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Delete Book4_Ch08_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_Ch8_01.py
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import matplotlib.pyplot as plt
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import numpy as np
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def plot_shape(X,copy = False):
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if copy:
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fill_color = np.array([255,236,255])/255
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edge_color = np.array([255,0,0])/255
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else:
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fill_color = np.array([219,238,243])/255
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edge_color = np.array([0,153,255])/255
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plt.fill(X[:,0], X[:,1],
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color = fill_color,
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edgecolor = edge_color)
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plt.plot(X[:,0], X[:,1],marker = 'x',
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markeredgecolor = edge_color*0.5,
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linestyle = 'None')
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X = np.array([[1,1],
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[0,-1],
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[-1,-1],
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[-1,1]])
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# visualizations
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fig, ax = plt.subplots()
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plot_shape(X) # plot original
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# translation
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t1 = np.array([3,2]);
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Z = X + t1
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plot_shape(Z,True) # plot copy
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t2 = np.array([-3,-2]);
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Z = X + t2
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plot_shape(Z,True) # plot copy
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t3 = np.array([-2,3]);
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Z = X + t3
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plot_shape(Z,True) # plot copy
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t4 = np.array([3,-3]);
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Z = X + t4
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plot_shape(Z,True) # plot copy
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# Decorations
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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plt.axis('equal')
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plt.axis('square')
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plt.axhline(y=0, color='k', linewidth = 0.25)
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plt.axvline(x=0, color='k', linewidth = 0.25)
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plt.xticks(np.arange(-5, 6))
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plt.yticks(np.arange(-5, 6))
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ax.set_xlim(-5,5)
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ax.set_ylim(-5,5)
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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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plt.xlabel('$x_1$')
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plt.ylabel('$x_2$')
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@@ -1,68 +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_Ch8_02.py
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import matplotlib.pyplot as plt
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import numpy as np
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def plot_shape(X,copy = False):
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if copy:
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fill_color = np.array([255,236,255])/255
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edge_color = np.array([255,0,0])/255
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else:
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fill_color = np.array([219,238,243])/255
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edge_color = np.array([0,153,255])/255
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plt.fill(X[:,0], X[:,1],
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color = fill_color,
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edgecolor = edge_color)
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plt.plot(X[:,0], X[:,1],marker = 'x',
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markeredgecolor = edge_color*0.5,
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linestyle = 'None')
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X = np.array([[1,1],
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[0,-1],
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[-1,-1],
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[-1,1]]) + np.array([3,3])
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# visualizations
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thetas = np.linspace(30, 330, num=11)
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for theta in thetas:
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fig, ax = plt.subplots()
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theta = theta/180*np.pi;
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# rotation
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R = np.array([[np.cos(theta), np.sin(theta)],
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[-np.sin(theta), np.cos(theta)]])
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Z = X@R;
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plot_shape(Z,True) # plot copy
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plot_shape(X) # plot original
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# Decorations
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ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
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plt.axis('equal')
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plt.axis('square')
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plt.axhline(y=0, color='k', linewidth = 0.25)
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plt.axvline(x=0, color='k', linewidth = 0.25)
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plt.xticks(np.arange(-5, 6))
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plt.yticks(np.arange(-5, 6))
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ax.set_xlim(-5,5)
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ax.set_ylim(-5,5)
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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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plt.xlabel('$x_1$')
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plt.ylabel('$x_2$')
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@@ -1,118 +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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import plotly.graph_objects as go
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import numpy as np
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from plotly.subplots import make_subplots
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import streamlit as st
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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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n = m = 20
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fig = make_subplots(rows=1, cols=2, horizontal_spacing=0.035)
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xv = []
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yv = []
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for k in range(-n, n+1):
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xv.extend([k, k, np.nan])
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yv.extend([-m, m, np.nan])
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lw= 1 #line_width
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fig.add_trace(go.Scatter(x=xv, y=yv, mode="lines", line_width=lw,
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line_color = 'red'), 1, 1)
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#set up the lists of horizontal line x and y-end coordinates
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xh=[]
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yh=[]
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for k in range(-m, m+1):
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xh.extend([-m, m, np.nan])
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yh.extend([k, k, np.nan])
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fig.add_trace(go.Scatter(x=xh, y=yh, mode="lines", line_width=lw,
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line_color = 'blue'), 1, 1)
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with st.sidebar:
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st.latex(r'''
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R = \begin{bmatrix}
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\cos(\theta) & -\sin(\theta)\\
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\sin(\theta) & \cos(\theta)
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\end{bmatrix}''')
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theta = st.slider('Theta degree: ',-180, 180, step = 5, value = 0)
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theta = theta/180*np.pi
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R = np.array([[np.cos(theta), -np.sin(theta)],
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[np.sin(theta), np.cos(theta)]], dtype=float)
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#get only the coordinates from -3 to 3
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# X = np.array(xv[6:-6])
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# Y = np.array(yv[6:-6])
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X = np.array(xv)
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Y = np.array(yv)
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# transform by T the vector of coordinates [x, y]^T where the vector runs over the columns of np.stack((X, Y))
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Txvyv = R@np.stack((X, Y)) #transform by T the vertical lines
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# X = np.array(xh[6:-6])
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# Y = np.array(yh[6:-6])
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X = np.array(xh)
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Y = np.array(yh)
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Txhyh = R@np.stack((X, Y))# #transform by T the horizontal lines
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st.latex(r'R = ' + bmatrix(R))
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r1 = R[:,0].reshape((-1, 1))
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r2 = R[:,1].reshape((-1, 1))
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st.latex(r'''
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r_1 = R e_1 = ''' + bmatrix(R) +
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'e_1 = ' + bmatrix(r1)
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)
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st.latex(r'''
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r_2 = R e_2 = ''' + bmatrix(R) +
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'e_2 = ' + bmatrix(r2)
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)
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st.latex(r'\begin{vmatrix} R \end{vmatrix} = ' + str(np.linalg.det(R)))
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fig.add_trace(go.Scatter(x=Txvyv[0], y=Txvyv[1],
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mode="lines", line_width=lw,
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line_color = 'red'), 1, 2)
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fig.add_trace(go.Scatter(x=Txhyh[0], y=Txhyh[1],
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mode="lines", line_width=lw,
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line_color = 'blue'), 1, 2)
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fig.update_xaxes(range=[-4, 4])
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fig.update_yaxes(range=[-4, 4])
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fig.update_layout(width=800, height=500, showlegend=False, template="none",
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plot_bgcolor="white", yaxis2_showgrid=False, xaxis2_showgrid=False)
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st.plotly_chart(fig)
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@@ -1,132 +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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import plotly.graph_objects as go
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import numpy as np
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from plotly.subplots import make_subplots
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import streamlit as st
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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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n = m = 20
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fig = make_subplots(rows=1, cols=2, horizontal_spacing=0.035)
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xv = []
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yv = []
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for k in range(-n, n+1):
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xv.extend([k, k, np.nan])
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yv.extend([-m, m, np.nan])
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lw= 1 #line_width
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fig.add_trace(go.Scatter(x=xv, y=yv, mode="lines", line_width=lw,
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line_color = 'red'), 1, 1)
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#set up the lists of horizontal line x and y-end coordinates
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xh=[]
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yh=[]
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for k in range(-m, m+1):
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xh.extend([-m, m, np.nan])
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yh.extend([k, k, np.nan])
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fig.add_trace(go.Scatter(x=xh, y=yh, mode="lines", line_width=lw,
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line_color = 'blue'), 1, 1)
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with st.sidebar:
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st.latex(r'''
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A = \begin{bmatrix}
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a & b\\
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c & d
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\end{bmatrix}''')
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a = st.slider('a',-2.0, 2.0, step = 0.1, value = 1.0)
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b = st.slider('b',-2.0, 2.0, step = 0.1, value = 0.0)
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c = st.slider('c',-2.0, 2.0, step = 0.1, value = 0.0)
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d = st.slider('d',-2.0, 2.0, step = 0.1, value = 1.0)
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theta = np.pi/6
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A = np.array([[a, b],
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[c, d]], dtype=float)
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#get only the coordinates from -3 to 3
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# X = np.array(xv[6:-6])
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# Y = np.array(yv[6:-6])
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X = np.array(xv)
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Y = np.array(yv)
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# transform by T the vector of coordinates [x, y]^T where the vector runs over the columns of np.stack((X, Y))
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Txvyv = A@np.stack((X, Y)) #transform by T the vertical lines
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# X = np.array(xh[6:-6])
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# Y = np.array(yh[6:-6])
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X = np.array(xh)
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Y = np.array(yh)
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Txhyh = A@np.stack((X, Y))# #transform by T the horizontal lines
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st.latex(r'A = ' + bmatrix(A))
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a1 = A[:,0].reshape((-1, 1))
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a2 = A[:,1].reshape((-1, 1))
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st.latex(r'''
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a_1 = Ae_1 = ''' + bmatrix(A) +
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'e_1 = ' + bmatrix(a1)
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)
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st.latex(r'''
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a_2 = Ae_2 = ''' + bmatrix(A) +
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'e_2 = ' + bmatrix(a2)
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)
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st.latex(r'\begin{vmatrix} A \end{vmatrix} = ' + str(np.linalg.det(A)))
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theta_array = np.linspace(0, 2*np.pi, 101)
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circle_x = np.cos(theta_array)
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circle_y = np.sin(theta_array)
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circle_array = np.stack((circle_x, circle_y))
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fig.add_trace(go.Scatter(x=circle_x, y=circle_y,
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fill="toself", line_color='orange'), 1, 1)
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A_times_circle_array = A@circle_array
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fig.add_trace(go.Scatter(x=A_times_circle_array[0,:],
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y=A_times_circle_array[1,:],
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fill="toself", line_color='orange'), 1, 2)
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fig.add_trace(go.Scatter(x=Txvyv[0], y=Txvyv[1],
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mode="lines", line_width=lw,
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line_color = 'blue'), 1, 2)
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fig.add_trace(go.Scatter(x=Txhyh[0], y=Txhyh[1],
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mode="lines", line_width=lw,
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line_color = 'red'), 1, 2)
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fig.update_xaxes(range=[-4, 4])
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fig.update_yaxes(range=[-4, 4])
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fig.update_layout(width=800, height=500, showlegend=False, template="none",
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plot_bgcolor="white", yaxis2_showgrid=False, xaxis2_showgrid=False)
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st.plotly_chart(fig)
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