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Book4_Ch02_Python_Codes/Bk4_Ch2_01.py

@@ -9,12 +9,22 @@
 # Bk4_Ch2_01.py
 
 import numpy as np
+import matplotlib.pyplot as plt
 
-a = np.array([[4, 3]])
-b = np.array([[5, -2]])
+def draw_vector(vector,RBG): 
+    array = np.array([[0, 0, vector[0], vector[1]]])
+    X, Y, U, V = zip(*array)
+    plt.quiver(X, Y, U, V,angles='xy', scale_units='xy',scale=1,color = RBG)
 
-a_dot_b = np.inner(a, b)
+fig, ax = plt.subplots()
 
-a_2 = np.array([[4], [3]])
-b_2 = np.array([[5], [-2]])
-a_dot_b_2 = a_2.T@b_2
+draw_vector([4,3],np.array([0,112,192])/255)
+draw_vector([-3,4],np.array([255,0,0])/255)
+
+plt.ylabel('$x_2$')
+plt.xlabel('$x_1$')
+plt.axis('scaled')
+ax.set_xlim([-5, 5])
+ax.set_ylim([-5, 5])
+ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
+plt.show()

Book4_Ch02_Python_Codes/Bk4_Ch2_02.py

@@ -9,11 +9,11 @@
 # Bk4_Ch2_02.py
 
 import numpy as np
-a = np.array([[2,3],
-              [3,4]])
 
-b = np.array([[3,4],
-              [5,6]])
+# define two column vectors
+a = np.array([[4], [3]])
+b = np.array([[-3], [4]])
 
-a_@_b = np.dot(a,b)
-# a@b
+# calculate L2 norm
+a_L2_norm = np.linalg.norm(a)
+b_L2_norm = np.linalg.norm(b)

Book4_Ch02_Python_Codes/Bk4_Ch2_03.py

@@ -6,14 +6,31 @@
 # Beijing, China, 2022
 ###############
 
-# Bk4_Ch2_03.py
+# Bk4_Ch1_03.py
 
+import matplotlib.pyplot as plt
 import numpy as np
-a = np.array([[1,2],
-              [3,4]])
 
-b = np.array([[3,4],
-              [5,6]])
+x1 = np.linspace(-10, 10, num=201);
+x2 = x1;
 
-a_dot_b = np.vdot(a,b)
-# [1,2,3,4]*[3,4,5,6].T
+xx1, xx2 = np.meshgrid(x1,x2)
+p = 2
+zz = ((np.abs((xx1))**p) + (np.abs((xx2))**p))**(1./p)
+
+fig, ax = plt.subplots(figsize=(12, 12))
+
+ax.contour(xx1, xx2, zz, levels = np.arange(11), cmap='RdYlBu_r')
+
+ax.axhline(y=0, color='k', linewidth = 0.25)
+ax.axvline(x=0, color='k', linewidth = 0.25)
+ax.set_xlim(-12, 12)
+ax.set_ylim(-12, 12)
+ax.spines['top'].set_visible(False)
+ax.spines['right'].set_visible(False)
+ax.spines['bottom'].set_visible(False)
+ax.spines['left'].set_visible(False)
+ax.set_xlabel('$x_1$')
+ax.set_ylabel('$x_2$')
+ax.set_aspect('equal', adjustable='box')
+plt.show()

Book4_Ch02_Python_Codes/Bk4_Ch2_04.py

@@ -6,17 +6,21 @@
 # Beijing, China, 2022
 ###############
 
-# Bk4_Ch2_04.py
+# Bk4_Ch1_04.py
 
 import numpy as np
 
-a, b = np.array([[4], [3]]), np.array([[5], [-2]])
+# define two column vectors
+a = np.array([[-2], [5]])
+b = np.array([[5], [-1]])
 
-# calculate cosine theta
-cos_theta = (a.T @ b) / (np.linalg.norm(a,2) * np.linalg.norm(b,2))
+# calculate vector addition
+a_plus_b = a + b
+a_plus_b_2 = np.add(a,b)
 
-# calculate theta in radian
-cos_radian = np.arccos(cos_theta)
+# calculate vector subtraction
+a_minus_b = a - b
+a_minus_b_2 = np.subtract(a,b)
 
-# convert radian to degree
-cos_degree = cos_radian * ((180)/np.pi)
+b_minus_a = b - a
+b_minus_a_2 = np.subtract(b,a)

Book4_Ch02_Python_Codes/Bk4_Ch2_05.py

@@ -8,30 +8,10 @@
 
 # Bk4_Ch2_05.py
 
-from scipy.spatial import distance
-from sklearn import datasets
 import numpy as np
 
-# import the iris data
-iris = datasets.load_iris()
+# define a column vector
+a = np.array([[2], [2]])
 
-# Only use the first two features: sepal length, sepal width
-X = iris.data[:, :]
-
-# Extract 4 data points
-x1_data = X[0,:]
-x2_data = X[1,:]
-x51_data = X[50,:]
-x101_data = X[100,:]
-
-# calculate cosine distance
-x1_x2_cos_dist = distance.cosine(x1_data,x2_data)
-x1_norm = np.linalg.norm(x1_data) 
-x2_norm = np.linalg.norm(x2_data)
-x1_dot_x2 = x1_data.T@x2_data
-x1_x2_cos = x1_dot_x2/x1_norm/x2_norm
-
-
-x1_x51_cos_dist = distance.cosine(x1_data,x51_data)
-
-x1_x101_cos_dist = distance.cosine(x1_data,x101_data)
+b = 2*a
+c = -1.5*a

Book4_Ch02_Python_Codes/Bk4_Ch2_06.py

@@ -9,16 +9,12 @@
 # Bk4_Ch2_06.py
 
 import numpy as np
-a = np.array([-2, 1, 1])
-b = np.array([1, -2, -1])
-# a = [-2, 1, 1]
-# b = [1, -2, -1]
 
-# calculate cross product of row vectors
-a_cross_b = np.cross(a, b)
+a = np.array([[4, 3]])
+b = np.array([[5, -2]])
 
-a_col = np.array([[-2], [1], [1]])
-b_col = np.array([[1], [-2], [-1]])
+a_dot_b = np.inner(a, b)
 
-# calculate cross product of column vectors
-a_cross_b_col = np.cross(a_col,b_col,axis=0)
+a_2 = np.array([[4], [3]])
+b_2 = np.array([[5], [-2]])
+a_dot_b_2 = a_2.T@b_2

Book4_Ch02_Python_Codes/Bk4_Ch2_07.py

@@ -9,19 +9,11 @@
 # Bk4_Ch2_07.py
 
 import numpy as np
-a = np.array([-2, 1, 1])
-b = np.array([1, -2, -1])
-# a = [-2, 1, 1]
-# b = [1, -2, -1]
+a = np.array([[2,3],
+              [3,4]])
 
+b = np.array([[3,4],
+              [5,6]])
 
-# calculate element-wise product of row vectors
-a_times_b = np.multiply(a, b)
-a_times_b_2 = a*b
-
-a_col = np.array([[-2], [1], [1]])
-b_col = np.array([[1], [-2], [-1]])
-
-# calculate element-wise product of column vectors
-a_times_b_col = np.multiply(a_col,b_col)
-a_times_b_col_2 = a_col*b_col
+a_@_b = np.dot(a,b)
+# a@b

Book4_Ch02_Python_Codes/Bk4_Ch2_08.py

@@ -8,33 +8,12 @@
 
 # Bk4_Ch2_08.py
 
-import matplotlib.pyplot as plt 
 import numpy as np
-import seaborn as sns
+a = np.array([[1,2],
+              [3,4]])
 
-def plot_heatmap(x,title):
+b = np.array([[3,4],
+              [5,6]])
 
-    fig, ax = plt.subplots()
-    ax = sns.heatmap(x,
-                     cmap='RdYlBu_r',
-                     cbar_kws={"orientation": "horizontal"}, vmin=-1, vmax=1)
-    ax.set_aspect("equal")
-    plt.title(title)
-
-a = np.array([[0.5],[-0.7],[1],[0.25],[-0.6],[-1]])
-b = np.array([[-0.8],[0.5],[-0.6],[0.9]])
-
-a_outer_b = np.outer(a, b)
-a_outer_a = np.outer(a, a)
-b_outer_b = np.outer(b, b)
-
-# Visualizations
-plot_heatmap(a,'a')
-
-plot_heatmap(b,'b')
-
-plot_heatmap(a_outer_b,'a outer b')
-
-plot_heatmap(a_outer_a,'a outer a')
-
-plot_heatmap(b_outer_b,'b outer b')
+a_dot_b = np.vdot(a,b)
+# [1,2,3,4]*[3,4,5,6].T

Book4_Ch02_Python_Codes/Bk4_Ch2_09.py

@@ -0,0 +1,22 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch2_09.py
+
+import numpy as np
+
+a, b = np.array([[4], [3]]), np.array([[5], [-2]])
+
+# calculate cosine theta
+cos_theta = (a.T @ b) / (np.linalg.norm(a,2) * np.linalg.norm(b,2))
+
+# calculate theta in radian
+cos_radian = np.arccos(cos_theta)
+
+# convert radian to degree
+cos_degree = cos_radian * ((180)/np.pi)

Book4_Ch02_Python_Codes/Bk4_Ch2_10.py

@@ -0,0 +1,37 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch2_10.py
+
+from scipy.spatial import distance
+from sklearn import datasets
+import numpy as np
+
+# import the iris data
+iris = datasets.load_iris()
+
+# Only use the first two features: sepal length, sepal width
+X = iris.data[:, :]
+
+# Extract 4 data points
+x1_data = X[0,:]
+x2_data = X[1,:]
+x51_data = X[50,:]
+x101_data = X[100,:]
+
+# calculate cosine distance
+x1_x2_cos_dist = distance.cosine(x1_data,x2_data)
+x1_norm = np.linalg.norm(x1_data) 
+x2_norm = np.linalg.norm(x2_data)
+x1_dot_x2 = x1_data.T@x2_data
+x1_x2_cos = x1_dot_x2/x1_norm/x2_norm
+
+
+x1_x51_cos_dist = distance.cosine(x1_data,x51_data)
+
+x1_x101_cos_dist = distance.cosine(x1_data,x101_data)

Book4_Ch02_Python_Codes/Bk4_Ch2_11.py

@@ -0,0 +1,24 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch2_11.py
+
+import numpy as np
+a = np.array([-2, 1, 1])
+b = np.array([1, -2, -1])
+# a = [-2, 1, 1]
+# b = [1, -2, -1]
+
+# calculate cross product of row vectors
+a_cross_b = np.cross(a, b)
+
+a_col = np.array([[-2], [1], [1]])
+b_col = np.array([[1], [-2], [-1]])
+
+# calculate cross product of column vectors
+a_cross_b_col = np.cross(a_col,b_col,axis=0)

Book4_Ch02_Python_Codes/Bk4_Ch2_12.py

@@ -0,0 +1,27 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch2_12.py
+
+import numpy as np
+a = np.array([-2, 1, 1])
+b = np.array([1, -2, -1])
+# a = [-2, 1, 1]
+# b = [1, -2, -1]
+
+
+# calculate element-wise product of row vectors
+a_times_b = np.multiply(a, b)
+a_times_b_2 = a*b
+
+a_col = np.array([[-2], [1], [1]])
+b_col = np.array([[1], [-2], [-1]])
+
+# calculate element-wise product of column vectors
+a_times_b_col = np.multiply(a_col,b_col)
+a_times_b_col_2 = a_col*b_col

Book4_Ch02_Python_Codes/Bk4_Ch2_13.py

@@ -0,0 +1,40 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+# Bk4_Ch2_13.py
+
+import matplotlib.pyplot as plt 
+import numpy as np
+import seaborn as sns
+
+def plot_heatmap(x,title):
+
+    fig, ax = plt.subplots()
+    ax = sns.heatmap(x,
+                     cmap='RdYlBu_r',
+                     cbar_kws={"orientation": "horizontal"}, vmin=-1, vmax=1)
+    ax.set_aspect("equal")
+    plt.title(title)
+
+a = np.array([[0.5],[-0.7],[1],[0.25],[-0.6],[-1]])
+b = np.array([[-0.8],[0.5],[-0.6],[0.9]])
+
+a_outer_b = np.outer(a, b)
+a_outer_a = np.outer(a, a)
+b_outer_b = np.outer(b, b)
+
+# Visualizations
+plot_heatmap(a,'a')
+
+plot_heatmap(b,'b')
+
+plot_heatmap(a_outer_b,'a outer b')
+
+plot_heatmap(a_outer_a,'a outer a')
+
+plot_heatmap(b_outer_b,'b outer b')