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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6
votes
2answers
563 views

Faster Eigenvalues with lower precision goal

I compute all eigenvalues of a large matrix, and I decide that the speed is more important than the precision. Then the question is, can I speed up Eigenvalues[] by ...
5
votes
1answer
401 views

How to speed up calculations with large number of replacement rules?

In my program I have an expression which looks like: ...
6
votes
1answer
314 views

How to avoid unpacking from Language`ExtendedFullDefinition

Consider this code: LaunchKernels[]; On["Packing"] a = RandomReal[{0., 1.}, {64, 30000}]; ParallelMap[Fourier, a]; // AbsoluteTiming Developer...
9
votes
1answer
308 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: ...
7
votes
2answers
270 views

How can I speed up my compiled RBF interpolating function?

Overview I have a function that acts like the Interpolation on sparse $n$-dimensional data using a simple implementation of RBF interpolation method. I want my ...
3
votes
1answer
200 views

Optimization of power tower fractal generator [closed]

I tried to optimize the code for generating power tower fractals from here. As the author suggested, I tried to memorize the points already tested in a list. Here is my code : ...
17
votes
3answers
2k views

How can I efficiently “remap” an image?

Many image processing libraries like OpenCV, Intel Performance Primitives or Octave have a useful function called "remap", that takes an image, an array with X coordinates and an array with Y ...
8
votes
1answer
300 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}]; ...
9
votes
0answers
230 views

Improving the performance of a package for working with rational functions

As Mathematica gets slow for large symbolic calculations, the cost of putting terms over a common denominator (Together), in particular, gets too high. It occurred ...
1
vote
0answers
244 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
4
votes
5answers
348 views

How to generalize and speed up this program?

There is a vector whose length is $n*m$, we can part it into $n$ sections in order. I want to define a function to compare the $i$-th and $i+1$-th section and find the minimum. The program for $n=m=3$ ...
3
votes
2answers
479 views

How can I track the execution time of an evaluating Manipulate cell?

In Wolfram's tutorial on Advanced Manipulate Functionality, a nice example of a continually evaluating Manipulate cell is presented: ...
6
votes
2answers
210 views

Consecutive Print to target same output Cell

Is it possible to conveniently direct the output of consecutive Print statements to the same output without actually accumulating the output in a temporary string/variable. This would be useful in ...
6
votes
0answers
89 views

Does one need to be careful about loading multiple (many) contexts or packages in the same session?

I have a number of large pieces of precomputed data which I am considering putting into individual packages in order to load them (via DeclarePackage) and unload ...
7
votes
3answers
2k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
2
votes
2answers
203 views

Time differences between code using user-defined probability distribution and code using built-in distribution

Why is the reponse time of of kernel significantly different when I use the first code rather than the second? Shouldn it not be the same? Is there any way that the response time can be made smaller ...
9
votes
1answer
100 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? ...
2
votes
1answer
120 views

What is the best way to produce a symmetric semi-definite matrix using as few variables as possible?

As we know, there are only $\frac{n(n+1)}{2}$ variables in a symmetric $n$-dimensional semi-definite matrix. Is it possible to produce a $n$-dimensional semi-definite matrix whose trace is $1$ using ...
4
votes
1answer
234 views

How do I put a Monitor into CDF?

I would like to keep track of progress of a database request in an Enterprise CDF, but it won't allow PrintTemporary or ...
10
votes
1answer
360 views

Mathematica9: NDSolve slows down after repeated calls

I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, slows down considerably after some time. Apparently, the problem is NDSolve itself and it seems to be related to ...
9
votes
2answers
343 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 ...
20
votes
1answer
475 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
2
votes
0answers
100 views

Speed improvement in string distance function

I'm using this distance function to compare distance between strings: ...
5
votes
1answer
559 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: ...
5
votes
2answers
179 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
717 views
5
votes
1answer
162 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
114 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
108 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 ...
21
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
104 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 ";". ...
4
votes
2answers
478 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
925 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
54 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
106 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 ...
1
vote
2answers
256 views

How can I speed up this plot manipulation? Why does Evaluate not help?

If I were able to "Save" the computed inverse function somewhere and then plot it, the manipulation would become faster. As I understand, Evaluate should do the job, but for some reason it does not. ...
5
votes
1answer
643 views

Why is parallel slower?

I always assumed that distributing a computation is faster, but it isn't necessarily true. When I do Sum[i,{i,10^4}] I retrieve an answer much faster then if I do ...
9
votes
4answers
635 views

NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
28
votes
0answers
465 views

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

Here are a few: AppendTo[data, elem], Sort[data, test], in some cases use of ___ (as ...
3
votes
3answers
239 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 ...
2
votes
0answers
138 views

Frontend cursor movement speed depends on the position in large notebook file

I run Mathematica v9 on my Atom laptop (don't ask) and I got used to the fact that everything is slower. Except for one annoying thing: cursor movement (in text) is slower than the keyboard key repeat ...
1
vote
0answers
292 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: ...
17
votes
1answer
1k 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 ...
1
vote
1answer
787 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
363 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
195 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 ...
3
votes
1answer
195 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 ...
22
votes
1answer
400 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 ...