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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5
votes
1answer
515 views

Montgomery Modular Exponentiation

I'm trying to write a Montgomery exponentiation based on this which can compete with Mathematica PowerMod. We know that PowerMod ...
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 ...
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 ...
1
vote
0answers
673 views

How can I speed up numerical integration of multidimensional integral?

I am numerically solving an integral equation that contains a double integral. I have managed to get a solution but it takes forever. I am wondering if there is a way to speed up numerical integration ...
1
vote
2answers
239 views

What ways are there to convert an Integer to a list of digits?

How can I convert an Integer to list of numbers? For example: 781049 ==> {7, 8, 1, 0, 4, 9} What are the possible ways of ...
8
votes
2answers
219 views

How to read off coefficients of tensor-like expression in a speedy way?

I am considering identities involving t[a, b, c, d, ...], where number of indices is fixed. t has the cyclic property so that ...
6
votes
1answer
321 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 ...
2
votes
2answers
266 views

Efficient code for building a big list

I would like replace the following code ...
-1
votes
1answer
341 views

Integral evaluation taking too long [closed]

When I try to evaluate the following integral, it runs for a much longer time than I think is should without producing a result. What might be the problem? Can anybody please point it out? ...
9
votes
1answer
301 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 ...
5
votes
2answers
161 views

Speed up plot of $\sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$

I'm a beginner at Mathematica. I would like to plot the following function: $${n\over2} \sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$$ However the following code is just too slow: ...
2
votes
3answers
206 views

Speeding up a simple simulation with random extractions

I wonder if anybody can help, I need a hand with a simple simulation I am writing with Mathematica (I am using version 8). Basically it creates a list (called l) with numbers from 1 to n and a random ...
2
votes
0answers
126 views

Is there documentation on the comparative performance of Mathematica functions? [duplicate]

Recently I have been solving some Project Euler problems. I find there are always several ways to do the same thing. For example, one could join two lists like this: ...
8
votes
3answers
420 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: ...
5
votes
1answer
184 views

Why is Flattening a CoefficientArray so slow?

I have a vector of $n$ degree $n$ polynomials in $(x,y,z)$, each of whose coefficients is an inhomogenous linear expression in $3 n^2$ variables. I want to write down the linear equations in these $3 ...
7
votes
4answers
234 views

Why does array packing in Table behave like this?

Consider the following example, which generate two identical arrays. Why sometimes the array is packed and sometimes it doesn't? And why they perform differently? Here the arrays are packed: ...
10
votes
1answer
665 views

Modular arithmetic - efficiently calculating the remainders of factorials

When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code. ...
16
votes
4answers
515 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: ...
3
votes
0answers
237 views

Project Euler (memory and speed issues)

Let n be a positive integer. An integer triple (a, b, c) is called a factorisation triple of n if: 1 ≤ a ≤ b ≤ c a·b·c = n. Define f(n) to be a + b + c for the factorisation triple (a, b, c) of n ...
21
votes
3answers
3k views

Fastest way to calculate matrix of pairwise distances

It is a very common problem that given a distance function $d(p_1,p_2)$ and a set of points pts, we need to construct a matrix ...
8
votes
5answers
418 views

Efficiently finding the positions of a large list of targets in another, even larger list

I have a big list. It contains nearly 60,000 sub-lists. It's structured like bigList = {{x1,y1,z1},{x2,y2,z2},{x3,y3,z3},.....,{x60000,y60000,z60000}}; I have ...
12
votes
5answers
390 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: ...
1
vote
1answer
122 views

Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
0
votes
1answer
189 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
16
votes
5answers
831 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 ...
1
vote
1answer
122 views

PDF on TransformedDistribution of two BinomialDistribution too slow

I'd been doing my own convolutions of distributions for some calculations, decided to use built-ins. With ...
7
votes
2answers
324 views

Using a given colour table with Image?

Context I would like to represent large images with a given colour table. Now, if I use Image ...
32
votes
5answers
2k views

How to efficiently find positions of duplicates?

Is there an efficient way to find the positions of the duplicates in a list? I would like the positions grouped according to duplicated elements. For instance, given ...
11
votes
3answers
685 views

Efficient implementation of a linear complexity measure of binary sequences

For a implementation of testing the quality of random number generators I implemented the NIST test suite in Mathematica based on the nice workbook by Ilja Gerhardt. However I took up the challenge ...
7
votes
2answers
335 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 ...
3
votes
1answer
198 views

EmpiricalDistribution for Gini Coefficient Runs Slow

I am repurposing code that I found in this blog post (http://datavoreconsulting.com/sports/gini-coefficients-and-the-olympic-medal-race/) to generate the Gini coefficient for other data sets I am ...
6
votes
1answer
220 views

Does pass-by-value affect the performance of function calls?

I only have a little coding experience in C, and I remember I was told that pass by reference is more efficient than pass by value since the parameters don't need to be copied. Since there is no pass ...
6
votes
2answers
404 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), ...
4
votes
1answer
457 views

A Faster way to combine two Lists of different structures into one of a different structure [duplicate]

I have the following two lists (each containing over 500,000 elements). Here is a sample: ...
2
votes
1answer
324 views

Speeding up code by avoiding repeated evaluation of a function

I want to speed up my code and I have two ideas, but I don't know how I can implement them. Here is a little part of my code, which I want to improve: ...
6
votes
2answers
500 views

CorrelationFunction for vectors

Mathematica 9 has a new CorrelationFunction. Sadly the joy does not last long, as I can't get it to work with vectors. I would like to make a velocity correlation ...
8
votes
1answer
280 views

Optimizing the performance of an algorithm

First - a bit of an introduction. If you're only interested in the code, you can skip this section. The following question is drawn from Dennis E. Shasha's Puzzling Adventures, and is listed under ...
2
votes
3answers
647 views

Selecting subsets of a list containing a specific element

I'm trying to generate all the subsets of a set containing a specific element. For example, for the set {1, 2, 3, 4}, with the specific element I want inside each subset being 4, the required answer ...
6
votes
2answers
308 views

Fastest way to test if a numerical array has complex elements

I am looking for the fastest way to test whether an n-dimensional numerical (NumericQ) array (in the ArrayQ sense) is complex or ...
9
votes
2answers
363 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way ...
4
votes
2answers
275 views

How can this DivisorSigma code be made fast?

Since Project Euler problems are now fair game for questions I have a question of my own. A certain problem* states: For a positive integer n, let σ2(n) be the sum of the squares of its ...
9
votes
4answers
1k views

Passing large list by reference

I have the following problem: I would like to control evaluation of a variable that points to a list. For example, frequently in the code I have functions of the form that are supposed to work on ...
9
votes
5answers
591 views

Counting the population of integers

Suppose that myData is a list of sublists. Each sublist has a length of one or greater and contains any number of replicates of the integers 1, 2, 3, and 4. I ...
14
votes
3answers
428 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:- ...
5
votes
4answers
179 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: ...
7
votes
2answers
999 views

Elegant way to handle columns operations

Inspired by this question from @sjdh and by my recurrent use of columns operations in database sets, I was looking for one way to make columns operations more symetric, so I can handle with matrix and ...
1
vote
0answers
791 views

Speed up Numerical Integration

EDIT: I need to evaluate a very complicated multi-dimensional Integral. The dimension of the Integral depends on a variable j. Let's make my point clear with the ...
11
votes
2answers
677 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 ...
2
votes
1answer
178 views

Understanding a slowdown associated with wrapping a set of nested Do loops with a ParallelDo expression

I have a set of set of nested Do loops that require data from three different arrays (though the position from each array is fixed per cycle of the outer Do loop). Let's call these arrays: ListA, ...