cofactor.py

from itertools import permutations, combinations

import numpy as np
from numpy.linalg import det

from matplotlib.patches import FancyArrowPatch
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import proj3d
from mpl_toolkits.mplot3d import Axes3D


def draw(X, color, alpha=0.2):
    a = np.arange(0, 1, 0.01)
    S = np.array(np.meshgrid(a, a)).reshape(2, -1)
    indices = np.arange(3)
    for i in range(3):
        k = np.delete(indices, i)
        V = surface(X[:, k], S)
        ax.plot(V[0], V[1], V[2], alpha=alpha, color=color)
        V = V + X[:, [i]]
        ax.plot(V[0], V[1], V[2], alpha=alpha, color=color)


def surface(X, S):
    return np.dot(X, S)


def mask(X, row, column):
    X = np.copy(X)
    assert(X.shape[0] == X.shape[1])
    indices = np.arange(0, X.shape[0])
    c = np.delete(indices, column)
    X[row, c] = 0
    r = np.delete(indices, row)
    X[r, column] = 0
    # X[row, column] = pow(-1, row + column + 2) * X[row, column]
    return X


X = np.array([
    [1, -1, 0],
    [1, 0, -1],
    [1, 1, 2]
])

X = 2 * X


U, V, W = [mask(X, 2, c) for c in range(3)]
print(X, det(X))
print(U, det(U))
print(V, det(V))
print(W, det(W))
xrange, yrange, zrange = [-3, 3], [-3, 3], [0, 9]

fig = plt.figure()
ax = fig.add_subplot("111", projection='3d')
ax.set_aspect('equal')
ax.set_xlim(xrange)
ax.set_ylim(yrange)
ax.set_zlim(zrange)

draw(X, color="y")
draw(U, color="r")
draw(V, color="g")
draw(W, color="b")
plt.show()