# 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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### For loop catastrophe

I know that Mathematica prefers a functional programming way but I still have some problems for the following example. Supposing we generate a Fibonacci sequence of 10^6 elements. NestList or FoldList ...
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### Performance of Extract-Transform operations

I'm doing simple data analysis, where I load some "date-time" data from a file. The data is a simple list, but there are 41,000 values in total. Here's a short sample: ...
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### How to make Graphics3D with multiple lighting sources being rendered faster

I have a very "precise"(through setting "SpherePoints") Sphere illuminated by hundreds of random color lighting sources. The ...
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### Generate Degeneracies in List [duplicate]

I have a list with n entries and I would like to duplicate this list p times. In my case because of the Degeneracy of my Eigenvalues. For example I have {3,2,1} and it is five-fold-degenerate so that ...
322 views

### How can I Integrate large trigonometric expressions more efficiently?

I have a requirement to integrate some large symbolic expressions containing products of trigonometric functions. A single integration is averaging 7 minutes, and I have 2628 expressions to integrate, ...
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### More on performance of Sum[]

There is an interesting discussion on performance of Sum[] in this question. I actually wanted to reproduce findings from this answer. So, I entered: ...
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### Apply functions to functions yields slow execution speed

I'm trying to write a function that parametrizes a curve c(t) by its arc length. Technicly I'm finished but if I plot the result for an example curve like ...
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### Speed optimization of Mean calculation in a previous calculated data range

I have following problem: My calculations work quite well with the shown testdata, the only problem is the speed of it. My original dataset is about 64000 datapoints, and it takes several minutes to ...
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### Why does this line increase the consumed memory?

Probably this is a simple question, however I really don't understand this behavior in Mathematica. It particularly leads to a memory leak in a huge program I have to do processing of 3D images. I ...
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### Slowdown of Flat attributed function

I was trying to write an associative function f using the attribute Flat. ...
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### Mathematica taking too long to calculate recursive function

I have been trying to plot those specific recursively defined functions p1 and q1 in Mathematica: ...
286 views

### The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
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### Use Compile to speed up evaluation

I have read, that using Compile command can speed up evaluations in mathematica. I have a mathematical expression, which I evaluate using following command: ...
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### How to handle Indeterminate TimeConstrain

I have to use Timeconstrained[aux] first for avoid some bigs calculation that dont need and it use a lot of time of calculate, so i can't do this. ...
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### Over 30mins to generate the first eigenvector?

Is it normal for Mathematica to take over 30mins to try to compute the first eigenvector of a 100x100 matrix? The matrix is reasonably sparse - about 90% of the cells are 0s and each column sums to ...
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### Improve on timing of NMinimize

I got a little performance problem with the function NMinimize (it takes mathematica approximately 10 minutes to compute the results). Here i s my sample code: ...
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### Neighbourhood - Calculations

SeedRandom[0]; n = 5; (m = N @ RandomInteger[{1, 3}, {n, n}]) // MatrixForm result1 = MeanFilter[m, 1] // MatrixForm ...
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### Division by zero is slow

Suppose I have two arrays of data, which I want to divide: ...
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### How to get “Signature” of each element of “Permutation” output

I need to sum over all possible permutations, multiplied by the Signature of each permutation of a given list of symbols. But, I don't know how to determine the <...
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### Speeding up the generation of all k-edge-coloring of a graph

A $k$-edge-coloring of a graph $G=(V,E)$ is a function from $E$ to $\{1,\ldots,k\}$, so in other words every edge of $G$ receives one of the $k$ colors available. (In particular, note that we are not ...
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### Speed up numerical optimization (for plotting and solving)?

Briefly speaking, I want to plot a function PIfun[], which its value is based on numerical optimization using NMaximize. It ...
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### How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
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### Why some built-in functions are slow

I just wonder why some built-in functions are slower compared to some other ways using more than one built-in functions for doing same job. consider this example: ...
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### Calculating eigensystem of a matrix containing very small numbers [duplicate]

I'm dealing with a matrix containing very small numbers like 10^(-370). When I compute the eigensystem of my matrix, it takes too much time, though the matrix size is not large. Can anyone explain ...
531 views

### Colorize Grayscale Image

I have a grayscale image that contains two objects. The grayscale pixel values can be divided into three intervals where two of them represent objects and the third represents the background. The ...
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### Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
564 views

### Total much slower in version 10

Issue introduced in version 10, fixed in 10.0.2 Compilation nowadays may give very fast functions. Here is an example for finding the sum of a list of machine numbers, just as the built-in function ...
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### How to remove recursion, and write it functional and efficient way?

I wish to implement the following recursion efficiently. ...
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### Paralleizing the Plot function internally

I have a function of several parameters, funct(a,b,c,d,f,...). Mathematica deals with this function fine but it takes a minute or so to make a data point. I want to plot graphs of funct using code ...
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### Faster Integer Approximation of pi

I'd like to speed up this calculation: First[Sort[Table[{k,Abs[Round[k/Pi]Pi - k]1.{k,1,100000}],#1[[2]]<#2[[2]] &]] The code above generates a list of ...
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### Speedup of KL Divergence by Monte Carlo Simulation

I started with Mathematica about just a week, so I don't know how to take all of this environment. What I want to know is if there is a way to speedup my code to compute the KL-Divergence of Gaussian ...
272 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: ...
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### How smart is Solve? Figuring out what tricks I should try

I'm trying to solve a large system (~10000) of linear equations using Solve, but the process keeps failing. As-is, I don't know whether it's failing because it's using too much memory or too much time ...
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### Optimizing code containing an infinite sum

I have the following expression. It's based on the negative-log-likelihood of a Poisson-Gaussian noise model, i.e. a convolution of a Poisson & Normal distribution. The value $x_{i}$ is the ...
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### Better way to test that a matrix is upper-triangular?

Today, I got to thinking about how to test that a matrix was upper-triangular. So I had a try at it. Algorithm $\quad \quad a_{ij}=0$ Or $i \leq j$ $\Rightarrow$ $True$ My solution is ...
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### Export[] performance

Consider this sequence of commands: ...
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### NSolve for complicated equation involving double cross product

I have the following issue. I am trying to solve a 3-vector equation for the vector slx, sly, and ...
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### Listable on first level [duplicate]

I have some function which take List as input. f[l_List]:=someActions[l] I need apply this function to a list of lists. Now I ...
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### Speed of ConvexHullMesh

Pick $N$ random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in $N,$ ...
I've read here that Mathematica 10 can Obtain symbolic solutions to delay differential equations. Would that help in numericaly evaluating Dickman's function $\rho(u)$ ? It is a delay differential ...