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Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_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 numpy as np
+from sympy import lambdify, diff, exp, latex, simplify, symbols
+import numpy as np
+import plotly.figure_factory as ff
+import plotly.graph_objects as go
+import streamlit as st
+
+x1,x2 = symbols('x1 x2')
+num = 301; # number of mesh grids
+x1_array = np.linspace(-3,3,num)
+x2_array = np.linspace(-3,3,num)
+xx1,xx2 = np.meshgrid(x1_array,x2_array)
+
+# f_xy = x*exp(- x**2 - y**2);
+f_x =  3*(1-x1)**2*exp(-(x1**2) - (x2+1)**2)\
+    - 10*(x1/5 - x1**3 - x2**5)*exp(-x1**2-x2**2)\
+    - 1/3*exp(-(x1+1)**2 - x2**2) 
+
+f_x_fcn = lambdify([x1,x2],f_x)
+f_zz = f_x_fcn(xx1,xx2)
+
+st.latex('f(x_1, x_2) = ' + latex(f_x))
+
+#%% gradient
+
+#take the gradient symbolically
+grad_f = [diff(f_x,var) for var in (x1,x2)]
+
+#turn into a bivariate lambda for numpy
+grad_fcn = lambdify([x1,x2],grad_f)
+
+x1__ = np.linspace(-3,3,40)
+x2__ = np.linspace(-3,3,40)
+# coarse mesh
+xx1_, xx2_ = np.meshgrid(x1__,x2__)
+V = grad_fcn(xx1_,xx2_)
+
+#%% 
+
+#%% visualizations
+
+fig_surface = go.Figure(go.Surface(
+    x = x1_array,
+    y = x2_array,
+    z = f_zz,
+    showscale=False,
+    colorscale = 'RdYlBu_r'))
+fig_surface.update_layout(
+    autosize=False,
+    width =800,
+    height=600)
+
+st.plotly_chart(fig_surface)  
+
+#%% gradient vector plot
+
+f = ff.create_quiver(xx1_, xx2_, 
+                     V[0], V[1], 
+                     arrow_scale=.1,
+                     scale = 0.03)
+
+f_stream = ff.create_streamline(x1__,x2__, 
+                                V[0], V[1], 
+                                arrow_scale=.1)
+
+trace1 = f.data[0]
+trace3 = f_stream.data[0]
+trace2 = go.Contour(
+    x = x1_array,
+    y = x2_array,
+    z = f_zz,
+    showscale=False,
+    colorscale = 'RdYlBu_r')
+
+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)  
+
+#%% streamlit plot
+
+data2=[trace3,trace2]
+fig2 = go.FigureWidget(data2)
+fig2.update_layout(
+    autosize=False,
+    width =800,
+    height=800)
+
+
+fig2.add_hline(y=0, line_color = 'black')
+fig2.add_vline(x=0, line_color = 'black')
+
+fig2.update_xaxes(range=[-2, 2])
+fig2.update_yaxes(range=[-2, 2])
+fig2.update_coloraxes(showscale=False)
+
+st.plotly_chart(fig2)