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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-2
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1answer
66 views

Manipulate aborts the computation of NDSolve with the Piecewise function after curtain time [closed]

I'm facing the problem with performance: Manipulate is working fine till end time =60 sec, after that it aborts. There is NDSolve inside Manipulate with Piecewise function, and the plot of the ...
3
votes
0answers
66 views

NelderMeadMinimize for 2D Gaussian fitting

I would like to fit a large number (10^5-10^6) of small images to 2D gaussians by taking advantage of the NelderMeadMinimize package from Oleksandr: Shaving the last 50 ms off NMinimize. The ...
8
votes
0answers
120 views

What are the time and space complexities of Classify/Predict?

Does anyone have knowledge of the O(n) time & space complexities for various model types supported by Classify[] and ...
0
votes
1answer
81 views

Slow sum computation

I'm doing a simple OLS regression and I strikes my attention that this very simple computation takes several seconds to perform in Mathematica ...
4
votes
2answers
123 views

How can I make this code to count Hamiltonian paths faster?

I have this very basic code to count Hamiltonian paths in a graph: ...
15
votes
3answers
485 views

Generating Tuples with restrictions

I am interested in a certain subset of all tuples. Generating all with Tuples and then filtering is wasteful, and will "blow up" very quickly. For a concrete ...
3
votes
1answer
50 views

Replacing elements of a matrix

I'm trying to write a program that takes a given matrix $A$ of 1's and 0's and flips a designated amount of 1's to -1's. ...
39
votes
9answers
2k views

What would you ask Mathematica to do on a big system?

Our hardware supplier has given us the opportunity to test Mathematica on a big Windows system. The specs will be 1 to 4 TB of working memory and 12 sockets with 18 cores each. I got 1 full week of ...
1
vote
0answers
57 views

Solving a polynomial equation with an approximate constraint is slower than the symbolic solution

Why do these two operations have such different timing, when the only difference is specifying r as approximate $0.1$ vs arbitrary-precision $1/10$? Here are the ...
6
votes
1answer
182 views

Fast loading of png files

I need to process through 600 images that are stored as png-files. Each file has 8.3-ish Mb and 2400x2400 pixel (Real32). For a single processor it takes 0.93sec per image to be loaded with Import (...
6
votes
1answer
152 views

Finding mean brightness, standard deviation, count of pixels in gray scale images

I have many sequential gray scale images (2048*2048 pixels, 8bit). To determine the brightness, standard deviation, and count of pixels with in two bins, zero and non-zero brightness, I use the code ...
9
votes
3answers
309 views

Implementation of a matrix formula

For the Bézier surface, which owns the following matrix definition: $$\begin{align*} S(u,v)&=\sum_{i=0}^m \sum_{j=0}^n P_{i,j} B_{m,i}(u) B_{n,j}(v)\\ &=\small \begin{pmatrix}B_{m,0}(u)&\...
3
votes
0answers
61 views

Why is a LibraryLink function, which returns a list, not parallelizing with ParallelTable?

First example: librarylink function return a list of two element ...
16
votes
5answers
629 views

Easiest/most efficient way to delete duplicates from one list at the positions of another?

This question is somewhat related to How to efficiently find positions of duplicates? , although I'm interested in something a little bit simpler since I'm not really interested in a list of all the ...
2
votes
2answers
82 views
2
votes
2answers
336 views

How to optimize this code?

I am implementing a code that works correctly but it takes too much time. I did not see how to optimize it to be run quickly. Here is my code: ...
3
votes
2answers
353 views

Mandelbrot set—efficiently iterate over a list of initial points

OP edit: This is a Mathematica-specific question about an approach it attempted for a fractal visualization problem described HERE. I'm using the Mandelbrot set there and here as an example, but the ...
1
vote
1answer
96 views

How to do this Function with compile

There is 4 lists, 3 of them are at same length (l0, l1 and l3). ...
1
vote
1answer
246 views

Histograms of gray scale images

I have a large set of subsequent 8bit gray scale png images (50 Hz). They show the noise of a CMOS camera, with the lens covered. A subset of 50 images is available here: https://goo.gl/Sa3P9P I ...
3
votes
1answer
145 views

How to speed up filling a matrix as much as possible in a loop?

In order to find the solution of an $n\times n$ system of nonlinear equations by the method $x_{k+1}=x_k-D_k^{-1}f(x_k)$ where $D_k$ is an approximation of the Jacobian and defined by \begin{equation}...
11
votes
1answer
248 views

Why does Outer sometimes return a packed array, and sometimes not?

For example In[342]:= test3 = Flatten[Outer[Plus, Range[1000], Range[1000]], 1]; // AbsoluteTiming Out[342]= {0.0198735, Null} returns PackedArray (...
1
vote
1answer
92 views

Manipulating Some Lists in Compile

Consider a list of lists, such as: Z={{1,4,3},{2,1,3},{3,1,4}} Z is an $n \times n$ matrix (here $3 \times 3$) which ...
2
votes
1answer
99 views

Product of $N\ 2 \times 2$ matrices and subsequently solving an equation dependent on the product

I have $N\ 2 \times 2$ matrices, each one containing one variable energy which may be complex. I want to muliply them all together to a single matrix ...
1
vote
1answer
28 views

Coefficient of function with general argument

I would like to obtain the coefficients of a general function f in a list. For example, the coefficient list of ...
15
votes
1answer
270 views

Why is SatisfiabilityCount faster than SatisfiableQ?

Consider the following (large) Boolean expression, which arose in a SAT problem. (The expression is not satisfiable.) ...
1
vote
0answers
54 views

Compilation error: “Could not complete external evaluation at…”

I'm pretty new to trying to use Compile[], and I just can't see why I'm getting this error. I have two functions to define beforehand; one of them is a bit odd: <...
1
vote
1answer
70 views

How can I obtain the same result without using any loop?

I have a piece of code as below: For[i = 1; t = x, i^2 < 10, i++, t = t^2 + i; Print[t]] and the result is: ...
11
votes
2answers
297 views

How to “inform” successive ContourPlot calculations?

I need to draw some contour plots of very non-linear functions. As a simple example, take a Mandelbrot Set divergence contour near $z\approx i$. (Just to be clear, I'm not trying to write a ...
5
votes
5answers
167 views

How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
9
votes
1answer
227 views

Speed up construction of a dense matrix

I wish to find the numerical eigenvalues of a relatively small (100 dimensional) Hermitian matrix. While the eigenvalue calculation itself is fast, the construction of the matrix is taking longer than ...
6
votes
0answers
134 views

Call Magma in Mathematica

I've written some code in Mathematica, related to some group theory questions I have. Subsequently, I found that part of the code could be significantly sped up if I could just call a routine in ...
4
votes
0answers
95 views

Is it possible to prohibit unnecessary CopyTensor in Compile? Just like .noalias() in Eigen library?

Turn on Needs["CompiledFunctionTools`"] First example ...
4
votes
1answer
137 views

How to increase the evaluation speed of this somewhat complicated table / matrix operation?

I'd like to calculate the following one-dimensional array: OneDimArray = Table[(Norm[Sum[ MatrixA[[i,j]]VectorB[[j]],{j,N}]])^2,{i,N}] However this takes a very ...
0
votes
1answer
56 views

Invoking functions in other kernels

Suppose one wants to parallelize as much as possible N tasks, each task produces a graphics via ParametricPlot or something like that. If the system is allowed to ...
9
votes
1answer
172 views

What kind of patterns in a list of rules would benefit from being Dispatched?

I have a long list of rules for manipulating expressions. They are of the form: ...
6
votes
1answer
103 views

How does Internal`PolynomialFunctionQ work?

I found that Internal`PolynomialFunctionQ performs much better than PolynomialQ. Here is a huge random polynomial in 12 ...
1
vote
0answers
41 views

Speedup ListCorrelation when using generalized correlation function

ImageCorrelation provides several general function that can be used to replace the default Dot function. For example, in the documentation of ImageCorrelation, ...
6
votes
1answer
133 views

Extracting PNG images from AVI movie

I have written the following code to extract all images from an uncompressed AVI movie and to save them as sequential PNGs. ...
3
votes
1answer
120 views

Randomly generate points on a van der Waals surface

I'm looking to randomly place an atom $\mathbf{A}$ onto a van der Waals surface formed by atoms $\mathbf{B}$, such that the distance between the randomly-generated atom $\mathbf{A}$ and the nearest ...
5
votes
1answer
204 views

How to compile this code?

Could somebody teach me how to compile this code? ...
8
votes
2answers
195 views

Evolution of a trait in an asexual population (performance tuning)

I just coded a simple simulation module that looks at the evolution of a continuous trait in a haploid asexually reproducing population under density dependent competition in discrete time (i.e. non-...
5
votes
1answer
137 views

Find random $n$ combinations of values with a given sum

This problem is described in the related StackOverflow question: Find all combinations of coins when given some dollar value. I would like generate a list of $n$ combinations of values that sum up to ...
15
votes
2answers
306 views

Which elements of a large array are part of a set?

I have a large integer packed array arr. My array is multidimensional, but for simplicity let's consider 1D arrays for now. ...
3
votes
2answers
202 views

Tracing 2d coordinates by using Nearest function

In 5 digital images I have determined the 2d coordinates of detected objects. The resulting coordinate list can be downloaded from here: http://pastebin.com/7bE0CEJ5 ...
6
votes
1answer
89 views

Faster square test for integers

This question was asked already in Jan '12 and the most recent answer is from Oct '12, so it's several Mathematica versions out of date. What is a faster test for whether an integer is a perfect ...
3
votes
3answers
177 views

Optimizing a series of basic matrix operations—scaling doesn't seem right with matrix size

I have a simple operation that I'd like to apply to an n×n matrix. My problem (well, one of them...) is that it runs in, say, 4 seconds for a 100×100 matrix, but it took five and a half minutes to run ...
1
vote
1answer
83 views

How to make this code involving Hypergeometric functions to run faster?

This question is followed up from this Question. I would like to thank Dr. Hintze and I_Mariusz for the comments and help. I am pretty new to mathematica ( I just learned it 4 days ago) so I would ...
3
votes
1answer
113 views

Generate a 3D grid data table

I would like to generate a 3D Grid, not for displaying, but to do computations on it, so no draw functions I guess. I have a simple version of what I am thinking, however, it is terribly slow: ...
0
votes
1answer
53 views

Timing and memory use is critical:fast partitioning of binary sparse array

I do experiments were I measure a signal, and I need to know at what time points it is above a threshold. If at a given time point, the signal is above the threshold, then a '1' gets put into the ...