# Tagged Questions

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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### 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 ...
174 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), ...
206 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 ...
227 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 ...
141 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 ...
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### 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 ...
203 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 ...
108 views

### A simple For loop visibly slowing down. Advice to fix?

I have run into a unique problem. I am going to try and describe my code and what is happening as understandably as possible. I have a For loop that does the same set of calculations over and over ...
139 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 ...
291 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 ...
336 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 ...
270 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:- ...
124 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: ...
324 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 ...
239 views

### Vlookup function as Excel in Mathematica

How to create a Vlookup function, similar to what we have in Excel. So if we have a table a and another b, we could add columns ...
97 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, ...
144 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 ...
367 views

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### 1D Random Walk with Excluded Sites and Variable Time-Step

Here is the physical problem I would like to simulate: Consider the following variations to the 1d random walk: allow for certain, random sites to be excluded with probability 1/2. allow for the ...
201 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: ...
497 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 ...
212 views

### Efficiently extracting an array subset given a separate array

I have two arrays. The first array consists of tens of millions of rows and three columns with a string, a number, and a string. ...
191 views

### Correct way to generate large data sets (i.e.forward yield curve )

I would like to generate a set of forward yield curve matrix of size 1000 x 100. First I defined my SparseArray of 1000 x100: ...
490 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 ...
189 views

### How can I improve my code with efficient mathematica built-in functions?

I have written a module for my assignment like below. V[n + 1] = rk[x[n], y[n] ,z[n], V[n]]; vs = V[n].V[n+1]; V[n + 1] = I want to modify it with efficient ...
150 views

### Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...
909 views

### xkcdConvert routines perform slower in Mathematica 9

I am experiencing some rather large performance decreases in Mathematica version 9.0 using the xkcd-styled plotting routines. I had used the xkcdConvert code ...
405 views

### Speed optimization

I have a part of a program that I have to repeatedly call many times (about 2000 to 10000 times) ...
223 views

### How can I find the lines that go through?

I have a 80 x 80 x 50 dataset. From this dataset, I get some curves. These curves are randomly seeded, by which I mean that their starting points have been chosen randomly. Below, you can find an ...
187 views

### how can I avoid CPU waste (by master kernel) using WaitNext?

I'm using WaitNext in Mathematica for parallel processing on Mac OS X. I have 4 processors on my MacBook and LaunchKernels[] ...
376 views

### Fast Sieve Implementation

I'm going to write a code to compete in performance with NewPGen. The goal is to sieve numbers that have small factors. Mine is very slow in compare with NewPGen. Here's my code: ...
414 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 ...
138 views

### Best Parallel Kernel Configuration

I wrote a code snippet which counts prime numbers in any given interval because the built-in PrimePihas a limited bounds. ...
139 views

### FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
155 views

### How to do the polynomial stuff over finite fields extensions fast?

This question is raised from the problem of package FiniteFields being very slow (please, see the corresponding question): I have had an evidence that Mathematica ...
98 views

### Is there a faster way to compute the endpoint for a DateRange given the start, step, and length?

Say I am given a date start an increment step (possibly mixed radix) and a desired number of steps ...
288 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: ...
236 views

### Reading in Huge Text Files

I would like to read in really large text files (about 2GB) into Mathematica. The structure of the file is such that the first row and the first column are text i.e strings. Rest is all numbers. Is it ...
174 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 ...
162 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 ...
130 views

### How can I use the overhang argument to Partition to avoid using PadLeft and PadRight here?

Say I have a list of values v = {v1, v2, v3, ... }. I need to partition these values to perform operations with a sliding window (think ...
113 views

### Computing closest set of points to each point in large set — running out of memory (arrays unpacking)

I have a large set of points in 3D and I'm trying to identify all the points that lie within a certain distance of each point. Then using this data store the vector between the pairs of points. I ...
309 views

### Fast Trial Division

I'm going to write a custom Trial Division primality test. I know that PrimeQ will first try trial division and then switches to ...
194 views

### speed up iteration with conditionals plus optimize memory usage

Given list1 and list2 whose elements are vectors of a certain (fixed) dimension, I am interested in the behaviour of a scalar ...
174 views

### Extracting Pareto elements from a list

How can I extract the Pareto elements from a list? For example, for that list: ...