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.

learn more… | top users | synonyms (4)

25
votes
7answers
753 views

Faster position list construction from a “take instructions” list

Take some list, e.g., {1,2,3,4,5}, and a "take instructions" list, say {1,1,2,1,1}. The latter is read as "take the first ...
25
votes
5answers
742 views

Compiling ColorFunction for faster complex phase-amplitude plots

I have gotten into the habit of plotting complex-valued functions on a plane using a color-function along the lines of ...
25
votes
4answers
1k views

How to collect result continuously (interruptible calculation) when running parallel calculations?

This is the most common pattern to compute a table of results: Table[function[p], {p, parameters}] (regardless of how it's implemented, it could be a ...
25
votes
0answers
555 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 ...
24
votes
4answers
1k views

What is the fastest way to count square-free words?

Background A word is a string of letters in an alphabet. A square-free word has no adjacent repeating substring. For example, (in the ternary alphabet of {0,1,2}) the words 00, 012121, and 0212012021 ...
24
votes
5answers
914 views

Can (compiled) matrix permanent evaluation be further sped-up?

Update III  Mathematica 10.2.0 now ships with a predefined System`Permanent function, which the PermanentCode package ...
24
votes
5answers
913 views

More efficient way of generating list of occurrence counts?

Given a list, e.g., target = {a, b, c, b, c, d, c, d, e, f, a, h, g}, I want to generate a list containing the occurrence count of the corresponding element of the ...
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 ...
24
votes
2answers
608 views

Efficiently generating 2-D Gaussian random fields on the sphere

Context A couple of years ago I posted this question for an efficient code to generate an n-D Gaussian random field (sometimes called processes in other fields of research), which has applications in ...
23
votes
6answers
2k views

efficient way to count the number of zeros at the (right) end of a very large number

If I want to count the number of zeros at the (right) end of a large number, like $12345!$, I can use something like: Length[Last[Split[IntegerDigits[12345!]]]] ...
23
votes
4answers
3k views

Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. Attempt I wrote the ...
23
votes
4answers
872 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
23
votes
3answers
2k views

Reading periodic elements from a large file

I have a large binary data file (big endian) with 100+ million "rows" of 11 elements, combination of floats and integers. This is the format: ...
23
votes
3answers
2k views

Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...
23
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
23
votes
1answer
689 views

Efficient lazy weak compositions

In Mathematica all weak k-compositions of integer n can be generated using permutations of integer partitions: ...
22
votes
2answers
2k 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: ...
22
votes
6answers
2k views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
22
votes
1answer
408 views

A fast, robust DropWhile

For reasons that have never been entirely clear to me, Mathematica has had a built-in TakeWhile function since version 6.0, but has no equivalent ...
22
votes
1answer
553 views

Total much slower in version 10

Issue introduced in version 10, fixed in 10.0.2 Compilation nowadays may give very fast functions. Here is an example for finding the sum of a list of machine numbers, just as the built-in function ...
22
votes
0answers
344 views

Why is ListPlot so slow here?

While examining How can I monitor the progress of a Plot? I was surprised to discover that in some cases ListPlot in version 10.0 and 10.1 is orders of magnitude ...
22
votes
0answers
2k views

Mathematica performance on Mac

I recently got a trial version of both Mathematica 9 and MATLAB 13a for Windows. I was stunned by the performance difference in the Windows and the Mac version. It was a simple test in matrix ...
21
votes
3answers
452 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 ...
21
votes
1answer
372 views

Progress bar for FullSimplify

Sometimes FullSimplify takes a really long time and it is not really clear if it makes sense to wait another half an hour in hopes for it to finish, or if it will ...
21
votes
2answers
410 views

Speeding up the built-in Rudin-Shapiro and Thue-Morse sequence functions

Version 10.2 introduced two well-studied sequences as functions: the (Golay-)Rudin-Shapiro sequence (RudinShapiro[]) and the (Prouhet-)Thue-Morse sequence (...
21
votes
4answers
1k views

Efficient circular buffer?

I wish to create an efficient circular buffer. That is, I wish to keep a fixed length list while appending a new value and dropping the oldest, repeatedly. As we know lists in Mathematica are ...
21
votes
2answers
1k views

Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
21
votes
1answer
420 views

Why some built-in functions are slow

I just wonder why some built-in functions are slower compared to some other ways using more than one built-in functions for doing same job. consider this example: ...
21
votes
1answer
854 views

Has this implementation of FDM touched the speed limit of Mathematica?

Still, I'll use the implementation of the 1D FDTD method (you can simply understand it as a kind of explicit finite difference scheme for the Maxwell's equation) as the example. Just for completeness, ...
21
votes
2answers
264 views
21
votes
1answer
405 views

Is there an NDSolve`ProcessEquations analog for NIntegrate?

NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving algorithm each time. This can improve ...
21
votes
0answers
348 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 ...
20
votes
3answers
2k views

Fastest way to measure Hamming distance of integers

I am looking for a fast and robust way to calculate the Hamming distance of integers. The Hamming distance of two integers is the number of matching bits in their binary representations. I expect that ...
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 ...
20
votes
2answers
1k views

Efficient way of finding shortest distance between two sets of points in mathematica

I have two sets of 3D points, say a = RandomReal[1, {10, 3}]; b = RandomReal[1, {10, 3}]; I wanna find the first N pairs that have shortest distance between the ...
20
votes
1answer
326 views

Performance of compiled functions

I am trying to find the fastest way to calculate two values where both of them are sum of different expressions. I combine both calculations in one Sum[]. I'm ...
20
votes
1answer
488 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
2answers
1k views

How to quickly calculate intersections of filled curves?

I am trying to quickly calculate the intersection of polygons with more than 6,000 points. A compiled solution would be preferable. Here is one example of the problem: ...
19
votes
5answers
485 views

Partitioning a list when the cumulative sum exceeds 1

I have a long list of say 1 million Uniform(0,1) random numbers, such as: dat = {0.71, 0.685, 0.16, 0.82, 0.73, 0.44, 0.89, 0.02, 0.47, 0.65} I want to ...
19
votes
5answers
674 views

How to delete subsets quickly?

I have some data like this: ...
19
votes
4answers
470 views

Function that caches when it returns unevaluated

How would you go about implementing a function that caches not the result but the fact that it didn't match a pattern? So that it doesn't waste time recomputing a complex time-consuming pattern ...
19
votes
4answers
581 views

Getting lengths of sublists that sum to more than one

I have a long list of numbers, and I'm interested in finding the length of each sublist that totals to more than 1, so for the list ...
19
votes
1answer
426 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 ...
19
votes
3answers
476 views

Is there a faster way to create a matrix of indices from ragged data?

I have data that is given as a list of ordered pairs mixed with scalars. The pairs can contain infinite bounds. My goal is to convert the data into an index used in future computations. ...
19
votes
1answer
639 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 ...
18
votes
3answers
879 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 ...
18
votes
5answers
2k views

How to speed up my Project Euler code

The evaluation speed of Mathematica often depresses me. It did it again when I wrote a code to solve a Project Euler problem. https://projecteuler.net/problem=206 Here's my code: ...
18
votes
3answers
699 views

Why is calling Dot with many arguments so inefficient?

Say I want to multiply a reasonably large list of symbolic matrices. ...
18
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 ...
18
votes
1answer
645 views

Use Compile to improve performance

I've recently discovered Compile as a way to optimize my code. I wrote a program to learn something new about Compile. I have a ...