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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14
votes
3answers
692 views

Nearest neighbor search in n-dimensions

Suppose a list of items such as: L1 = RandomReal[{0, 100}, 1000]; I need to find the position of each k-neighbor in the original list. And very quickly if ...
14
votes
5answers
3k views

Division by zero is slow

Suppose I have two arrays of data, which I want to divide: ...
14
votes
2answers
947 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
3answers
468 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
518 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
6answers
447 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 ...
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. ...
14
votes
1answer
437 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 ...
14
votes
4answers
289 views

Fast Selections Testing on Inequality

Is there a functional idiom for fast selections testing on inequality? For example, finding values from list a & b where the key is less than or equal to a value, in this case 4 or 9. An ...
14
votes
2answers
251 views

Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
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
4answers
370 views

How to evaluate the second argument of Cases only once

I'd like to find a fast but readable way to achieve the following: ...
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: ...
13
votes
3answers
505 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
2answers
372 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
4answers
528 views

Can you recommend an efficient method for finding the least integer satisfying my inequality?

I tried find the minimum make $\frac{1}{2}+\frac{1}{2+\sqrt{2}}+\frac{1}{3 +\sqrt{3}}+...+\frac{1}{n+\sqrt{n}}>15$ Following code is so slow when I use condition ...
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 ...
13
votes
3answers
543 views

Particles bouncing in a 3D box

I made this Manipulate code which shows a pack of particles randomly moving inside a box. It has a huge performance issue. What should be the best way in doing "...
13
votes
3answers
590 views

Benchmarking expressions

It often happens that I'd like to know which of two or more alternative expressions (that should evaluate to the same value) is fastest. For example, below are three ways to define a function: ...
13
votes
3answers
682 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/...
13
votes
3answers
1k 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 ...
13
votes
3answers
1k views

What is the most efficient way to map a linked list?

In order to work with lists effectively using common recursive patterns from functional programming, it's often most convenient to worked with the "linked list" representation, that looks like this: <...
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. ...
13
votes
1answer
385 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 <...
13
votes
1answer
223 views

Unexpected slowness checking for empty list?

I thought I had a firm understanding of the differences between Equal and SameQ, but this has me puzzled: ...
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 ...
13
votes
2answers
353 views

Why is NeighborhoodGraph so slow?

To get neighboring vertices I first tried: gg = GridGraph[{10, 10, 10, 10}]; VertexList[NeighborhoodGraph[gg, 1, 1]] // AbsoluteTiming {5.539308, {1, 2, 11, ...
13
votes
2answers
243 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 ...
13
votes
2answers
382 views

How to speed up the plotting of B-spline curve?

Three months ago, I asked a quesion about B-Spline basis function here, Today, I used this function to plot B-spline curve. The definition of $N_{i,p}$ ...
13
votes
1answer
310 views

Wiggly and imprecise animated gif output

Trying to make animated gif of zooming into famous Ford circles. With the code ...
13
votes
1answer
544 views

the more effective method to find 21 digits armstrong number

In recreational number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number(after Michael F. Armstrong) or a plus perfect number) is a number that is ...
13
votes
2answers
335 views

Parallelization of distinct array write access from subkernels

I'm working on an implementation of a multivariate FFT, which is (or at least should be) highly parallelizable due to the row-column-algorithm. However, i can't figure out how to implement that. The ...
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 ...
12
votes
4answers
2k views

3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me, but it is extremely slow. Does anyone have any suggestions on how I could speed ...
12
votes
5answers
475 views

How would you efficiently implement BinListsBy?

Let's say I have a list like this: data = {{21, "Alice"}, {27, "Bob"}, {22, "Charles"}, {34, "Dora"}, {75, "Eliza"}} containing ages and names of persons. What I ...
12
votes
3answers
357 views

Taking Top K Occurrences

Having millions of numbers in a list, I want to take top K occurrences. MMA Commonest is very slow so I write my own versions: <...
12
votes
5answers
433 views

Faster way to convert triangle list to edge list with no duplicates

I have a list of triangles returned by a Delaunay triangulator, in the following format: ...
12
votes
2answers
5k views

How to calculate the mode of a probability distribution

I was wondering if there is any command to get the mode of the probability distributions. Calculating manually, the mode is (alpha-1)/(alpha+beta-2) While the mean, median or variance of the beta ...
12
votes
3answers
256 views

How to implement a more efficient inverse triangular recursion?

Consider the following inverse triangular formula $$\left( \begin{array}{ccccc} & & & & N_{i-p,p}\left(u_0\right) \\ & & N_{i-2,2}\left(u_0\right) & & ...
12
votes
2answers
202 views

Faster trimming of leading/trailing zeroes in rectangular array

Given a (large) rectangular array, e.g. (small for example case): ...
12
votes
2answers
210 views

why MeanFilter is nearly 100 times slower than MovingAverage for 1D array?

I used to average over my data with MeanFilter before I learn about MovingAverage and thought that these two functions are similar except that MeanFilter is more powerful for its ability to deal with ...
12
votes
2answers
645 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 ...
12
votes
2answers
305 views

Efficient conversion between two partition representations

I have a list of distinct expressions. We can represent a partitioning of list in two ways: As a list of sublists ...
12
votes
3answers
577 views

Riffle and Partition

At some point I noticed that I was using Riffle and Partition together a lot. I would do things like ...
12
votes
1answer
1k views

How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
12
votes
1answer
233 views

Choosing among different function definitions without sacrificing speed

I'm working on some code that numerically integrates a function, let's call it G, which calls another function, F, that can be ...
12
votes
2answers
334 views

How to make geometric intersection faster for geographic borders?

I have developed a solution to identify geographic regions bordering a region in this post (94723). Can this functionality be made to execute any faster? Find which entities in a set border other ...
11
votes
4answers
641 views

In a list of points, how to efficiently delete points which are close to other points?

Consider a list of points: pts = Partition[RandomReal[1, 10000], 2]; ListPlot[pts] I'd like to delete points so that the minimum distance between two points is ...
11
votes
3answers
2k views

Speed up ordering digit code?

My goal is given an integer number to deduce if its digits increase (or remain the same) from left to right or not. Example: $1236, 123336$ are both considered numbers with increasing digits, but $...
11
votes
4answers
410 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. ...