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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9
votes
3answers
351 views

Faster Alternatives to DateDifference

I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following: Input: A time/date specified by ...
9
votes
2answers
217 views

Additive SparseArray Assembly

The goal is to assemble a SparseArray in an additive fashion. Let us assume we have a large List of indices (some will be ...
9
votes
2answers
192 views

Export[] performance

Consider this sequence of commands: ...
9
votes
2answers
134 views

vectorized operations is not efficient?

Consider the following example: ...
9
votes
2answers
366 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
2answers
932 views

Rapidly binning 3D data

I have a set of data (about 20 million datapoints for my real data) of the form {x, y, z, m}. There are 3 spatial coordinates x, ...
9
votes
3answers
238 views

Improving selection of elements from large multidimensional array

Frequently in my profession I deal with large arrays of data. Typically these are mixed types including integers, strings, dates, and reals. To recreate a typical data array: ...
9
votes
1answer
246 views

Creating a NearestFunction that returns an index

I use Nearest repeatedly for large data sets. For example pts = RandomReal[{-1, 1}, {1000, 3}]; Nearest[pts, {0, 0, 0}] I ...
9
votes
1answer
149 views

Slow work of SQLInsert with MS SQL Server in V10

This question is very similar to: Slow work of SQLInsert with SQLite, but for MS SQL Server. Unfortunately the use of SQLBeginTransaction and ...
9
votes
3answers
411 views

Slow work of SQLInsert with SQLite

I want to store my data in SQLite database, but writing large numbers of data its too slow. For example: ...
9
votes
1answer
97 views

IntegerDigits has Listable attributes, but not fast

See this example, a function has Listable attributes often more efficient than Map,but why is this one is an exception? ...
9
votes
2answers
305 views

Complement on pre-sorted lists

Is there any way to instruct Complement to skip the sorting part? If the answer is no (likely), the next question would be: how can I remove from a sorted list ...
9
votes
1answer
309 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
9
votes
2answers
279 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: ...
9
votes
1answer
767 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 ...
9
votes
1answer
331 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 ...
9
votes
2answers
239 views

Extracting values with multiple keys

I want to extract sorted data from a huge database based upon two (or more) keys in a very timely manner. Here is a reproducible toy example for two keys only: ...
9
votes
2answers
227 views

Relaxation of Mass-Spring System with Pinned Masses

Problem Assume that four masses are connected to each other by springs while two of them are pinned down at their initial positions. Find the position of masses when system is at its minimum ...
9
votes
1answer
359 views

Speed up DensityHistogram rendering (display)

When I tried to present some pre-calculated density histograms inside Manipulate I noticed that the display of DensityHistogram is extremely slow. Here is a simple ...
9
votes
4answers
301 views

How can I efficiently check if a graph is unit distance?

A unit distance graph is a graph that is embeddable in the plane so that every edge has length 1. ...
9
votes
1answer
796 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 ...
9
votes
1answer
294 views

Why I only get 2X speedup when parallelized with 16 kernels

I'm trying to parallelize a function by ParallelTable, and it seems the speedup is not very good. I have 16 parallel kernels on my computer node: ...
9
votes
3answers
402 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 ...
9
votes
0answers
97 views

Mathematica is getting slow when repeatedly calling an external program

I found a strange phenomenon that Mathematica is getting slow when I repeatedly called an external program by using ReadList. For example, the following code will display a significant increase of CPU ...
9
votes
0answers
129 views

Efficient image stacking

I have a list of lists of images that I would like to stack and create mean images for each list of images. Images are .jpg files 2592x1944 pixels large. Each list ...
9
votes
0answers
113 views

Fast two dimensional version of Range[] [duplicate]

I have need of a two dimensional version of Range[]. I have a few ideas of varying speeds, and I was wondering if anyone knew a better way to do this. ...
9
votes
0answers
258 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 ...
8
votes
4answers
368 views

Slow plotting of trigonometric functions

I have two sets of solutions for a and b. I'm plotting solution only if it is positive for both ...
8
votes
5answers
2k views

Something faster than Do loops with AppendTo

I am an "old" programmer used to Fortran and Pascal. I can't get rid of For, Do and While ...
8
votes
4answers
526 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 ...
8
votes
3answers
373 views

Making sure that Timing[] isn't thrown off by caching

In playing with and comparing the various answers to my question here, I tried applying Timing[] to see how fast things ran, but it seemed that some of the answers ...
8
votes
5answers
420 views

Efficiently finding the positions of a large list of targets in another, even larger list

I have a big list. It contains nearly 60,000 sub-lists. It's structured like bigList = {{x1,y1,z1},{x2,y2,z2},{x3,y3,z3},.....,{x60000,y60000,z60000}}; I have ...
8
votes
3answers
315 views

Pairwise distances of points and classification using GraphDistanceMatrix

The challenge Given $n$ points in $\mathbf{R}^3$ and a cutoff distance, $d$, I would like to determine all pairs of points that are separated by less than the given cutoff distance, $d$, and all ...
8
votes
4answers
421 views

Fast method to select matrix elements based on a vector of positions

There is an operation for which I have long wanted to find a better solution. Let: a be a matrix of dimensions $m\times n$ ...
8
votes
3answers
429 views

Benchmarking expressions

It often happens that I'd like to know which of two or more alternative expressions (that should evaluate to the same value) is fastest. For example, below are three ways to define a function: ...
8
votes
2answers
218 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
8
votes
2answers
2k views

Easier program for period of Fibonacci sequence modulo p

For a little project I need to calculate the period of a Fibonacci sequence modulo p, for which p is a prime number. For example, the Fibonacci sequence modulo 19 would be: $$0, 1, 1, 2, 3, 5, 8, 13, ...
8
votes
3answers
562 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: ...
8
votes
6answers
250 views

Faster list duplicate 'limiter'

Given some list, e.g., {5, 3, 2, 3, 1, 0, 1, 3, 5, 5, 4, 5, 1, 2, 5, 2, 2, 0, 1, 4}, I need to limit the duplicates, if any, to an arbitrarily chosen number. The ...
8
votes
3answers
173 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
4answers
138 views

ImageApply Performance Difference

How come the timing difference between these calls is so big? (0.2 and 39 seconds on my computer) ImageApply[q3, img] ImageApply[q3[#] &, img] Where ...
8
votes
2answers
144 views

why MeanFilter is nearly 100 times slower than MovingAverage for 1D array?

I used to average over my data with MeanFilter before I learn about MovingAverage and thought that these two functions are similar except that MeanFilter is more powerful for its ability to deal with ...
8
votes
1answer
582 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
8
votes
1answer
204 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
738 views

Working with large data, pass-by-reference, compiled functions

I think I know the answer to this, but after two days of Googling, this is my last effort before going down an unwanted path... I have a function that takes lots of large data as arguments as well as ...
8
votes
1answer
230 views

Why is `Block` significantly faster than `ReplaceAll` for inputting variable values

Given that the documentation for FindMinimum uses ReplaceAll for its various examples of what to do with the found solution to ...
8
votes
2answers
768 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 ...
8
votes
1answer
229 views

Why is building a table of function values so much slower than just plotting the function?

Here is a function that take some time to evaluate: n = 1000; coeffs = RandomVariate[NormalDistribution[], n]; f[x_] := Sum[coeffs[[k]] Sin[k x]/k, {k, 1, n}]; ...
8
votes
2answers
228 views

How to read off coefficients of tensor-like expression in a speedy way?

I am considering identities involving t[a, b, c, d, ...], where number of indices is fixed. t has the cyclic property so that ...
8
votes
2answers
759 views

Mathematica rule substitution memory

First I present the specific programming question, and then I provide further background details. Given an expression in Mathematica, say f=3x+7y, there are two ...