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Delete Book4_Ch02_Python_Codes directory
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Iris Series: Visualize Math -- From Arithmetic Basics to Machine Learning
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_01.py
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import numpy as np
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import matplotlib.pyplot as plt
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def draw_vector(vector,RBG):
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array = np.array([[0, 0, vector[0], vector[1]]])
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X, Y, U, V = zip(*array)
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plt.quiver(X, Y, U, V,angles='xy', scale_units='xy',scale=1,color = RBG)
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fig, ax = plt.subplots()
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draw_vector([4,3],np.array([0,112,192])/255)
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draw_vector([-3,4],np.array([255,0,0])/255)
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plt.ylabel('$x_2$')
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plt.xlabel('$x_1$')
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plt.axis('scaled')
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ax.set_xlim([-5, 5])
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ax.set_ylim([-5, 5])
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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plt.show()
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_02.py
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import numpy as np
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# define two column vectors
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a = np.array([[4], [3]])
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b = np.array([[-3], [4]])
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# calculate L2 norm
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a_L2_norm = np.linalg.norm(a)
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b_L2_norm = np.linalg.norm(b)
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@@ -1,36 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch1_03.py
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import matplotlib.pyplot as plt
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import numpy as np
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x1 = np.linspace(-10, 10, num=201);
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x2 = x1;
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xx1, xx2 = np.meshgrid(x1,x2)
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p = 2
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zz = ((np.abs((xx1))**p) + (np.abs((xx2))**p))**(1./p)
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fig, ax = plt.subplots(figsize=(12, 12))
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ax.contour(xx1, xx2, zz, levels = np.arange(11), cmap='RdYlBu_r')
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ax.axhline(y=0, color='k', linewidth = 0.25)
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ax.axvline(x=0, color='k', linewidth = 0.25)
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ax.set_xlim(-12, 12)
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ax.set_ylim(-12, 12)
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ax.spines['top'].set_visible(False)
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ax.spines['right'].set_visible(False)
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ax.spines['bottom'].set_visible(False)
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ax.spines['left'].set_visible(False)
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ax.set_xlabel('$x_1$')
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ax.set_ylabel('$x_2$')
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ax.set_aspect('equal', adjustable='box')
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plt.show()
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch1_04.py
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import numpy as np
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# define two column vectors
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a = np.array([[-2], [5]])
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b = np.array([[5], [-1]])
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# calculate vector addition
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a_plus_b = a + b
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a_plus_b_2 = np.add(a,b)
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# calculate vector subtraction
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a_minus_b = a - b
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a_minus_b_2 = np.subtract(a,b)
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b_minus_a = b - a
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b_minus_a_2 = np.subtract(b,a)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_05.py
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import numpy as np
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# define a column vector
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a = np.array([[2], [2]])
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b = 2*a
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c = -1.5*a
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_06.py
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import numpy as np
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a = np.array([[4, 3]])
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b = np.array([[5, -2]])
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a_dot_b = np.inner(a, b)
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a_2 = np.array([[4], [3]])
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b_2 = np.array([[5], [-2]])
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a_dot_b_2 = a_2.T@b_2
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_07.py
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import numpy as np
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a = np.array([[2,3],
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[3,4]])
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b = np.array([[3,4],
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[5,6]])
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a_@_b = np.dot(a,b)
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# a@b
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_08.py
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import numpy as np
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a = np.array([[1,2],
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[3,4]])
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b = np.array([[3,4],
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[5,6]])
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a_dot_b = np.vdot(a,b)
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# [1,2,3,4]*[3,4,5,6].T
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_09.py
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import numpy as np
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a, b = np.array([[4], [3]]), np.array([[5], [-2]])
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# calculate cosine theta
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cos_theta = (a.T @ b) / (np.linalg.norm(a,2) * np.linalg.norm(b,2))
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# calculate theta in radian
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cos_radian = np.arccos(cos_theta)
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# convert radian to degree
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cos_degree = cos_radian * ((180)/np.pi)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_10.py
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from scipy.spatial import distance
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from sklearn import datasets
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import numpy as np
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# import the iris data
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iris = datasets.load_iris()
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# Only use the first two features: sepal length, sepal width
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X = iris.data[:, :]
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# Extract 4 data points
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x1_data = X[0,:]
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x2_data = X[1,:]
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x51_data = X[50,:]
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x101_data = X[100,:]
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# calculate cosine distance
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x1_x2_cos_dist = distance.cosine(x1_data,x2_data)
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x1_norm = np.linalg.norm(x1_data)
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x2_norm = np.linalg.norm(x2_data)
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x1_dot_x2 = x1_data.T@x2_data
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x1_x2_cos = x1_dot_x2/x1_norm/x2_norm
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x1_x51_cos_dist = distance.cosine(x1_data,x51_data)
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x1_x101_cos_dist = distance.cosine(x1_data,x101_data)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_11.py
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import numpy as np
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a = np.array([-2, 1, 1])
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b = np.array([1, -2, -1])
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# a = [-2, 1, 1]
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# b = [1, -2, -1]
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# calculate cross product of row vectors
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a_cross_b = np.cross(a, b)
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a_col = np.array([[-2], [1], [1]])
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b_col = np.array([[1], [-2], [-1]])
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# calculate cross product of column vectors
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a_cross_b_col = np.cross(a_col,b_col,axis=0)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_12.py
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import numpy as np
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a = np.array([-2, 1, 1])
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b = np.array([1, -2, -1])
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# a = [-2, 1, 1]
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# b = [1, -2, -1]
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# calculate element-wise product of row vectors
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a_times_b = np.multiply(a, b)
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a_times_b_2 = a*b
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a_col = np.array([[-2], [1], [1]])
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b_col = np.array([[1], [-2], [-1]])
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# calculate element-wise product of column vectors
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a_times_b_col = np.multiply(a_col,b_col)
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a_times_b_col_2 = a_col*b_col
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch2_13.py
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import matplotlib.pyplot as plt
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import numpy as np
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import seaborn as sns
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def plot_heatmap(x,title):
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fig, ax = plt.subplots()
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ax = sns.heatmap(x,
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cmap='RdYlBu_r',
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cbar_kws={"orientation": "horizontal"}, vmin=-1, vmax=1)
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ax.set_aspect("equal")
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plt.title(title)
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a = np.array([[0.5],[-0.7],[1],[0.25],[-0.6],[-1]])
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b = np.array([[-0.8],[0.5],[-0.6],[0.9]])
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a_outer_b = np.outer(a, b)
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a_outer_a = np.outer(a, a)
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b_outer_b = np.outer(b, b)
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# Visualizations
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plot_heatmap(a,'a')
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plot_heatmap(b,'b')
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plot_heatmap(a_outer_b,'a outer b')
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plot_heatmap(a_outer_a,'a outer a')
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plot_heatmap(b_outer_b,'b outer b')
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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import streamlit as st
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import numpy as np
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from plotly.subplots import make_subplots
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import plotly.graph_objects as go
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import plotly.express as px
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def bmatrix(a):
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"""Returns a LaTeX bmatrix
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:a: numpy array
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:returns: LaTeX bmatrix as a string
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"""
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if len(a.shape) > 2:
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raise ValueError('bmatrix can at most display two dimensions')
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lines = str(a).replace('[', '').replace(']', '').splitlines()
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rv = [r'\begin{bmatrix}']
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rv += [' ' + ' & '.join(l.split()) + r'\\' for l in lines]
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rv += [r'\end{bmatrix}']
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return '\n'.join(rv)
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#%%
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with st.sidebar:
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num_a = st.slider('Number of rows, a:',
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3,6,step = 1)
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num_b = st.slider('Number of rows, b:',
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3,6,step = 1)
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a = np.random.uniform(0,1,num_a).reshape((-1,1))
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a = np.round(a,1)
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b = np.random.uniform(0,1,num_b).reshape((-1,1))
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b = np.round(b,1)
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show_number = False
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with st.sidebar:
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show_number = st.checkbox('Display values')
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tensor_a_b = a@b.T
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#%% visualization
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st.latex('a = ' + bmatrix(a))
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st.latex('b = ' + bmatrix(b))
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st.latex('a \otimes b = ab^{T}')
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st.latex( bmatrix(a) + '@' + bmatrix(b.T) + ' = ' + bmatrix(tensor_a_b))
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col1, col2, col3 = st.columns(3)
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with col1:
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fig_a = px.imshow(a, text_auto=show_number,
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color_continuous_scale='viridis',
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aspect = 'equal')
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fig_a.update_layout(height=400, width=300)
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fig_a.layout.coloraxis.showscale = False
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st.plotly_chart(fig_a)
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with col2:
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fig_b = px.imshow(b, text_auto=show_number,
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color_continuous_scale='viridis',
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aspect = 'equal')
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fig_b.update_layout(height=400, width=300)
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fig_b.layout.coloraxis.showscale = False
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st.plotly_chart(fig_b)
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with col3:
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fig_ab = px.imshow(tensor_a_b, text_auto=show_number,
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color_continuous_scale='viridis',
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aspect = 'equal')
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fig_ab.update_layout(height=400, width=400)
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fig_ab.layout.coloraxis.showscale = False
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st.plotly_chart(fig_ab)
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