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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13
votes
9answers
609 views

Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
11
votes
4answers
394 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
729 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
278 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 ...
19
votes
6answers
1k views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
5
votes
3answers
673 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. ...
13
votes
1answer
355 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 ...
25
votes
5answers
4k 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. ...
10
votes
1answer
941 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 ...
10
votes
2answers
540 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
3
votes
3answers
488 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
4k 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 ...
15
votes
1answer
467 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
109 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
396 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 ...
0
votes
2answers
504 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), ...
3
votes
1answer
1k 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
535 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
283 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 ...
6
votes
2answers
627 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 ...
3
votes
1answer
428 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
334 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
476 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 ...
4
votes
2answers
1k views

Why is my animation so slow?

I have an animated plot of the kind ...
1
vote
2answers
328 views

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 ...
26
votes
1answer
851 views

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 ...
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 ...
15
votes
2answers
2k views

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 ...
21
votes
6answers
2k views

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 ...
8
votes
1answer
335 views

Compiled version of (Norm/@coordinates)

Here I define (NormCoordinates). ...
9
votes
3answers
464 views

Compiled function error - nontensor object created

I'm trying to optimize code that uses Position MANY times. The following toy code works: ...
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}} ...
6
votes
0answers
547 views

Optimizing NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
3
votes
1answer
2k 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? ...
10
votes
3answers
933 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 ...
19
votes
1answer
561 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 ...
15
votes
5answers
3k 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 ...
55
votes
1answer
2k 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?
9
votes
3answers
344 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
768 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 ...
34
votes
9answers
2k 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 ...
26
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
474 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
846 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
683 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
154 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
578 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
323 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 ...
36
votes
2answers
2k 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 ...
9
votes
4answers
440 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 ...