# 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.

101 views

### How to implement Bresenhamâ€™s algorithm as a system of equations?

Bresenham's line drawing algorithm is usually implemented via loops. But in Mathematica we can take advantage of its ability to solve Diophantine equations. From educational viewpoint it is quite ...
50 views

### Speeding Up RandomVariate

Consider the following code where we first take 1000 independent samples from a Poisson distribution, and then take 1000 independent samples from 1000 different Poisson distributions: ...
94 views

### Sorting eigenvectors according to its projection

The problem I'm trying to calculate the eigenvalues and eigenvectors of a matrix that depends on a parameter x. As x changes, I ...
28 views

### Number triangle programming challenge, separate columns

I am about to enter this number triangle https://oeis.org/draft/A262964 in the oeis, but I don't know how to program it properly. This is partly a mathematics question so I could ask it at math se ...
117 views

### PixelValues along a straight Line [duplicate]

UPDATE to the question I have reformulated the question in order to make it distinct from the one suggested as a duplicate: "Line Intensity Profile From Image." The key difference is that I'm ...
57 views

### Purchasing a laptop to fit Mathematica system requirements [on hold]

I need to buy a new laptop and I intend to run the latest student edition of Mathematica (I am not sure if that is equivalent to Mathematica 10). What I don't understand are the specifications needed ...
300 views

### sudden increase in timing when summing over 250 entries

I see a sudden increase of Timing by a factor of thousands when I sum over 250 elements of a matrix rather than over 249. So for instance, this table contains sums ...
52 views

### Mathematica computes too slowly at the start of a session [on hold]

Everyone, I'm a Mathematica new user. I find it a problem that, when I start a new Mathematica session, it executes too slowly for the first command (say, "1+1", it may take a few seconds before it ...
57 views

### Why is this function taking so much more time when its argument reaches 250? [duplicate]

I am observing something which I do not understand with the following function function: ...
267 views

### How to make geometric intersection faster for geographic borders?

I have developed a solution to identify geographic regions bordering a region in this post (94723). Can this functionality be made to execute any faster? Find which entities in a set border other ...
1k views

### Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
108 views

### 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. ...
6k views

### Finding Local Minima / Maxima in Noisy Data

I'm trying to find local minima / maxima in noisy data, consisting of data values taken at certain time intervals. Ideally, the function should take a pair of lists (one containing time values and one ...
45 views

### Fast way to get edge-list of graph in terms of vertex indices (not vertex names)

I am looking for the fastest way to achieve the following: Given a Graph, retrieve its edge list in terms of vertex indices (not actual vertices). For example, ...
34 views

### NIntegrate within NMinimize - how to optimize the code?

How I can optimize these numerical calculations? Most annoying is encountering instabilities (numerical errors). I have a predefined function: ...
198 views

### Efficient conversion between two partition representations

I have a list of distinct expressions. We can represent a partitioning of list in two ways: As a list of sublists ...
605 views

### In a list of points, how to efficiently delete points which are close to other points?

Consider a list of points: pts = Partition[RandomReal[1, 10000], 2]; ListPlot[pts] I'd like to delete points so that the minimum distance between two points is ...
167 views

### Compiled function crashes kernel when trying to list over different length arguments

Bug introduced in 8.0 and fixed in 10.0 I'm trying to speed up a tally/binning operation that I have to run many times. I have many lists of between 1 and 10 numbers from the range [1,5] and I ...
70 views

### Speed up rendering of ContourPlot3D object

Please can you advise me how to speed up the rendering of the following two planes? When I click and drag to rotate the plot, its movement is quite jerky. Presumably it is working harder than I need ...
346 views

### Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
468 views

### Efficiently generating 2-D Gaussian random fields on the sphere

Context A couple of years ago I posted this question for an efficient code to generate an n-D Gaussian random field (sometimes called processes in other fields of research), which has applications in ...
35 views

### Plotting precise intersections involving singular functions

I have pseudo-elliptic functions defined on a parallelogram within $\mathbb{C}$ and I would like to clearly highlight the path within this parallelogram which satisfies the real part of my ...
157 views

### How to populate a large sparse array efficiently

I am trying to populate a large 2D sparse array and sum up all the columns at the end. I tried generating a set of rules and then generate a matrix using SparseArray or break the data into chunks but ...
32 views

### Evaluation of likelihood very slow

I am trying to implement a simple statistical model for the first time in Mathematica. My model is made my one random variable which is the sum of background and signal. Background is an exponential ...
62 views

### Closing over array values makes Compile choke with CompilationTarget -> “C”

When I attempt to Compile a closure which contains an array of the appropriate type, it works just fine with ...
83 views

### Recursive calculation is very slow

I've got a recursive definition of Arcs that shares equal length and a several other dependencies to each respective predecessor. (Imagine a book being bent.) I formulated all necessary things here: ...
81 views

### Optimization of a voxel projection function

I implemented a function to check if a voxel (3D pixel) is well projected on the space of a image (black and white silhouette) through a perspective camera. The function does the work but It need more ...
57 views

### Eigenvalues FEAST method - performance is very variable

I am running the FEAST method option for Eigenvalues on sparse matrices of dimension around 500,000. I look for about 50 ...
687 views

### Numerical integration — Mathematica vs Python (w/ Scipy) performance

I'm about to tackle a problem that involves a lot of (multi-dimensional) numerical integrations and also subsequent optimizations, and so I want to make sure at least the integration step is as fast ...
43 views

### More efficient way to generate lattice graph with edges between visible vertices?

Given a nXn lattice, I need to generate the graph such that there is an edge between two vertices iff they are directly "visible" to each other, i.e., there is no vertex between them. I'm using ...
77 views

### How to speed up summing a large number of vectors

First let me explain what I am trying to do in my code. Assume that I send a very short chirp (2,000 ms long) into a domain filled with 20,000 particles randomly scattered in the domain. The ...
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 ...
111 views

### Strategy to build efficiently an image using parts of many images

I have about 1000 images of 1000px $\times$ 1000px and a list which contains the coordinates of the pixels to select, for each of the 1000 images. Each pixel is used once, so the final image is a full ...
151 views

### Is it possible to speed up the user-defined function CAGDBezierSurface?

For given control net of points $P_{i,j} \quad i=0,2, \cdots m, \quad j=0,2,\cdots, n$, the BÃ©zier surface is defined by the following equation: ...
279 views

### How can this resampling code be made faster?

Suppose I have a matrix: sbt = RandomInteger[{0, 2^16 - 1}, {5202, 3465}]; It represents an image and I would like to do "pixel binning" on it, where I take ...
195 views

### Slightly increasing complexity of function increases calculation time by magnitudes

I am trying to calculate an impedance value from voltage and current functions. The calculation method is based on how an actual measurement device performs it. I have two different current function, ...
630 views

### How to delete subsets quickly?

I have some data like this: ...
2k views

### Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. Attempt I wrote the ...
334 views

### How to speed up the plotting of B-spline curve?

Three months ago, I asked a quesion about B-Spline basis function here, Today, I used this function to plot B-spline curve. The definition of $N_{i,p}$ ...
41 views

### NIntegrate option for FourierSeries

I would like to use FourierSeries but it is very slow. My guess is that it is because it uses symbolic integration: ...
388 views

### Looping through 3 million elements of a list to 'Set' values is slow

I am looping through the 3 million elements of a time-series (v1, o1) and corresponding values (v2, o2). v1 contains a uniformly increasing timestamp (e.g. 1 to 3,000,000 in increments of 1) o1 ...
112 views

### Is this a reliable method for getting a list of very large primes?

As noted here, both PrimePi and Prime are documented as having their limits somwhere around $10^{15}.$ ...
173 views

### Finding planetary conjunctions with Mathematica (project-level) [closed]

Summary: What's an efficient way of finding planetary conjuctions with Mathematica using the SPICE kernels, and without using AstronomicalData (which I believe is less efficient). NASA publishes ...
4k views

### File-backed lists/variables for handling large data

Background Currently I am working with some large data (most of it generated by Mathematica itself). I usually find it a hassle to do this. For example, I just exported a large amount of data to ...
195 views

### Is there a PrimeQ whose accuracy guarantee you can adjust?

Say I have a list of a million integers each with a million digits, and I want a crude sieve to see which have a chance at being prime. Mathematica has a PrimeQ function, which appears to be slow ...
104 views

Has anyone benchmarked LibraryLink vs MathLink when passing large arrays? Specifically I would like to know how performance compares when using the following to pass and return a large array: ...
540 views

### Efficient lazy weak compositions

In Mathematica all weak k-compositions of integer n can be generated using permutations of integer partitions: ...
137 views

### My evaluation is taking a lot of time

I was evaluating the roots of a transcendental equation, when I noticed that Mathematica never finishes but stays in the running state. The following is the code that I was using: ...
Let list be a list of lists, the elements of which are random integers in the interval $[1,c]$. Each element $i$ has a probability ...