# Tagged Questions

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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### EvaluationMonitor slows down NDSolve considerably

Hi guys I'm solving a nonlinear system of ODEs with NDSolve. Since the dimension of the system ranges from 2700 to 20000 equations, depending on the parameters, the time required to solve the entire ...
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### NDSolve with default settings solves much faster than classic Runge-Kutta 4

NDSolve with default parameters takes 0.25 s for the first run. With Runge Kutta 4 specified, it takes about 4.6 s, ...
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I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and $\... 0answers 43 views ### Is there a clean way to parallelize multi-index tables? The documentation of ParallelTable indicates that if you want to parallelize the evaluation of a table of more than one dimension, such as ... 0answers 78 views ### Improve recursive function (memoization) These days I am trying to rewrite the following recursive function, in order to gain some speed. It is crucial because I end up using 4-5 similar functions, and I need to decrease execution time. ... 1answer 114 views ### What are the main differences between RawArray and PackedArray? What I know: PackedArray is documented (to some extent) in "Developer Utilities Package", RawArray is just mentioned in ... 1answer 70 views ### Code optimizations with functions inside Module I wrote a small code by using functions inside Module: ... 2answers 216 views ### General solution for a linear ODE set with complicated coefficient This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ... 1answer 178 views ### How to turn off depth sorting of 3D curves for Manipulate? Is there a way to turn off the default depth sorting of curves in a 3D output of several complicated curves ? Currently, I suspect that depth sorting has a very strong impact on performances on my ... 1answer 253 views ### Complicated symbolic coefficient slows down equation solving Here's a simple example for Solve: ... 1answer 153 views ### How can I optimize the search between two lists, one that is changing length? I'm trying to identify unique arrays by comparing two lists, one which is growing in length. The number of elements in the list grows as 2^n^2, where ... 0answers 187 views ### Best approach for 'manual' common subexpression elimination I have working code, but am looking for ways to make it more elegant. I have a fairly large expression with plenty of repetition and structure. A shortened toy example is ... 3answers 132 views ### Lazy form of Tuples/Outer to loop over list of lists This is less a question and more asking if someone has implemented this already, with more skill. I need to perform the Outer-like generalized outer product of a ... 0answers 65 views ### Data acquisition from TCP socket At last (since 10.3) we have straightforward/documented access to TCP sockets. It's been a long wait. So far there is very little discussion of the new feature. Although some older posts are still ... 0answers 32 views ### Solving for limit of integration with a piecewise function (FindRoot vs NSolve) [duplicate] I am trying to solve for the limits of integration using a piecewise function. I'm doing this in a loop over a list of data, mostly because I'm not well-versed enough in Mathematica to make this a ... 3answers 132 views ### Indexing all elements of permutations$S_n$I have this Table that gives all elements of$S_n$, I would like to know how to improve efficiency. ... 1answer 139 views ### Why does Compile not make my function faster? I need to speed up a large program that repeatedly calls the module below (I've not trimmed the code for this question to ensure there is enough calculation to show a speed improvement.) The obvious ... 2answers 248 views ### Speed-up the computation of this sum of small matrices Given a matrix mat with a large number of rows (a few thousands) and a few columns (between 2 and 10), I'd like to compute the sum of the "small" matrices obtained ... 1answer 271 views ### Speed up RegionPlot I want to plot a system of equalities and inequalities. I used a combination of ImplicitRegion and RegionPlot (since RegionPlot cannot plot lines or points). But this method is very slow than using ... 5answers 132 views ### How to efficiently stream words and whitespace from a large text file I want to tokenize a large (~20 MB) file, opening it and streaming the words, but preserving the whitespace as well. Example: ... 2answers 229 views ### Primes Race (Mathematica Efficiency) I am currently working with a paper that deals with this concept of Prime Races. You essentially create a large list of prime numbers and then split that list into two teams. You are assigned to ... 2answers 571 views ### Improve speed in this tree - memoization won't suffice I have two functions, one of which calls the other. I need to do some calculations but I was unable to optimize my code to do it efficiently. In search I came across the memoization technique, which ... 3answers 103 views ### Counting runs in bits, along with their starts and lengths, in functional style Here is some code to visualize Project Euler Problem 502. The code scans for runs of bits in the binary representation of an integer, and outputs the beginning position of each run and the length of ... 1answer 159 views ### Problem with convergence of limiting value in Manipulate I created a nice Manipulate box of the magnetic field outside and inside a spherical shell placed in an homogeneous magnetic field. The code is working great, but it has a problem at a limiting value,... 1answer 101 views ### efficient element wise multiplication of SparseArray vector and matrix I have a large SparseArray$P$of dimensions$\{d,d\}$and I want to multiply a vector (also a SparseArray)$v$of length$d$... 0answers 45 views ### Prepending a sequence with zeros gives FindGeneratingFunction hard time Asking for FindGeneratingFunction[{1, 3, 11, 43, 171, 683, 2731, 10923, 43691, 174763}, t] gives the answer (namely ... 6answers 450 views ### Given a large binary matrix, find the largest submatrix containing non-zero elements I'm looking for a way to reduce a binary matrix containing zeros at some positions into a matrix that contains no zeros by deleting rows and columns of the original matrix until only non-zero values ... 2answers 268 views ### What is the fastest way to compute digits of$\pi$using Mathematica? There are a lot of ways to calculate digits of$\pi$using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ... 1answer 41 views ### Customized ParallelTable - Automate ParallelSubmit - Possibly an issue with HoldAllComplete attribute Related to this question and in particular its answer I am trying to wrap everything into a new parallelTab function that takes into account some cost per job, ... 1answer 102 views ### Speed up Dynamic for graphical interface I am trying to create a user interface where I can click on certain points in a set of data and save them into a list that can be used later in my code. The problem is it is currently sluggish. Is ... 4answers 183 views ### Find the minimum positive-integer value which meet the requirement If the equation is Mod[515 Sum[10^(3 d), {d, 0, n}], 53] == 0 Then I can get the minimum positive-integer value of n. ... 1answer 231 views ### How to speed up calculation of this equation (FindRoot) I have come up with the following functions, and I need to calculate a value, in order to have a condition valid. In my problem, all data are given, and I need to calculate variable l. I am using ... 2answers 136 views ### How to optimize my own BezierFunction? A few months ago, I asked a question about the implementation of Bezier surface. Please see here for a full detail. I also know that BezierFunction[] is built-in ... 2answers 229 views ### Elegant way to partition list to be faster than ParallelTable (using ParallelSubmit), or some alternative? Suppose you have a function fun[x_] := (Pause[.05*x]; x^2); of which you know that its evaluation time increases with its argument - in this case obviously ... 1answer 215 views ### Error with FindMinimum. The Message is FindMinimum::cnpcons I want to run a rather demanding check of feasibility. I have 3565 non-negativity constraints for my variables, and one that makes them sum to a certain budget they shall not surpass. I also have ... 0answers 177 views ### Slow JoinAcross performance Bug introduced in 10.3 I am using JoinAcross to combine two datasets, where the key is an Integer. ... 0answers 61 views ### Speeding up ImageData[image,“Byte”] For my image analysis I need the Byte values of many sequential 8bit PNG images. To obtain the Byte data I use: ... 2answers 286 views ### Why is ListPlot[] so slow for coordinate pairs? Can we speed it up? I compared the time it took to create a plot in two different ways. I expected the first method to be slower, but I was surprised at how much. Is this an inherent limitation or the function, or are ... 1answer 57 views ### why URLFetch is slow when encapsulated by module and how to fix it [closed] I'm using Mathematica 10.0.2 on Win7. I'm writing some program to crawl etymology of words on http://www.etymonline.com/. Below lies the example code: ... 1answer 116 views ### Memory limit hit: optimize code for finding twin primes I need some help optimizing a Mathematica code so that it'll not max out RAM. Here's the code: Cell 1 ... 1answer 37 views ### Access variable middle of the run [duplicate] I execute a Table[] that need large time to be finished. If I abort it I loose what evaluated until now. Does it possible to stop running and save what evaluated ... 1answer 98 views ### How to improve speed of the following code The following code do what I needed, but it takes too long ... 0answers 59 views ### Is this problem parametrically solvable or it can just be solved for specific$\sigma$and$\theta\$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
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### How to efficiently find all combinations of the letters in an alphabet given a condition

Problem: I want to find all unique expressions with n number of terms that contain all the digits (or characters) in alphabet. ...
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### Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?

I've noticed that, while ListConvolve is very fast, it becomes much slower when you use anything but the standard Times,Plus as ...
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### Why is Random faster than RandomReal?

As of version 6, Random[] was superseded by RandomReal[ ] etc, but both still work perfectly well. Playing with some timing ...
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### Partitioning a list when the cumulative sum exceeds 1

I have a long list of say 1 million Uniform(0,1) random numbers, such as: dat = {0.71, 0.685, 0.16, 0.82, 0.73, 0.44, 0.89, 0.02, 0.47, 0.65} I want to ...
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### FindInstance—why doesn't it work with my expression?

I want to find arbitrary solution of a system of equations: ...