Basic linear transformations

matrix_transformation.py

from math import cos,sin,radians
import matplotlib.pyplot as plt
import numpy as np

vec = np.array([-5,-8]) #YOUR VECTOR

k = 1 #decide K for shear

# Transformations
def custom_transf (vector, m1,m2,m3,m4):
    result = np.dot(np.matrix([[m1,m2],[m3,m4]], vector))
    return result

def nullvec(vector):
    result = np.dot(np.matrix([[1,0],[0,1]]), vector)
    return result

def mirrored_x (vector):
    result = np.dot(np.matrix([[1,0],[0,-1]]), vector)
    return result

def mirrored_y(vector):
    result = np.dot(np.matrix([[-1,0],[0,1]]), vector)
    return result

def shear_x(vector, k):
    result = np.dot(np.matrix([[1,k],[0,1]]), vector)
    return result

def shear_y(vector, k):
    result = np.dot(np.matrix([[1,0],[k,1]]), vector)
    return result

def rotation90(vector):
    result = np.dot(np.matrix([[0,1],[-1,0]]), vector)
    return result

def proj_on_y(vector):
    result = np.dot(np.matrix([[0,0],[0,1]]), vector)
    return result

def proj_on_x(vector):
    result = np.dot(np.matrix([[1,0],[0,0]]), vector)
    return result

def reflection(vector):
    result = np.dot(np.matrix([[-1,0],[0,-1]]), vector)
    return result


ax = plt.gca()
#Cartesian plane
ax.spines['top'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
plt.scatter(vec[0], vec[1])

labels = ["reflection","shear_x", "shear_y", "mirrored_Y", "mirrored_X", "proj_on_X", "proj_on_Y", "rotation90",
          "custom_transf", "vector"]

custom = custom_transf(vec, cos(radians(-90)),sin(radians(-90)),-sin(radians(-90)),cos(radians(-90)))

values = [reflection(vec),shear_x(vec,k), shear_y(vec,k),mirrored_y(vec),mirrored_x(vec), proj_on_x(vec),proj_on_y(vec),rotation90(vec),
          custom, nullvec(vec)] #ADD VALUES TO CUSTOM_TRANSF

# PLOT ALL THE POINTS
plt.scatter(reflection(vec)[0,0], reflection(vec)[0,1])
plt.scatter(shear_x(vec,k)[0,0], shear_x(vec,k)[0,1])
plt.scatter(shear_y(vec,k)[0,0], shear_y(vec,k)[0,1])
plt.scatter(mirrored_y(vec)[0,0], mirrored_y(vec)[0,1])
plt.scatter(mirrored_x(vec)[0,0], mirrored_x(vec)[0,1])
plt.scatter(proj_on_x(vec)[0,0], proj_on_x(vec)[0,1])
plt.scatter(proj_on_y(vec)[0,0], proj_on_y(vec)[0,1])
plt.scatter(rotation90(vec)[0,0], rotation90(vec)[0,1])
plt.scatter(custom[0,0], custom[0,1])
print(values[0][0,0])

# THESE ARE FOR LABELS
vals1 = [x[0,0] for x in values]
vals2 = [x[0,1] for x in values]


for x in range(0, len(values)):
    #PLOT LINES FROM THE TRANSFORMATIONS
    # TO ORIGINAL VECTOR
    plt.plot((nullvec(vec)[0][0,0] , values[x][0,0]),
             (nullvec(vec)[0][0,1] , values[x][0,1]),
             linestyle="dashed", alpha=0.5)
    # PLOT LINES FROM POINTS TO ORIGIN
    plt.plot((0 , values[x][0,0]),
             (0 , values[x][0,1]),
             color="black", alpha=0.5)


for label, x, y in zip(labels, vals1, vals2):
    #ADD LABELS
    plt.annotate(
        label,
        xy=(x, y), xytext=(-20, 20),
        textcoords='offset points', ha='right', va='bottom',
        bbox=dict(boxstyle='round,pad=0.5', fc='yellow', alpha=0.5),
        arrowprops=dict(arrowstyle = '-', connectionstyle='arc3,rad=0'))

# Keep ticks in the range of possible transformations
plt.xticks(range(-(abs(vec[0])+8),(abs(vec[0])+9)))
plt.grid()
plt.yticks(range(-(abs(vec[1])+8),(abs(vec[1])+9)))

plt.show()