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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4
votes
2answers
195 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 ...
16
votes
2answers
420 views

Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
2
votes
1answer
143 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 ...
11
votes
2answers
262 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 ...
1
vote
1answer
260 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 ...
5
votes
1answer
108 views

Number of divisors visualized with the QPochhammer function, how improve performance of code?

I have this code that originally is Jeffrey Stopple's code for the Riemann zeta function in the complex plane. Because I discovered yesterday that the number of divisors can be generated with the ...
1
vote
3answers
134 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 ...
1
vote
0answers
94 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. ...
4
votes
1answer
272 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 ...
10
votes
1answer
228 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). ...
10
votes
2answers
684 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 ...
4
votes
1answer
160 views

Ruth-Aaron quadruple challenge

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." ...
0
votes
1answer
100 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? ...
4
votes
2answers
322 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 ...
5
votes
1answer
111 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): ...
2
votes
1answer
108 views

Optimizing alphametrics code

First of all, thank you all in this great community. I have been reading a lot of threads about Mathematica optimization learning things like using Compile ...
4
votes
2answers
202 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: ...
4
votes
1answer
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 ...
0
votes
1answer
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 ...
2
votes
1answer
122 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 ...
4
votes
1answer
273 views

Mathematica 10 issue: working with Entities slows down recurrence equations [duplicate]

I was looking at the Mathematica code given at http://community.wolfram.com/groups/-/m/t/326240 where example code is given to simulate the spreading of a supposed Ebola outbreak in Nigeria: ...
0
votes
0answers
49 views

Order of evaluation when using Solve and Minimize

I have to solve numerically an integral, that ends up being more or less as follows: Solve[f[x]==a*Sum[Sin[x-i]*(f[i]-f[i-1]),{i,1,x}],f[x]] (not actual ...
4
votes
1answer
112 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: ...
3
votes
2answers
239 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 ...
3
votes
3answers
133 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: ...
2
votes
0answers
147 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 . ...
9
votes
1answer
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 ...
1
vote
1answer
54 views

Performance of Extract-Transform operations

I'm doing simple data analysis. I load some date-time data from a file, it's a simple list: ...
8
votes
0answers
109 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 ...
0
votes
1answer
72 views

Duplicate values n-times [closed]

I already asked how I can take the list {1,2,3} and get {1,1,1,2,2,2,3,3,3} out of it, adding degeneracy to the problem. So far ...
1
vote
1answer
35 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 ...
5
votes
1answer
263 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, ...
0
votes
0answers
50 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: ...
1
vote
1answer
103 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 ...
1
vote
1answer
53 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 ...
15
votes
1answer
330 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 ...
4
votes
1answer
96 views

Slowdown of Flat attributed function

I was trying to write an associative function f using the attribute Flat. ...
3
votes
1answer
104 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: ...
5
votes
3answers
259 views

The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
1
vote
1answer
115 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: ...
2
votes
1answer
81 views

How to handle Indeterminate TimeConstrain

I have to use Timeconstrained[aux] first for avoid some bigs calculation that dont need and it use a lot of time of calculate, so i can't do this. ...
0
votes
0answers
41 views

Faster way to build a specific height in a thickness plane graph? [duplicate]

Test image can be a Plot, ParametricPlot, RegionPlot, ...
5
votes
1answer
484 views

Over 30mins to generate the first eigenvector?

Is it normal for Mathematica to take over 30mins to try to compute the first eigenvector of a 100x100 matrix? The matrix is reasonably sparse - about 90% of the cells are 0s and each column sums to ...
0
votes
0answers
90 views

Improve on timing of NMinimize

I got a little performance problem with the function NMinimize (it takes mathematica approximately 10 minutes to compute the results). Here i s my sample code: ...
2
votes
1answer
137 views

Neighbourhood - Calculations

SeedRandom[0]; n = 5; (m = N @ RandomInteger[{1, 3}, {n, n}]) // MatrixForm result1 = MeanFilter[m, 1] // MatrixForm ...
14
votes
5answers
3k views

Division by zero is slow

Suppose I have two arrays of data, which I want to divide: ...
6
votes
3answers
205 views

How to get “Signature” of each element of “Permutation” output

I need to sum over all possible permutations, multiplied by the Signature of each permutation of a given list of symbols. But, I don't know how to determine the ...
2
votes
2answers
156 views

Speeding up the generation of all k-edge-coloring of a graph

A $k$-edge-coloring of a graph $G=(V,E)$ is a function from $E$ to $\{1,\ldots,k\}$, so in other words every edge of $G$ receives one of the $k$ colors available. (In particular, note that we are not ...
0
votes
0answers
70 views

Speed up numerical optimization (for plotting and solving)?

Briefly speaking, I want to plot a function PIfun[], which its value is based on numerical optimization using NMaximize. It ...