quadproj 0.0.3

A package to project onto quadratic hypersurface.

quadproj

A simple library to project a point onto a quadratic surface, or quadric.

How to use quadproj?

The class Quadric from the quadrics module allows to create a non-empty, non-cylindrical, and central quadric.

We can use the project function from the project module to find (one of) the projection of some point onto the quadric.

from quadproj import quadrics
from quadproj.project import project

import matplotlib.pyplot as plt
import numpy as np


# creating random data
dim = 3
_A = np.random.rand(dim, dim)
A = _A + _A.T  # make sure that A is positive definite
b = np.random.rand(dim)
c = -1


param = {'A': A, 'b': b, 'c': c}
Q = quadrics.Quadric(param)

x0 = np.random.rand(dim)
x_project = project(Q, x0)

if dim <= 3:
    fig, ax = Q.plot()
    plt.show()

Supported quadrics

Ellipsoid

show = True
dim = 3
A = np.eye(dim)
A[0, 0] = 2
A[1, 1] = 0.5

b = np.zeros(dim)
c = -1
param = {'A': A, 'b': b, 'c': c}
Q = quadrics.Quadric(param)
Q.plot(show=show)

To ease visualisation, the function get_gif lets you write gif.

Q.get_gif(step=2, gif_path=Q.type+'.gif')

Remark that the sphere is a particular case of the ellipsoid with three equal eigenvalues.

One-sheet hyperboloid

A one-sheet hyperboloid is a 3D quadratic surface with two positive eigenvalues and one negative.

A[0, 0] = -4
param = {'A': A, 'b': b, 'c': c}
Q = quadrics.Quadric(param)
Q.plot(show=show)
Q.get_gif(step=2, gif_path=Q.type+'.gif')

Two-sheet hyperboloid

A Two-sheet hyperboloid is a 3D quadratic surface with two positive eigenvalues and one negative.

A[0, 0] = 4
A[1, 1] = -2
A[2, 2] = -1

b = np.random.rand(dim)  # it will rotate the quadric

param = {'A': A, 'b': b, 'c': c}


Q = quadrics.Quadric(param)
Q.plot(show=show)
Q.get_gif(step=2, gif_path=Q.type+'.gif')

Dependencies

See requirements.txt.