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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8
votes
2answers
756 views

Why is Mathematica's expansion of expressions with square roots so slow?

Mathematica expansion of expressions with symbols isn't slow, but with square roots it is very slow. In Maple or Mupad both are fast: with square roots they both take less than a second. Here is an ...
4
votes
3answers
2k views

Definite integral takes a very long time

I'm trying to integrate the following function: $$r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}$$ where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
7
votes
1answer
311 views

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 ...
5
votes
1answer
556 views

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 ...
15
votes
1answer
322 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: ...
20
votes
4answers
898 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 ...
5
votes
3answers
441 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. ...
9
votes
2answers
278 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: ...
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 ...
0
votes
1answer
280 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 ...
8
votes
4answers
523 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 ...
1
vote
1answer
258 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 ...
31
votes
3answers
1k 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 ...
3
votes
3answers
568 views

Speed optimization

I have a part of a program that I have to repeatedly call many times (about 2000 to 10000 times) ...
4
votes
2answers
283 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 ...
7
votes
1answer
246 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[] ...
8
votes
3answers
557 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: ...
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 ...
2
votes
0answers
317 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 ...
4
votes
1answer
533 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 ...
3
votes
2answers
123 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 ...
14
votes
2answers
457 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: ...
5
votes
1answer
452 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 ...
9
votes
2answers
299 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 ...
7
votes
1answer
286 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 ...
8
votes
3answers
171 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 ...
3
votes
1answer
240 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 ...
3
votes
2answers
457 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 ...
4
votes
1answer
255 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 ...
4
votes
3answers
316 views

Extracting Pareto elements from a list

How can I extract the Pareto elements from a list? For example, for that list: ...
5
votes
2answers
450 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 ...
23
votes
3answers
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: ...
11
votes
2answers
537 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 ...
7
votes
1answer
663 views

Speeding up numerical Fourier Transform

I wrote this function NFourierTransform, which takes a function $f(k)$ and numerically calculates the fourier transform integral for discrete values of $k \in ...
1
vote
1answer
160 views

Optimization of correlation calculation

How can I make the following line of code run faster? Is there a way to do this calculation as a matrix vs vector than vector vs vector? In the code below, f is a ...
4
votes
1answer
277 views

Performance of a Do-Loop of variable length

If I'm changing a basis depending on a (non quadratic) matrix $\mathbf{M}\in\mathbb Z^{d\times k}$ and some $\mu\in\mathbb N^k$, i.e. i have an array a of the same ...
7
votes
2answers
311 views

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 ...
3
votes
1answer
326 views

Why can't Mathematica parallelize this?

The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation." ...
1
vote
3answers
113 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: ...
7
votes
2answers
321 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 ...
11
votes
2answers
564 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 ...
10
votes
2answers
286 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, ...
9
votes
2answers
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 ...
4
votes
3answers
574 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, ...
8
votes
0answers
334 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 ...
17
votes
2answers
2k 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: ...
4
votes
1answer
389 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 ...
14
votes
9answers
625 views

Thread over list in different levels

I have these two lists, both with the same length in the first dimension: ...
11
votes
4answers
396 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. ...
9
votes
1answer
746 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 ...