Questions tagged [performance-tuning]

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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Find all non-isomorphic trees with $n$ nodes

I would like to compute all non-isomorphic trees with n nodes efficiently. I use the following approach: I create all possible trees ( Visualizing Cayley's Formula in Mathematica) and filter the ...
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Copy DateListPlot ticks in ListLinePlot (for large data)

It is not very surprising that plotting a PackedArray is faster to plot than a list of pairs (date, value), nonetheless the plotting time may be prohibitive with <...
I have the following code which solves for Integers the equation $$a_1+a_2+a_3+a_4+b_1+b_2+b_3+b_4+c_1+c_2+c_3+c_4=tot$$ with $$-4<a_i\in \mathbb{Z}<4$$ $$-7<b_i\in \mathbb{Z}<7$$ $$-4&... 0answers 38 views Problem with the return type of Compile [closed] Can I return anything other than a real number with a compiled function ? In the example below, I use Compile on a toy function to illustrate my problem, the real ... 1answer 71 views Minimize Number of Boolean Formulas that Evaluate to True I'm interested in a MinSat variant: given a list of boolean formulas like ... 2answers 276 views Using compile to speed up evaluation of a While loop I want to calculate a loop. For speed, I compiled my code. Even after the compilation, it is still very slow in getting the results. Are there any further improvements that can be made to my code? <... 1answer 150 views Performance of select from a 3d list - Mathematica slower than Python I am creating a random 3d data set in Matematica 12.1. Then I am selecting all points that are in a certain range of one axis. The same I am doing in Python (same computer, Python 3.8.5, numpy 1.19.2) ... 0answers 101 views Repeated calling of a ParametricNDSolve result in a faster way? I recently learned of ParametricNDSolve and found that I need to compute it once and then call its result sol at different ... 1answer 87 views Multiply lists: element-wise but matrix-like in the last 2 levels How can I do the following computation more efficiently? We have nested lists and want to multiply element-wise, where the 'element' is the deepest 2 levels treated like normal matrix multiplication. ... 1answer 90 views Fastest way to compute the solution of this equation I am looking for the solutions to the equation :$$a_1+...+a_n =x$$with$$ -3 \leq a_i\in \mathbb {Z} \leq 3 \ \ \ \ \ \forall ix \in \mathbb Z$$Mathematica will get you the solutions ... 1answer 110 views GroebnerBasis internals and runtime dependence on variable list ordering I have a problem I have reduced to asking for a Gröbner basis. For some reason, Mathematica is able to solve this in minutes, while other programs more dedicated to these types of calculations run for ... 1answer 51 views understanding this timing result I got two timings which I do not understand. ... 2answers 141 views Unexpected timing result of Total and Part performance of packed array Define a = RandomReal[1., {2, 100, 100, 100}]; then Total[a, Infinity]; // RepeatedTiming {0.00183727, Null} and ... 1answer 169 views How to speed up by Compile? I need to NDSolve a system many times by scanning some of its parameters and do some matrix calculation with the (discretized) solutions. The example is the ... 2answers 699 views Why is mathematica so slow when tables reach a certain length So Here is an example: I have a table full of numbers: foo = Table[Table[RandomComplex[], {i, 1000}], {j, 8192}]; No I want to do things with some elements of this ... 1answer 96 views Memoization of functions with optional arguments Consider the following function that generates a sparse diagonal matrix: ... 1answer 53 views Speeding Up ImageApply / Binarize? I have a 5Kx4K image. I'm wanting to binarize it. At the moment, I have a simple binarization function, but it's taking 6 seconds or 8 seconds to binarize. ... 4answers 153 views How to use function GeneratingFunction  to solve this combinatorial problem efficiently? Divide the 14 elements {A, B, C, C, C, C, D, D, D, D, E, E, E, E} into 7 groups (one group all have two elements), and I want to find out how many kinds of methods ... 1answer 200 views Program for efficient computation of given functional: I need to plot the following functional with accuracy:$$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy,s) − F(x −\mathrm iy,s)}{\mathrm e^{2πy}-1}, $$Where  F(z,s) = \dfrac{1}{z^s\Gamma(\... 2answers 110 views Most efficient strategy for integrating over removable poles? I am finding many situations where I have to numerically integrate some function f(x) of the form:$$f(x)=f_{s}(x)-ax^{-n},$$where f_s is a special function with a finite-order pole that is ... 1answer 77 views Improving performace of GeoDistance and NearestNeighborGraph I am trying to construct a NearestNeighborGraph of the 3143 US counties, using their latitude and longitude positions. ... 4answers 421 views How to reduce the time to solve this system of equations? I am trying to solve the system of equations. My code ... 2answers 124 views Best way to write a system of conditions Quite simply, I am wondering if there is a cleaner (and more easily altered) way to write a system of conditions for an evaluation. For instance, suppose I have something like (I don't think a real ... 0answers 44 views Setting up constraints in NMaximize I have an optimization problem for which I'm using NMaximize. For the constraints I need the variables to belong to a particular set. ... 1answer 168 views Finding invariant matrix given group elements I have a question about speeding up / optimising the following calculation. I have a feeling there is a way to rewrite it but I can't quite see what to do. In d=3 dimensions, given a set of ... 1answer 131 views why does wolframscript start an instance of Mathematica frontend? The following wls file surprisingly creates an instance of Mathematica (v12.1) on OS X 10.15.7: ... 3answers 180 views generating lists of integers with constraint Suppose you have the list a=(k_1,k_2,k_3, \dots, k_N) such that k_{i}\; (i=1,\ldots, N) are non negative integers. How can you get all the lists that satisfy the constraint \sum_{i=1}^{N} k_{i}=M... 0answers 78 views Fast definition of sparse tensor I'm defining a sparse array through ... 0answers 117 views Replacing an part in a dataset I have a nested dataset, which has been created to be the correct size from using Table, and I wish to replace parts of the dataset with the data. My dataset would look like (with placeholder values ... 1answer 95 views Improve running speed of FullSimplify function How can I make this code faster? The checking with FullSimplify takes a lot of time. ... 2answers 333 views Speedup calculation of the largest eigenvalue and eigenvector of a 400×400 matrix? [duplicate] Actually, the matrix is an adjacency matrix of a network. The code is: ... 2answers 80 views Matrix which gives the existence in a graph of a path of length k In a graph G, for some k, I am looking to get a 0-1 matrix whose ij^{\text{th}} entry is 1 whenever vertex i has a path of length k to vertex j in G, and is otherwise zero. I have been ... 1answer 113 views Speeding up code doing random sampling I have a particular probability distribution (that is a function of a parameter \phi), that I would like to sample from and then do a listplot for that function. Here is the code that I came up with:... 0answers 54 views Slow evaluation of derivative of Solution of NDSolve I need to perform a Fourier Transform on the results of a ParametricNDSolve function as well as on the derivative of one of the coefficients. Now I do this by ... 1answer 93 views speed up symbolic summation I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ... 3answers 585 views Faster "Closest Pair of Points Problem" implementation? The closest pair of points problem is a common computational geometry problem: given n points, find a pair of points with the smallest distance between them. A naive algorithm of finding distances ... 1answer 172 views (Non)LinearModelFit hangs on "trivial" linear fit (Fit succeeds) A simplified version of my function and a simplified subset of my data (real data also has weights, if that matters, but I tested both with and without those): ... 3answers 491 views Improve running speed for DeleteDuplicates How to make this faster? I want to remove elements that satisfy the condition below but it's way too slow. ... 0answers 50 views Finding if a number is perfect square [duplicate] I used the following code to found if a specific number is a perfect square: ... 1answer 152 views Reducing execution time without compromising on accuracy and precision I have the following NDSolve code, and it is extremely time consuming for me to run it, even when I set both AccuracyGoal and <... 2answers 123 views Can I improve performance of compiled deleteDuplicates? I'm working on a project to compute pairs of complex numbers and need to delete the duplicates (within some tolerance, 10^-5 below). I was wondering if the performance of my compiled version can be ... 0answers 32 views Easiest Way To Parallelize Derivatives What I would like to do I have a Lagrangian (a scalar). Of this function I take the derivative w.r.t. to metric-components. Of the result, I take again a derivative. The formula looks like \partial_a\... 1answer 169 views Why does the Frontend slow down in long sessions? I'm running Mathematica 12.1.1 on my Windows 10 laptop (Dell Latitude E5550 with Intel iCore 5, 8 GB RAM). My MMA sessions tend to be very long, sometimes extending on over days and weeks, interrupted ... 2answers 389 views Ways to speed up numerical integration This first code block is just to create the functions I'm considering. Actual problem follows. ... 1answer 50 views loop execution time difference after Map operation I am box filtering data from a DNS simulation. When filtering the original data read from a file, this is fast. When filtering a function of these data after applying Map, it is 10 times slower. If I ... 0answers 56 views Making animation more efficient I created some code to create a nice animation. However, it takes a considerable amount of time to run it. I would like to make it run in the least amount of time possible. First, I load two packages ... 2answers 268 views Generate random lines that don't be too crowded between the intersections It's easy to generate random lines, such as this ... 0answers 63 views How to evaluate the following integral faster? I have a problem with the time required for evaluating the multi-dimensional integral and would be grateful for any help in reducing this time. First of all, there are some pre-definitions used in the ... 0answers 38 views Solving Kronecker-structured linear equations I need to approximately solve the following underdetermined system of n linear equations$$y_i=a_i^T X b_i Where $X$ is $d\times d$ unknown matrix, $a_i$ and $b_i$ are given vectors and $n=d$. Is ...
Christmas is around the corner! In preparation, consider the polynomial f[x_,y_]:= 1/10 (4 - x^2 - 2 y^2)^2 + 1/2 (x^2 + y^2) and define $r=(f_x,f_y)$ using the ...