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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5
votes
1answer
470 views

Efficiently generating histograms with large numbers of bins

I'm trying to generate a histogram for a large data set with the following lines of code: ...
4
votes
2answers
162 views

Replace function call with expression resulting from the symbolic evaluation of the function when defining a second function?

Suppose the evaluation of a function f[x_, y_] := ... takes a very long time, but the output is a not-so-complicated polynomial in ...
3
votes
2answers
584 views
5
votes
1answer
147 views

Force Dispatch to generate dispatch tables

Dispatch creates hash tables only for lists of length larger than 3. Is there any way to force MMA to create hash tables even for lists of length smaller than 4? ...
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. ...
4
votes
1answer
106 views

Strange behavior of Mathematica regarding calculation time

Today I witnessed the following strange behavior of Mathematica, when it comes to calculation time involving larger nested lists. The following is the short example that I setup, I am sure one can ...
14
votes
0answers
1k views

Mathematica performance on Mac

I recently got a trial version of both Mathematica 9 and MATLAB 13a for Windows. I was stunned by the performance difference in the Windows and the Mac version. It was a simple test in matrix ...
4
votes
0answers
92 views

2X slower with ; — LibraryLink performance problem [duplicate]

This is the continued problem of the LibraryLink memory usage question here and here. In the following code, there is a 2X performance difference with only the change of ";". ...
1
vote
2answers
404 views

Collatz Tool Box — any speed ups possible?

I have created a tool box for experimenting with the Collatz conjecture. Info here: Wolfram MathWorld and here: Wikipedia The patterns I have found allow us to make the conjecture jump through some ...
4
votes
2answers
605 views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
0
votes
0answers
52 views

Fastest way to add a constant column into a array [duplicate]

What is the fastest way to add a constant (1 in this test) into a array? There is my attempt: ...
3
votes
1answer
98 views

Slow CreateDialog when passing image sequence

I'm attempting to display an image sequence of 40 images inside of a Manipulate that cycles through each frame with a slider. I would like the ...
23
votes
0answers
361 views

What Mathematica features and idioms have $n^2$ complexity or worse

Here are a few: AppendTo[data, elem], Sort[data, test], in some cases use of ___ (as ...
3
votes
3answers
213 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
1
vote
0answers
213 views

Making simultaneous equation solving more efficient

I am trying to solve a system of several simultaneous equations that have been generated by a series of modules and functions, using this module: ...
16
votes
1answer
924 views

Slow import of multigigabyte TIF image stacks

Update 6: After contacting Wolfram Technical Support, I was advised that the frame-to-frame import timing variability can be eliminated by reading in the frame stack from frame to frame with the ...
0
votes
1answer
622 views

ParallelTable 70 times slower on 16 cores than Table on single core

Consider these code(sorry it's messy), why the ParallelTable version is 70 times slower than the Table version? ...
-1
votes
2answers
324 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...
0
votes
2answers
165 views

Can I speed up the following plotting code?

I have the following Mathematica code. I do get the output graphs, but it takes like 12 seconds, on my computer. Longer still if I increase the value of n1. Are ...
9
votes
1answer
1k views

Hardware Performance Metrics for Mathematica

Dear Mathematica users I am looking into buying a new computer and Mathematica is one of the main applications I run. To help me assess the overwhelming welter of choice out there: I'd like to know ...
2
votes
1answer
188 views

Parallelization of the stochastic Euler scheme

I wrote a simulation to approximate the law of a stochastic differential equation via a Monte Carlo method using the stochastic Euler scheme. Then I thought, it would be a good idea to speed up ...
20
votes
1answer
351 views

A fast, robust DropWhile

For reasons that have never been entirely clear to me, Mathematica has had a built-in TakeWhile function since version 6.0, but has no equivalent ...
7
votes
1answer
840 views

Exporting a sequence of graphs as video efficiently

I have a sequence of graphs that are being created within Mathematica which I'm exporting to create an animated plot of the graph, as follows. ...
0
votes
0answers
97 views

Inconsistent results in fits from NArgMin

EDIT: Just realized I had misspelled "inconsistent." I'm using version 7.0. I'm trying to fit a (noisy) data set to a large-order polynomial. (Just for context: there isn't a model for the ...
1
vote
0answers
242 views

Get path to end nodes in directed (partially cyclic) graph

I have a large directed graph containing small loops. I would like to extract all paths to all end nodes (no VertexOutComponent) with a given path length $n$. I ...
6
votes
2answers
123 views

DictionaryLookup very slow

I'm trying to plot, given a list of words, how many words belongs to each language. I'm using the following code: ...
18
votes
1answer
264 views

Performance of compiled functions

I am trying to find the fastest way to calculate two values where both of them are sum of different expressions. I combine both calculations in one Sum[]. I'm ...
4
votes
0answers
125 views

Efficient Generation of Subgraphs (or, unfriend a friend a day)

NB: If you're not interested in the back-story, you could simply jump forward to the code which I'm seeking to optimize. Also, I believe this code would only work for MMA 8.0 and above. My friends ...
0
votes
2answers
244 views

Seeking faster method than using Table and If together [duplicate]

See the example below. Is there any way to make this execute much faster and still get the same output ? I have read Conditionals slower than operators? but it didn't really help me as I can't seem to ...
5
votes
1answer
177 views

What is the fastest way to maintain a large set of expressions?

In my algorithm I need to maintain a set (an unordered list of distinct elements) of expressions supporting two operations: Test an expression for membership in the set Adding a new expression to ...
8
votes
1answer
831 views

Integration strategies for oscillatory multidimensional function

I am seeking to integrate a highly oscillatory, multidimensional function. I am currently using NIntegrate's QuasiMonteCarlo approach. However, this is time-consuming and, given my current resources, ...
2
votes
0answers
208 views

why version 9 is much slower than version 8 in producing these graphics

Consider this example(taken from Thomas's question here) ...
1
vote
1answer
155 views

Improving the plotting time of a very complicated expression

The quatity $R$ is defined by a complicated expression in terms of $a_1,a_2,\ldots,a_n$. Now each $a_i$ is a function of $x$, $a_i(x)$. I would like to know what is the most efficient way to ...
1
vote
0answers
80 views

Is the TCPIP link type compressed?

Since I'm already piping a MathLink connection in a ssh tunnel (connect back is a pain!), I wonder if it makes sense to compress the data in the stream (ssh -C). As ...
11
votes
3answers
982 views

Every second evaluation in notebook front end is slow

I'm having a rather baffling problem that Wolfram was unable to help me diagnose, and I'm hoping one of you geniuses in residence here can figure it out. (I don't get access to the Technical Support ...
31
votes
1answer
582 views

Why is StringExpression faster than RegularExpression?

Edit: as noted by Albert Retey the performance difference is only seen when sub expression extraction is performed. If this test is used below the timings are similar: ...
5
votes
0answers
92 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
2
votes
0answers
210 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
8
votes
2answers
130 views

vectorized operations is not efficient?

Consider the following example: ...
14
votes
1answer
299 views

How to create internally optimized expression for computing with high WorkingPrecision?

I have large dataset and need to fit rather complicated function on it with different values of one of its parameters (this parameter must be fixed in every fit). I use the ...
9
votes
1answer
232 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 ...
2
votes
3answers
342 views

Using ImageTransformation[] with a lookup table

I need to transform images by ImageTransformation in a time critical application. Therefore I precalculate a lookup table lut of ...
3
votes
2answers
215 views

How to replace Do loops by Inner

I need to replace Do loops by something else because it takes forever with big programs. I have been hinted towards Inner, but ...
25
votes
3answers
803 views

Common subexpression from two expressions

I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
2
votes
2answers
435 views

Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν: expr = 3nu*kx*ky+ ...
3
votes
1answer
125 views

Optimizing a simple calculus using a list of matrices - Repeated dot product between a vector and a list of matrices [closed]

I want to make the following operation : $$ \begin{bmatrix} \dot q_1\\\dot q_2 \end{bmatrix} + \begin{bmatrix} \begin{bmatrix} q_1 & q_2 \end{bmatrix} \mathbf A_1 \begin{bmatrix} q_1\\ q_2 ...
4
votes
4answers
551 views

Remove linear trend from data

I have a large data set with 150k lines and two data columns. I noticed that there is a linear trend, which I want to remove. So, I do the following: first fit with a linear model ...
24
votes
3answers
565 views

How to flush machine underflows to zero and prevent conversion to arbitrary precision?

I'm working on some pretty intense computation in Mathematica; when my code started running slowly, I tracked the source of the problem to Exp[]. I need to ...
4
votes
1answer
147 views

Why is this code in functional style is slower than procedural style?

I know that in Mathematica a functional programming style is often more efficient than procedural style programming using For loops. But the code shown below seems ...