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#!/usr/bin/env python3
"""
Plot a single sample from the 2D Poisson equation dataset.
Visualizes the forcing function, solution field, and boundary conditions
for a single randomly generated Poisson boundary value problem.
"""
import numpy as np
import matplotlib.pyplot as plt
from dataset import PoissonDataset
def plot_poisson_sample(sample, save_path="sample_plot.png"):
"""
Plot a single sample from the 2D Poisson equation dataset.
Creates a 3-panel visualization showing:
1. Forcing function f(x,y)
2. Solution field u(x,y)
3. Boundary conditions
"""
fig = plt.figure(figsize=(15, 5))
ax1 = plt.subplot(1, 3, 1)
ax2 = plt.subplot(1, 3, 2)
ax3 = plt.subplot(1, 3, 3)
# Extract data from dataset return dictionary
X, Y = sample["spatial_coordinates"] # Shape: (2, Nx, Ny)
solution = sample["solution_field"] # Shape: (Nx, Ny)
forcing = sample["forcing_function"] # Shape: (Nx, Ny)
bc_bottom = sample["boundary_condition_bottom"] # Shape: (Nx,)
bc_top_grad = sample["boundary_condition_top_gradient"] # Shape: (Nx,)
# Plot 1: Forcing function f(x,y)
im1 = ax1.pcolormesh(
X, Y, forcing, cmap="RdBu_r", shading="gouraud", rasterized=True
)
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.set_title("Forcing Function f(x,y)")
ax1.set_aspect("equal")
plt.colorbar(im1, ax=ax1, label="f(x,y)")
# Plot 2: Solution field u(x,y)
im2 = ax2.pcolormesh(
X, Y, solution, cmap="viridis", shading="gouraud", rasterized=True
)
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.set_title("Solution u(x,y)")
ax2.set_aspect("equal")
plt.colorbar(im2, ax=ax2, label="u(x,y)")
# Plot 3: Boundary conditions
# X has shape (Nx, Ny), we want x-coordinates along boundaries
x_bottom = X[:, 0] # x-coordinates along bottom boundary (y=0)
x_top = X[:, -1] # x-coordinates along top boundary (y=Ly)
# Flatten boundary condition arrays if needed
bc_bottom_flat = bc_bottom.ravel() if bc_bottom.ndim > 1 else bc_bottom
bc_top_grad_flat = bc_top_grad.ravel() if bc_top_grad.ndim > 1 else bc_top_grad
ax3.plot(x_bottom, bc_bottom_flat, "b-", linewidth=2, label="u(x,0) = g(x)")
ax3.plot(x_top, bc_top_grad_flat, "r--", linewidth=2, label="∂u/∂y(x,Ly) = h(x)")
ax3.set_xlabel("x")
ax3.set_ylabel("Boundary values")
ax3.set_title("Boundary Conditions")
ax3.legend()
ax3.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig(save_path, dpi=200, bbox_inches="tight")
plt.close()
print(f"Sample visualization saved to {save_path}")
if __name__ == "__main__":
# Set random seed for reproducibility
np.random.seed(42)
# Create dataset instance
dataset = PoissonDataset()
# Generate a single sample
dataset_iter = iter(dataset)
sample = next(dataset_iter)
sample = next(dataset_iter)
print("Sample keys:", list(sample.keys()))
for key, value in sample.items():
if hasattr(value, "shape"):
print(f"{key}: shape {value.shape}")
else:
print(f"{key}: {type(value)} - {value}")
# Plot the sample
plot_poisson_sample(sample)
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