# Questions tagged [implementation-details]

For questions regarding the underlying implementation of built-in functions.

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166 views

### Finding NDSolve method details

I have eqs about the NDSolve, I know this code given the solving automatically. How can I find out what method is used behind the scenes? How can I gauge the ...
185 views

### Which FFT algorithm does Fourier[…] use?

Does anyone know which Fast Fourier Transform algorithm Mathematica uses to compute a Discrete Fourier Transform using Fourier[...], and is there any option to ...
124 views

### Why does Fourier give me a different picture than ImagePeriodogram?

I want to take a 2D fourier transform of some data, but when I try this I get unexpected results. When I use ImagePeriodogram I get something that looks like I ...
865 views

### What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
137 views

### Definition of WignerD function?

On Wikipedia, elements of Wigner's D-matrix are defined as D_{m'm}^{j}(\alpha,\beta,\gamma)=\langle jm'|e^{-i\alpha J_z}e^{-i\beta J_y}e^{-i\gamma J_z}|jm\rangle=e^{-im'\alpha}d_{m'm}^j (\beta)e^{-...
138 views

### How to find which automatic method is used by FindMinimum?

This question has already been addressed here and here. The second link consists of an answer by halirutan, which clearly states which method is used in which situation. However, while trying to check ...
193 views

### Listable built-in functions - Why are they so fast on numerical vectors?

Consider the following small example, where I calculate Exp on a large vector by employing the listability which many mathematical built-in functions have: ...
43 views

### Proper implementation of numerically integrated function inside a differential equation

I have a numerically-inverted function TP which is then fed to the differential equation below. My question is: What is the right way to implement this ...
230 views

### Difference between NSolve and FindRoot?

While it is clear what FindRoot does (start at a point and look for local extremum using gradient), how does NSolve work? Also, ...
58 views

### Details of NDSolve calling LSODA

Inspired by my question regarding the computation time of NDSolve using the LSODA backend I was wondering how NDSolve is actually calling LSODA (what arguments are sent to LSODA), i.e. what are the ...
252 views

### How does Mathematica determine when to use scientific notation?

I have code that takes an initial guess for a set of parameters to use in a function that I want to minimize, calculates the function, prints the value, recalculates new parameters via the gradient ...
2k views

### What stopwords list is the Wolfram language using?

The documentation of DeleteStopwords only says that it "uses a standard, built-in list of stopwords". So what is it exactly? Update Now that it is said "standard"...
96 views

### “Exporting” Plot Theme “Classic”

I really like the 3D plots in Mathematica with the PlotTheme option set to "Classic". I wonder if there's a way to export the ...
470 views

### Which algorithm does Mathematica use for “RandomSearch”?

Recently I have used Mathematica for minimization of certain functions and I have realized that even though it lasts much longer, the method "RandomSearch" functions much better than the other methods ...
429 views

### FindMinimum: How can I know which method Mathematica has used?

I have been using FindMinimum to find a local minimum of a non-linear function within a constrained region. How can I know which method Mathematica has selected to find the local minimum? Thanks in ...
92 views

### The actual polynomial behind a BezierFunction [duplicate]

Let's say I have the following Mathematica code pts = {{0, 0}, {1, 1}, {2, -1}, {3, 0}}; F = BezierFunction[pts] How can I find the actual polynomial of the <...
44 views

### How to reconstruct the result of ColorBalance manually?

I want to know about the mathematics behind white balance. I understand that it should be 3 different constants being applied to the red/green/blue channels. Thus I used ...
179 views

### Finding Root of BesselJ [closed]

When I work on some physical problem I needed to know how to get all of first 100 roots of BesselJ[n,x] function -which is a quasi periodic function-, as a List. I ...
58 views

### Evaluation Time of RandomVariate Function

This question is about the runtime of the function RandomVariate. Take a simple normalized Gaussian distribution G on the real line, I tried to generate N random ...
157 views

### How is the Hessian computed using ExperimentalNumericalFunction?

Here and here it was explained how to use ExperimentalNumericalFunction to compute the Hessian of a numerical function. I would like to know how this undocumented ...
126 views

### The algorithm behind InputForm for machine numbers

There are several questions on this site about implementing fast CSV/TSV export for machine numbers without loss of precision. Recently I discovered that Export ...
59 views

### What GraphRepresentations does Mathematica use?

Mathematica can use multiple internal representations for Graphs. Normally, we don't need to care about this. But the specific representation used can influence the ...
62 views

### Why doesn't the low-level box representation of a graph with VertexLabels use GraphicsComplex?

Compare following two low-level box representations of a graph without VertexLabels and one with VertexLabels set to ...
32 views

### LatticeReduce (2D) more than two vector [duplicate]

I wonder how LatticeReduce works when I use more than two vector arguments each one in 2D. I know the Gauss algorithm to reduce two vectors. However, how ...
119 views

### Confusing periodic boundary condition with PeriodicInterpolation

When using NDSolve to solve a PDE with a periodic boundary condition, for example, $y(0,t)=y(L,t)$ using ...
108 views

### underlying data for QuantilePlot[]

What is the best way to produce the actual pairs of points shown by QuantilePlot? Would anyone have an implementation? (I am interested in the simplest possible ...
176 views

### Does DegreeGraphDistribution sample uniformly?

Bug introduced in 10.0 or earlier and persisting through 12.0 The first symptom (histogram below) is gone in 12.0. The second (fraction of connected graphs) persists, showing that the sampling is ...
52 views

### How does DominantColors work?

I'm trying to understand the algorithms behind DominantColors[]. Unfortunately Trace[] and ...
82 views

### Mathematica’s algorithm for limits of multivariable functions

What algorithm does Mathematica use to compute limits for functions in $\mathbb{R}^n$ with $n\geq2$? Here I refer to limits that present indeterminate forms. How can it test every possible path? Does ...
3k views

### How was Nothing implemented?

How was Nothing implemented in Wolfram language at the language level? For example, {a, b, Nothing, c, d, Nothing} will return <...
58 views

### What method does FindGraphCommunities use with Method -> “Centrality”?

Cross-posted to W Community I would like to know what method FindGraphCommunities uses with the option Method -> "Centrality"...
130 views

### How does Mathematica draw 2D and 3D graphics?

I'd like to know Mathematica draws 3D graphics with respect to platform it's running on? For Windows: Is it using Diret3D(DirectX)? For Linux/Solaris: Is it Using OpenGL or Vulkan? For Mac OS X: ...
173 views

### What is Mathematica's ML Linear Regression Method?

When I run p = Predict[trainingSet, Method -> "LinearRegression"];, how is that different from just running ordinary least squares? It's quite slow on a ...
2k views

### What's the default colormap (or color scheme) used in mathematica?

For example, the colors used on this page: http://reference.wolfram.com/language/ref/ContourStyle.html or here: https://www.wolfram.com/mathematica/new-in-10/plot-themes/default.html or here: ...
147 views

### Formulation of skewness and kurtosis calculated from Smooth Kernel Distribution

I would like to know the formulation used to calculate skewness and kurtosis in Mathematica. I see that for a discrete data set, skewness is calculated as ...
491 views

### How does Mathematica numerically integrate to infinity?

Suppose you have a function that can only be evaluated numerically. I.e., you call $f[x]$ with a particular value of $x$ and get a value after a brief amount of time, but there is no good way of ...
190 views

### How FindRoot is implemented

I am trying to reproduce my mathematica code in java, the problem is that I use FindRoot to solve either equations or non linear systems of equations (3*3 speciically). For example ...
60 views

### What image adjustments are made when importing raw camera data?

I am trying to use Mathematica to import and process raw camera data in the Canon CR2 format. What I would like is data which has a linear relationship to exposure. I am thinking that the closest I ...