Add files via upload

Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py

@@ -0,0 +1,130 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+
+import streamlit as st
+import plotly.graph_objects as go
+import sympy
+import numpy as np
+from scipy.stats import multivariate_normal
+
+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)
+
+with st.sidebar:
+    
+    st.latex(r'''
+             \Sigma = \begin{bmatrix}
+    \sigma_1^2 & 
+    \rho \sigma_1 \sigma_2 \\
+    \rho \sigma_1 \sigma_2 & 
+    \sigma_2^2
+    \end{bmatrix}''')
+    
+    
+    st.write('$\sigma_1$')
+    sigma_1 = st.slider('sigma_1',1.0, 2.0, step = 0.1)
+
+    st.write('$\sigma_2$')
+    sigma_2 = st.slider('sigma_2',1.0, 2.0, step = 0.1)
+    
+    st.write('$\u03C1$')
+    rho_12 = st.slider('rho',-0.9, 0.9, step = 0.1)
+        
+#%%
+
+st.latex(r'''
+   f(x) = \frac{1}{\sqrt{2\pi} \sigma} 
+          \exp\left( -\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{\!2}\,\right)
+          ''')
+  
+st.latex(r'''
+   f(x) = \frac{1}{\left( 2 \pi \right)^{\frac{D}{2}} 
+          \begin{vmatrix}
+          \Sigma 
+          \end{vmatrix}^{\frac{1}{2}}} 
+          \exp\left( 
+         -\frac{1}{2}
+          \left( x - \mu \right)^{T} \Sigma^{-1} \left( x - \mu \right)
+          \right)
+          ''')
+          
+#%%
+x1 = np.linspace(-3,3,101)
+x2 = np.linspace(-3,3,101)
+
+xx1, xx2 = np.meshgrid(x1,x2)
+pos = np.dstack((xx1, xx2))
+
+Sigma = [[sigma_1**2, rho_12*sigma_1*sigma_2], 
+         [rho_12*sigma_1*sigma_2, sigma_2**2]]
+rv = multivariate_normal([0, 0], 
+                         Sigma)
+PDF_zz = rv.pdf(pos)
+
+#%%
+
+Sigma = np.array(Sigma)
+
+D,V = np.linalg.eig(Sigma)
+D = np.diag(D)
+
+st.latex(r'''\Sigma = \begin{bmatrix}%s & %s\\%s & %s\end{bmatrix}''' 
+         %(sigma_1**2, 
+           rho_12*sigma_1*sigma_2, 
+           rho_12*sigma_1*sigma_2, 
+           sigma_2**2))
+
+st.latex(bmatrix(Sigma) + '=' + 
+         bmatrix(np.around(V, decimals=3)) + '@' + 
+         bmatrix(np.around(D, decimals=3)) + '@' + 
+         bmatrix(np.around(V.T, decimals=3)))
+
+#%% Plot 3D surface
+
+fig_surface = go.Figure(go.Surface(
+    x = x1,
+    y = x2,
+    z = PDF_zz))
+fig_surface.update_layout(
+    autosize=False,
+    width=500,
+    height=500)
+st.plotly_chart(fig_surface)
+
+#%% Plot 2D contour
+
+fig_contour = go.Figure(
+    go.Contour(
+        z=PDF_zz,
+        x=x1,
+        y=x2
+    ))
+
+fig_contour.update_layout(
+    autosize=False,
+    width=500,
+    height=500)
+
+st.plotly_chart(fig_contour)       
+        
+        
+        
+