# Questions tagged [implementation-details]

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

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### How is the reference line in QuantilePlot defined?

We know that, when using QuantilePlot to visualize data, a reference line will be added by default. For example the red line below: ...
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115 views

### Orientation of 1st order 2D boundary mesh is counter-clockwise but 2nd order one is clockwise, any deep reason?

Consider this toy example: ...
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35 views

### The "StandardGaussian" bandwidth selection method in the SmoothKernelDistribution function

I have a list of points which follow the Gaussian distribution: ...
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1 vote
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### On ContinuedFraction

The code p = Integrate[E^-x^2, {x, 0, 1}] p // ContinuedFraction produces Does this mean that (i) Mathematica knows that a terminating or periodic continued ...
141 views

### Understanding NDSolve's implementation of the method of lines

In order to better understand the MethodOfLines flag, I tried comparing the results of NDSolve for a driven heat equation with a ...
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1 vote
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### A request on the kernel of the function ”SpheroidalEigenvalue“ in Mathemitica 11

I want to understand the algorithm of the function "SpheroidalEigenvlaue" in Mathematica 11, especially the code of the following command. Then I will try to use this algorithm to reproduce ...
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105 views

### How is the analytical continuation for the HurwitzZeta function implemented?

Following up on this question, I am trying to understand the implementation details of the HurwitzZeta[x,y] function in Mathematica, particularly when the first ...
152 views

### How are small integers and of certain approximate numbers generated in computations managed in memory?

In the documentation tutorial/SomeNotesOnInternalImplementation, it says: Most raw objects such as strings and numbers are allocated separately; however, unique ...
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290 views

### What do the arguments of a generated BSplineFunction mean?

For example, if we evaluate this: BSplineFunction@{{0,100},{200,50},{200,0}} we'll get ...
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812 views

### FEM doesn't output exactly the same solution for exactly the same code?

Consider this toy example: ...
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333 views

### How is the zoom tooltip in the "Coordinates Tool" implemented?

I notice that the built-in "Coordinates Tool" has a very efficient zoom tooltip displaying an enlarged portion of the image along with coordinates and row/column indices: How to get the ...
188 views

### Interior point method for unconstrained problems

I was recently working on applying the FindMinimum function to $f(x)=(x+1)(x-1)$, and chose the interior point method as the 'method', which yielded $x=0$. I would like to better understand how the ...
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2k views

### What happens if you don't Reap what you've Sown?

As I understand it, when using Sow[expr] you throw the expr on some private stack which you can ...
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227 views

### Inverse Laplace Algorithm used in Mathematica [closed]

I have a general question. I want to know what algorithm (The name of this numerical method) is already used to calculate a numerical Inverse Laplace in Mathematica. I used the function ...
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108 views

### What is LatticeReduce minimizing?

According to the manual page on LatticeReduce, The product of the norms of lattice vectors will decrease. The claim seems to be true for small lattices, but, I cannot confirm this for higher ...
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### Which model behind SequencePredictorFunction?

Is the SequencePredictorFunction based on Hidden Markov Model? If so, how does the model estimate the number of hidden states?
419 views

### Solving hyperbolic equation with parallelization in python by elucidating Mathematica algorithm [closed]

So! I have what seems like a rather basic hyperbolic equation to be solved written in Mathematica, with an integer input ‘n’, for which I am seeking the First {x,y} Integer solution to satisfy the ...
83 views

I don't quite understand how SessionSubmit[ScheduledTask[expr,spec]] works. We can create a background task, which can go without interfering with the main loop. If ...
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185 views

### Are derivatives from interpolating functions created by NDSolve using derivatives of the spline or numerics from solving DE

For example given the code: ...
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112 views

### Theory behind CountRoots

According to this page, one can compute the number of zeros of a meromorphic function over an interval in Mathematica. I am working with univariate functions of x, which are meromorphic elementary ...
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109 views

### Does RandomArrayLayer implement the reparameterization trick?

I want to backpropagate through random operations (e.g. learn the mean and variance of a Gaussian random variable). I assumed that ...
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495 views

### Is K is a function? [duplicate]

Some of the capitalized single letters are functions. Starting a fresh kernel and typing in the 24 capital letters, the following letters turn black since they are special functions, ...
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190 views

### How does FindRoot decide if a solution has converged?

I am solving a 1D non-linear differential equation using the finite element method with NDSolve. From the documentation I understand that the equation is discretized and then solved with FindRoot, I ...
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786 views

### Mathematica internal source code for a numerical method

I read this (Six Reasons Why the Wolfram Language Is (Like) Open Source), which inspired me to re-investigate Mathematica's implementation of some numerical methods. I would like to see the code that ...
1 vote
152 views

### How is MatrixPower computed?

How does Mathematica compute MatrixPower[m,n]? The documentation states it is equivalent to Dot @@ ConstantArray[m, {n}], but ...
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263 views

### Why does NMinimize using NelderMead without PostProcessing always stop at the nearest decade of iterations, e.g. 100, 110, 120

Why does NMinimize using NelderMead without PostProcessing always stop at the nearest decade of iterations, e.g. 100, 110, 120... Perhaps Catch Throw can prevent this e.g., see this answer, but that ...
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304 views

### RandomReal vs Random[Real

Let's say I need random numbers with increasing precision to simulate a particular function, so I try: ...
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93 views

### My construction of additive compound matrices doesn't work sometimes; why?

Using the multiplicative compound matrix --see definition at Are compound matrices implemented in mathematica? one may define also additive compound matrices ...
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### Construction of an additive compound matrix

I want to construct an additive compound matrix which has the following form as output : ...
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1 vote
67 views

### Can LinearOptimization (ex. LinearProgramming) support other methods (Ellipsoid method)?

Can LinearOptimization (ex. LinearProgramming) support methods other than "InteriorPoint", "Simplex", "RevisedSimplex"? Specifically, I need the Ellipsoid Method. Are ...
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1 vote
145 views

### Spelunking yields <<kernel function>> [closed]

This is in the spirit of the old but excellent thread: What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools) Using ...
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