# 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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### Random number generation with specific distribution

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
380 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. Let'...
1k 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 ...
478 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. ...
289 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: ...
574 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 ...
326 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 ...
548 views

### Efficient code for the Ten True Sentences puzzle

I am trying to solve Ten True Sentences Puzzle. Take a look at the following sentences: The number of times the digit 0 appears in this puzzle is _. The number of times the digit 1 ...
271 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 ...
2k 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 ...
601 views

### Speed optimization

I have a part of a program that I have to repeatedly call many times (about 2000 to 10000 times) ...
287 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 ...
267 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[] ...
611 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: ...
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 ...
407 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 ...
728 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 ...
132 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 ...
495 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: ...
632 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 ...
359 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 ...
336 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 ...
182 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 ...
285 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 ...
495 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 ...
261 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 ...
425 views

### Extracting Pareto elements from a list

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

### Fast Karatsuba Squaring, how to?

I want to improve timing of squaring for big numbers. So I asked What is the fastest way to split a number into parts and What is the most efficient way to add zeros to end of a number with several ...
2k views

### Reading periodic elements from a large file

I have a large binary data file (big endian) with 100+ million "rows" of 11 elements, combination of floats and integers. This is the format: ...
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 ...
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### Compiling a spatial predator-prey model and optimising it for speed

I just made a spatial predator-prey model but it runs a little slow and I am seeking some advice on how to compile it to optimise it for speed. I first define matrix with 0 for an empty site, 1 for a ...
433 views

### Why can't Mathematica parallelize this?

The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation." ...
123 views

### Timing display of Graphics (Front End timing)

I want to know how much wall-time it takes to display a Graphics For example this one: ...
360 views

### Use of Cellular Automaton or Discrete Convolution to calculate Potts Energy of a 2D Matrix

In a project of Monte Carlo Modelling of Grain Growth (Link) one of the most costly subroutines is the calculation of the Potts-Energy of an Monte Carlo Grid cell by comparing the center cell value ...
673 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 ...
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, ...
2k views

### Convolution with interpolated function

I have some problems to calculate in reasonable speed the convolution of an interpolated function with a Gauss function. I have here (ExampleData.txt, alternate Pastebin link) data which I ...
716 views

### How to make brute force coding more efficient?

Hi guys and guysettes, The little Mathematica I've been using/seen so far, it seems to be all about neat "one-liners" using the underlying functions and working with lists & maps to solve issues, ...
396 views

### Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
3k views

### Difference between AbsoluteTiming and Timing

I need to evaluate the efficiency of my code. Therefore I would like to evaluate the time the code need for some calculations. Mathematica gives me two possibilities for this kind of evaluation: <...
483 views

### using interpolation functions in ParallelMap

Edit I am editing the question to give a simple workable example. It is at the bottom under the heading Example. The original question is now headed withe Background. Background I am trying to ...
714 views

### Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
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. ...
892 views

### Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
302 views

### Speed up iterated manipulations of a graph / table

I am trying to generate a version of Watts' model of cascading shocks to a network following the discussion on p. 20-25 of this article. The basic premise is to use the ...