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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33
votes
5answers
8k views

Finding Local Minima / Maxima in Noisy Data

I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
17
votes
2answers
485 views

How to create internally optimized expression for computing with high WorkingPrecision?

I have large dataset and need to fit rather complicated function on it with different values of one of its parameters (this parameter must be fixed in every fit). I use the ...
13
votes
6answers
998 views

Efficient conditional Mean[] on a large data set

Consider a list, AK6, that has 382 sublists of length varying from 2500 to 3000. Each "subsublist" is as such : ...
13
votes
3answers
683 views

Considerations when determining efficiency of Mathematica code

I have two segments of code that do the same thing and I want to determine the which is more efficient. What are the considerations when determining efficiency of Mathematica code? Correctness/...
27
votes
2answers
626 views

Why is Query so much slower than Part?

Time for another of these(1),(2) as yet another new-in-10 function appears to have poor performance compared to older alternatives. This time: Query appears to be ...
13
votes
3answers
1k views

Function does not compile with Greater in it

I have to speed up a matrix-calculation and would like to use Compile for it, though it fails and produces an unknown error message: ...
12
votes
3answers
346 views

Memoization of Rounded inputs

Memoization is a technique for improving performance by having a function remember its previous arguments. For example, f[x_]:=f[x]=mySlowFunction[x] will be ...
11
votes
2answers
686 views

Speeding up construction of simple tridiagonal matrix

I have the following code to construct a tridiagonal matrix: ...
10
votes
1answer
347 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 ...
9
votes
3answers
402 views

Faster Alternatives to DateDifference

I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following: Input: A time/date specified by <...
7
votes
2answers
393 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 ...
9
votes
4answers
537 views

Plotting the components of a function that returns a list in different colors without redundant evaluations of the function

I have a function f which takes a number as input, and returns a list of numbers (the length of the list is constant). f is hard ...
4
votes
2answers
229 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 ...
40
votes
10answers
2k views

Happy 2K prime question

This being the Q number 2K in the site, and this being the day we got the confirmation of mathematica.se graduating soon, I think a celebration question is in order. So... What is the fastest way to ...
44
votes
2answers
3k views

Benchmarking Mathematica performance on the Raspberry Pi

It is not surprising that Mathematica on the Raspberry Pi is slow and clunky. In Stephen Wolfram's words, the command line is "quite zippy" but the notebook interface is "a trifle sluggish by modern ...
18
votes
3answers
898 views

Select performance

I am fairly new to mathematica and working my way thru Paul Wellins book on Mathematica programming so experimenting with various language constructs. I was experimenting with ...
29
votes
1answer
366 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 ...
22
votes
2answers
3k views

Difference between AbsoluteTiming and Timing

I need to evaluate the efficiency of my code. Therefore I would like to evaluate the time the code need for some calculations. Mathematica gives me two possibilities for this kind of evaluation: <...
17
votes
2answers
916 views

Efficiently collecting results inside a compiled function

When we don't know the number of results that will be generated, the usual way to collect results is Reap/Sow. Another ...
16
votes
1answer
656 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 ...
13
votes
3answers
483 views

With versus Function

I've seen people compare Block with Module and With as scoping constructs, and try to figure ...
8
votes
3answers
3k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
19
votes
3answers
714 views

Why is calling Dot with many arguments so inefficient?

Say I want to multiply a reasonably large list of symbolic matrices. ...
14
votes
3answers
469 views

Quick multiple selections from a list

What is the fastest way to make multiple selections from a list? Compiled methods included. For example, here are two methods for selecting a subset, compared:- ...
13
votes
2answers
840 views

Vlookup function as Excel in Mathematica

How can we create a Vlookup function, similar to what we have in Excel? So if we have a table a and another b, we could add ...
9
votes
2answers
323 views

How to avoid an expensive subset of a Manipulate computation when dependent variables have not changed?

I have a Manipulate where a portion of the calculation that ends up displayed is dependent on a subset of the Manipulate control ...
6
votes
1answer
556 views

How to speed up calculations with large number of replacement rules?

In my program I have an expression which looks like: ...
13
votes
3answers
506 views

Collatz optimization

I'm VERY new to Mathematica programming (and by new I mean two days), and was solving Project Euler question 12, which states: Which starting number, under one million, produces the longest [...
13
votes
1answer
306 views

Why does partitioning increase Dot execution speed?

I have noticed that multiplying a list of matrices can be significantly sped up by partitioning the list, calculating the product of the partitions matrices, and then multiplying the results. ...
16
votes
4answers
628 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: ...
9
votes
2answers
300 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 <...
4
votes
3answers
246 views

How to compile a diagonal array efficiently?

For example, if we use some functions defined prior to Compile, we usually have the main evaluators in the compiled codes, pointing to the definition of the ...
14
votes
1answer
733 views

Space-efficient null space of sparse array

I have a roughly 100,000 × 3,000 matrix (as a SparseArray) that I'd like to find the kernel (null space) of. It has about 500,000 nonzero entries, all -1 or 1. ...
10
votes
1answer
384 views

Mathematica9: NDSolve slows down after repeated calls

I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, slows down considerably after some time. Apparently, the problem is NDSolve itself and it seems to be related to ...
9
votes
2answers
371 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 ...
4
votes
1answer
724 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 ...
2
votes
2answers
361 views

NIntegrate over a list of functions

This question is the result of these other two questions. Question 1 and 2. I thought it would be better to ask a new question rather than deleting previous one. I think When ...
9
votes
2answers
288 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 ...
4
votes
3answers
555 views

SparseArray row operations

Given a large (very) sparse matrix, A, how can I efficiently "operate" on only the nonzeros in a given row? For example: For each row in A, generate a list of column indices that have a magnitude (...
4
votes
1answer
231 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 ...
2
votes
3answers
379 views

Re-arranging / selecting of a data table very slow in For loop [duplicate]

My task is quite simple; I have a table of data like M = {{1,2}, {1,3}, {3,4}, {5,1}, {6,9}, {6,8}, {6,1}}; so the table is sorted with respect to the first ...
18
votes
1answer
2k views

Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
19
votes
1answer
644 views

How can I effectively performance-profile Dynamics?

How to optimize performance-wise a complex dynamic expression (like a GUI) with lots of dynamically updated components, which require different update-frequencies? I was hesitant to ask this question ...
30
votes
1answer
405 views

Exporting extremely large images; arrays generated via TensorProduct use 5 times as much RAM as expected?

I am generating plots of the roots of certain classes of polynomials, in the spirit of the multicolored visuals on the Wiki page on algebraic numbers. I've thus far been able to make some extremely ...
20
votes
1answer
499 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
20
votes
5answers
4k views

Best way to create symmetric matrices

From time to time I need to generate symmetric matrices with relatively expensive cost of element evaluation. Most frequently these are Gram matrices where elements are $L_2$ dot products. Here are ...
19
votes
1answer
1k views

Faster way to compute the distance from a point to a surface in 3D

I am trying to compute the shortest distance between a point and a triangle in 3D ...
19
votes
1answer
452 views

Faster binary Hamming weight for big integers?

While working on an answer to Count the sequences in an array I found that DigitCount was the bottleneck in my code when used as ...
26
votes
1answer
3k views

Finding long strings of identical digits in transcendental numbers

Introduction Describing the three main streams of present-day mathematical philosophy (formalism, Platonism and intuitionism) in a well-known book, The Emperor's New Mind, R. Penrose says: ...it ...
25
votes
0answers
573 views

Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...