# Questions tagged [implementation-details]

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

336 questions
Filter by
Sorted by
Tagged with
770 views

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

Consider this toy example: ...
• 58.5k
247 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 ...
• 60.7k
127 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 ...
• 31
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 ...
• 1,196
138 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 ...
• 141
70 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 ...
• 351
87 views

### Which model behind SequencePredictorFunction?

Is the SequencePredictorFunction based on Hidden Markov Model? If so, how does the model estimate the number of hidden states?
322 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 ...
1 vote
66 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 ...
• 375
44 views

### Choice of initial values for FindMinimum

I have been using the FindMinimum function in Mathematica to implement nonlinear regression (for function $f(x,y)$, say). I am curious to find how the starting ...
• 31
111 views

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

For example given the code: ...
• 801
79 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 ...
• 137
94 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 ...
• 101
247 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, ...
• 1,967
167 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 ...
• 147
632 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
114 views

### How is MatrixPower computed?

How does Mathematica compute MatrixPower[m,n]? The documentation states it is equivalent to Dot @@ ConstantArray[m, {n}], but ...
• 1,735
234 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 ...
• 635
183 views

### RandomReal vs Random[Real

Let's say I need random numbers with increasing precision to simulate a particular function, so I try: ...
• 25k
76 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 ...
• 1,250
109 views

### Construction of an additive compound matrix

I want to construct an additive compound matrix which has the following form as output : ...
• 173
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 ...
• 622
1 vote
122 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 ...
• 323
147 views

I am wondering how FunctionConvexity was implemented in Wolfram Mathematica. I am trying to prove the convexity of the function $A(v)$: $$A(v) = -\dfrac{k-1}{\... • 81 2 votes 1 answer 171 views ### How is this asymptotic expansion of an integral calculated? I am strongly impressed by this example from New in 13 as = AsymptoticIntegrate[ (t^10 + 3) Exp[I λ (t^5 + t + 1)], {t, -2, 2}, {λ, Infinity, 2} ] <... • 20.4k 7 votes 1 answer 199 views ### Exactly recreating image NetEncoder output I need to run an exported NetChain in ONNX, surprisingly the model exports and runs successfully, but there's a discrepancy in the image loading stage (the NetEncoder'ing that must be written manually)... • 3,685 1 vote 0 answers 82 views ### How does Mathematica compute PseudoInverse? [closed] What is the algorithm that is used in computing the PseudoInverse in Mathematica? • 501 1 vote 0 answers 96 views ### How does Mathematica numerically evaluate Gaussian Hypergeometric function _2F_1(a,b,c,z) where a,b,c \in \mathbb{C} [closed] Gaussian hypergeometric function _2F_1(a,b,c,z) usually takes a,b,c \in \mathbb{R} and z \in \mathbb{C}. But using Barnes integral representation, one can analytically continue the _2F_1(a,b,c,... • 111 4 votes 1 answer 59 views ### NetNestOperator with custom input / output ports I'd like to use NetNestOperator on a NetGraph that has custom input / output port names, such as ... • 2,015 1 vote 0 answers 43 views ### How is the Riemann-Siegel Z function evaluated in Mathematica? How is the Riemann-Siegel Z function evaluated in Mathematica? Is it calculated using the first so many terms of its power series or by other means? • 285 4 votes 2 answers 495 views ### How does mathematica numerically evaluate the Meijer G-function? The Meijer G-function is defined as a contour integral in the complex plane. Mathematica is able to numerically evaluate such a function quickly and accurately. How does she do that? 5 votes 0 answers 55 views ### What are the valid options for the "ParametricCaching" option in ParametricNDSolve? I am using ParametricNDSolve as part of the calculation of an objective function for an optimization, so I am trying to strike a balance between memory usage and ... • 13.9k 2 votes 2 answers 135 views ### How does Plot choose the points in a figure? Taking a simple example, ... • 491 1 vote 0 answers 308 views ### Is anyone aware of Mathematica implementation of OpenAI's GPT-3 API? Is anyone aware of Mathematica's implementation of OpenAI's GPT-3 API? • 361 19 votes 2 answers 1k views ### How do the functions Reap and Sow actually work behind the scenes? I have read that using Reap and Sow to generate a list of unknown length is much more efficient than using AppendTo over and over. I believe AppendTo works by creating a new list that is one element ... • 344 1 vote 1 answer 73 views ### AsymptoticOutputTracker to Matlab-Simulink What is the structural scheme for AsymptoticOutputTracker in Mathematica? I need this in order to transfer the feedback signals received with the help of ... • 2,256 10 votes 3 answers 291 views ### Why does ReliefPlot not have a version for functions? TL, DR: Use the LightingAngle option to DensityPlot to achieve the same shadows effect as ... • 790 6 votes 1 answer 133 views ### GroebnerBasis internals and runtime dependence on variable list ordering I have a problem I have reduced to asking for a Gröbner basis. For some reason, Mathematica is able to solve this in minutes, while other programs more dedicated to these types of calculations run for ... • 63 9 votes 1 answer 187 views ### Automatic Method for FindMinimum with constraints What is the default method used by FindMinimum with constraints? The documentation says: "Currently, the only method available for constrained optimization is ... • 93 4 votes 0 answers 179 views ### NMinimize differential evolution: how do search points and initial points really work? I am puzzled by the settings of a specific method for NMinimize called DifferentialEvolution, given for example here. The ... • 1,521 3 votes 0 answers 81 views ### Algorithm used by Mathematica for evaluating partial sums Today, while using mathematica, I entered the command Sum[1/Factorial[n], {n, 0, x}] and found that:$$\sum_{x\geq n\geq0}\frac{1}{n!}=\frac{e\Gamma(x+1,1)}{\Gamma(... 138 views

### Is there any way to change the box-formatting behavior thoroughly?

Background The box-formmating behavior is affected by the downvalues of the symbol MakeBoxes. But the formatting behavior is not exactly ...
• 573
281 views

### Implementation of quantum Uhlmann Fidelity in Mathematica

I want to implement the quantum Uhlmann fidelity $$F(\rho, \sigma) := \mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]^2.$$ in Mathematica as a measure of "closeness" between ...
• 201
135 views

### Why Does Subsets[...,{n}] not Output a Packed List, Even Though it Doesn't Unpack?

Assume list is packed. I expect Subsets[] is a structural operation because it depends on the number of elements, not on what ...
• 1,587
45 views

### How algebraic (or more general) expression is represented (memory level, data structure) in Mathematica?

This is not a question about the usage of Mathematica, it is more about implementation. Mathematica is a very huge system, it can provide a series of very advanced operation against a Mathematica ...
439 views

### How is Grad defined for array particularly in non-Cartesian coordinates?

This question can be viewed as a follow-up of What is the definition of Curl in Mathematica? First argument of Grad can be an array, but what definition does ...
• 58.5k
431 views

### Which methods are available for NDEigensystem?

I am trying to find out what methods/options are available for NDEigensystem and descriptions of their use. Perusing the help, online Q&As, Mathematica's in-...
• 7,359
1 vote
62 views

### How does Mathematica determine if a multivariate polynomial is absolutely irreducibile?

I am working with a collection of multivariate polynomials over Q in 5 or more indeterminates, all of which are irreducible over Q. However, after testing their absolute irreducibility via ...
• 225
107 views

### What algorithm(s) are used by MoleculeModify's GenerateConformers?

Starting with Mathematica 12, the MoleculeModify function has a "GenerateConformers" option. What is the algorithm used to ...
• 2,370