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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15
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2answers
2k 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
1answer
486 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
2answers
151 views

HDF5 importing large arrays

I have some computations that output a 300,000,000 element array of long unsigned ints, so about 2.4GB, in an h5 file. Mathematica handles files south of 2GB fine, albeit taking very long to import ...
15
votes
1answer
343 views

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

Bug introduced in 9.0.0 and fixed in 10.0.0 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. ...
15
votes
1answer
330 views

Why does this line increase the consumed memory?

Probably this is a simple question, however I really don't understand this behavior in Mathematica. It particularly leads to a memory leak in a huge program I have to do processing of 3D images. I ...
15
votes
2answers
401 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
176 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
9answers
631 views

Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
14
votes
6answers
1k 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
3answers
614 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
395 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
14
votes
3answers
635 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
3answers
448 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
457 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
866 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
1answer
193 views

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

Problem remains in 10.1 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: ...
14
votes
2answers
458 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
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
896 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
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
351 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
168 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
1answer
362 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 ...
13
votes
1answer
530 views

Making a “cached” version of `Manipulate[]`?

I have a function that is a bit too slow for Manipulate[]. Right now I plan to cache outputs outside the manipulation and just have the manipulator select among ...
13
votes
0answers
195 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 ...
12
votes
3answers
311 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
5answers
455 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
900 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
4answers
508 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 ...
12
votes
3answers
455 views

With versus Function

I've seen people compare Block with Module and With as scoping constructs, and try to figure ...
12
votes
3answers
354 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
395 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
4k 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
769 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: ...
12
votes
3answers
885 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 ...
12
votes
3answers
537 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? ...
12
votes
1answer
264 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. ...
12
votes
1answer
342 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 ...
12
votes
2answers
197 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 ...
12
votes
1answer
230 views

The efficiency compare between Flatten[#, 1] & and Join @@ # &

Err..Often I met the situation to join lists at the first level and I used to just Flatten[#, 1] &@ them. However, I found(when glance over the mathematica.stackexchange.com) someone else prefer ...
12
votes
1answer
421 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 ...
12
votes
2answers
300 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
1answer
221 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 ...
11
votes
6answers
570 views

How to find all the positions of max value of a list efficiently?

For Example, list=RandomInteger[{1,100},2000]. Yes,I know Position[list,Max[list]] can do. But it's based on pattern ...
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
398 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. ...
11
votes
4answers
566 views

How to write this without For loop

Suppose I have a few lists of numbers and want to exponentiate element-wise, then sum up everything into a polynomial. For example, if I have ...
11
votes
5answers
412 views

Most efficient way of making pair list from a list

I have a bunch of datasets which looks like: 3 7 1 6 5 8 2 4 1 2 8 1 5 2 5 ... and I need to make a list of pairs such that the first element makes a pair with ...
11
votes
2answers
571 views

Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...