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.
13
votes
4answers
486 views
How to collect result continuously (interruptible calculation) when running parallel calculations?
This is the most common pattern to compute a table of results:
Table[function[p], {p, parameters}]
(regardless of how it's implemented, it could be a ...
13
votes
1answer
269 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 ...
13
votes
2answers
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:
...
12
votes
6answers
612 views
Efficient conditional Mean[] on a large data set
Consider a list, AK6, that has 382 sublists of length varying from 2500 to 3000. Each "subsublist" is as such : ...
12
votes
3answers
579 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
12
votes
3answers
495 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 ...
12
votes
5answers
198 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:
...
12
votes
2answers
415 views
Efficiently collecting results inside a compiled function
When we don't know the number of results that will be generated, the usual way to collect results is Reap/Sow. Another ...
12
votes
4answers
351 views
How to reduce the InterpolatingFunction building overhead?
I want a linear interpolation from the following example list:
...
12
votes
1answer
222 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 ...
12
votes
2answers
232 views
Parallelization of distinct array write access from subkernels
I'm working on an implementation of a multivariate FFT, which is (or at least should be) highly parallelizable due to the row-column-algorithm. However, i can't figure out how to implement that. The ...
11
votes
3answers
219 views
Memoization of Rounded inputs
Memoization is a technique for improving performance by having a function remember its previous arguments. For example,
f[x_]:=f[x]=mySlowFunction[x]
will be ...
11
votes
4answers
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
...
11
votes
3answers
211 views
Plot on command within DynamicModule?
Suppose I have a DynamicModule with all sorts of controls to set some parameters for a graphics object.
...
11
votes
3answers
279 views
What compilers are “suitable” for CompilationTarget->“C”?
The documentation for CompilationTarget says, "if you do not have a suitable C compiler then you will not be able to set CompilationTarget to C". Well at this time, I don't have a compiler installed ...
11
votes
2answers
563 views
Speeding up random walk for many particles
I am trying to speed up this code for many particles to take a random walk. I'm not sure why it is so slow for such a simple task.
I got a few hints from colleagues to reduce the precision of the ...
11
votes
1answer
315 views
Space-efficient null space of sparse array
I have a roughly 100,000 × 3,000 matrix (as a SparseArray) that I'd like to find the kernel (null space) of.
It has about 500,000 nonzero entries, all -1 or 1.
...
11
votes
1answer
331 views
What is the fastest way to find an integer-valued row echelon form for a matrix with integer entries?
Let me begin by saying that this is my first post on StackExchange. I apologize in advance if I unwittingly break any of its unwritten rules of etiquette.
Recently, I've been trying to understand an ...
11
votes
1answer
225 views
Are there rules of thumb for knowing when RandomVariate is more efficient than RandomReal?
Please consider the following:
From a fresh Mathematica kernel, RandomVariate is more efficient for NormalDistribution but ...
11
votes
2answers
119 views
How do you determine the optimal autocompilation length on your system
When you pack lists there is an overhead therefore packing a list with, say, 2 elements is likely to cost more than you get back in efficiency. Mathematica has default list lengths for which functions ...
11
votes
1answer
179 views
Choosing among different function definitions without sacrificing speed
I'm working on some code that numerically integrates a function, let's call it G, which calls another function, F, that can be ...
10
votes
5answers
494 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 ...
10
votes
4answers
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
...
10
votes
3answers
426 views
Function does not compile with Greater in it
I have to speed up a matrix-calculation and would like to use Compile for it, though it fails and produces an unknown error message:
...
10
votes
5answers
898 views
Best way to create symmetric matrices
From time to time I need to generate symmetric matrices with relatively expensive cost of element evaluation. Most frequently these are Gram matrices where elements are $L_2$ dot products. Here are ...
10
votes
3answers
239 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 ...
10
votes
4answers
340 views
Finding Local Minima / Maxima in Noisy Data
I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
10
votes
2answers
196 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, ...
10
votes
1answer
177 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 ...
10
votes
1answer
215 views
Memory Leak in RowReduce?
Recently I tried to do what I thought was a fairly small (relative to the 6 GB of RAM that I have on my machine) row reduction calculation on a matrix representing an undetermined linear system and ...
10
votes
2answers
220 views
9
votes
3answers
366 views
Improve speed for calculating a recursive sequence
I want to calculate following recursive sequence:
$\alpha_{0}=0,\\
\cos(\alpha_{i})=\cos(\alpha_{i-1})\cdot\cos(\beta_{i})+\sin(\alpha_{i-1})\cdot\sin(\beta_{i})\cdot\cos(\gamma_{i}).$
In ...
9
votes
3answers
272 views
Compiled function error - nontensor object created
I'm trying to optimize code that uses Position MANY times.
The following toy code works:
...
9
votes
2answers
264 views
Speeding up construction of simple tridiagonal matrix
I have the following code to construct a tridiagonal matrix:
...
9
votes
2answers
839 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 ...
9
votes
4answers
198 views
Efficient way to turn a subset into a permutation
For an input vector $\{a_1,a_2,\ldots,a_n,b_{1},b_2,\ldots,b_{m}\}$ and a list of ordered positions $\{k_1,k_2,\ldots, k_n\}$, such that $1\leqslant k_1 < k_2 < \ldots < k_n \leqslant ...
9
votes
3answers
383 views
How can I speed up SQL queries in Mathematica?
I have an application that queries a MySQL database many times for data. At the moment, Mathematica and MySQL are running on the same box and yet it takes over 1.6 seconds for the query to run and ...
9
votes
1answer
152 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.
...
9
votes
2answers
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 ...
9
votes
1answer
306 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 ...
9
votes
2answers
168 views
Update only one element in a dynamic grid?
I've got a grid of buttons that each display an image from an array. When a button is clicked, its image changes.
...
9
votes
1answer
391 views
How to tell mathematica not to resolve stiffness issues
Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
8
votes
5answers
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 ...
8
votes
4answers
289 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. ...
8
votes
4answers
215 views
Plotting the components of a function that returns a list in different colors without redundant evaluations of the function
I have a function f which takes a number as input, and returns a list of numbers (the length of the list is constant). f is hard ...
8
votes
3answers
236 views
Faster Alternatives to DateDifference
I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following:
Input: A time/date specified by ...
8
votes
4answers
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 ...
8
votes
3answers
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 ...
8
votes
1answer
151 views
Reducing the memory footprint of lists of machine numbers
I have a large 1D dataset of double precision numbers that are stored in many external database files. In order to load the whole dataset into Mathematica 8 I iterate over the files ...
8
votes
2answers
313 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 ...
