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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3
votes
1answer
118 views

Randomly generate points on a van der Waals surface

I'm looking to randomly place an atom $\mathbf{A}$ onto a van der Waals surface formed by atoms $\mathbf{B}$, such that the distance between the randomly-generated atom $\mathbf{A}$ and the nearest ...
5
votes
1answer
197 views

How to compile this code?

Could somebody teach me how to compile this code? ...
3
votes
2answers
198 views

Tracing 2d coordinates by using Nearest function

In 5 digital images I have determined the 2d coordinates of detected objects. The resulting coordinate list can be downloaded from here: http://pastebin.com/7bE0CEJ5 ...
18
votes
1answer
1k views

Slow import of multigigabyte TIF image stacks

Update 6: After contacting Wolfram Technical Support, I was advised that the frame-to-frame import timing variability can be eliminated by reading in the frame stack from frame to frame with the ...
29
votes
1answer
364 views

Why is multidimensional Reverse slow?

Bug introduced in 6.0 or earlier and persisting through 10.3.1 I have found that multidimensional Reverse is ~10 times slower than exact ...
15
votes
2answers
306 views

Which elements of a large array are part of a set?

I have a large integer packed array arr. My array is multidimensional, but for simplicity let's consider 1D arrays for now. ...
6
votes
1answer
87 views

Faster square test for integers

This question was asked already in Jan '12 and the most recent answer is from Oct '12, so it's several Mathematica versions out of date. What is a faster test for whether an integer is a perfect ...
3
votes
3answers
175 views

Optimizing a series of basic matrix operations—scaling doesn't seem right with matrix size

I have a simple operation that I'd like to apply to an n×n matrix. My problem (well, one of them...) is that it runs in, say, 4 seconds for a 100×100 matrix, but it took five and a half minutes to run ...
1
vote
1answer
81 views

How to make this code involving Hypergeometric functions to run faster?

This question is followed up from this Question. I would like to thank Dr. Hintze and I_Mariusz for the comments and help. I am pretty new to mathematica ( I just learned it 4 days ago) so I would ...
1
vote
1answer
117 views

Speeding up Integrate and the numerical solution

I want to compute the drag of a plate Below is the code I am using to integrate the function ...
3
votes
1answer
110 views

Generate a 3D grid data table

I would like to generate a 3D Grid, not for displaying, but to do computations on it, so no draw functions I guess. I have a simple version of what I am thinking, however, it is terribly slow: ...
3
votes
1answer
99 views

Fast evaluation of a function in many points

I need to feed to an external program a number of points (in Complex128 format) generated from the numerical evaluation of some function, e.g. $e^{i ...
1
vote
0answers
132 views

Autocorrelation of 3D Points

I'm trying to compute the autocorrelation of a list of points $(x,y,z)$ in 3D. Can the CorrelationFunction or maybe ...
0
votes
0answers
129 views

Random generation of three-non-collinear and four-non-coplanar points in 3D space

Please, take a look to this code. How it can be improved so that the time execution becomes smaller? ...
0
votes
0answers
142 views

Manipulate for Electric Field

I'm kind of new to Mathematica but I'm getting the hang of it slowly. Anyways, I'm trying to do a project on the electric field of two particles so my professor helped me with this code (sorry in ...
6
votes
3answers
140 views

How to remove duplicate elements from two separated lists efficiently?

I have two lists of elements: indices = {Prime /@ Range[5000], Prime /@ Range[100, 300]} // Flatten; values = RandomReal[100, 3] & /@ Range[Length[indices]]; ...
3
votes
1answer
93 views

Extreme Slowdown with Fold

I am doing a finite difference model, and need to create a list recursively. For a small list, Fold is extremely fast, but when the list becomes large enough, Fold becomes extremely slow. Here is the ...
0
votes
0answers
98 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial ...
5
votes
2answers
89 views

Overlap between lists of sublists with different dimensions

I have two lists of sublists. The sublists in the first list contain three elements while the points in the second list contain four e.g.: ...
11
votes
1answer
350 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
15
votes
5answers
549 views

A quicker than outer

I need to get a matrix $\{a(x_i-x_j)\}$, where $x_i$ form a partition of an interval, $a(x)$ is a given function. I use ...
0
votes
1answer
164 views

Which platform is ideal for performance?

I have been using NDSolve, and I noticed that when you decrease the MaxStepSize, possible singularities are resolved. If I ...
6
votes
2answers
214 views

Speeding up code for lattice generation

Below is a lattice point generation code I write ...
16
votes
1answer
1k views

Numerical integration — Mathematica vs Python (w/ Scipy) performance

I'm about to tackle a problem that involves a lot of (multi-dimensional) numerical integrations and also subsequent optimizations, and so I want to make sure at least the integration step is as fast ...
1
vote
1answer
105 views

Evaluation time is always 0.23 s [closed]

Following the instructions in this documentation page, I'm setting EvaluationCompletionAction -> "Show Timing" in the option inspector so that Mathematica prints ...
7
votes
1answer
75 views

When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?

I wanted to use Mathematica to compute areas and volumes of various implicitly defined regions, so I ran a simple test case using the unit circle: ...
0
votes
0answers
79 views

Speed up the Eliminate

I have problem of eliminating some variables from a set of equations, which contain logarithmic function, in order to obtain a differential equation. These are the parameter and functions in ...
0
votes
0answers
83 views

Nestlist inside Compile

My question is a continuation of question1 and question2, but I think it may be considered as a self-contained one. I am interested to make the following code faster ...
10
votes
1answer
308 views

Using Compile to speed up Function with PermutationProduct [closed]

I have the following fairly simple routine dot involving PermutationProduct that I wish to speed up using ...
21
votes
3answers
453 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 ...
13
votes
1answer
307 views

Wiggly and imprecise animated gif output

Trying to make animated gif of zooming into famous Ford circles. With the code ...
5
votes
1answer
120 views

Why are so many built-in numerical function doesn't check its argument is packed array or not? [closed]

This question is brought by this one. Outer[Times, RandomReal[1., 1000000], {1., 2.}]; is much slower than ...
4
votes
4answers
482 views

Creating a fast random array generator

I want to create N x N array of random numbers. (N is an integer). The constraints are, each element should be between 0 to l(integer) ( here 0<= l <= N) and the sum of elements in each row ...
6
votes
1answer
155 views

Strange performance of Outer

The following takes 0.07 seconds on my laptop. list1 = RandomReal[1.,1000000]; (Outer[Times, list1, RandomReal[1., 2]];) // AbsoluteTiming But this takes 1.2 ...
1
vote
1answer
69 views

Improving strategy to solve this constrained root-finding problem

I am looking for roots of the function eqs defined below. It has $2k$ unknowns and returns a vector of $2k-1$ components. The sole purpose of the following block ...
3
votes
2answers
78 views

union several arrays of same flag(date for example) efficiently

Suppose I have several arrays from data files which look like: arrayi = {{datei1, xi11, xi21, ...}, {datei2, xi12, xi22, ...}, ..., {datein, xi1n, xi2n ,...}} ...
2
votes
0answers
91 views

Solving this system of nonlinear equations

Edit Interestingly, I realized solving my problem with $2n$ equations appeared to be more efficient than using mathematical results on the solutions to reduce the problem to $n$ equations (the $n$ ...
7
votes
1answer
204 views

How to terminate early a functional computation

Problem description: Given a list $A=\{1,2,0,7,0,-1,2,6,\ldots\}$ and a list $B=\{0,7,0\}$ write a program that determines whether $B$ appears in $A$ or not. Note: the order of $B$'s items does ...
2
votes
1answer
106 views
3
votes
1answer
148 views

default RGB coloring

I am playing with some basic genetic algorithms to recreate input images by transparent plane figures (similar like here:). Everything would work great but the speed is terrible. I was looking for a ...
4
votes
0answers
146 views

strange timing result of LinearAlgebra`BLAS` in mathematica? [closed]

BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context ...
0
votes
0answers
45 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...
1
vote
0answers
163 views

Exceeding time constraint of 300 seconds when taking coefficients of some expressions from schur polynomial [closed]

I have written a code that takes coefficients of some expressions from schur function, but it seems to take a lot of time, and Mathematica will stop after 300 seconds saying that it's over the time ...
6
votes
1answer
209 views

My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page [http://young.physics.ucsc.edu/115/]{http://young.physics.ucsc.edu/115/}. I've tried: ...
1
vote
2answers
97 views

Finding matrix given null space

Suppose I input a very large $n$ integer vectors and I wish to compute the matrix whose nullspace is spanned uniquely by these vectors. Is there an appropriate command/module to do this using ...
4
votes
2answers
146 views

How to be more efficient/faster with this MatrixExp-vector multiplication?

I am looking for expertise that helps to improve speed of the code below. First, a little bit of background: There is some system of differential equations $\dot{\vec{m}}(t)=S(t)\vec{m}(t)$. In order ...
0
votes
1answer
71 views

Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily ...
2
votes
0answers
44 views

Performance of different Count patterns

The two pieces of code below are functionally equivalent, and I would have expected similar performance. (The only difference between the two is the form of the pattern used.) But the second piece of ...