ml-algorithms/linear-transform at main · karmveer-ranawat/ml-algorithms · GitHub

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Program: -
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
#Create X and Y vectors
X = np.linspace(-2, 2, 100)
Y = 2 * X + 1
print(X);print("-"*80);print(Y)


plt.figure()
plt.xlabel("X")
plt.ylabel("Y")
# Set x-axis rangeplt.xlim((-7,7))
# Set y-axis rangeplt.ylim((-7,7))
# Draw lines to split quadrants
plt.plot([-6,6],[0,0], linewidth=2, color='black')
plt.plot([0,0],[6,-6], linewidth=2, color='black' )
plt.plot(X, Y)
plt.show()


X = np.linspace(-2, 2, 100)
Y = 2 * X + 1
Y1 = 2 * X + 3
print(X);print("-"*80);print(Y);print("-"*80);print(Y1)


plt.figure()
plt.xlabel("X")
plt.ylabel("Y")
# Set x-axis rangeplt.xlim((-7,7))
# Set y-axis rangeplt.ylim((-7,7))
# Draw lines to split quadrants
plt.plot([-6,6],[0,0], linewidth=2, color='black')
plt.plot([0,0],[6,-6], linewidth=2, color='black' )
plt.title('Quadrant plot')
plt.plot(X,Y)
plt.plot(X,Y1)


x = np.arange(-10, 10, 1)
y = np.arange(-10, 10, 1)
xx,yy = np.meshgrid(x, y)
print(xx,yy)


Geometric Interpretation:
Input: -
plt.scatter(xx, yy, s=20, c=xx+yy)
plt.xlabel("XX")
plt.ylabel("YY")
# Set x-axis rangeplt.xlim((-10,10))
# Set y-axis rangeplt.ylim((-10,10))
# Draw lines to split quadrants
plt.plot([-9,9],[0,0], linewidth=2, color='black')
plt.plot([0,0],[9,-9], linewidth=2, color='black' )


T = np.array([[-1 0],
[0, -1]
])
xy = np.vstack([xx.flatten(), yy.flatten()])
xy.shape


T @ xy[:, 0]


trans = T @ xy
trans.shape


xx_transformed = trans[0].reshape(xx.shape)
yy_transformed = trans[1].reshape(yy.shape)
f, axes = plt.subplots(1, 2, figsize=(6, 3))
#[...] Add axis, x and y witht the same scale
axes[0].scatter(xx, yy, s=10, c=xx+yy)
axes[0].set_xlabel("XX");axes[0].set_ylabel("YY")
axes[0].plot([-9,9],[0,0],linewidth=2,color = "lightgray")
axes[0].plot([0,0],[9,-9],linewidth=2,color = "lightgray")
axes[1].scatter(xx_transformed, yy_transformed, s=10, c=xx+yy)
axes[1].set_xlabel("XX")
axes[1].plot([-9,9],[0,0],linewidth=2,color = "lightgray")
axes[1].plot([0,0],[9,-9],linewidth=2,color = "lightgray")


T = np.array([ [1.3,-2.4],
[0.1, 2]
])
trans = T @ xy
xx_transformed = trans[0].reshape(xx.shape)yy_transformed = trans[1].reshape(yy.shape)
f, axes = plt.subplots(1, 2, figsize=(6, 3))
axes[0].scatter(xx, yy, s=10, c=xx+yy) axes[0].set_xlabel("XX")
axes[0].set_ylabel("YY")
axes[0].plot([-9,9],[0,0],linewidth=2,color = "lightgray")
axes[0].plot([0,0],[9,-9],linewidth=2,color = "lightgray")
axes[1].scatter(xx_transformed, yy_transformed, s=10, c=xx+yy)
axes[1].set_xlabel("XX")
axes[1].plot([-40,40],[0,0],linewidth=1,color = "lightgray")
axes[1].plot([0,0],[40,-40],linewidth=1,color = "lightgray")


T= np.array
([[1.3, -2.4],
[0.1, 2]])
27
trans = T @ xy
T_inv = np.linalg.inv(T)
un_trans = T_inv @ T @ xy
f, axes = plt.subplots(1, 3, figsize=(9, 3),dpi = 100)
axes[0].scatter(xx, yy, s=10, c=xx+yy) axes[0].set_xlabel("XX")
axes[0].set_ylabel("YY")
axes[0].plot([-15,15],[0,0],linewidth=2,color = "lightgray")
axes[0].plot([0,0],[15,-15],linewidth=2,color = "lightgray")
axes[0].set_title("Initial")
axes[1].scatter(trans[0].reshape(xx.shape),trans[1].reshape(yy.shape),s=10,c=xx+yy)
axes[1].set_xlabel("XX");
axes[1].plot([-40,40],[0,0],linewidth=1,color = "lightgray")
axes[1].plot([0,0],[40,-40],linewidth=1,color = "lightgray")
axes[1].set_title("Transformed")
axes[2].scatter(un_trans[0].reshape(xx.shape),un_trans[1].reshape(yy.shape),s=10,c=xx+yy)
axes[2].set_xlabel("XX");
axes[2].plot([-15,15],[0,0],linewidth=2,color = "lightgray")
axes[2].plot([0,0],[15,-15],linewidth=2,color="lightgray") axes[2].set_title("Transformed
back with inverse")


T = np.array([
[3, 6],
[2, 4],
])
trans = T @ xy
f, axes = plt.subplots(1, 2, figsize=(6, 3),dpi = 100)
axes[0].scatter(xx, yy, s=10, c=xx+yy) axes[0].set_xlabel("XX");
axes[0].set_ylabel("YY")
axes[0].plot([-15,15],[0,0],linewidth=2,color = "lightgray")
axes[0].plot([0,0],[15,-15],linewidth=2,color = "lightgray")
axes[0].scatter(trans[0].reshape(xx.shape),trans[1].reshape(yy.shape),s=10,c=xx+yy)
axes[1].axes[1].set_xlabel("XX");
axes[1].plot([-50,50],[0,0],linewidth=2,color = "lightgray")
axes[1].plot([0,0],[50,-50],linewidth=2,color = "lightgray")