post two of my fastest ideas (tab and mat), although they are not really fast. Thanks in ...
4
votes
2answers
310 views

Comparing LetL and Module efficiency

I was recently introduced to the LetL macro thanks to Leonid's answer to one of my prior questions. I was, needless to say, impressed by the simplicity of its ...
7
votes
2answers
819 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 ...
5
votes
2answers
501 views

How to speed up drawing a tangent plane?

I have this code to produce an interactive visualization of a tangent plane to a function: ...
4
votes
1answer
474 views

Efficient way to perform elementary integration step with NDSolve internal method

I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
8
votes
1answer
408 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 ...
2
votes
1answer
566 views

How to solve simultaneous equations faster with Compile?

I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
20
votes
2answers
1k views

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: ...
4
votes
2answers
1k views

Why is my animation so slow?

I have an animated plot of the kind ...