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Book4_Ch05_Python_Codes/Bk4_Ch5_01.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+# Bk4_Ch5_01.py
+
+import numpy as np
+
+A = np.array([[1, 2, 3, 0,  0],
+              [4, 5, 6, 0,  0],
+              [0, 0, 0, -1, 0],
+              [0, 0 ,0, 0,  1]])
+
+# NumPy array slicing
+
+A_1_1 = A[0:2,0:3]
+
+A_1_2 = A[0:2,3:]
+# A_1_2 = A[0:2,-2:]
+A_2_1 = A[2:,0:3]
+# A_2_1 = A[-2:,0:3]
+A_2_2 = A[2:,3:]
+# A_2_2 = A[-2:,-2:]
+
+# Assemble a matrix from nested lists of blocks
+
+A_ = np.block([[A_1_1, A_1_2],
+               [A_2_1, A_2_2]])

Book4_Ch05_Python_Codes/Bk4_Ch5_02.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+# Bk4_Ch5_02.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)
+
+# Generate matrices A and B
+A = np.random.random_integers(0,40,size=(6,4))
+A = A/20 - 1
+
+B = np.random.random_integers(0,40,size=(4,3))
+B = B/20 - 1
+
+# visualize matrix A and B
+plot_heatmap(A,'A')
+
+plot_heatmap(B,'B')
+
+# visualize A@B
+C = A@B
+plot_heatmap(C,'C = AB')
+
+C_rep = np.zeros_like(C)
+
+# reproduce C
+
+for i in np.arange(4):
+    C_i = A[:,[i]]@B[[i],:];
+    title = 'C' + str(i + 1)
+    plot_heatmap(C_i,title)
+    
+    C_rep = C_rep + C_i
+
+# Visualize reproduced C
+plot_heatmap(C_rep,'C reproduced')
+

Book4_Ch05_Python_Codes/Bk4_Ch5_03.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+# Bk4_Ch5_03.py
+
+import numpy as np
+from matplotlib import pyplot as plt
+import seaborn as sns
+
+A = np.array([[-1,  1],
+              [0.7, -0.4]])
+
+B = np.array([[0.5, -0.6],
+             [-0.8, 0.3]])
+
+A_kron_B = np.kron(A, B)
+
+fig, axs = plt.subplots(1, 5, figsize=(12, 5))
+
+plt.sca(axs[0])
+ax = sns.heatmap(A,cmap='RdYlBu_r',vmax = 1,vmin = -1,
+                 cbar_kws={"orientation": "horizontal"})
+ax.set_aspect("equal")
+plt.title('A')
+
+plt.sca(axs[1])
+plt.title('$\otimes$')
+plt.axis('off')
+
+plt.sca(axs[2])
+ax = sns.heatmap(B,cmap='RdYlBu_r',vmax = 1,vmin = -1,
+                 cbar_kws={"orientation": "horizontal"})
+ax.set_aspect("equal")
+plt.title('B')
+
+plt.sca(axs[3])
+plt.title('=')
+plt.axis('off')
+
+plt.sca(axs[4])
+ax = sns.heatmap(A_kron_B,cmap='RdYlBu_r',vmax = 1,vmin = -1,
+                 cbar_kws={"orientation": "horizontal"})
+ax.set_aspect("equal")
+plt.title('C')