Add files via upload

Book4_Ch17_Python_Codes/Streamlit_Bk4_Ch17_01.py

@@ -0,0 +1,85 @@
+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+import sympy
+import numpy as np
+from sympy.functions import exp
+import streamlit as st
+import plotly.figure_factory as ff
+import plotly.graph_objects as go
+
+#define symbolic vars, function
+x1,x2 = sympy.symbols('x1 x2')
+
+f_x = x1*exp(-(x1**2 + x2**2))
+
+st.latex('f(x_1, x_2) = ' + sympy.latex(f_x))
+
+#take the gradient symbolically
+grad_f = [sympy.diff(f_x,var) for var in (x1,x2)]
+st.latex(r'\nabla f = ' + sympy.latex(grad_f) + '^T')
+
+f_x_fcn = sympy.lambdify([x1,x2],f_x)
+
+#turn into a bivariate lambda for numpy
+grad_fcn = sympy.lambdify([x1,x2],grad_f)
+
+x1_array = np.linspace(-2,2,100)
+x2_array = np.linspace(-2,2,100)
+
+xx1, xx2 = np.meshgrid(x1_array,x2_array)
+
+# coarse mesh
+xx1_, xx2_ = np.meshgrid(np.linspace(-2,2,20),np.linspace(-2,2,20))
+V = grad_fcn(xx1_,xx2_)
+
+ff_x = f_x_fcn(xx1,xx2)
+
+
+#%% visualizations
+
+fig_surface = go.Figure(go.Surface(
+    x = x1_array,
+    y = x2_array,
+    z = ff_x,
+    showscale=False))
+fig_surface.update_layout(
+    autosize=False,
+    width =800,
+    height=800)
+
+st.plotly_chart(fig_surface)  
+
+
+f = ff.create_quiver(xx1_, xx2_, V[0], V[1])
+trace1 = f.data[0]
+trace2 = go.Contour(
+    x = x1_array,
+    y = x2_array,
+    z = ff_x,
+    showscale=False)
+
+data=[trace1,trace2]
+fig = go.FigureWidget(data)
+fig.update_layout(
+    autosize=False,
+    width =800,
+    height=800)
+
+
+fig.add_hline(y=0, line_color = 'black')
+fig.add_vline(x=0, line_color = 'black')
+
+fig.update_xaxes(range=[-2, 2])
+fig.update_yaxes(range=[-2, 2])
+fig.update_coloraxes(showscale=False)
+
+st.plotly_chart(fig)  
+
+