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

learn more… | top users | synonyms

3
votes
1answer
264 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 ...
6
votes
1answer
266 views

The default ColorFunction of DensityPlot before v10?

The default ColorFunction of Plot, Plot3D before v10 is respectively mentioned here and ...
3
votes
0answers
136 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
171 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 ...
2
votes
1answer
139 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 ...
9
votes
1answer
458 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
139 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 ...
7
votes
0answers
139 views

How does Mathematica resolve symbolic systems of inequalities? [closed]

Before getting into my question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A major part of the ...
5
votes
2answers
1k views

what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
1
vote
0answers
40 views

Apparent issue with derivative of FractionalPart [duplicate]

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 ...
4
votes
1answer
259 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
273 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 ...
3
votes
0answers
249 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
164 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
290 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
55 views

Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
6
votes
1answer
309 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 ...
2
votes
0answers
76 views

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

I recently asked this question on the Mathematics SE. Does anyone know, as a follow up, what algorithm Mathematica uses to calculate the betweenness centrality vector (of $N$ elements) for an ...
4
votes
1answer
472 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 ...
18
votes
2answers
542 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 ...
4
votes
1answer
147 views

The algorithm of ListGraphs[n,m]

I'm not sure if this is a Mathematica problem, math problem or a CS problem, so if this is off-topic please transfer it. In the package Combinatorica there is a ...
6
votes
9answers
942 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 ...
1
vote
0answers
103 views

How to find matrix exponential using RootSum? [duplicate]

From what I've been able to deduce, Mathematica uses a root sum scheme to determine the exponential of a matrix. Can someone please explain to me the theory behind this? I've searched, but have had no ...
4
votes
1answer
143 views

What is the formula Mathematica uses for ZetaZero?

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

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

CreateTemporary can generate a unique file name like ...
3
votes
1answer
571 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
1answer
158 views

References on functions FindGraphPartition and FindGraphCommunties

Does somebody have some interesting references on the FindGraphPartition and FindGraphCommunties[.., Method -> "Spectral"] ...
4
votes
0answers
140 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 ...
3
votes
0answers
71 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
147 views

How to write my own interpolation method [duplicate]

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
9
votes
1answer
248 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 ...
11
votes
1answer
689 views

What type of solver does Mathematica use in LinearSolve

I have a question regarding linear equation solvers. For a specific 9-diagonal matrix, every method I tried in C++ (Gaus, GCC, BICGTAB) didn't work (even though they worked for other matrices). But in ...
6
votes
2answers
141 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
133 views

Why does $Failed have attribute HoldAll?

Why does $Failed have attribute HoldAll? Are there typical situations where $Failed is ...
20
votes
1answer
688 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 ...
10
votes
1answer
329 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
3
votes
1answer
753 views

Specific Mathematica algorithms, for example LU Decomposition

Where I can find detailed information on algorithms used by Mathematica, especially for numerical methods. The Manual doesn't seem to iclude specifics in most cases. For example I get a different LU ...
1
vote
0answers
38 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
102 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? ...
12
votes
1answer
371 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 ...
15
votes
1answer
1k 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 ...
10
votes
1answer
984 views

How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
1
vote
1answer
646 views

FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
4
votes
1answer
2k views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
3
votes
2answers
380 views

How does Accumulate work?

Accumulate can be used to compute the partial sums of a list. The partial sums can also be computed using a For loop but this ...
4
votes
0answers
89 views

JewishNewYear date limitation

The documentation for the function "JewishNewYear" in the "calendar" package declares that the year argument must be between 1900 and 2100. No explanation is given for this limitation. The function ...
7
votes
0answers
168 views

Finding hidden treasure (aka finding undocumented functions) [duplicate]

I was searching for a way to determine if a point is within a polygon and stumbled upon rm -rf's answer. (actually, I really wanted to find a point within a ...
21
votes
2answers
894 views

Blend code for built-in ColorData schemes

Hi I want to get a blend similar to "SunsetColors". To make those slight modifications, I would like to know the precise blend of that color scheme. My try: ...
20
votes
1answer
488 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
14
votes
1answer
440 views

What is the real default CellEvaluationFunction?

The default CellEvaluationFunction is Identity but one can quickly see that this is handled specially as an equivalent function, ...