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Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.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 streamlit as st
+import plotly.graph_objects as go
+import sympy
+import numpy as np
+
+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'''
+             A = \begin{bmatrix}
+    a & b\\
+    b & c
+    \end{bmatrix}''')
+    
+    st.latex(r'''
+             f(x_1,x_2) = ax_1^2 + 2bx_1x_2 + cx_2^2
+             ''')
+    
+    
+    a = st.slider('a',-2.0, 2.0, step = 0.1)
+    b = st.slider('b',-2.0, 2.0, step = 0.1)  
+    c = st.slider('c',-2.0, 2.0, step = 0.1)  
+    
+#%%
+
+x1_ = np.linspace(-2, 2, 101)
+x2_ = np.linspace(-2, 2, 101)
+
+xx1,xx2 = np.meshgrid(x1_, x2_)
+
+#define symbolic vars, function
+x1,x2 = sympy.symbols('x1 x2')
+
+A = np.array([[a, b],
+              [b, c]])
+
+D,V = np.linalg.eig(A)
+D = np.diag(D)
+
+st.latex(r'''A = \begin{bmatrix}%s & %s\\%s & %s\end{bmatrix}''' %(a, b, b, c))
+
+st.latex(bmatrix(A) + '=' + 
+         bmatrix(np.around(V, decimals=3)) + '@' + 
+         bmatrix(np.around(D, decimals=3)) + '@' + 
+         bmatrix(np.around(V.T, decimals=3)))
+
+x = np.array([[x1,x2]]).T
+
+f_x = a*x1**2 + 2*b*x1*x2 + c*x2**2
+
+st.latex(r'''f(x_1,x_2) = ''')
+st.write(f_x)
+
+f_x_fcn = sympy.lambdify([x1,x2],f_x)
+
+ff_x = f_x_fcn(xx1,xx2)
+
+#%% Plot 3D surface
+
+fig_surface = go.Figure(go.Surface(
+    x = x1_,
+    y = x2_,
+    z = ff_x))
+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=ff_x,
+        x=x1_,
+        y=x2_
+    ))
+
+fig_contour.update_layout(
+    autosize=False,
+    width=500,
+    height=500)
+
+st.plotly_chart(fig_contour)
+