# Tagged Questions

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

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 ...
531 views

### How does Mathematica calculate the nth prime?

When I enter Prime[2000000000000], the two-trillionth prime, Mathematica gives 61427839512211 for the answer after several ...
94 views

### What is the default ColorFunction for MatrixPlot?

I think the the default ColorFunction for ArrayPlot is ColorNegate[RGBColor[{#, #, #}]] &...
74 views

### Classifying text and number features

I am new to the ML algorithms and I am checking the Classify function of Mathematica. I understand the math for the random forest algorithm, but I have a question ...
283 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 ...
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 ...
91 views

### Why patterns names aren't scoped by default?

In a recent question [1] OP asked how to make Module scope working inside Set, so how to get: ...
143 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 ...
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 ...
393 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 ...
221 views

### How does RootOfUnityQ work?

How does Mathematica's RootOfUnityQ function work? That is, how does Mathematica know if a number is a root of unity? Example: Let $x = \frac{1-i \sqrt{2+\sqrt{5}}}{1+i \sqrt{2+\sqrt{5}}}$. Then <...
313 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 ...
334 views

### Daubechies scaling function

In Mathematica in wavelet package with the following codes Phi[x_, j_, k_] := 2^(j/2) WaveletPhi[DaubechiesWavelet[3], 2^(j) x - k] Mathematica computes ...
113 views

### How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute ...
812 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 ...
91 views

### What kind of preprocessing does Mathematica do when I use EdgeDetect on an image?

I am doing my own implementation of Canny and Sobel in another language (not in Mathematica). I was testing the EdgeDetect method (Sobel and Canny), and my own, and ...
43 views

### What is the Chebyshev method for InterpolationFunction?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
94 views

### FrobeniusSolve: how does it work?

Can someone suggest any reference to read? I would like to understand how the algorithm works.
30 views

### Where do DistributeDefinitions and ParallelNeeds put their definitions for newly-launched kernels to find

I'm sorry to keep banging on the definition distribution bell, but here is another (hopefully well-focused enough) question on that vein. If one is trying to distribute the definitions in a package ...
72 views

### What CPU instruction set extensions does Mathematica support?

Most CPUs in desktops and laptops nowadays are backwards compatible with the x86-64 instruction sets. But newer CPUs also have additional instruction set extensions like AVX 2, FMA3, and BMI/BMI2 ...
92 views

### What am I missing in this highly oscillatory integral?

I want to numerically integrate this equation (in python without calling Mathematica): $\int_0^\infty {\rm d}k f(k) J_v(r k) J_n(s k)$ where $f(k)$ is a non-smooth function, $J_v$ are the Bessel ...
94 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.
150 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 ...
272 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 ...
72 views

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 ...
490 views

### How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? (...
73 views

### What is the encoding used when exporting images as MOV with “VideoEncoding” -> “MPEG-4 Video”?

I have a few rasterised images generated in Mathematica, and I want to output them in a video file, ideally using H.264 encoding. I found the following command. ...
77 views

### Is there a method to look inside at the internal code of Built-In functions? [duplicate]

How can I look at the code of built-in functions? Is there something like this: LookInsideFunction[SubsetQ] RETURNS ...
161 views

### Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
35 views

### What is the default SignificanceTest setting for FindClusters with Optimize method?

According to the documentation, the default value of FindCluster's Method option is Optimize....
200 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 ...
158 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 ...
52 views

### Documentation for the Bounded option of SmoothKernelDistribution

I have found the Bounded option useful in the SmoothKernelDistribution function, but I can't find any documentation for exactly ...
504 views

### Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
660 views

### Method used by FindFit

Using FindFit, Mathematica selects an optimal algorithm when Automatic is selected. I'd like to know the name of the method ...
56 views

### Rationalize error

The docs state that "Rationalize[x,dx] yields the rational number with smallest denominator that lies within dx of x." However, testing this out it appears to be false. ...
95 views

### How does Mathematica compute the determinant of a matrix? [closed]

I have been trying to write efficient code for calculating the matrix determinant for some time now. I noticed last night that Mathematica is able to compute the determinant of a $200 \times 200$ ...
63 views

### Algorithm used by Fit[]

Does anyone know what algorithm Mathematica's basic Fit[] function uses? Is it proprietary? I'm trying to do some pretty basic, linear, polynomial data fitting (...
78 views

### How can I access the Criterion function of KI method in FindThreshold for a dataset?

I want to find a threshold for some data set, using Kittler-Illingworth minimum error thresholding method (KI method). To do so, I use the Mathematica built-in function ...
56 views

### SetSystemOptions is obsolete? What is next？ [closed]

When running the following code on Mathematica 10.2 SetSystemOptions[ "CompileOptions" -> "CompileReportExternal" -> True]; I received the message: ...
170 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?
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. ...
81 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 ...
103 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? ...
171 views

### PowersRepresentations Algorithm

I'm trying to understand the mathematics behind counting the number of representations of a positive integer by $n$ distinct $k$th powers, i.e. I would really like to know how to do the Mathematica ...
124 views

### NIntegrate evaluates its 1st argument while it has the attribute HoldAll?

NIntegrate owns the attribute HoldAll: Attributes@NIntegrate (* {HoldAll, Protected} *) ...
700 views

### FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
103 views

### Does FindFit use symbolic differentiation?

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