Questions tagged [simplex]
The simplex tag has no usage guidance.
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Uniform sampling from intersection of hypercube and simplex [migrated]
Background
Discussion from http://blog.geomblog.org/2005/10/sampling-from-simplex.html and Uniform sampling from a simplex have shown algorithms of sampling from unit simplex uniformly:
Let $X_i \sim ...
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Sort array of 3D points to maximize number of tetrahedra in the array
Let $P$ be a indexable set(array) of points in $\mathbb{R}^3$ s.t. $P = \{p_0,p_1,p_2,...,p_n\}, p_i \in\mathbb{R}^3$.
I want to sort $P$ so that every 4 consecutive points forms a non-coplanar ...
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Periodic 4D Triangulations
I am looking for references and/or algorithms for generating 4-dimensional periodic triangulations on unit 4 lattices. That is, generating a space filling triangulation of the 4D integer lattice (Z^4) ...
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How does Bowyer-Watson algorithm for Delaunay triangulation run in $O(n^2)$ but runs over all the simplexes?
The Bowyer-Watson algorithm for Delaunay triangulation is known to run in $O(n^2)$ according to the authors, where $n$ is the number of data points in $\mathbb R^d$.
In addition, the algorithm (for ...
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Solving linear programming problem with mixed type of constraints
I have a query in solving the problem below:
An automobile company has two factories. One factory has 400 cars (of a certain model)
in stock and the other factory has 300 cars (of the model) in stock. ...
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What algorithm do SVMs use to minimize their objective function?
Support Vector Machines turn machine learning linear classification tasks into a linear optimization problems.
$$ \text{minimize } J(\theta,\theta_0) = \frac1n \sum_1^n \text{HingeLoss}(\theta,\...
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Better way to decide if a set is a pure simplicial complex
Setup
I am trying to write a function that determines if a set of vertices, edges and faces is a pure simplicial complex.
A pure simplicial complex is a set where all facets have the same degree, a ...
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In a LP problem Ax = b, how to solve for A instead of x?
I have a multi-objective linear programming problem of the form Ax = b, where A is a matrix and x and b are vectors. x is known, and I'm looking to minimise each row of b by solving for A.
Constraints ...
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How to uniformly sample a sorted simplex
I am looking for an algorithm to uniformly generate a descending array of N random numbers, such that the sum of the N numbers is 1, and all numbers lie within 0 and 1. For example, N=3, the random ...
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