# Tagged Questions

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

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### Functionality of FindMaximumFlow

I know that the superseeded function NetworkFlow (needs Combinatorica) uses Goldberg-Tarjan's Push-Relabel-Algorithm but i cant find any information on Mathematica's built-in-function (...
1answer
367 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 ...
1answer
139 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 ...
1answer
184 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: ...
1answer
318 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 ...
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165 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?
1answer
170 views

### BoxWhiskerChart Notched: how is the notch calculated?

I am aware of one convention for the uncertainty in a median: it is 1.58 * IQR / Sqrt[n], where IQR is the inter-quartile range and n is the number of data points. This was proposed by McGill, Tukey, ...
0answers
91 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.
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### 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 ...
0answers
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### 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 ...
0answers
55 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 <...
1answer
233 views

### Default algorithm in NonlinearModelFit

Does anyone know the default algorithm used in NonlinearModelFit? The documentation gives several possible algorithms, but I can't figure out what it uses if you do not specify the algorithm. Thanks.
2answers
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### Does FindFit use symbolic differentiation?

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

### What method does NIntegrate use by default?

There is a variety of algorithms for performing numerical integration (See wiki). What method does NIntegrate use by default? I looked at the documentation page ...
1answer
288 views

### The default ColorFunction of DensityPlot before v10?

The default ColorFunction of Plot, Plot3D before v10 is respectively mentioned here and here,...
0answers
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### 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 ...
2answers
190 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 ...
1answer
152 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 ...
1answer
518 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 ...
1answer
148 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 ...
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145 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 ...
2answers
1k views

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

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
0answers
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### 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 ...
1answer
278 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 ...
1answer
277 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 ...
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264 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 ...
3answers
172 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. ...
2answers
294 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 ...
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. ...
1answer
321 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 ...
0answers
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### 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 ...
1answer
491 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 ...
2answers
564 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 ...
1answer
149 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 ...
9answers
946 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 ...
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 ...
1answer
144 views

### What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
2answers
613 views

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

CreateTemporary can generate a unique file name like ...
1answer
606 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 ...
1answer
174 views

### References on functions FindGraphPartition and FindGraphCommunties

Does somebody have some interesting references on the FindGraphPartition and FindGraphCommunties[.., Method -> "Spectral"] ...
0answers
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### 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 ...
0answers
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### 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 ...
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 ...
1answer
263 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 suppose)...
1answer
709 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 ...
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 ...
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### 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 ...
1answer
331 views

### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
1answer
803 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 ...