# Tagged Questions

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.

329 views

### Check whether array has only constant entries?

I have an array arr with n entries. Now I want to check whether ...
139 views

### Making table of matrix product and efficiency

I want to make a table in which each element is a matrix product: ...
57 views

### Complex input for Compile makes it slow

I asked a question here and then tried to use Compile for the solution to gain even more speed. Inside Compile there is a loop ...
203 views

### Generate lists that satisfy a condition in an efficient way

The following code produces lists of sublists with maximum length 5 that shuffle zeros around an ordered list (here {1,2}). It produces all permutations while ...
162 views

### How to speed up my code about Divisors?

This code is about PE496 In[21]:= ParallelSum[n*Count[Divisors[n^2], a_ /; n < a < 2 n], {n, 1, 10^5}] // AbsoluteTiming Out[21]= {5.987342,10724527832} I ...
328 views

### Lookup construction using data matrix and Reap/Sow versus AppendTo`s

I am a user of MMA9 and made my own kind of Lookup, which is now a standard command in Version 10. In my program there is a section in which by means of a StringReplace[ ]-command containing a lot of ...
314 views

### Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
141 views

### Speed up replacement using Rule Dispatch Associtation

I knew that this has asked many times, but I hope there is something more could be done to speed this up. The expression kappa is here. ...
514 views

### Fast matrix multiplication in MMA and GPU

Matlab multiplies two 3000by3000 matrix around 0.18s faster than MMA. While for just a few matrix multiplications the speed difference is not important, it becomes crucial when I want to do those ...
175 views

This a computational challenge, to find an efficient algorithm to discover a quadruple $(n,n+1,n+2,n+3)$ with the same sum of prime factors as described in the MO question, "Ruth-Aaron triples, etc." ...
283 views

### Max element of a list with a custom ordering function

I need a function to find max element of a list according to some custom ordering function, assuming that the function implements a total order (elements being compared might not even be numbers). ...
495 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 ...
737 views

### Rendering thousands of points

I am trying to render an image with some 120,000 Points. Technically it's just 10,000 points, plus their reflection, plus 5 rotations of both of those sets, but I'm ...
151 views

### How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
107 views

### How to speed up execution of this function?

How can I speed up the execution of following function, specifically for larger values of n? ...
77 views

404 views

### Speed up calculation

First of all thanks to: rm -rf, Mr.Wizard, Simon Woods, Pickett, Piotr Wendykier, Mac, Yves Klett, belisarius, halirutan, bill s, nikie, wxffles, ... Everybody of you helped me (a mathematica ...
142 views

### Why is C-compiled (but not WVM-compiled) code so slow in Manipulate?

Here is a small section of code from this SE question which computes the real part of the dilogarithm (the upper limit of the sum is increased for demonstration purposes): ...
243 views

### Animate skips frames and hard to control speed.

I browsed similar questions related to Animate jerkiness like here, but haven't found the right options to control animation rate while also displaying all frames: ...
138 views

### How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
70 views

### Extend a function to all polynomials ( just 2 variables) when one knows its values on monomials

I need your help to make my code faster. I have a formula for computing a value from any monomial $x^i y^j$, say formular1[i_,j_]:=(Gamma[i]/Gamm[j] ). It is just ...
113 views

### How do I understand this big difference in speed:

A friend of mine found a huge difference in runtime speed between these two ...
272 views

### A bug in Commonest in version 10

Bug introduced in 10.0.0 and fixed in 10.0.2 m_goldberg demonstrated that in Mathematica 10 Commonest does not behave as the documentation indicates that it will....
399 views

### Help at speeding up simplification/nested symbolic integration

I have the following problem: I want to compute an integral of the form $$\int\limits_0^{t_g}\mathrm{d}t_2\int\limits_0^{t_2}\mathrm{d}t_1\left[A(t_1),A(t_2)\right],$$where $\left[B,C\right]=BC-CB$ is ...
202 views

### Use Compile to speed up evaluation

I have read, that using Compile command can speed up evaluations in mathematica. I have a mathematical expression, which I evaluate using following command: ...
134 views

### Most efficient searching algorithm in a table

I am completely new in Mathematica (and in data analysis in general) and I find it really useful, although I still do not use it properly. I have the following question related to data manipulation: ...
249 views

### Best way to create symmetric matrices with block structure and additional symmetries of the submatrices

Update: you can now skip the "My attempted solution" part and jump to "My first attempt for improvement" in the end of the question. My question is related to Best way to create symmetric matrices . ...
147 views

### How to pick the maximum of a list? Improving efficiency

I need to find the element of a list, with the highest weight. Example: ...
1k views

### For loop catastrophe

I know that Mathematica prefers a functional programming way but I still have some problems for the following example. Supposing we generate a Fibonacci sequence of 10^6 elements. NestList or FoldList ...
1k views

### Can a Trie be implemented efficiently?

What is the most space and time efficient way to implement a Trie in Mathematica? Will it be practically faster than what is natively available in appropriate cases?
695 views

### Why is StringExpression faster than RegularExpression?

Edit: as noted by Albert Retey the performance difference is only seen when sub expression extraction is performed. If this test is used below the timings are similar: ...
42 views

### Generate Degeneracies in List [duplicate]

I have a list with n entries and I would like to duplicate this list p times. In my case because of the Degeneracy of my Eigenvalues. For example I have {3,2,1} and it is five-fold-degenerate so that ...
679 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 errors/...
238 views

### Mathematica taking too long to calculate recursive function

I have been trying to plot those specific recursively defined functions p1 and q1 in Mathematica: ...
360 views

### Why does this line increase the consumed memory?

Probably this is a simple question, however I really don't understand this behavior in Mathematica. It particularly leads to a memory leak in a huge program I have to do processing of 3D images. I ...
322 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 ...
330 views

### How can I Integrate large trigonometric expressions more efficiently?

I have a requirement to integrate some large symbolic expressions containing products of trigonometric functions. A single integration is averaging 7 minutes, and I have 2628 expressions to integrate, ...
58 views

### More on performance of Sum[]

There is an interesting discussion on performance of Sum[] in this question. I actually wanted to reproduce findings from this answer. So, I entered: ...
145 views

### Apply functions to functions yields slow execution speed

I'm trying to write a function that parametrizes a curve c(t) by its arc length. Technicly I'm finished but if I plot the result for an example curve like ...
10k views

### How can I use Mathematica's graph functions to cheat at Boggle?

Boggle is a word game played with 16 dice and a 4x4 tray. This question is inspired by a Stack Overflow question about Boggle that I decided to solve using Mathematica. In addition to Mathematica, I ...
69 views

### Issuing user-defined messages takes a long time (Message is slow)

Issuing messages takes a very long time in version 9 and version 10. Can others reproduce this? Is there a fix? Update: This is slow only when using the front end, but not when running the kernel ...
60 views

### Speed optimization of Mean calculation in a previous calculated data range

I have following problem: My calculations work quite well with the shown testdata, the only problem is the speed of it. My original dataset is about 64000 datapoints, and it takes several minutes to ...
101 views

### Slowdown of Flat attributed function

I was trying to write an associative function f using the attribute Flat. ...
307 views

### Combining images with CUDA

SMALL UPDATE: This question is left as unanswered, because none of the existing answers as of yet actually use CUDA (though, whilst being very useful). 2nd Edition: To make it a bit more clear, and ...
290 views

### The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
1k views

### What is the most efficient way to map a linked list?

In order to work with lists effectively using common recursive patterns from functional programming, it's often most convenient to worked with the "linked list" representation, that looks like this: <...
3k views

### Division by zero is slow

Suppose I have two arrays of data, which I want to divide: ...
2k views

### Hardware Performance Metrics for Mathematica

Dear Mathematica users I am looking into buying a new computer and Mathematica is one of the main applications I run. To help me assess the overwhelming welter of choice out there: I'd like to know ...