From 23a3fc463aba446f0a6c00c232314545d4b205f3 Mon Sep 17 00:00:00 2001 From: Visualize-ML <105787223+Visualize-ML@users.noreply.github.com> Date: Thu, 22 Sep 2022 22:30:54 -0400 Subject: [PATCH] Add files via upload --- .../Streamlit_Bk4_Ch20_04.py | 130 ++++++++++++++++++ .../Streamlit_Bk4_Ch21_02.py | 107 ++++++++++++++ ...和正定性__矩阵力量__从加减乘除到机器学习.pdf | Bin 1407319 -> 1415547 bytes 3 files changed, 237 insertions(+) create mode 100644 Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py create mode 100644 Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py diff --git a/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py b/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py new file mode 100644 index 0000000..11055ff --- /dev/null +++ b/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) + + + + \ No newline at end of file diff --git a/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py b/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py new file mode 100644 index 0000000..9b4c1da --- /dev/null +++ b/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py @@ -0,0 +1,107 @@ + +############### +# 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) + diff --git a/Book4_Ch21_曲面和正定性__矩阵力量__从加减乘除到机器学习.pdf b/Book4_Ch21_曲面和正定性__矩阵力量__从加减乘除到机器学习.pdf index 4c8ba6b8d6a745dd7449917297a3c892c4831065..023d6b7f71290f1e893be9038727cc72d08b3928 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