Updates

app.py

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+import streamlit as st
+import torch
+import numpy as np
+import plotly.graph_objects as go
+
+st.set_page_config(layout="wide")
+
+st.title("Bivariate Normal Distribution")
+
+# Sidebar for controls
+with st.sidebar:
+    st.header("Controls")
+    mu_x = st.slider("Mean of X (μx)", -2.0, 2.0, 0.0)
+    mu_y = st.slider("Mean of Y (μy)", -2.0, 2.0, 0.0)
+    sigma_x = st.slider("Std Dev of X (σx)", 0.1, 2.0, 1.0)
+    sigma_y = st.slider("Std Dev of Y (σy)", 0.1, 2.0, 1.0)
+    rho = st.slider("Correlation (ρ)", -0.9, 0.9, 0.0)
+
+# Covariance matrix
+cov_matrix = torch.tensor([[sigma_x**2, rho * sigma_x * sigma_y],
+                           [rho * sigma_x * sigma_y, sigma_y**2]])
+mean_vector = torch.tensor([mu_x, mu_y])
+
+# Create distribution
+distribution = torch.distributions.MultivariateNormal(mean_vector, cov_matrix)
+
+# Generate grid
+x = torch.linspace(-4, 4, 100)
+y = torch.linspace(-4, 4, 100)
+X, Y = torch.meshgrid(x, y, indexing='xy')
+pos = torch.stack((X, Y), dim=-1)
+
+Z = torch.exp(distribution.log_prob(pos))
+
+# Compute marginal distributions
+marginal_x = torch.distributions.Normal(mean_vector[0], torch.sqrt(cov_matrix[0, 0]))
+marginal_y = torch.distributions.Normal(mean_vector[1], torch.sqrt(cov_matrix[1, 1]))
+
+pdf_x = torch.exp(marginal_x.log_prob(x))
+pdf_y = torch.exp(marginal_y.log_prob(y))
+
+# Convert to numpy for plotting
+X, Y, Z = X.numpy(), Y.numpy(), Z.numpy()
+
+# Create 3D surface plot
+fig = go.Figure()
+fig.add_trace(go.Surface(z=Z, x=X, y=Y, colorscale='Viridis', opacity=0.9, name='Density'))
+
+# Marginal distributions on the walls
+fig.add_trace(go.Scatter3d(x=x.numpy(), y=np.full_like(x.numpy(), -4), z=pdf_x.numpy() / np.max(pdf_x.numpy()) * np.max(Z), mode='lines', line=dict(color='red', width=4), name='Marginal X'))
+fig.add_trace(go.Scatter3d(x=np.full_like(y.numpy(), 4), y=y.numpy(), z=pdf_y.numpy() / np.max(pdf_y.numpy()) * np.max(Z), mode='lines', line=dict(color='blue', width=4), name='Marginal Y'))
+
+fig.update_layout(
+    scene=dict(
+        xaxis_title='X',
+        yaxis_title='Y',
+        zaxis_title='Density',
+    ),
+    margin=dict(l=0, r=0, t=20, b=20),
+    legend=dict(x=0.8, y=0.9, font=dict(size=14)),
+    width=1100, height=800
+)
+
+# Main display
+st.plotly_chart(fig, use_container_width=True)

requirements.txt

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+streamlit
+matplotlib
+torch
+plotly