# Tagged Questions

Questions about optimizing code for faster results, or how to do faster computations.

910 views

### Why is the new PositionIndex horribly slow?

This issue has largely been mitigated in 10.0.1. New timings for the final test below are: ...
1k views

### 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 ...
495 views

### Why is Query so much slower than Part?

Time for another of these(1),(2) as yet another new-in-10 function appears to have poor performance compared to older alternatives. This time: Query appears to be ...
472 views

### Total much slower in version 10

Issue introduced in version 10, fixed in 10.0.2 Compilation nowadays may give very fast functions. Here is an example for finding the sum of a list of machine numbers, just as the built-in function ...
824 views

### DeleteDuplicatesBy is not performing as I'd hoped. Am I missing something?

Déjà vu: a new-in-v10 function should provide a better solution to an old problem, but my enthusiasm is curbed when I run timings. This time the function is ...
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: ...
349 views

### Why some built-in functions are slow

I just wonder why some built-in functions are slower compared to some other ways using more than one built-in functions for doing same job. consider this example: ...
1k views

### How to speed up my Project Euler code

The evaluation speed of Mathematica often depresses me. It did it again when I wrote a code to solve a Project Euler problem. https://projecteuler.net/problem=206 Here's my code: ...
437 views

### Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
718 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 ...
401 views

### Is there a better way to add elements to a Graphics expression repeatedly?

Consider simple example where a set of points is generated and some are displayed. ...
170 views

### Exp is slower for some number ranges

I get a hit on performance with the Exp function depending on the range of my inputs. for example, with: ...
597 views

### Why is calling Dot with many arguments so inefficient?

Say I want to multiply a reasonably large list of symbolic matrices. ...
188 views

### Why is ListPlot so slow here?

While examining How can I monitor the progress of a Plot? I was surprised to discover that in some cases ListPlot in version 10.0 and 10.1 is orders of magnitude ...
209 views

### Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...
249 views

### Why does partitioning increase Dot execution speed?

I have noticed that multiplying a list of matrices can be significantly sped up by partitioning the list, calculating the product of the partitions matrices, and then multiplying the results. ...
561 views

### How to find all the positions of max value of a list efficiently?

For Example, list=RandomInteger[{1,100},2000]. Yes,I know Position[list,Max[list]] can do. But it's based on pattern ...
2k views

### Speed up ordering digit code?

My goal is given an integer number to deduce if its digits increase (or remain the same) from left to right or not. Example: $1236, 123336$ are both considered numbers with increasing digits, but ...
563 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 ...
260 views

### Choose between Apply and Map

Even though this might be too general question(or not answerable), I want to get some advice here. I apologize in advance if it is not a relevant question. I frequently have to process large list of ...
752 views

### 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 ...
312 views

### Replacing matrix values

I want to find the n largest values in a matrix and replace all others with zero. The solution I found uses ReplaceAll and becomes very slow as the size of ...
749 views

### Fast way of finding position of Interval containing an Integer

I have a large list (about 2.2 million) of pairs of integers. Each pair defines an Interval[{}]. Given some integer x, I need to ...
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 ...
137 views

### Slow work of SQLInsert with MS SQL Server in V10

This question is very similar to: Slow work of SQLInsert with SQLite, but for MS SQL Server. Unfortunately the use of SQLBeginTransaction and ...
370 views

### Slow work of SQLInsert with SQLite

I want to store my data in SQLite database, but writing large numbers of data its too slow. For example: ...
230 views

### Extracting values with multiple keys

I want to extract sorted data from a huge database based upon two (or more) keys in a very timely manner. Here is a reproducible toy example for two keys only: ...
218 views

### Relaxation of Mass-Spring System with Pinned Masses

Problem Assume that four masses are connected to each other by springs while two of them are pinned down at their initial positions. Find the position of masses when system is at its minimum ...
293 views

### 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. ...
401 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 ...
89 views

### Mathematica is getting slow when repeatedly calling an external program

I found a strange phenomenon that Mathematica is getting slow when I repeatedly called an external program by using ReadList. For example, the following code will display a significant increase of CPU ...
363 views

### Slow plotting of trigonometric functions

I have two sets of solutions for a and b. I'm plotting solution only if it is positive for both ...
417 views

### Efficiently finding the positions of a large list of targets in another, even larger list

I have a big list. It contains nearly 60,000 sub-lists. It's structured like bigList = {{x1,y1,z1},{x2,y2,z2},{x3,y3,z3},.....,{x60000,y60000,z60000}}; I have ...
406 views

### Fast method to select matrix elements based on a vector of positions

There is an operation for which I have long wanted to find a better solution. Let: a be a matrix of dimensions $m\times n$ ...
987 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 ...
133 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 ...
222 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}]; ...
537 views

### NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
879 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, ...
113 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 ...
107 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 ...
508 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 ...
169 views

### How do I speed up a plotting of NIntegrate when repeated multiple times inside Plot?

I am studying a set of functions (many of which I know only as a definite integral) and I have assembled into a list. Here is a sample: ...
225 views

### Is there a faster way to Map an Association?

Consider mapping an existing Association in a manner such as this: ...
106 views

### Why does Rescale performance vary significantly based on the real number values in a list?

I have a list of the form: testList = Table[{Flatten[RandomReal[{-200, 200}, {1, 2}], 1], RandomReal[{-200, 200}, {69, 2}]}, {i, 1, 100}]; And I would like to ...
567 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 ...
278 views

### Porting code from MATLAB

I'd like to switch from MATLAB to Mathematica for my research in digital signal processing. I used Mathematica a lot during the '90s but I haven't used it since then, so I might as well be a complete ...
321 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 ...
Pick $N$ random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in $N,$ ...