plot_sample.py

#!/usr/bin/env python3
"""
Plot a single sample from the Schrödinger equation dataset.

Visualizes quantum wave packet evolution including:
- Real and imaginary parts
- Probability density |ψ|²
- Potential well
- Energy conservation
"""

import numpy as np
import matplotlib.pyplot as plt
from dataset import SchrodingerDataset


def plot_schrodinger_sample(sample, save_path="sample_plot.png"):
    """Plot a single sample from the Schrödinger dataset"""
    fig = plt.figure(figsize=(16, 12))

    # Create subplot layout
    gs = fig.add_gridspec(3, 2, height_ratios=[1, 1, 0.8], hspace=0.3, wspace=0.3)

    # Extract data
    x = sample["spatial_coordinates"]
    t = sample["time_coordinates"]
    psi_r = sample["psi_r_trajectory"]
    psi_i = sample["psi_i_trajectory"]
    prob = sample["probability_density"]
    V = sample["potential"]
    energy = sample["total_energy"]

    # Colors for consistency
    color_real = "#1f77b4"
    color_imag = "#ff7f0e"
    color_prob = "#2ca02c"
    color_potential = "#d62728"

    # Plot 1: Initial and final wavefunction components
    ax1 = fig.add_subplot(gs[0, 0])
    ax1.plot(x, psi_r[0], color=color_real, linewidth=2, label="ψᵣ(x,t=0)")
    ax1.plot(x, psi_i[0], color=color_imag, linewidth=2, label="ψᵢ(x,t=0)")
    ax1.plot(
        x,
        psi_r[-1],
        "--",
        color=color_real,
        alpha=0.7,
        linewidth=2,
        label=f"ψᵣ(x,t={t[-1]:.1f})",
    )
    ax1.plot(
        x,
        psi_i[-1],
        "--",
        color=color_imag,
        alpha=0.7,
        linewidth=2,
        label=f"ψᵢ(x,t={t[-1]:.1f})",
    )
    ax1.set_xlabel("Position x")
    ax1.set_ylabel("ψ(x)")
    ax1.set_title("Wavefunction Components")
    ax1.grid(True, alpha=0.3)
    ax1.legend()

    # Plot 2: Probability density evolution
    ax2 = fig.add_subplot(gs[0, 1])
    ax2.plot(x, prob[0], color=color_prob, linewidth=2, label="|ψ(x,t=0)|²")
    ax2.plot(
        x,
        prob[-1],
        "--",
        color=color_prob,
        alpha=0.7,
        linewidth=2,
        label=f"|ψ(x,t={t[-1]:.1f})|²",
    )

    # Add potential well (scaled for visibility)
    V_scaled = V / np.max(V) * np.max(prob[0]) * 0.3
    ax2.fill_between(
        x, V_scaled, alpha=0.2, color=color_potential, label="V(x) (scaled)"
    )

    ax2.set_xlabel("Position x")
    ax2.set_ylabel("Probability Density")
    ax2.set_title("Quantum Probability |ψ|²")
    ax2.grid(True, alpha=0.3)
    ax2.legend()

    # Plot 3: Real part space-time evolution
    ax3 = fig.add_subplot(gs[1, 0])
    vmax = np.max(np.abs(psi_r))
    im1 = ax3.pcolormesh(
        x, t, psi_r, cmap="RdBu", vmin=-vmax, vmax=vmax, shading="gouraud"
    )
    ax3.set_xlabel("Position x")
    ax3.set_ylabel("Time t")
    ax3.set_title("Real Part Evolution ψᵣ(x,t)")
    plt.colorbar(im1, ax=ax3, label="ψᵣ")

    # Plot 4: Imaginary part space-time evolution
    ax4 = fig.add_subplot(gs[1, 1])
    vmax = np.max(np.abs(psi_i))
    im2 = ax4.pcolormesh(
        x, t, psi_i, cmap="RdBu", vmin=-vmax, vmax=vmax, shading="gouraud"
    )
    ax4.set_xlabel("Position x")
    ax4.set_ylabel("Time t")
    ax4.set_title("Imaginary Part Evolution ψᵢ(x,t)")
    plt.colorbar(im2, ax=ax4, label="ψᵢ")

    # Plot 5: Bottom spanning plots - Probability density heatmap and energy
    ax5 = fig.add_subplot(gs[2, 0])
    im3 = ax5.pcolormesh(x, t, prob, cmap="viridis", shading="gouraud")
    ax5.set_xlabel("Position x")
    ax5.set_ylabel("Time t")
    ax5.set_title("Probability Density Evolution |ψ(x,t)|²")
    plt.colorbar(im3, ax=ax5, label="|ψ|²")

    # Plot 6: Energy conservation
    ax6 = fig.add_subplot(gs[2, 1])
    ax6.plot(t, energy, "o-", color="darkgreen", linewidth=2, markersize=4)
    ax6.set_xlabel("Time t")
    ax6.set_ylabel("Total Energy")
    ax6.set_title("Energy Conservation")
    ax6.grid(True, alpha=0.3)

    # Add energy statistics
    E_mean = np.mean(energy)
    E_std = np.std(energy)
    ax6.axhline(
        E_mean, color="red", linestyle="--", alpha=0.7, label=f"Mean: {E_mean:.3f}"
    )
    ax6.text(
        0.02,
        0.95,
        f"σ/⟨E⟩ = {E_std/E_mean:.2e}",
        transform=ax6.transAxes,
        bbox=dict(boxstyle="round", facecolor="white", alpha=0.8),
        verticalalignment="top",
    )
    ax6.legend()

    # Add main title with physical parameters
    hbar = sample["hbar"]
    mass = sample["mass"]
    omega = sample["omega"]
    fig.suptitle(
        f"Quantum Harmonic Oscillator (ℏ={hbar}, m={mass}, ω={omega})",
        fontsize=16,
        fontweight="bold",
    )

    plt.savefig(save_path, dpi=200, bbox_inches="tight")
    plt.close()

    print(f"Schrödinger sample visualization saved to {save_path}")


if __name__ == "__main__":
    # Set random seed for reproducibility
    np.random.seed(42)

    # Create dataset with reasonable parameters for visualization
    dataset = SchrodingerDataset(Lx=20.0, Nx=256, stop_sim_time=2.0, timestep=1e-3)

    # 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_schrodinger_sample(sample)