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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0
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0answers
42 views

Finding minima of a function: Ways to speed up the code [duplicate]

I am quite new to Mathematica. I tried to calculate all minima of the function of interest as follows: ...
0
votes
1answer
66 views
3
votes
1answer
152 views

How can I optimize the search between two lists, one that is changing length?

I'm trying to identify unique arrays by comparing two lists, one which is growing in length. The number of elements in the list grows as 2^n^2, where ...
3
votes
2answers
133 views

Summing matrix products

I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and ...
34
votes
5answers
3k views

Is it possible to speed up ContourPlot on multi-core machines?

It is not very difficult to face a function for which ContourPlot works too slow. And it seems natural that this function can be parallelized well. Anyway, naive ...
0
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0answers
87 views

NDSolve with default settings solves much faster than classic Runge-Kutta 4

NDSolve with default parameters takes 0.25 s for the first run. With Runge Kutta 4 specified, it takes about 4.6 s, ...
3
votes
0answers
53 views

EvaluationMonitor slows down NDSolve considerably

Hi guys I'm solving a nonlinear system of ODEs with NDSolve. Since the dimension of the system ranges from 2700 to 20000 equations, depending on the parameters, the time required to solve the entire ...
4
votes
0answers
38 views

Is there a clean way to parallelize multi-index tables?

The documentation of ParallelTable indicates that if you want to parallelize the evaluation of a table of more than one dimension, such as ...
5
votes
0answers
71 views

Improve recursive function (memoization)

These days I am trying to rewrite the following recursive function, in order to gain some speed. It is crucial because I end up using 4-5 similar functions, and I need to decrease execution time. ...
9
votes
6answers
490 views

Efficiently finding the positions of a large list of targets in another, even larger list

I have a big list. It contains nearly 60,000 sub-lists. It's structured like bigList = {{x1,y1,z1},{x2,y2,z2},{x3,y3,z3},.....,{x60000,y60000,z60000}}; I have ...
2
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0answers
185 views

Best approach for 'manual' common subexpression elimination

I have working code, but am looking for ways to make it more elegant. I have a fairly large expression with plenty of repetition and structure. A shortened toy example is ...
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 ...
9
votes
1answer
104 views

What are the main differences between RawArray and PackedArray?

What I know: PackedArray is documented (to some extent) in "Developer Utilities Package", RawArray is just mentioned in ...
2
votes
1answer
66 views

Code optimizations with functions inside Module

I wrote a small code by using functions inside Module: ...
21
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0answers
346 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 ...
-3
votes
1answer
177 views

How to turn off depth sorting of 3D curves for Manipulate?

Is there a way to turn off the default depth sorting of curves in a 3D output of several complicated curves ? Currently, I suspect that depth sorting has a very strong impact on performances on my ...
5
votes
3answers
125 views

Lazy form of Tuples/Outer to loop over list of lists

This is less a question and more asking if someone has implemented this already, with more skill. I need to perform the Outer-like generalized outer product of a ...
0
votes
0answers
25 views

Smartest way to choose number of kernels? Which kernels are launched by `LaunchKernels`? [on hold]

Suppose you have something like below. hermMat is some hermitian matrix of dimensions {dim,dim} and ...
2
votes
0answers
63 views

Data acquisition from TCP socket

At last (since 10.3) we have straightforward/documented access to TCP sockets. It's been a long wait. So far there is very little discussion of the new feature. Although some older posts are still ...
0
votes
1answer
262 views

Speed up RegionPlot

I want to plot a system of equalities and inequalities. I used a combination of ImplicitRegion and RegionPlot (since RegionPlot cannot plot lines or points). But this method is very slow than using ...
4
votes
3answers
128 views

Indexing all elements of permutations $S_n$

I have this Table that gives all elements of $S_n$, I would like to know how to improve efficiency. ...
0
votes
0answers
32 views

Solving for limit of integration with a piecewise function (FindRoot vs NSolve) [duplicate]

I am trying to solve for the limits of integration using a piecewise function. I'm doing this in a loop over a list of data, mostly because I'm not well-versed enough in Mathematica to make this a ...
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: ...
6
votes
1answer
140 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
3
votes
1answer
133 views

Why does Compile not make my function faster?

I need to speed up a large program that repeatedly calls the module below (I've not trimmed the code for this question to ensure there is enough calculation to show a speed improvement.) The obvious ...
5
votes
2answers
241 views

Speed-up the computation of this sum of small matrices

Given a matrix mat with a large number of rows (a few thousands) and a few columns (between 2 and 10), I'd like to compute the sum of the "small" matrices obtained ...
10
votes
2answers
225 views

Primes Race (Mathematica Efficiency)

I am currently working with a paper that deals with this concept of Prime Races. You essentially create a large list of prime numbers and then split that list into two teams. You are assigned to ...
10
votes
0answers
163 views

Slow JoinAcross performance

Bug introduced in 10.3 I am using JoinAcross to combine two datasets, where the key is an Integer. ...
3
votes
3answers
97 views

Counting runs in bits, along with their starts and lengths, in functional style

Here is some code to visualize Project Euler Problem 502. The code scans for runs of bits in the binary representation of an integer, and outputs the beginning position of each run and the length of ...
14
votes
6answers
405 views

Given a large binary matrix, find the largest submatrix containing non-zero elements

I'm looking for a way to reduce a binary matrix containing zeros at some positions into a matrix that contains no zeros by deleting rows and columns of the original matrix until only non-zero values ...
9
votes
2answers
568 views

Improve speed in this tree - memoization won't suffice

I have two functions, one of which calls the other. I need to do some calculations but I was unable to optimize my code to do it efficiently. In search I came across the memoization technique, which ...
1
vote
1answer
150 views

Problem with convergence of limiting value in Manipulate

I created a nice Manipulate box of the magnetic field outside and inside a spherical shell placed in an homogeneous magnetic field. The code is working great, but it has a problem at a limiting ...
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 ...
1
vote
1answer
83 views

efficient element wise multiplication of SparseArray vector and matrix

I have a large SparseArray $P$ of dimensions $\{d,d\}$ and I want to multiply a vector (also a SparseArray) $v$ of length $d$ ...
1
vote
1answer
97 views

Computing the coefficients for Gaussian integral

I wrote a small script to find the Gaussian integral points and weights: ...
5
votes
2answers
230 views

How to improve efficiency when classifying lists according to certain laws

I have a function that generates lists: f[n_] := Join @@ Permutations /@ PadLeft@IntegerPartitions[n]; For example f[3] ...
24
votes
1answer
667 views

How to work with Experimental`NumericalFunction?

This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?" Oleksandr R. correctly states in the comment: A ...
2
votes
1answer
212 views

Error with FindMinimum. The Message is FindMinimum::cnpcons

I want to run a rather demanding check of feasibility. I have 3565 non-negativity constraints for my variables, and one that makes them sum to a certain budget they shall not surpass. I also have ...
6
votes
2answers
367 views

Memory management and speed for Fast GCD

Let's say that we have some $300\,\text{K}$ digits (arbitrary function) and want to trial factor with $100{,}000{,}000$ first prime numbers. ...
16
votes
4answers
613 views

How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
3
votes
0answers
42 views

Prepending a sequence with zeros gives `FindGeneratingFunction` hard time

Asking for FindGeneratingFunction[{1, 3, 11, 43, 171, 683, 2731, 10923, 43691, 174763}, t] gives the answer (namely ...
10
votes
2answers
258 views

What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
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 ...
11
votes
1answer
98 views

Speed up Dynamic for graphical interface

I am trying to create a user interface where I can click on certain points in a set of data and save them into a list that can be used later in my code. The problem is it is currently sluggish. Is ...
1
vote
1answer
35 views

Customized `ParallelTable` - Automate `ParallelSubmit` - Possibly an issue with `HoldAllComplete` attribute

Related to this question and in particular its answer I am trying to wrap everything into a new parallelTab function that takes into account some cost per job, ...
9
votes
3answers
292 views

Implementation of a matrix formula

For the Bézier surface, which owns the following matrix definition: $$\begin{align*} S(u,v)&=\sum_{i=0}^m \sum_{j=0}^n P_{i,j} B_{m,i}(u) B_{n,j}(v)\\ &=\small ...
3
votes
4answers
165 views

Find the minimum positive-integer value which meet the requirement

If the equation is Mod[515 Sum[10^(3 d), {d, 0, n}], 53] == 0 Then I can get the minimum positive-integer value of n. ...
0
votes
1answer
69 views

Slow sum computation

I'm doing a simple OLS regression and I strikes my attention that this very simple computation takes several seconds to perform in Mathematica ...