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

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11
votes
1answer
423 views

What function generates random numbers in a compiled function?

I am writing a simulation for 2D random walk. I wrote several version of code, and found that the speed is like this (fastest to slowest): C++, Mathematica compiled procedural code, Mathematica ...
6
votes
1answer
208 views

Algorithms behind implemented Mathematica functions [duplicate]

When I use Mathematica for analysis and I write a publication, readers often ask me: "What is the algorithm behind your calculation?". I answer that I did it with Mathematica and if they are ...
5
votes
1answer
80 views

Actual bins used for Pearson Chi Square Test

PearsonChiSquareTest[data, dist] computes bins for data as a step towards calculating the test statistic. For continuous ...
-2
votes
1answer
119 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
8
votes
1answer
167 views

Possible Method for MatrixExp

Well, probably a hard question, but I think it's better to cry out loud :). I noticed that MatrixExp owns Method option when ...
2
votes
0answers
49 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
3
votes
0answers
49 views

How does Mathematica automatically choose which classifier method to use?

I'm interested in what heuristics are used in Classify's choice of method.
5
votes
0answers
94 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
0
votes
0answers
35 views

Algorithm for converting truth tables to Boolean functions

The function BooleanFunction is able to convert a truth table into a Boolean function. Does anyone know what is the mathematical background and/or algorithm that ...
0
votes
0answers
52 views

How to make work Plus function? [duplicate]

I have a little problem. I have k = 1.56343*10^9; r = 9.10492*10^18. And I should receive a (2*r*r-k*k)/2*r*r, it equals to ...
6
votes
2answers
183 views

Built in function without Attributes Listable works as if it has Attributes Listable

Can Built-in function works as if it has Attributes Listable even if it doesn't have that ...
-3
votes
1answer
67 views

Miller-Rabin algorithm [closed]

I want to implement the Miller-Rabin algorithm in Mathematica to check if a number is prime with at least 99.99% probability. I used this: ...
1
vote
2answers
95 views

Does FindFit use symbolic differentiation?

Does FindFit use symbolic differentiation when optimizing by least squares a non-linear function?
3
votes
1answer
208 views

What method does `NIntegrate` uses by default?

There is a variety of algorithm for performing numerical integration (See wiki). What method does NIntegrate uses by default? I looked on the documentation page and I saw that the function ...
4
votes
1answer
135 views

The default ColorFunction of DensityPlot before v10?

The default ColorFunction of Plot, Plot3D before v10 is respectively mentioned here and ...
2
votes
0answers
80 views

PlotRange->Automatic the exact function used to calculate outliers

I know that PlotRange->Automatic does the following: "the distribution of coordinate values is found, and any points sufficiently far out in the distribution ...
2
votes
2answers
120 views

Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
0
votes
0answers
61 views

Plot function failure, and understanding how mathematica selects recursion points for correction

I think it is best to start out by directing everyone to this link. The discussion concerns why the Plot function fails to accurately generate a simple sine wave for given parameters. The answer given ...
2
votes
1answer
103 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
8
votes
1answer
237 views

How to know the internal algorithms of functions like Predict or Classify?

The document centre seems only explain how to use these functions, but just in an very brief way. I know Mathmatica is not open source, so we can not expect to see the code of the function, but are ...
0
votes
1answer
73 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
1
vote
0answers
29 views

Apparent issue with derivative of FractionalPart

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
3
votes
1answer
156 views

Root finding: zeroes of Mathieu function

I am finding the roots of the Mathieu sine function, and find Mathematica and Maple do not agree on the solutions. For example, consider the solutions of ...
14
votes
1answer
257 views

Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
0
votes
0answers
61 views

Birch clustering in Mathematica

I want to implement birch clustering in Mathematica. MAthematica only has 4 methods of clustering, is there any implementation for Birch clustering? Birch clustering is much faster than K means ...
3
votes
0answers
160 views

Distance Time Warp (DTW) function implementation in mathematica

The DTW (Distance time warp) is given here http://en.wikipedia.org/wiki/Dynamic_time_warping There is an implementation of DTW in R as well as MATLAB. However i am unable to find something for DTW in ...
3
votes
3answers
143 views

Pick bug? level 0 matching

A previous discussion of this issue (Is there a bug in Pick?) accepted that matching at level 0 is not a bug in Pick. Was that correct? I am not yet persuaded. ...
7
votes
2answers
254 views

Get name of hidden inbuilt functions (like Ticks drawing)

how do I get the name and definition of a builtin Mathematica functions? For instance, I would like to see how default Tick plotting function is implemented. However, it is not clear where it is and ...
2
votes
0answers
52 views

Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
5
votes
0answers
201 views

Citation of the algorithms used in FindGraphCommunities

For my research work I need to put a comparison of different community detection algorithms. Instead of implementing all those algorithms once again, I would like to use the methods already provided ...
0
votes
0answers
55 views

What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

Recently asked this question http://math.stackexchange.com/questions/888369/betweenness-centrality-how-long-does-mathematica-take on the Mathematics SE. Does anyone know, as a follow up, what ...
4
votes
1answer
345 views

Use of Strassen's algorithm

Strassen's algorithm is an algorithm for matrix multiplication that is asymptotically faster than the naive one. In practice, the matrices involved have to be quite large before Strassen's algorithm ...
5
votes
2answers
286 views

Where can I get detailed information on how the Plot command works?

The command Plot[x^2, {x, -3, 3}, PlotStyle -> Arrowheads[{-.025, .025}]] /.Line -> Arrow produces this output. What I don't understand is what ...
6
votes
9answers
895 views

Find the smallest positive integer that satisfies a certain condition

I know Mathematica is really powerful when it comes to functional operations like applying a list of tasks to a list of variables. Sometimes I feel like it isn't the most powerful tool when it comes ...
4
votes
1answer
135 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
1
vote
2answers
299 views

How to generate a unique file name similar as that created by CreateTemporary

CreateTemporary can generate a unique file name like ...
0
votes
0answers
293 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm mathematica uses. It's probabaly similiar to ...
4
votes
0answers
126 views

Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
2
votes
0answers
58 views

Can BreadthFirstScan be modified?

I would like to obtain a "slick" implementation of A*-search algorithm on Graph objects, using the built-in BreadthFirstScan (if that is possible at all). I noticed that BreadthFirstScan is static in ...
1
vote
0answers
143 views

How to write my own interpolation method

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
4
votes
1answer
156 views

What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I ...
6
votes
2answers
130 views

Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...
9
votes
1answer
114 views

Why does $Failed have attribute HoldAll?

Why does $Failed have attribute HoldAll? Are there typical situations where $Failed is ...
5
votes
0answers
304 views

How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
8
votes
1answer
291 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
1
vote
0answers
36 views

Internals of Prime function [duplicate]

Does anyone knows how exactly Prime works ? For example how Prime[1000000000] is calculated ? The only information I found was ...
2
votes
0answers
84 views

What are the limits of the Prime-functions? [duplicate]

Will Prime and PrimePi test up to 3 * 10^12? Where can I find the limits for these funtions? ...
11
votes
1answer
237 views

What is the default ColorFunction for Image3D?

What is the default ColorFunction for Image3D? I find it a bit confusing that the most intense colour is not shown where the ...
9
votes
1answer
969 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...