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
279 views

How can this DivisorSigma code be made fast?

Since Project Euler problems are now fair game for questions I have a question of my own. A certain problem* states: For a positive integer n, let σ2(n) be the sum of the squares of its ...
9
votes
2answers
305 views

Complement on pre-sorted lists

Is there any way to instruct Complement to skip the sorting part? If the answer is no (likely), the next question would be: how can I remove from a sorted list ...
6
votes
2answers
166 views

Speed and the MapThread function

Can anyone help explain why MapThread is so slow in this simple case? ...
5
votes
2answers
144 views

Speed up image coloring with ReplaceImageValue

I have about 200000 rgb-images of such format (2160*577 pixels): I want to colorize in each image some parts in white color: ...
2
votes
0answers
87 views

When does Mathematica automatically use dispatch tables for function evaluation? [closed]

I've read the documentation for Dispatch, and it says: Lists of rules produced by assignments made with = and := are automatically optimized with dispatch ...
10
votes
1answer
670 views

Modular arithmetic - efficiently calculating the remainders of factorials

When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code. ...
2
votes
1answer
149 views

How to determine whether an expression can act as a “good” function?

It's not easy to see whether an expression can act as a "good" function. A good function refers to an operater that transforms symbolic entities like 1+x^2 or ...
11
votes
5answers
412 views

Most efficient way of making pair list from a list

I have a bunch of datasets which looks like: 3 7 1 6 5 8 2 4 1 2 8 1 5 2 5 ... and I need to make a list of pairs such that the first element makes a pair with ...
16
votes
2answers
290 views

How to improve performance of BesselJ to the level of GSL?

Consider the following code: zs = N /@ Range[0, 12, 10^-5]; AbsoluteTiming[bessels = BesselJ[1, #] & /@ zs;] Length@zs I've tried to measure only computation ...
1
vote
1answer
59 views

How to perform multi-columns selection and/or !MemberQ on large lists with speed?

This question (2 subquestions) is connected to How to speed up Select with MemberQ for large lists? Q1: I would like to have an alternate version of the form below to do a multi-columns selection on ...
19
votes
1answer
355 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: ...
9
votes
2answers
224 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 ...
1
vote
0answers
54 views

Efficient way for solving a matrix equation

I am looking for a more effcient method to perform the following analysis. I did my best, but running the following code on my machine takes 9.766s. I need to perform this analysis several times. ...
4
votes
3answers
2k views

Definite integral takes a very long time

I'm trying to integrate the following function: $$r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}$$ where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
1
vote
2answers
120 views

Slow program- Mathematica shuts down

I've been trying to draw dynamic pictures of level sets of certain polynomials. The code right now looks like that : ...
5
votes
2answers
124 views

How to speed up Select with MemberQ for large lists?

I have two large lists: list1 and list2. I would like to select elements of list1 only if they appear in list2. Since the list1 has dimensions of (335000, 2) and list2 : (122000, 4), it's taking a ...
6
votes
1answer
91 views

SameQ for unsorted lists

I have to compare two or more lists and check if they are the same, but their elements can be in different position. For instance ...
2
votes
1answer
96 views

Compiling a summation

I have a sum over Legendre polynomials which I'm trying to speed up. I've come across the suggestion of using Compile to speed up code in previous answers around ...
6
votes
0answers
100 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
5
votes
4answers
638 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
2
votes
3answers
150 views

Efficient matrix multiplication

I have a list of vectors vecs = {vec1, vec2, ..., vecN} where veci is a list with length $N$. Now I have a matrix $N\times N$ ...
4
votes
1answer
120 views

StreamPlot slow in version 10

In version, 10 StreamPlot seems to calculate many more points along each streamline than necessary, compared to version 7. For example, from Mathematica ...
13
votes
0answers
195 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 ...
1
vote
1answer
79 views

Apply NonlinearModelFit to an image

I have several images (in FITS format), which I want to fit with a 2D-Gaussian distribution. The problem is that NonlinearModelFit expects data in the form of a ...
8
votes
2answers
225 views

How to read off coefficients of tensor-like expression in a speedy way?

I am considering identities involving t[a, b, c, d, ...], where number of indices is fixed. t has the cyclic property so that ...
5
votes
1answer
120 views

Reap, Sow with Parallelize: bad performance, why?

I have a question about the performance of Reap and Sow with Parallelize. I am aware of the following questions How to collect result continuously (interruptible calculation) when running parallel ...
4
votes
0answers
72 views

How to perform Bayesian optimization with Mathematica?

Does Mathematica have any Bayesian optimization methods for learning hyper-parameters? Practical Bayesian Optimization of Machine Learning Algorithms Jasper Snoek, Hugo Larochelle and Ryan P. ...
5
votes
1answer
110 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 ...
6
votes
3answers
176 views

Speed up derivative evaluation

I'm trying to calculate the normal vectors and the tangent vectors at the discrete points of a suface. For example: ...
16
votes
1answer
460 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 ...
3
votes
1answer
166 views

How to further accelerate arithmetic with Fermat Pseudoprime and Fibonacci number

I've been working on this all night, and I have made this go pretty fast, compared to my first iteration of the program, but now I'm out of ideas. I'm trying to write a program to test (by good ...
4
votes
2answers
248 views

Why does having many Print statements slow down my code?

I have a code that I need to debug. I have put a Print[] into it that should give about 10^4 prints for table entries. I know that 10^4 is large, and this exposes ...
1
vote
1answer
130 views

Making ReplaceAll faster

I have a list of functions ncalc that is calculated by ...
10
votes
1answer
293 views

Drop selection of columns from a ragged array

I have an application where I need to drop some arbitrary list of columns from a ragged array (where of course the shortest array rows have at least all the specified columns). E.g., given a ragged ...
5
votes
1answer
155 views

Force Dispatch to generate dispatch tables

Dispatch creates hash tables only for lists of length larger than 3. Is there any way to force MMA to create hash tables even for lists of length smaller than 4? ...
17
votes
0answers
231 views

Can code optimize code?

Are there functions, programs or packages that deal with optimizing mathematica code i.e. re-writing ineffecive or convoluted code. -This question has haunted me since I joined SE. The background for ...
1
vote
0answers
54 views

Fast construction and reshaping of large tensors

I'm trying to construct a large matrix which is derived from some higher rank tensor (the rank of interest to me changes case by case, so it needs to be a general method). Currently, the process of ...
7
votes
2answers
327 views

Using a given colour table with Image?

Context I would like to represent large images with a given colour table. Now, if I use Image ...
14
votes
1answer
193 views

Major slowdown when using a ColorFunction with more than one named scheme

Problem remains in 10.1 Earlier Kuba noted a major slowdown with code Simon Woods posted. Here is a simplified example. First a color function using two different named gradient schemes: ...
25
votes
0answers
405 views

What Mathematica features and idioms have $n^2$ complexity or worse

Here are a few: AppendTo[data, elem], Sort[data, test], in some cases use of ___ (as ...
4
votes
1answer
90 views

How to create fast functions based on units?

Using units is a good means for rapidly developing code, since it provides some error control. Hovewer, using Mathamatica functions containing units appears to be copmutationally inefficient. ...
11
votes
6answers
569 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 ...
0
votes
0answers
74 views

NIntegrate gives message NIntegrate::vars:

As seen in the code below, I initially constructed a list of functions of two variables ζ and t0. These functions are pure ...
1
vote
0answers
61 views

Orthogonality relations of Hermite polynomials

The Hermite polynomials are orthogonal. $$ \int_{-\infty}^\infty H_m(x) H_n(x) e^{-x^2}\, \mathrm{d}x = \sqrt{ \pi} 2^n n! \delta_{nm} $$ Does Mathematica not use this relationship? Because running ...
14
votes
3answers
614 views

Why is calling Dot with many arguments so inefficient?

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