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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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 ...
4
votes
2answers
114 views

Factor out invariant code from Plot

Given a simple Gaussian kernel UnscaledKernel[a_, b_, sigma_] := Exp[-(((a - b)/sigma).((a - b)/sigma))/2] and un-normalized smoothing function ...
4
votes
1answer
202 views

How to speed up calculation of this equation (FindRoot)

I have come up with the following functions, and I need to calculate a value, in order to have a condition valid. In my problem, all data are given, and I need to calculate variable l. I am using ...
4
votes
1answer
353 views

Very slow mathematica finite differences

I have a simple code which solves an equation by an explicit method (FTCS). It takes mathematica several minutes (mathematica 10.0.2) to finish the calculation while the same code in Fortran runs less ...
4
votes
2answers
230 views

Finding large Collatz Sequences, trying to improve speed

Background: I am already very much in love with Mathematica but I am also a novice. So far I have only gathered experience in procedural programming in Python. Generally speaking I am trying to ...
4
votes
2answers
200 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 ...
4
votes
2answers
233 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
2answers
196 views

Time-efficient creation of matrix

I have expressions like xx1=FF[1, 1] GG[1, 1] + FF[1, 1] GG[2, 2] + FF[2, 2] GG[2, 2] xx2=2*FF[1, 2] GG[1, 1] + FF[1, 1] GG[1, 2] + FF[2, 2] GG[2, 2] and I want ...
4
votes
2answers
1k views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
4
votes
1answer
155 views

Why is this code in functional style is slower than procedural style?

I know that in Mathematica a functional programming style is often more efficient than procedural style programming using For loops. But the code shown below seems ...
4
votes
2answers
203 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
4
votes
2answers
218 views

Elegant way to partition list to be faster than `ParallelTable` (using `ParallelSubmit`), or some alternative?

Suppose you have a function fun[x_] := (Pause[.05*x]; x^2); of which you know that its evaluation time increases with its argument - in this case obviously ...
4
votes
1answer
237 views

Calculate the covariance of a large matrix

I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ...
4
votes
5answers
298 views

Can I generate a “piecewise” list from a list in a fast and elegant way?

Suppose we have a number list a: n = 1000000; a = RandomReal[{0, 1}, {n}]; We want to generate a list ...
4
votes
2answers
310 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 ...
4
votes
2answers
1k views

Why is my animation so slow?

I have an animated plot of the kind ...
4
votes
2answers
102 views

Want Manipulate to be low resolution enough to render fast but no so low resolution that it is useless

When using Manipulate to graph a simple surface (sum of 2 sine waves) with Plot3D, setting PerformanceGoal->"Quality" makes it take about 1/3 second to render, while "Speed" sets it at such a low ...
4
votes
2answers
108 views

How can I make this code to count Hamiltonian paths faster?

I have this very basic code to count Hamiltonian paths in a graph: ...
4
votes
1answer
190 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
4answers
465 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 ...
4
votes
2answers
524 views

Colorize Grayscale Image

I have a grayscale image that contains two objects. The grayscale pixel values can be divided into three intervals where two of them represent objects and the third represents the background. The ...
4
votes
1answer
104 views

How to increase the evaluation speed of this somewhat complicated table / matrix operation?

I'd like to calculate the following one-dimensional array: OneDimArray = Table[(Norm[Sum[ MatrixA[[i,j]]VectorB[[j]],{j,N}]])^2,{i,N}] However this takes a very ...
4
votes
2answers
109 views

Ordering and summing elements of a list based on their indexes

Suppose I have a vector. I assign to every vector index a four-element array, in such a way that index i corresponds to ...
4
votes
1answer
86 views

Speed up rendering of ContourPlot3D object

Please can you advise me how to speed up the rendering of the following two planes? When I click and drag to rotate the plot, its movement is quite jerky. Presumably it is working harder than I need ...
4
votes
1answer
168 views

Usage of Block in Compile

When is there an advantage to using Block in Compile? For instance, if I have a multiple-step code, how do I decide which ...
4
votes
1answer
108 views

Strange behavior of Mathematica regarding calculation time

Today I witnessed the following strange behavior of Mathematica, when it comes to calculation time involving larger nested lists. The following is the short example that I setup, I am sure one can ...
4
votes
1answer
83 views

Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?

I've noticed that, while ListConvolve is very fast, it becomes much slower when you use anything but the standard Times,Plus as ...
4
votes
2answers
186 views

PixelValues along a straight Line [duplicate]

UPDATE to the question I have reformulated the question in order to make it distinct from the one suggested as a duplicate: "Line Intensity Profile From Image." The key difference is that I'm ...
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 ...
4
votes
1answer
342 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: ...
4
votes
1answer
132 views

Example from Mathematica documentation (ExtremeValueDistribution) seems to be evualting “forever”

I am referring to this example at the reference page for the extreme value distribution: http://reference.wolfram.com/mathematica/ref/ExtremeValueDistribution.html#6764486 The first three commands ...
4
votes
1answer
282 views

How could I improve this Central Limit Theorem demonstration speed- and content-wise?

My purpose is to demonstrate the Central Limit theorem by assuming two custom distributions, taking some random samples, calculating their means and ploting the results. Ideally, the histograms should ...
4
votes
2answers
286 views

How can I find the lines that go through?

I have a 80 x 80 x 50 dataset. From this dataset, I get some curves. These curves are randomly seeded, by which I mean that their starting points have been chosen randomly. Below, you can find an ...
4
votes
2answers
491 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 ...
4
votes
1answer
1k views

MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...
4
votes
2answers
100 views

Efficiently strip off coefficients in front of variables?

I am working with multivariate polynomials and need a very efficient way to decompose monomials into coefficients and pure monomials. for instance consider variables ...
4
votes
1answer
129 views

Find random $n$ combinations of values with a given sum

This problem is described in the related StackOverflow question: Find all combinations of coins when given some dollar value. I would like generate a list of $n$ combinations of values that sum up to ...
4
votes
1answer
224 views

Select elements of list

I have a list of lists list={l1,l2,l3,l4,...}; and two elements e1,e2. I want to select from lists ...
4
votes
1answer
143 views

Fast way to get edge-list of graph in terms of vertex indices (not vertex names)

I am looking for the fastest way to achieve the following: Given a Graph, retrieve its edge list in terms of vertex indices (not actual vertices). For example, ...
4
votes
2answers
294 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 ...
4
votes
1answer
465 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 ...
4
votes
1answer
129 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: ...
4
votes
1answer
429 views
4
votes
2answers
137 views

Values (or positions) of array row elements within a specified number of positions from target value

I have the need to collect values from the rows of rectangular arrays of arbitrary precision integers, given a target element value and allowed "distance" (positions +/- within the row from found ...
4
votes
2answers
314 views

DynamicModule/Dynamic CheckboxBar Slow for Large Lists

I am trying to create a dynamic construct that takes a large list of expressions and allows the user to interactively select any number of entries for further manipulation. This is what I have ...
4
votes
1answer
282 views

MapThread Alternatives

I want to add two matrices, the first one containing a 2D vector at each position the other one a list of 2D vectors. The 2D vector from the first matrix should be added to each of the 2D vectors at ...
4
votes
1answer
703 views

How to do the polynomial stuff over finite fields extensions fast?

This question is raised from the problem of package FiniteFields being very slow (please, see the corresponding question): I have had an evidence that Mathematica ...
4
votes
1answer
463 views

using interpolation functions in ParallelMap

Edit I am editing the question to give a simple workable example. It is at the bottom under the heading Example. The original question is now headed withe Background. Background I am trying to ...
4
votes
5answers
125 views

How to efficiently stream words and whitespace from a large text file

I want to tokenize a large (~20 MB) file, opening it and streaming the words, but preserving the whitespace as well. Example: ...
4
votes
2answers
140 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 ...