import matplotlib.pyplot as plt
import matplotlib.patches as patches
import numpy as np

# Vi ser p? virkningen av en 2x2-matrise A: R^2 --> R^2.

# Permutering
P = np.array([[0,1],
              [1,0]])

# Skalering
q = 2
S = np.array([[q,0],
              [0,1]])

# Forskyvning
k = 1/2
F = np.array([[1,k],
              [0,1]])

# Rotasjon om origo
theta = -np.pi/6
rho = [[np.cos(theta),-np.sin(theta)],
       [np.sin(theta),np.cos(theta)]]

# Speiling om linje y = c*x
c = -1
R = [[(1-np.power(c,2))/(np.power(c,2)+1),2*c/(np.power(c,2)+1)],
     [2*c/(np.power(c,2)+1),(np.power(c,2)-1)/(np.power(c,2)+1)]]

# Velg din matrise
A = [[2,-2],
     [1, 2]]

A = R

# Setter opp figur for "input" R^2.
fig1 = plt.figure()
ax1 = fig1.add_subplot(aspect='equal')
r = np.sqrt(2)    # For ? ha god plass.
ax1.set_xlim(-r, r)
ax1.set_ylim(-r, r)

# Vi deler [-1,1] i fire kvadrater som vi farger bl?, r?d, gul og gr?nn.
points = [[0, 0], [0, 1], [1, 1], [1, 0]]
ax1.add_patch(plt.Polygon(points, fill=True, color='blue'))
points = [[0, 0], [0, 1], [-1, 1], [-1, 0], [0,0]]
ax1.add_patch(plt.Polygon(points, fill=True, color='red'))
points = [[0, 0], [0, -1], [-1, -1], [-1, 0]]
ax1.add_patch(plt.Polygon(points, fill=True, color='green'))
points = [[0, 0], [0, -1], [1, -1], [1, 0]]
ax1.add_patch(plt.Polygon(points, fill=True, color='yellow'))

# Setter opp figur for "output" R^2
fig2 = plt.figure()
ax2 = fig2.add_subplot(aspect='equal')
rA = np.linalg.norm(A,2) * np.sqrt(2)   # For ? ha god plass.
ax2.set_xlim(-rA, rA)
ax2.set_ylim(-rA, rA)

# Vi bruker A p? de fire kvadratene og tegner parallellogrammene i samme farge.
points = [np.matmul(A,[0, 0]), np.matmul(A,[0, 1]), np.matmul(A,[1, 1]), np.matmul(A,[1, 0])]
ax2.add_patch(plt.Polygon(points, fill=True, color='blue'))
points = [np.matmul(A,[0, 0]), np.matmul(A,[0, 1]), np.matmul(A,[-1, 1]), np.matmul(A,[-1, 0]), np.matmul(A,[0,0])]
ax2.add_patch(plt.Polygon(points, fill=True, color='red'))
points = [np.matmul(A,[0, 0]), np.matmul(A,[0, -1]), np.matmul(A,[-1, -1]), np.matmul(A,[-1, 0])]
ax2.add_patch(plt.Polygon(points, fill=True, color='green'))
points = [np.matmul(A,[0, 0]), np.matmul(A,[0, -1]), np.matmul(A,[1, -1]), np.matmul(A,[1, 0])]
ax2.add_patch(plt.Polygon(points, fill=True, color='yellow'))