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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22
votes
2answers
466 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 ...
14
votes
2answers
835 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 ...
12
votes
2answers
1k views

How can I efficiently “remap” an image?

Many image processing libraries like OpenCV, Intel Performance Primitives or Octave have a useful function called "remap", that takes an image, an array with X coordinates and an array with Y ...
12
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 ...
17
votes
6answers
751 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 ...
12
votes
2answers
191 views

How do you determine the optimal autocompilation length on your system

When you pack lists there is an overhead therefore packing a list with, say, 2 elements is likely to cost more than you get back in efficiency. Mathematica has default list lengths for which functions ...
11
votes
4answers
388 views

What's fastest way of defining 10^5 down values?

I want to define isGood[___] = False; isGood[#] = True & /@ list where list is a list of several million integers. ...
8
votes
1answer
726 views

Integration strategies for oscillatory multidimensional function

I am seeking to integrate a highly oscillatory, multidimensional function. I am currently using NIntegrate's QuasiMonteCarlo approach. However, this is time-consuming and, given my current resources, ...
23
votes
6answers
1k 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!]]]] ...
19
votes
3answers
444 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. ...
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 ...
12
votes
1answer
165 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: ...
10
votes
2answers
518 views

FiniteFields package is very slow. Any fast substitute for Mathematica?

I want to compute the inverse of matrix, say with dimensions $100 \times 100$, defined over a large finite field extension such as $GF(2^{120})$. I am using the package FiniteFields, but Mathematica's ...
6
votes
2answers
404 views

Is there a Break[] equivalent for short-circuiting in Table?

I am running Mathematica 7. The following is admittedly a silly example, but suppose that I have a list list whose entries are either ...
5
votes
4answers
176 views

Performance: Collapsing repeated contiguous rows & cols from a matrix

In this answer I needed to remove contiguous zero-valued cols and rows from a matrix, leaving only two of them in place, no matter what the original number was. I made up this code: ...
4
votes
2answers
167 views

How can I speed up my compiled RBF interpolating function?

Overview I have a function that acts like the Interpolation on sparse $n$-dimensional data using a simple implementation of RBF interpolation method. I want my ...
15
votes
2answers
241 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 ...
11
votes
1answer
558 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. ...
11
votes
2answers
335 views

Memory leak in FE?

A very abridged example of what was originally a major leak ...
10
votes
2answers
355 views

Why is ParallelMap way slower than Map

I recently tried to use ParallelMap instead of Map and to my surprise encountered that ...
5
votes
2answers
378 views

Variant of the cutting-stock problem in Mathematica

I'm pretty new to Mathematica and am trying to learn to solve problems in a functional way. The problem I was solving was to list the ways in which I could sum elements from a list (with repetitions), ...
12
votes
1answer
324 views

Are there rules of thumb for knowing when RandomVariate is more efficient than RandomReal?

Please consider the following: From a fresh Mathematica kernel, RandomVariate is more efficient for NormalDistribution but ...
11
votes
1answer
718 views

What is the fastest way to find an integer-valued row echelon form for a matrix with integer entries?

Let me begin by saying that this is my first post on StackExchange. I apologize in advance if I unwittingly break any of its unwritten rules of etiquette. Recently, I've been trying to understand an ...
8
votes
2answers
720 views

Why is Mathematica's expansion of expressions with square roots so slow?

Mathematica expansion of expressions with symbols isn't slow, but with square roots it is very slow. In Maple or Mupad both are fast: with square roots they both take less than a second. Here is an ...
4
votes
1answer
131 views

Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
4
votes
3answers
403 views

Improve the performance of solutions to Project Euler (#14)

Problem I have following code, when n<=10^5 it's not slow, but n>2*10^5 it's became very slow. I think maybe some temp value greater than 2^31-1, so make compile invalid. Could you give any idea ...
4
votes
2answers
198 views

Setting a lower limit on calculation time

Sometimes it can come in handy to set a lower limit for a calculation. Consider for example an animation that is generated by some infinite loop, which would run way too fast to display properly for ...
4
votes
1answer
836 views

MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...
2
votes
1answer
266 views

AbsoluteTiming affected by surrounding code

In the process of simplifying code posted for another question, I noticed AbsoluteTiming returned different results for the same code being timed, ...
1
vote
0answers
52 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 ...
1
vote
1answer
124 views

Slow evaluation of NIntegrate when used as a pure function

I asked a perhaps related question here. Here is my code in below. The goal is that to define a function which must be integrated numerically. The function itself first is calculated over different ...
24
votes
3answers
1k views

Smooth Peter de Jong attractor

Today I was playing with Peter de Jong attractor. At the bottom of the page I've linked there are beautiful examples like: My attempts are not so great: It is around 10^5 points. For more than ...
17
votes
1answer
504 views

Fast DensityPlot

Is it possible to increase the perforamce the DensityPlot? For example, let's try to plot this "flower" ...
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 ...
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 ...
12
votes
3answers
805 views

What compilers are “suitable” for CompilationTarget->“C”?

The documentation for CompilationTarget says, "if you do not have a suitable C compiler then you will not be able to set CompilationTarget to C". Well at this time, I don't have a compiler installed ...
9
votes
2answers
278 views

Manually specifying distance metric to Nearest slows down calculation

Why does manually specifying the distance metric to Nearest slow down the calculation so much? This is relevant to my previous question. I've been using ...
12
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 ...
22
votes
5answers
582 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 ...
19
votes
2answers
974 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 ...
12
votes
3answers
829 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: ...
9
votes
1answer
344 views

Speed up DensityHistogram rendering (display)

When I tried to present some pre-calculated density histograms inside Manipulate I noticed that the display of DensityHistogram is extremely slow. Here is a simple ...
7
votes
2answers
304 views

Solving variant of the knapsack/money-changing problem

I'm trying to solve a variant of the knapsack/changing money problem where I have a set of a few numbers and I'm trying to find the linear (integer) combinations of them which are close to a given ...
7
votes
1answer
275 views

Compiling Map over expression that yields a ragged array

I'm trying to speed up a function that looks in the neighborhood of each 3D point in a large dataset and finds all the points within 1 unit in each direction, x, y, z. I've started by using ...
6
votes
1answer
293 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
9
votes
2answers
155 views

Export[] performance

Consider this sequence of commands: ...
9
votes
1answer
279 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
9
votes
3answers
386 views

Why is AstronomicalData so slow?

I'm having trouble getting some pretty simple functions using AstronomicalData to perform at anywhere near the speed I need them to. For example, I have many ...
9
votes
3answers
693 views

Improve speed for calculating a recursive sequence

I want to calculate following recursive sequence: $\alpha_{0}=0,\\ \cos(\alpha_{i})=\cos(\alpha_{i-1})\cdot\cos(\beta_{i})+\sin(\alpha_{i-1})\cdot\sin(\beta_{i})\cdot\cos(\gamma_{i}).$ In ...
8
votes
5answers
891 views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...