app.py

from matplotlib import pyplot as plt
import numpy as np
import streamlit as st
import pandas as pd
from utils import getSquareYVectorised, getCircle, transform, plotGridLines

np.set_printoptions(precision=3)
xlim = (-10,10)
ylim = (-10,10)

st.title("Eigen Values and Eigen Vectors")
st.write(
    "This app shows the effect of linear transformation with respect to eigen values and eigen vectors"
)

with st.sidebar:
    data = st.selectbox('Select type of dataset', ['Square', 'Circle'])
    st.write("---")
    st.text("Enter transformation matrix elements")
    minv = -5.0
    maxv = 5.0
    step = 0.1
    a_00 = st.slider(label = '$A_{0,0}$', min_value = minv, max_value=maxv, value=1.0, step=step)
    a_01 = st.slider(label = '$A_{0,1}$', min_value = minv, max_value=maxv, value=0.0, step=step)
    a_10 = st.slider(label = '$A_{1,0}$', min_value = minv, max_value=maxv, value=0.0, step=step)
    a_11 = st.slider(label = '$A_{1,1}$', min_value = minv, max_value=maxv, value=1.0, step=step)
    t = np.array([[a_00,a_01], [a_10, a_11]], dtype=np.float64)  

x = np.linspace(-1,1,1000)
y = getSquareYVectorised(x) if data == 'Square' else getCircle(x)

x_dash_up, y_dash_up = transform(x,y,t)
x_dash_down, y_dash_down = transform(x,-y,t)

evl, evec = np.linalg.eig(t)
fig, ax = plt.subplots()
ax.plot(x_dash_up,y_dash_up,'r')
ax.plot(x_dash_down,y_dash_down, 'g')
if not (np.iscomplex(evl).any() or np.iscomplex(evec).any()):
    ax.quiver(0,0,evec[0,0]*evl[0],evec[1,0]*evl[0],scale=1,scale_units ='xy',angles='xy', facecolor='yellow', label='$eigen\ vector_{\lambda_0}$')
    ax.quiver(0,0,evec[0,1]*evl[1],evec[1,1]*evl[1],scale=1,scale_units ='xy',angles='xy', facecolor='blue',label='$eigen\ vector_{\lambda_1}$')

plotGridLines(xlim,ylim,t)
ax.set_xlim(*xlim)
ax.set_ylim(*ylim)
ax.set_aspect('equal', adjustable='box')
fig.legend()
st.pyplot(fig)

df = pd.DataFrame({'Eigen Values': evl, 'Eigen Vectors': [str(evec[:,0]), str(evec[:,1])],\
    'Transformed Eigen Vectors': [str(evec[:,0]*evl[0]), str(evec[:,1]*evl[1])]})
st.table(df)

if np.iscomplex(evl).any() or np.iscomplex(evec).any():
    st.write("Due to complex eigen vectors or eigne values, the transformed eigen vectors are not\
        displayed...")