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| import streamlit as st | |
| import numpy as np | |
| from scipy.integrate import odeint | |
| import plotly.graph_objects as go | |
| import time | |
| import pandas as pd | |
| # Define the Lorenz system | |
| def lorenz_system(current_state, t, sigma, rho, beta): | |
| x, y, z = current_state | |
| dx_dt = sigma * (y - x) | |
| dy_dt = x * (rho - z) - y | |
| dz_dt = x * y - beta * z | |
| return [dx_dt, dy_dt, dz_dt] | |
| # Set up the sidebar | |
| st.sidebar.title('Lorenz System Parameters') | |
| sigma = st.sidebar.slider('Sigma', 0.0, 50.0, 10.0) | |
| rho = st.sidebar.slider('Rho', 0.0, 50.0, 28.0) | |
| beta = st.sidebar.slider('Beta', 0.0, 50.0, 2.67) | |
| x0_1 = st.sidebar.number_input('Initial x for 1st system', value=1.0) | |
| y0_1 = st.sidebar.number_input('Initial y for 1st system', value=1.0) | |
| z0_1 = st.sidebar.number_input('Initial z for 1st system', value=1.0) | |
| x0_2 = st.sidebar.number_input('Initial x for 2nd system', value=1.0) | |
| y0_2 = st.sidebar.number_input('Initial y for 2nd system', value=1.0) | |
| z0_2 = st.sidebar.number_input('Initial z for 2nd system', value=1.0) | |
| # Define the time points for the simulation | |
| t = np.linspace(0, 4, 1000) | |
| # Solve the Lorenz system | |
| solution_1 = odeint(lorenz_system, (x0_1, y0_1, z0_1), t, args=(sigma, rho, beta)) | |
| solution_2 = odeint(lorenz_system, (x0_2, y0_2, z0_2), t, args=(sigma, rho, beta)) | |
| # Create a 3D plot of the solutions | |
| plot_slot = st.empty() | |
| stop = st.checkbox('Stop') | |
| i = 0 | |
| while i < len(t) and not stop: | |
| fig = go.Figure(data=[ | |
| go.Scatter3d(x=solution_1[:i, 0], y=solution_1[:i, 1], z=solution_1[:i, 2], mode='lines', line=dict(color='red'), name='System 1'), | |
| go.Scatter3d(x=solution_2[:i, 0], y=solution_2[:i, 1], z=solution_2[:i, 2], mode='lines', line=dict(color='blue'), name='System 2') | |
| ]) | |
| fig.update_layout(scene=dict(xaxis=dict(range=[min(min(solution_1[:, 0]), min(solution_2[:, 0])), max(max(solution_1[:, 0]), max(solution_2[:, 0]))]), | |
| yaxis=dict(range=[min(min(solution_1[:, 1]), min(solution_2[:, 1])), max(max(solution_1[:, 1]), max(solution_2[:, 1]))]), | |
| zaxis=dict(range=[min(min(solution_1[:, 2]), min(solution_2[:, 2])), max(max(solution_1[:, 2]), max(solution_2[:, 2]))]), | |
| camera=dict(eye=dict(x=2*np.cos(i/10), y=2*np.sin(i/10), z=0.1))), | |
| width=800, height=600) | |
| plot_slot.plotly_chart(fig) | |
| i += 1 | |
| time.sleep(0.2) | |
| if st.button('Export Data'): | |
| df_1 = pd.DataFrame(solution_1, columns=['x_1', 'y_1', 'z_1']) | |
| df_2 = pd.DataFrame(solution_2, columns=['x_2', 'y_2', 'z_2']) | |
| df_1.to_csv('lorenz_data_1.csv') | |
| df_2.to_csv('lorenz_data_2.csv') | |
| st.write('Data exported successfully!') |