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b/Book4_Ch12_Python_Codes/Bk4_Ch12_01.py new file mode 100644 index 0000000..3908794 --- /dev/null +++ b/Book4_Ch12_Python_Codes/Bk4_Ch12_01.py @@ -0,0 +1,54 @@ + +############### +# Authored by Weisheng Jiang +# Book 4 | From Basic Arithmetic to Machine Learning +# Published and copyrighted by Tsinghua University Press +# Beijing, China, 2022 +############### + +# Bk4_Ch12_01.py + +import numpy as np +from matplotlib import pyplot as plt + +x1 = np.arange(-2,2,0.05) +x2 = np.arange(-2,2,0.05) + +xx1_fine, xx2_fine = np.meshgrid(x1,x2) + +a = 0; b = -1; c = 0; + +yy_fine = a*xx1_fine**2 + 2*b*xx1_fine*xx2_fine + c*xx2_fine**2 + +# 3D visualization + +fig, ax = plt.subplots() +ax = plt.axes(projection='3d') + +ax.plot_wireframe(xx1_fine,xx2_fine,yy_fine, + color = [0.8,0.8,0.8], + linewidth = 0.25) + +ax.contour3D(xx1_fine,xx2_fine,yy_fine,15, + cmap = 'RdYlBu_r') + +ax.view_init(elev=30, azim=60) +ax.xaxis.set_ticks([]) +ax.yaxis.set_ticks([]) +ax.zaxis.set_ticks([]) +plt.tight_layout() +ax.set_proj_type('ortho') +plt.show() + +# 2D visualization + +fig, ax = plt.subplots() + +ax.contourf(xx1_fine,xx2_fine,yy_fine,15, + cmap = 'RdYlBu_r') + +ax.xaxis.set_ticks([]) +ax.yaxis.set_ticks([]) +ax.set_aspect('equal') + +plt.show() diff --git a/Book4_Ch12_Python_Codes/Bk4_Ch12_02.py b/Book4_Ch12_Python_Codes/Bk4_Ch12_02.py new file mode 100644 index 0000000..21edd33 --- /dev/null +++ b/Book4_Ch12_Python_Codes/Bk4_Ch12_02.py @@ -0,0 +1,56 @@ + +############### +# Authored by Weisheng Jiang +# Book 4 | From Basic Arithmetic to Machine Learning +# Published and copyrighted by Tsinghua University Press +# Beijing, China, 2022 +############### + +# Bk4_Ch12_02.py + +import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import Axes3D +import numpy as np +import math as m + +cos_theta_12 = np.cos(m.radians(135)) +cos_theta_13 = np.cos(m.radians(60)) +cos_theta_23 = np.cos(m.radians(120)) + +P = np.array([[1, cos_theta_12, cos_theta_13], + [cos_theta_12, 1, cos_theta_23], + [cos_theta_13, cos_theta_23, 1]]) + +L = np.linalg.cholesky(P) +R = L.T + + +fig = plt.figure() +ax = fig.add_subplot(projection='3d') + +plt.plot(0,0,0,color = 'r', marker = 'x', + markersize = 12) + +colors = ['b', 'r', 'g'] +for i in np.arange(0,3): + + vector = R[:,i] + v = np.array([vector[0],vector[1],vector[2]]) + vlength=np.linalg.norm(v) + ax.quiver(0,0,0,vector[0],vector[1],vector[2], + length=vlength, color = colors[i]) + +ax.set_xlim([-1,1]) +ax.set_ylim([-1,1]) +ax.set_zlim([-1,1]) + +ax.set_xlabel('x') +ax.set_ylabel('y') +ax.set_zlabel('z') + +ax.xaxis.set_ticklabels([]) +ax.yaxis.set_ticklabels([]) +ax.zaxis.set_ticklabels([]) +ax.view_init(35, 60) +ax.set_proj_type('ortho') +ax.set_box_aspect([1,1,1])