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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20
votes
1answer
340 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 ...
20
votes
4answers
851 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 ...
19
votes
6answers
1k views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
19
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 ...
19
votes
2answers
990 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 ...
19
votes
3answers
450 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
358 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 ...
19
votes
1answer
553 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
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 ...
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
4answers
413 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 ...
18
votes
1answer
260 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 ...
18
votes
1answer
396 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 ...
17
votes
6answers
752 views

Split a string at specific positions

Given a string of alphanumerical characters, how to split it simply and quickly at the center of continuous letter-substrings? Is there an elegant and fast solutions out there in the "computational ...
17
votes
1answer
1k 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 ...
17
votes
4answers
470 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 ...
17
votes
1answer
513 views

Fast DensityPlot

Is it possible to increase the perforamce the DensityPlot? For example, let's try to plot this "flower" ...
16
votes
4answers
482 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: ...
16
votes
4answers
630 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
16
votes
1answer
896 views

Slow import of multigigabyte TIF image stacks

Update 6: After contacting Wolfram Technical Support, I was advised that the frame-to-frame import timing variability can be eliminated by reading in the frame stack from frame to frame with the ...
15
votes
5answers
793 views

Iterate until condition is met

I want to find the first 5 prime numbers of the form $n^6 + 1091$. I have used this code: Timing[Select[Table[n^6 + 1091, {n, 10000}], PrimeQ, 5]] Which gives ...
15
votes
3answers
689 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 ...
15
votes
2answers
245 views

A bug in Commonest in version 10

Bug introduced in 10.0.0 and fixed in 10.0.2 m_goldberg demonstrated that in Mathematica 10 Commonest does not behave as the documentation indicates that it ...
15
votes
2answers
1k 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 ...
15
votes
1answer
389 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 ...
15
votes
2answers
1k views

Fast Spherical Linear Interpolation of list of quaternions

An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...
15
votes
2answers
744 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 ...
15
votes
1answer
599 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, ...
15
votes
2answers
397 views

Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
15
votes
1answer
453 views

Using Evaluate and Evaluated -> True in Plot

A few use cases: (1) This, as expected, returns (almost) immediately: f[x_?NumericQ] := Evaluate[(Pause[1]; x)] Plot[f[x], {x, 0, 1}] (2) This takes ...
15
votes
1answer
311 views

Adding three integer sparse matrices is very slow. Adding only two is fast

Adding more than two sparse matrices in one step in Mathematica 9 is very slow (in fact I couldn't even wait for it to finish). Here's an example. Let's generate a large sparse matrix: ...
15
votes
2answers
397 views

Is there a better way to add elements to a Graphics expression repeatedly?

Consider simple example where a set of points is generated and some are displayed. ...
15
votes
0answers
312 views

What Mathematica features and idioms have n^2 complexity or worse

Here are a few: AppendTo[data, elem], Sort[data, test], in some cases use of ___ (as ...
14
votes
6answers
966 views

Integers which are the sum of both two and three consecutive squares

This is a math problem I came across the other day: $365$ can be written as a sum of two and also three consecutive perfect squares: $365=14^2+13^2=12^2+11^2+10^2$ What is the next ...
14
votes
5answers
3k 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 ...
14
votes
3answers
421 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:- ...
14
votes
2answers
842 views

Speeding up random walk for many particles

I am trying to speed up this code for many particles to take a random walk. I'm not sure why it is so slow for such a simple task. I got a few hints from colleagues to reduce the precision of the ...
14
votes
2answers
428 views

Better way to test that a matrix is upper-triangular?

Today, I got to thinking about how to test that a matrix was upper-triangular. So I had a try at it. Algorithm $\quad \quad a_{ij}=0 $ Or $i \leq j$ $\Rightarrow$ $True$ My solution is ...
14
votes
2answers
449 views

Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
14
votes
1answer
291 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 ...
14
votes
0answers
152 views

Exp is slower for some number ranges

I get a hit on performance with the Exp function depending on the range of my inputs. for example, with: ...
14
votes
0answers
1k 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 ...
13
votes
6answers
866 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
9answers
603 views

Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
13
votes
3answers
1k views

Can Mathematica's random number generation be improved?

Performance on Random Number generation is intolerable. Whenever you need many deviates from the same distribution but with different parameters it takes forever. Here is a thread on Poisson ...
13
votes
2answers
338 views

Bad performance of LengthWhile?

A friend of mine showed me this example, it's a test comparing LengthWhile to a self-made lengthwhile written in a direct and ...
13
votes
1answer
172 views

Major slowdown when using a ColorFunction with more than one named scheme

Earlier Kuba noted a major slowdown with code Simon Woods posted. Here is a simplified example. First a color function using two different named gradient schemes: ...
13
votes
1answer
351 views

Removing calls to MainEvalute when using inlined compiled closures

This question is tightly related to the answer Shaving the last 50 ms off NMinimize. There @OleksandR shows how inlined closures can be used to eliminate calls to ...
12
votes
3answers
293 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 ...
12
votes
3answers
837 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: ...