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.
2
votes
1answer
116 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
312 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
196 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
179 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
234 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 ...
16
votes
3answers
660 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:
...
9
votes
2answers
350 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 ...
1
vote
0answers
175 views
Vector computation instead of iterating over a list
I am 'Map'ping over a list. I would like to do the computation in one single iteration. Is it possible? Can 'Apply' be used here? In what way is it different from 'Map' especially in this case?
...
6
votes
1answer
283 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
130 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
186 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 ...
6
votes
2answers
201 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 ...
2
votes
1answer
151 views
Why can't Mathematica parallelize this?
The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation."
...
0
votes
3answers
80 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:
...
10
votes
2answers
198 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, ...
6
votes
0answers
149 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 ...
2
votes
1answer
202 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 ...
7
votes
8answers
330 views
Thread over list in different levels
I have these two lists, both with the same length in the first dimension:
...
8
votes
4answers
298 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. ...
6
votes
1answer
278 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
...
2
votes
1answer
198 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 ...
12
votes
3answers
602 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
4
votes
2answers
316 views
How to solve an eigensystem faster?
I have a module that I need to call 1-10 million times in my program. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help.
...
10
votes
1answer
185 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 ...
19
votes
5answers
847 views
Making fractals with Mathematica
I recently saw this post on math.stackexchange and was curious as to how to generate the image in Mathematica. I tried the following naive approach; however, it is extremely slow.
...
7
votes
1answer
417 views
How to speed up Minimum Spanning Tree algorithm?
How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here.
The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
9
votes
2answers
274 views
Speeding up construction of simple tridiagonal matrix
I have the following code to construct a tridiagonal matrix:
...
3
votes
3answers
187 views
How to sum up large number of elements in a table quickly?
I have been using Mathematica for some time now but I have a feeling that I am not using it as efficiently as it could be.
I have the following problem which I am unable to figure out and it would be ...
9
votes
2answers
918 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
1answer
226 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 ...
4
votes
2answers
97 views
Factor out invariant code from Plot
Given a simple Gaussian kernel
UnscaledKernel[a_, b_, sigma_] :=
Exp[-(((a - b)/sigma).((a - b)/sigma))/2]
and un-normalized smoothing function
...
7
votes
3answers
291 views
Why is AstronomicalData so slow?
I'm having trouble getting some pretty simple functions using AstronomicalData to perform at anywhere near the speed I need them to.
For example, I have many ...
0
votes
2answers
190 views
Launching remote kernels - will it help RAM needs?
Given the exasperating RAM needs of my Mathematica program, I contemplated launching remote kernels to run my Mathematica script. This is a two part question:
Part 1
If I launch a remote kernel(s), ...
4
votes
1answer
554 views
Improving NDSolve speed for heavily stiff problems
Having looked around the intergoogles and Mathematica.SE, I thought I'd pose a question with a minimum working example.
Here is the situation I am trying to improve:
I am solving a 4th order non ...
3
votes
4answers
457 views
Faster code for specific problem
Sorry, but I need the following code much faster and I'm running out of ideas. I do appreciate any help. I post two of my fastest ideas (tab and mat), although they are not really fast. Thanks in ...
6
votes
2answers
320 views
Web scraping and multi-threading in Mathematica
I'm working in some web scraping using Mathematica, and today, to speed-up the process, I used bash commands (xargs with parallel options with curl and wget) using ...
3
votes
1answer
281 views
Efficient way to perform elementary integration step with NDSolve internal method
I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
6
votes
1answer
134 views
Elementwise, compilable min function
I am trying to implement efficiently a transfer-matrix like algorithm. On each iteration, I have two vectors $x=\{x_1,\dots,x_n\}$, $y=\{y_1,\dots,y_n\}$ with real numbers and I need to compute the ...
2
votes
1answer
233 views
How to solve simultaneous equations faster with Compile?
I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
3
votes
2answers
367 views
1
vote
2answers
131 views
Combining lists with common elements efficiently [duplicate]
Possible Duplicate:
Computing the equivalence classes of the symmetric transitive closure of a relation
I am required to process sets consisting of 2-element subsets of integers by ...
15
votes
0answers
367 views
Fast Spherical Harmonics radiative transfer
This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me.
I am using ...
8
votes
0answers
182 views
Using Compile to speed up Function with PermutationProduct
I have the following fairly simple routine dot involving PermutationProduct that I wish to speed up using ...
14
votes
2answers
519 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 ...
19
votes
6answers
968 views
How to improve the performance of solutions to Project Euler (#39)?
This is the problem 39 of Project Euler, which I asked in the chat room two days ago. My original code runs as slowly as snails, and finally I got two answers from JM and Rojo. Unfortunately, both of ...
7
votes
1answer
303 views
9
votes
3answers
282 views
Compiled function error - nontensor object created
I'm trying to optimize code that uses Position MANY times.
The following toy code works:
...
7
votes
1answer
252 views
Very fast way to do a coordinate frame transform
I need a function that rotates and translates a huge amount of line segments.
For example, I have a set of line segments in the form {{x0,y0,z0},{x1,y1,z1}}
...
6
votes
0answers
234 views
Optimizing NIntegrate for higher PrecisionGoal
By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
3
votes
1answer
522 views
Methods to speed up numerical NDSolve, NIntegrate,
I am not very used to do numerical simulations on Mathematica. Do you have any ideas how to improve i.e. speed up my code?
...
