polytope | Geometric operations on polytopes of any dimension | Dataset library
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Geometric operations on polytopes of any dimension
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- R Return the vertices of a polytope
- Return a Polytope
- Check if a polynomial is empty
- Solve the LPS problem
- Return the Chebyshev ball of a polygon
- Plot a partition
- Plot the transition arrow
- Creates a new ax
- Run setup py
- Retrieve information about the current git branch
- Return the union of two sets
- Rotate the register
- Return the intersection of this polytope
- Compute a qtope
- Translate a polynomial
- Return a new register
- Convert bounding box to polytope
- Returns the union of two sets
- Bounding box
- Compute the adjacency matrix
- Returns unique equality set
- R Return a list of two regions
- Intersect two polytope
- R Return a sparse adjacency matrix
- Rotate a polygon
- Enumerate integral points
- Convert a list of simplices to polytopes
polytope Key Features
polytope Examples and Code Snippets
Community Discussions
Trending Discussions on polytope
QUESTION
I need to find a list of all the extreme points of a polytope given by a matrix relation Ax <= b, with x being non-negative. I know that 100% of the time, the polytope is non degenerate. The first solution I used was to generate a random non negative vector and run an LP with the vector being the objective function (so basically; optimizing in a random direction). This of course has many problems: take an insane amount of time and in the end I can't be sure the solution is correct.
Then I tried using the polytope toolbox; with the 'extreme' function. I ran it on an instance I already know well:
...ANSWER
Answered 2022-Apr-08 at 11:22Your question is not clear (cf my comment) but you should use pycddlib. I tried and I got something close to your expectation:
QUESTION
I have to figure out the percentage of overlap between polytopes in n-dimensional spaces, where my only available source of reference is a set of randomly sampled points within those polytopes.
Assume that the following two R objects are two sets of randomly sampled points from two different polytopes in 5 dimensions:
...ANSWER
Answered 2021-Jul-13 at 10:48So, the most straightforward way is to use the hypervolume package.
QUESTION
I have two 4D shapes: a polytope composed of two triangles with each side connected to the corresponding side on the other triangle (think triangular prism, but not necessarily straight) and a line segment.
I don't need to know where they intersect, just whether they intersect or not. How can I check for this?
...ANSWER
Answered 2020-Dec-21 at 10:03Your convex polytope is delimited by a number of hyperplanes, of equation ax+by+cz+dw+e = 0
. Considering a point inside the polytope, you can adjust the signs so that all inside points verify ax+by+cz+dw+e ≥ 0
for all hyperplanes.
Now a line segment will have parametric equations like
QUESTION
Later Edit: I uploaded here a sample of my original data. It's actually a segmentation image in the DICOM format. The volume of this structure as it is it's ~ 16 mL, so I assume the inner ellipsoid volume should be smaller than that. to extract the points from the DICOM image I used the following code:
...ANSWER
Answered 2020-May-18 at 17:05One, perhaps the mathematically standard, way to represent (the surface of) an ellipsoid is that it is the set
QUESTION
I am trying to run the Concorde on a TSP generated from a distance matrix. Here is my Code
...ANSWER
Answered 2020-Apr-19 at 22:48The standard conversion from similarity (or adjacency matrix) s to a dissimilarity d is d = 1/s - 1. Here is the complete code that also works for Concorde (in TSP version 1.1-10 or later):
QUESTION
I am working with Concorde to solve TSP problems. Here is my code
...ANSWER
Answered 2020-Apr-19 at 22:44The distance matrix you create is the problem for Concorde. Concorde should catch that and give an appropriate error message.
Here is an appropriate way to convert a graph represented as an edge list into a distance matrix and solve the TSP (using TSP version 1.1-10 or later):
Community Discussions, Code Snippets contain sources that include Stack Exchange Network
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Install polytope
You can use polytope like any standard Python library. You will need to make sure that you have a development environment consisting of a Python distribution including header files, a compiler, pip, and git installed. Make sure that your pip, setuptools, and wheel are up to date. When using pip it is generally recommended to install packages in a virtual environment to avoid changes to the system.
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