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Book4_Ch08_Python_Codes/Streamlit_Bk4_Ch8_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
+###############
+
+import plotly.graph_objects as go
+import numpy as np
+from plotly.subplots import make_subplots
+import streamlit as st
+
+
+def bmatrix(a):
+    """Returns a LaTeX bmatrix
+
+    :a: numpy array
+    :returns: LaTeX bmatrix as a string
+    """
+    if len(a.shape) > 2:
+        raise ValueError('bmatrix can at most display two dimensions')
+    lines = str(a).replace('[', '').replace(']', '').splitlines()
+    rv = [r'\begin{bmatrix}']
+    rv += ['  ' + ' & '.join(l.split()) + r'\\' for l in lines]
+    rv +=  [r'\end{bmatrix}']
+    return '\n'.join(rv)
+
+n = m = 20
+
+fig = make_subplots(rows=1, cols=2, horizontal_spacing=0.035)
+
+xv = []
+yv = [] 
+
+for k in range(-n, n+1):
+    xv.extend([k, k, np.nan])
+    yv.extend([-m, m, np.nan])
+lw= 1 #line_width
+fig.add_trace(go.Scatter(x=xv, y=yv, mode="lines", line_width=lw,
+                         line_color = 'red'), 1, 1)
+#set up  the lists  of  horizontal line x and y-end coordinates
+
+xh=[]
+yh=[]
+for k in range(-m, m+1):
+    xh.extend([-m, m, np.nan])
+    yh.extend([k, k, np.nan])
+    fig.add_trace(go.Scatter(x=xh, y=yh, mode="lines", line_width=lw,
+                             line_color = 'blue'), 1, 1)
+
+
+with st.sidebar:
+    
+    st.latex(r'''
+             A = \begin{bmatrix}
+    a & b\\
+    c & d
+    \end{bmatrix}''')
+    
+    a = st.slider('a',-2.0, 2.0, step = 0.1, value = 1.0)
+    b = st.slider('b',-2.0, 2.0, step = 0.1, value = 0.0)  
+    c = st.slider('c',-2.0, 2.0, step = 0.1, value = 0.0)  
+    d = st.slider('c',-2.0, 2.0, step = 0.1, value = 1.0) 
+
+theta = np.pi/6
+A = np.array([[a, b], 
+              [c, d]], dtype=float)
+
+#get only the coordinates from -3 to 3
+# X = np.array(xv[6:-6])
+# Y = np.array(yv[6:-6])
+
+X = np.array(xv)
+Y = np.array(yv)
+
+# transform by T the vector of coordinates [x, y]^T where the vector runs over the columns of np.stack((X, Y))
+Txvyv = A@np.stack((X, Y)) #transform by T the vertical lines
+
+# X = np.array(xh[6:-6])
+# Y = np.array(yh[6:-6])
+
+X = np.array(xh)
+Y = np.array(yh)
+
+Txhyh = A@np.stack((X, Y))# #transform by T the horizontal lines
+
+st.latex(r'A = ' + bmatrix(A))
+
+a1 = A[:,0].reshape((-1, 1))
+a2 = A[:,1].reshape((-1, 1))
+
+st.latex(r'''
+         a_1 = Ae_1 = ''' + bmatrix(A) + 
+         'e_1 = ' + bmatrix(a1)
+         )
+
+st.latex(r'''
+         a_2 = Ae_2 = ''' + bmatrix(A) + 
+         'e_2 = ' + bmatrix(a2)
+         )
+
+st.latex(r'\begin{vmatrix} A \end{vmatrix} = ' + str(np.linalg.det(A)))
+
+theta_array = np.linspace(0, 2*np.pi, 101)
+circle_x = np.cos(theta_array)
+circle_y = np.sin(theta_array)
+circle_array = np.stack((circle_x, circle_y))
+
+fig.add_trace(go.Scatter(x=circle_x, y=circle_y, 
+                         fill="toself", line_color='orange'), 1, 1)
+
+A_times_circle_array = A@circle_array
+
+fig.add_trace(go.Scatter(x=A_times_circle_array[0,:], 
+                         y=A_times_circle_array[1,:], 
+                         fill="toself", line_color='orange'), 1, 2)
+
+fig.add_trace(go.Scatter(x=Txvyv[0], y=Txvyv[1], 
+                         mode="lines", line_width=lw,
+                         line_color = 'blue'), 1, 2)
+
+fig.add_trace(go.Scatter(x=Txhyh[0], y=Txhyh[1], 
+                         mode="lines", line_width=lw,
+                         line_color = 'red'), 1, 2)
+fig.update_xaxes(range=[-4, 4])
+fig.update_yaxes(range=[-4, 4])
+fig.update_layout(width=800, height=500, showlegend=False, template="none",
+                   plot_bgcolor="white", yaxis2_showgrid=False, xaxis2_showgrid=False)
+
+st.plotly_chart(fig)