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https://github.com/Visualize-ML/Book4_Power-of-Matrix.git
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Visualize-ML
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# -*- coding: utf-8 -*-
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"""
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Created on Mon Sep 12 21:19:47 2022
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@author: Work
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"""
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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import pandas as pd
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import plotly.graph_objs as go
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import streamlit as st
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import plotly.graph_objects as go
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import numpy as np
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from plotly.subplots import make_subplots
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import streamlit as st
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def bmatrix(a):
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"""Returns a LaTeX bmatrix
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:a: numpy array
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:returns: LaTeX bmatrix as a string
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"""
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if len(a.shape) > 2:
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raise ValueError('bmatrix can at most display two dimensions')
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lines = str(a).replace('[', '').replace(']', '').splitlines()
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rv = [r'\begin{bmatrix}']
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rv += [' ' + ' & '.join(l.split()) + r'\\' for l in lines]
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rv += [r'\end{bmatrix}']
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return '\n'.join(rv)
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n = m = 20
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fig = make_subplots(rows=1, cols=2, horizontal_spacing=0.035)
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xv = []
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yv = []
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for k in range(-n, n+1):
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xv.extend([k, k, np.nan])
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yv.extend([-m, m, np.nan])
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lw= 1 #line_width
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fig.add_trace(go.Scatter(x=xv, y=yv, mode="lines", line_width=lw,
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line_color = 'red'), 1, 1)
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#set up the lists of horizontal line x and y-end coordinates
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xh=[]
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yh=[]
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for k in range(-m, m+1):
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xh.extend([-m, m, np.nan])
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yh.extend([k, k, np.nan])
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fig.add_trace(go.Scatter(x=xh, y=yh, mode="lines", line_width=lw,
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line_color = 'blue'), 1, 1)
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with st.sidebar:
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num = st.slider('Number of points for each dimension',
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max_value = 20,
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min_value = 10,
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step = 1)
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x1 = np.linspace(0,1,num)
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x2 = x1
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x3 = x1
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st.latex(r'''
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A = \begin{bmatrix}
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a & b\\
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c & d
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\end{bmatrix}''')
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a = st.slider('a',-2.0, 2.0, step = 0.1, value = 1.0)
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b = st.slider('b',-2.0, 2.0, step = 0.1, value = 0.0)
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c = st.slider('c',-2.0, 2.0, step = 0.1, value = 0.0)
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d = st.slider('c',-2.0, 2.0, step = 0.1, value = 1.0)
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xx1,xx2,xx3 = np.meshgrid(x1,x2,x3)
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theta = np.pi/6
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A = np.array([[a, b],
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[c, d]], dtype=float)
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x1_ = xx1.ravel()
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x2_ = xx2.ravel()
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x3_ = xx3.ravel()
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#get only the coordinates from -3 to 3
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# X = np.array(xv[6:-6])
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# Y = np.array(yv[6:-6])
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#%%
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df = pd.DataFrame({'X': x1_,
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'Y': x2_,
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'Z': x3_,
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'R': (x1_*256).round(),
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'G': (x2_*256).round(),
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'B': (x3_*256).round()})
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X = np.array(xv)
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Y = np.array(yv)
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trace = go.Scatter3d(x=df.X,
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y=df.Y,
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z=df.Z,
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mode='markers',
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marker=dict(size=3,
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color=['rgb({},{},{})'.format(r,g,b)
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for r,g,b in
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zip(df.R.values, df.G.values, df.B.values)],
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opacity=0.9,))
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# transform by T the vector of coordinates [x, y]^T where the vector runs over the columns of np.stack((X, Y))
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Txvyv = A@np.stack((X, Y)) #transform by T the vertical lines
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data = [trace]
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# X = np.array(xh[6:-6])
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# Y = np.array(yh[6:-6])
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layout = go.Layout(margin=dict(l=0,
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r=0,
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b=0,
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t=0),
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scene = dict(
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xaxis = dict(title='e_1'),
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yaxis = dict(title='e_2'),
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zaxis = dict(title='e_3'),),
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)
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X = np.array(xh)
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Y = np.array(yh)
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fig = go.Figure(data=data, layout=layout)
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Txhyh = A@np.stack((X, Y))# #transform by T the horizontal lines
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st.plotly_chart(fig)
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st.latex(bmatrix(A))
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a1 = A[:,0].reshape((-1, 1))
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a2 = A[:,1].reshape((-1, 1))
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st.latex(r'''
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a_1 = Ae_1 = ''' + bmatrix(A) +
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'e_1 = ' + bmatrix(a1)
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)
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st.latex(r'''
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a_2 = Ae_2 = ''' + bmatrix(A) +
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'e_2 = ' + bmatrix(a2)
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)
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fig.add_trace(go.Scatter(x=Txvyv[0], y=Txvyv[1],
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mode="lines", line_width=lw,
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line_color = 'blue'), 1, 2)
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fig.add_trace(go.Scatter(x=Txhyh[0], y=Txhyh[1],
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mode="lines", line_width=lw,
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line_color = 'red'), 1, 2)
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fig.update_xaxes(range=[-4, 4])
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fig.update_yaxes(range=[-4, 4])
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fig.update_layout(width=800, height=500, showlegend=False, template="none",
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plot_bgcolor="white", yaxis2_showgrid=False, xaxis2_showgrid=False)
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st.plotly_chart(fig)
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61
Book4_Ch07_Python_Codes/Streamlit_Bk4_Ch7_02.py
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61
Book4_Ch07_Python_Codes/Streamlit_Bk4_Ch7_02.py
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@@ -0,0 +1,61 @@
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# -*- coding: utf-8 -*-
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"""
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Created on Mon Sep 12 21:19:47 2022
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@author: Work
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"""
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import pandas as pd
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import plotly.graph_objs as go
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import streamlit as st
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import numpy as np
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with st.sidebar:
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num = st.slider('Number of points for each dimension',
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max_value = 20,
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min_value = 10,
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step = 1)
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x1 = np.linspace(0,1,num)
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x2 = x1
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x3 = x1
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xx1,xx2,xx3 = np.meshgrid(x1,x2,x3)
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x1_ = xx1.ravel()
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x2_ = xx2.ravel()
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x3_ = xx3.ravel()
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#%%
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df = pd.DataFrame({'X': x1_,
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'Y': x2_,
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'Z': x3_,
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'R': (x1_*256).round(),
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'G': (x2_*256).round(),
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'B': (x3_*256).round()})
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trace = go.Scatter3d(x=df.X,
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y=df.Y,
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z=df.Z,
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mode='markers',
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marker=dict(size=3,
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color=['rgb({},{},{})'.format(r,g,b)
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for r,g,b in
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zip(df.R.values, df.G.values, df.B.values)],
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opacity=0.9,))
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data = [trace]
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layout = go.Layout(margin=dict(l=0,
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r=0,
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b=0,
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t=0),
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scene = dict(
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xaxis = dict(title='e_1'),
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yaxis = dict(title='e_2'),
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zaxis = dict(title='e_3'),),
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)
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fig = go.Figure(data=data, layout=layout)
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st.plotly_chart(fig)
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