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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5
votes
3answers
441 views

Efficiently extracting an array subset given a separate array

I have two arrays. The first array consists of tens of millions of rows and three columns with a string, a number, and a string. ...
5
votes
1answer
248 views

Can we know the background code associated with basic mathematica functions

I wanted to know how computers calculate basic functions like Sqrt so first I checked how humans do it I found that they use something called "Newton's method" that ...
4
votes
2answers
131 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
227 views

About auto-compiling and performance between Do and Fold

I was investigating how Fold could improve performance vs Do. I tested the code ...
4
votes
1answer
207 views

How do I put a Monitor into CDF?

I would like to keep track of progress of a database request in an Enterprise CDF, but it won't allow PrintTemporary or ...
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 ...
3
votes
1answer
118 views

Efficient way to perform local Otsu thresholding on image

I have images of cell nuclei that have locally varying intensity distributions. Therefore, I need a robust local threshold algorithm. LocalAdaptiveBinarize works ...
3
votes
1answer
194 views

Parallelization of the stochastic Euler scheme

I wrote a simulation to approximate the law of a stochastic differential equation via a Monte Carlo method using the stochastic Euler scheme. Then I thought, it would be a good idea to speed up ...
2
votes
1answer
68 views

Memory usage optimization for a large Association/SparseArray

Reformulating my question in simpler terms. Take two lists list1 = RandomInteger[{1, 100000000}, 25000000]; list2 = RandomReal[{1, 10}, 25000000]; Make an ...
2
votes
1answer
131 views

Performance on Binomial Deviate is slow

I hope I won't get spanked for reposting. This is related to a previous question discussed here: Performance on Multinomial Deviate is slow. but this version is simpler because it is a binomial ...
2
votes
2answers
214 views

Reducing quality of Graphics3D scene to improve performance?

ProteinData["SERPINA1", "MoleculePlot"] gives the detailed Graphics3D plot below. I'd like to make many small copies of this ...
2
votes
1answer
247 views

Manipulate executes expressions multiple times

I am using Manipulate for a rather intricate front end for data visualization. I was getting very sluggish performance and was able to boil the problem down to a ...
2
votes
1answer
151 views

How can I place gui controls inside Grid? [duplicate]

In all my apps, I am facing a problem about placing the Gui controls inside Grid. For this purpose, I wrote three functions. The first function, ...
2
votes
2answers
348 views

Combining lists with common elements efficiently [duplicate]

Possible Duplicate: Computing the equivalence classes of the symmetric transitive closure of a relation I am required to process sets consisting of 2-element subsets of integers by ...
1
vote
1answer
197 views

Using Manipulate with a control variable for selective recalculation

I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed. I've also read ...
0
votes
1answer
174 views

My Baum-Welch algorithm is very slow. Is it due to Mathematica?

I've also posted this question here, since I'm not sure which community is more adequate for this type of question. I've programmed imperatively the Baum-Welch algorithm for a 2 state hidden Markov ...
9
votes
2answers
215 views

Additive SparseArray Assembly

The goal is to assemble a SparseArray in an additive fashion. Let us assume we have a large List of indices (some will be ...
8
votes
4answers
523 views

Efficient code for the Ten True Sentences puzzle

I am trying to solve Ten True Sentences Puzzle. Take a look at the following sentences: The number of times the digit 0 appears in this puzzle is _. The number of times the digit 1 ...
8
votes
2answers
756 views

Mathematica rule substitution memory

First I present the specific programming question, and then I provide further background details. Given an expression in Mathematica, say f=3x+7y, there are two ...
7
votes
1answer
198 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
7
votes
2answers
723 views

Working with large data, pass-by-reference, compiled functions

I think I know the answer to this, but after two days of Googling, this is my last effort before going down an unwanted path... I have a function that takes lots of large data as arguments as well as ...
6
votes
3answers
173 views

How to speed up the plotting of B-spline curve?

Three months ago, I asked a quesion about B-Spline basis function here, Today, I used this function to plot B-spline curve. The definition of $N_{i,p}$ ...
5
votes
1answer
108 views

Why does a heavy background slow LocatorPane from updating, even if only the locators are Dynamic?

I'm having some trouble getting a dynamic plot to operate efficiently, and I think I've tracked down at least part of the problem to some pretty weird behaviour on the part of ...
5
votes
1answer
183 views

What is the fastest way to maintain a large set of expressions?

In my algorithm I need to maintain a set (an unordered list of distinct elements) of expressions supporting two operations: Test an expression for membership in the set Adding a new expression to ...
4
votes
1answer
71 views

Speed up the auxiliary function magicSquare when $n$ is doubly-even

Today, I saw a question about magic square. Please see here When $n$ is doubly-even.Namely, Mod[n,4]==0 ...
4
votes
0answers
129 views

Efficient Generation of Subgraphs (or, unfriend a friend a day)

NB: If you're not interested in the back-story, you could simply jump forward to the code which I'm seeking to optimize. Also, I believe this code would only work for MMA 8.0 and above. My friends ...
4
votes
1answer
148 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
1answer
1k views

Improving NDSolve speed for heavily stiff problems

Having looked around the intergoogles and Mathematica.SE, I thought I'd pose a question with a minimum working example. Here is the situation I am trying to improve: I am solving a 4th order non ...
4
votes
2answers
286 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 ...
3
votes
1answer
112 views

Making table of matrix product and efficiency

I want to make a table in which each element is a matrix product: ...
3
votes
1answer
268 views
3
votes
2answers
602 views
3
votes
3answers
216 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
votes
1answer
125 views

Optimizing a simple calculus using a list of matrices - Repeated dot product between a vector and a list of matrices [closed]

I want to make the following operation : $$ \begin{bmatrix} \dot q_1\\\dot q_2 \end{bmatrix} + \begin{bmatrix} \begin{bmatrix} q_1 & q_2 \end{bmatrix} \mathbf A_1 \begin{bmatrix} q_1\\ q_2 ...
3
votes
2answers
457 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 ...
3
votes
1answer
326 views

Why can't Mathematica parallelize this?

The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation." ...
3
votes
4answers
539 views

Faster code for specific problem

Sorry, but I need the following code much faster and I'm running out of ideas. I do appreciate any help. I post two of my fastest ideas (tab and mat), although they are not really fast. Thanks in ...
2
votes
1answer
64 views

Performance of a bootstrap - time of computation not linear with number of iterations

I'm doing a bootstrap based on this thread with the following code (file.txt here): ...
2
votes
1answer
120 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 ...
2
votes
1answer
75 views

Faster way to extract partial data from AdjacencyMatrix

I am dealing with a lot of Graph objects. One task is to obtain an Id for each of them. So I first used ...
2
votes
0answers
113 views

Significant platform-dependent efficiency when importing data?

I'm curious, as I understand that answer this way: If you are using a Linux derivative or something like cygwin on Windows, then this is an efficient solution for reading only the third field ...
1
vote
0answers
54 views

Hashing by Equals instead of SameQ

I have some numerical code involving complex numbers representing points on a plane. Some of these are equal but not identical, ie ...
1
vote
0answers
665 views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
1
vote
1answer
320 views

how to reduce the time to calculate triple integral

i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long. anyone have an idea ? ...
1
vote
2answers
239 views

What ways are there to convert an Integer to a list of digits?

How can I convert an Integer to list of numbers? For example: 781049 ==> {7, 8, 1, 0, 4, 9} What are the possible ways of ...
1
vote
1answer
258 views

Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...
0
votes
1answer
110 views

Why does initialization slow down manipulate in this case?

I'm trying to manipulate a plot of function with some parameters. The function is a long expression, so I tried to put it inside the Initialization options of ...
0
votes
1answer
654 views

ParallelTable 70 times slower on 16 cores than Table on single core

Consider these code(sorry it's messy), why the ParallelTable version is 70 times slower than the Table version? ...
0
votes
2answers
510 views

Launching remote kernels - will it help RAM needs?

Given the exasperating RAM needs of my Mathematica program, I contemplated launching remote kernels to run my Mathematica script. This is a two part question: Part 1 If I launch a remote kernel(s), ...
-1
votes
2answers
328 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...