ICL_code/ICL_Jay_final/data/Sphere.py

import torch
import numpy as np
import os
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def get_or_generate_data_sphere(epoch, batch_size, n_samples, scale_rbf, k_nn, device, label_percent, context_size, k_feat, data_dir="./cached_data", force=False):
    """
    Check for cached sphere data, or generate new data if it doesn't exist.
    
    Args:
        epoch: Current training epoch
        batch_size: Batch size
        n_samples: Number of points per sample
        scale_rbf: RBF kernel scaling parameter
        k_nn: K nearest neighbors parameter
        device: Computation device
        label_percent: Percentage of labeled points
        context_size: Size of context for in-context learning
        k_feat: Number of eigenvector features to use
        data_dir: Directory for data caching
        force: Whether to force regeneration of data
    
    Returns:
        Tuple of all data tensors and indices:
        (raw_data, real_lap, labels_tensor, real_adj, labeled_indices, context_indices, query_indices, real_ev)
    """
    # Create cache directory if it doesn't exist
    os.makedirs(data_dir, exist_ok=True)
    
    # Build file path
    file_path = os.path.join(data_dir, f"sphere_data_epoch_{epoch}.pt")
    # import pdb
    # pdb.set_trace()
    try:
        if (not force) and os.path.exists(file_path):
            print(f"Loading cached sphere data for epoch {epoch}...")
            cached_data = torch.load(file_path)
            return (
                cached_data['raw_data'],
                cached_data['real_lap'],
                cached_data['labels_tensor'],
                cached_data['real_adj'],
                cached_data['labeled_indices'],
                cached_data['context_indices'],
                cached_data['query_indices'],
                cached_data['real_ev']
            )
        
        print(f"Generating new sphere data for epoch {epoch}...")
    except:
        print(f"Re Generating new cone data for epoch {epoch}...")
    # Generate new data
    raw_data_batch = []
    real_lap_batch = []
    labels_batch = []
    adjacency_batch = []
    
    for b in range(batch_size):
        L_true, xyz, labels_np, adjacency = generate_small_sphere_in_3d(
            n_samples=n_samples,
            scale_rbf=scale_rbf,
            k_nn=k_nn,
            seed=epoch*batch_size+b,  
            device=device
        )
        raw_data_batch.append(torch.from_numpy(xyz).float())
        real_lap_batch.append(L_true)
        labels_batch.append(torch.from_numpy(labels_np))
        adjacency_batch.append(torch.from_numpy(adjacency).float())
    
    raw_data = torch.stack(raw_data_batch, dim=0).to(device)    
    real_lap = torch.stack(real_lap_batch, dim=0).to(device)
    labels_tensor = torch.stack(labels_batch, dim=0).to(device)
    real_adj = torch.stack(adjacency_batch, dim=0).to(device)
    
    # Build labeled and unlabeled sets
    n_labeled = int(n_samples * label_percent / 100)
    labeled_indices = torch.stack([torch.randperm(n_samples)[:n_labeled] for _ in range(batch_size)], dim=0).to(device)
    context_indices = torch.stack([torch.randperm(n_labeled)[:context_size] for _ in range(batch_size)], dim=0).to(device)
    all_indices = torch.arange(n_labeled).expand(batch_size, n_labeled).to(device)
    mask = torch.zeros(batch_size, n_labeled, dtype=torch.bool).to(device)
    

    # labels_tensor = labels_tensor.gather(-1, labeled_indices)
    # import pdb
    # pdb.set_trace()
    
    for i in range(batch_size):
        mask[i].scatter_(0, context_indices[i], True)
    
    query_indices = all_indices[~mask].view(batch_size, n_labeled - context_size).to(device)
    
    # Compute real eigenvectors
    real_eigs = []
    for b in range(batch_size):
        _, vecs = torch.linalg.eigh(real_lap[b])
        real_eigs.append(vecs[:, :k_feat])
    real_ev = torch.stack(real_eigs, dim=0)
    
    # Save all data to disk
    cached_data = {
        'raw_data': raw_data,
        'real_lap': real_lap,
        'labels_tensor': labels_tensor,
        'real_adj': real_adj,
        'labeled_indices': labeled_indices,
        'context_indices': context_indices,
        'query_indices': query_indices,
        'real_ev': real_ev
    }
    
    torch.save(cached_data, file_path)
    print(f"Saved sphere data to {file_path}")
    
    return raw_data, real_lap, labels_tensor, real_adj, labeled_indices, context_indices, query_indices, real_ev


def generate_in_context_sphere_graphs(Z, batch_size, n_samples, k_values, max_edges, noise=0.0, base_seed=0, k_feat=4, label_percent=100, context_size=0, model=None, use_exact_ev=False):
    """
    Generate in-context learning data for sphere dataset. Similar to the Swiss roll version but using sphere data.
    
    This function stores:
    - Normalized Laplacian in Z[:, :, :n]
    - Adjacency in Z[:, :, n:2n]
    - Eigenvectors in Z[:, :, 2n:]
    
    Args:
        Z: Zero tensor to populate with data
        batch_size: Number of graphs to generate
        n_samples: Number of nodes per graph
        k_values: K nearest neighbors for graph construction
        max_edges: Maximum edges to consider
        noise: Amount of noise to add
        base_seed: Base random seed
        k_feat: Number of eigenvector features
        label_percent: Percentage of labeled nodes
        context_size: Size of context for in-context learning
        model: Optional model to predict eigenvectors
        use_exact_ev: Whether to use exact eigenvectors
        
    Returns:
        embedding, labeled_data, labeled_indices, context_indices, query_indices
    """
    assert label_percent > 0 and label_percent <= 100
    n_labeled = int(n_samples * label_percent / 100)
    
    assert context_size < n_labeled
    
    if isinstance(k_values, int):
        k_values = [k_values]

    if use_exact_ev:
        embedding = torch.zeros([batch_size, n_samples, k_feat], device=device)
    
    for i in range(batch_size):
        # Use the iteration number or base_seed + i as the seed
        seed = base_seed + i  # Ensures different seeds for each graph
        
        adj, L_test, eigenvals, eigenvecs = generate_weighted_sphere_graph(
            n_samples=n_samples,
            scale=10,
            k=k_values[0] if isinstance(k_values, list) else k_values,
            seed=seed,
            return_extra=False,
            device=device
        )

        # Use the normalized Laplacian directly
        lap = L_test.to(device)
        
        # Select and normalize eigenvectors
        eigenvecs_selected = eigenvecs[:, :k_feat]
        eigenvecs_selected /= (np.linalg.norm(eigenvecs_selected, axis=1, keepdims=True) + 1e-10)
        eigenvecs_selected = torch.from_numpy(eigenvecs_selected).float().to(device)

        # Fill Z
        Z[i, :, :n_samples] = lap                       # [n, n], normalized Laplacian
        Z[i, :, n_samples:2*n_samples] = adj.to(device) # [n, n], adjacency matrix
        Z[i, :, 2*n_samples:] = eigenvecs_selected      # [n, k_feat], eigenvectors

        if use_exact_ev:
            actual_embedding = eigenvecs[:, :k_feat]  # [n_samples, k_feat]
            embedding[i, :, :] = torch.from_numpy(actual_embedding / (np.linalg.norm(actual_embedding, axis=1, keepdims=True) + 1e-10)).float().to(device)
            
    if not use_exact_ev:
        # Make predictions with PE transformer
        model.eval()
        with torch.no_grad():
            output = model(Z)  # Shape: [batch_size, n_samples, n + (n+k)]
            # Extract predicted eigenvectors
            predicted_ev = output[:, :, -k_feat:].cpu().numpy()  # [batch_size, n_samples, k_feat]
        
        # Predicted embedding
        embedding = predicted_ev / (np.linalg.norm(predicted_ev, axis=1, keepdims=True) + 1e-10)
        embedding = torch.from_numpy(embedding).float().to(device)

    # Assign labels based on geodesic distance for sphere dataset
    # For sphere we need to generate labels differently than Swiss roll
    # Generate one sample of sphere data to get point positions
    t, data = gen_random_data(batch_size, n_samples, type='sphere')
    data = data.to(device)
    
    # Generate labels based on geodesic distance
    labels = torch.zeros(batch_size, n_samples, device=device)
    for b in range(batch_size):
        # Choose a random point as center
        center_idx = torch.randint(0, n_samples, (1,)).item()
        center_point = data[b, center_idx]
        
        # Calculate dot products and geodesic distances
        dots = torch.clamp(torch.sum(data[b] * center_point, dim=1), -1.0, 1.0)
        geodesic_dist = torch.acos(dots)
        
        # Create binary labels: points closer than π/3 are class 1, others are class 0
        labels[b] = (geodesic_dist < (torch.pi / 3)).long()
    
    # Get labeled indices
    labeled_indices = torch.stack([torch.randperm(n_samples)[:n_labeled] for _ in range(batch_size)]).to(device)
    labeled_data = labels.gather(1, labeled_indices)
    
    # Get context indices
    context_indices = torch.stack([torch.randperm(n_labeled)[:context_size] for _ in range(batch_size)]).to(device)
    
    all_indices = torch.arange(n_labeled).expand(batch_size, n_labeled).to(device)  # Shape [B, n_labeled]

    # Create a mask for indices present in the input tensor
    mask = torch.zeros(batch_size, n_labeled, dtype=torch.bool).to(device)
    mask.scatter_(1, context_indices, True)
            
    # Invert the mask to get query indices
    query_indices = all_indices[~mask].view(batch_size, n_labeled - context_size).to(device)  # Shape [B, n_labeled - context_size]

    return embedding, labeled_data, labeled_indices, context_indices, query_indices


def gen_random_data(n_batch, n_samples, type='swissroll'):
    """
    Generate random data of different types, including circles, swiss roll, line,
    and now sphere.
    
    Args:
        n_batch (int): Number of batches to generate
        n_samples (int): Number of samples per batch
        type (str): Type of data to generate ('circles', 'swissroll', 'line', or 'sphere')
        
    Returns:
        t (torch.Tensor): Parameter values used to generate the data.
                           For 'swissroll', this is the 1D parameter.
                           For 'sphere', this returns the polar angle theta.
        data (torch.Tensor): Generated data points.
    """
    if type=='circles':
        n0 = int(n_samples/5)
        r0 = 0.1
        r1 = 0.6

        t0 = torch.rand(size=(n_batch, 2*n0))
        t1 = torch.rand(size=(n_batch, n0))
        t2 = torch.rand(size=(n_batch, 2*n0))
        
        t0, _ = torch.sort(t0)
        t1, _ = torch.sort(t1)
        t2, _ = torch.sort(t2)

        t = torch.cat((t0, t1+1, t2+2), dim=1)

        x0 = r0*torch.cos(t0*2*torch.pi)
        y0 = r0*torch.sin(t0*2*torch.pi)

        x1 = torch.zeros_like(t1)
        y1 = r0 + t1 * (r1-r0)

        x2 = r1 * torch.cos(t2*2*torch.pi)
        y2 = r1 * torch.sin(t2*2*torch.pi)

        xs = torch.cat((x0, x1, x2), dim=1)
        ys = torch.cat((y0, y1, y2), dim=1)

        data = torch.cat((xs[:,:,None], ys[:,:,None]), dim=2)

    elif type=='swissroll':
        n0 = int(n_samples)

        t0 = torch.rand(size=(n_batch, n0))
        t0, _ = torch.sort(t0)
        t = t0

        x0 = t0**2*torch.cos(t0*4*torch.pi)
        y0 = t0**2*torch.sin(t0*4*torch.pi)

        data = torch.cat((x0[:,:,None], y0[:,:,None]), dim=2)

    elif type=='line':
        n0 = int(n_samples)

        t0 = torch.rand(size=(n_batch, n0))
        t0, _ = torch.sort(t0)
        t = t0

        x0 = torch.zeros_like(t0)
        y0 = t0

        data = torch.cat((x0[:,:,None], y0[:,:,None]), dim=2)
    
    elif type=='sphere':
        # Sample uniformly on the unit sphere using spherical coordinates.
        # u, v ~ Uniform(0,1)
        u = torch.rand(n_batch, n_samples)
        v = torch.rand(n_batch, n_samples)
        # theta in [0, pi] via inverse transform of cos(theta)
        theta = torch.acos(2*u - 1)
        # phi in [0, 2pi]
        phi = 2 * torch.pi * v
        
        x = torch.sin(theta) * torch.cos(phi)
        y = torch.sin(theta) * torch.sin(phi)
        z = torch.cos(theta)
        
        # t will be theta (analogous to the 1D parameter for the swiss roll)
        t = theta
        
        data = torch.cat([x.unsqueeze(2), y.unsqueeze(2), z.unsqueeze(2)], dim=2)
    else:
        raise ValueError(f"Unknown data type: {type}")

    return t, data


def random_data_to_adjacency(data, scale=4):
    """
    Convert data points to an adjacency matrix using RBF kernel.
    
    Args:
        data (torch.Tensor): Data points of shape [B, n_sample, dim]
        scale (float): Scale parameter for RBF kernel
        
    Returns:
        torch.Tensor: Adjacency matrix with RBF weights
    """
    B, n, d = data.shape
    # distance(vi, vj) = ||vi - vj||^2 = ||vi||^2 + ||vj||^2 - 2<vi,vj>
    norms = torch.norm(data, p=2, dim=2)**2
    euclidean_distances = norms[:,:,None] + norms[:,None,:] - 2 * torch.einsum('Bni,Bmi->Bnm', (data, data))
    inv_rbf_distances = torch.exp(-scale * euclidean_distances)
    
    return inv_rbf_distances


def smallest_k_indices(inv_distance_matrix, k):
    """
    Find the indices of the k largest values in each row of the inverse distance matrix.
    This corresponds to the k nearest neighbors in the original space.
    
    Args:
        inv_distance_matrix (torch.Tensor): Inverse distance matrix
        k (int): Number of nearest neighbors to find
        
    Returns:
        torch.Tensor: Indices of k-nearest neighbors for each node
    """
    # Mask the diagonal to exclude self-loops
    n = inv_distance_matrix.size(0)
    inv_distance_matrix = inv_distance_matrix.clone()  # Avoid modifying the original
    inv_distance_matrix.fill_diagonal_(float(-1))  # Set diagonal to a negative value
    
    # Find the indices of the k largest values in each row
    indices = torch.topk(inv_distance_matrix, k, dim=-1).indices
    
    return indices


def generate_small_sphere_in_3d(n_samples=100, scale_rbf=10, k_nn=6, seed=0, device=None):
    """
    Generate a 3D sphere with a normalized Laplacian.
    
    This function samples n_samples points uniformly from a sphere, computes the
    RBF adjacency based on Euclidean distances, builds a k-NN graph, and then computes
    the normalized Laplacian.
    
    Labels are assigned based on the geodesic (great-circle) distance on the sphere.
    A random point is chosen, and all points with geodesic distance (arccos(dot))
    less than a threshold (here 0.5 radians) are labeled as one class.
    
    Args:
        n_samples (int): Number of samples to generate
        scale_rbf (float): Scale parameter for RBF kernel
        k_nn (int): Number of nearest neighbors for graph construction
        seed (int): Random seed for reproducibility
        device (torch.device): Device to create tensors on
        
    Returns:
        L (torch.Tensor): Normalized Laplacian matrix
        xyz (numpy.ndarray): 3D coordinates of the points
        labels (numpy.ndarray): Binary labels for the points (0 or 1)
        adjacency (torch.Tensor): Optional adjacency matrix
    """
    if device is None:
        device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
        
    # Set random seeds for reproducibility
    torch.manual_seed(seed)
    np.random.seed(seed)

    # Generate 3D sphere data using the new type.
    n_batch = 1
    t, data3d = gen_random_data(n_batch, n_samples, type='sphere')
    data3d = data3d.to(device)  # shape [1, n_samples, 3]

    # Compute RBF adjacency using Euclidean distances in 3D.
    dist_sq = torch.cdist(data3d[0], data3d[0], p=2)**2
    A_rbf = torch.exp(-scale_rbf*dist_sq).to(device)

    # Build k-NN graph
    idx_topk = smallest_k_indices(A_rbf, k_nn)  # shape [n_samples, k_nn]
    adjacency = torch.zeros((n_samples, n_samples), device=device)
    for i in range(n_samples):
        for j in idx_topk[i]:
            adjacency[i, j] = A_rbf[i, j]
            adjacency[j, i] = A_rbf[j, i]  # Ensure symmetry

    # Compute normalized Laplacian: L = I - D^(-1/2) A D^(-1/2)
    deg = adjacency.sum(dim=1)
    deg[deg < 1e-10] = 1e-10  # Avoid division by zero
    D_inv_sqrt = torch.diag(deg.pow(-0.5))
    L = torch.eye(n_samples, device=device) - D_inv_sqrt @ adjacency @ D_inv_sqrt

    # Create labels based on geodesic distance on the sphere.
    # Randomly choose one point from the dataset as the center.
    chosen_idx = np.random.randint(0, n_samples)
    chosen_point = data3d[0, chosen_idx]  # shape [3]
    # Compute dot products between chosen_point and all points (they lie on the unit sphere)
    dots = torch.clamp(torch.matmul(data3d[0], chosen_point), -1.0, 1.0)
    # Geodesic distance on a sphere: arccos(dot)
    geodesic_distances = torch.acos(dots)
    # Use threshold = 0.5 (radians); points with geodesic distance less than 0.5 are class 1, else 0.
    labels = (geodesic_distances < 0.5).long().cpu().numpy()
    xyz = data3d[0].cpu().numpy()  # shape [n_samples, 3]

    return L, xyz, labels, adjacency.cpu().numpy()


def generate_weighted_sphere_graph(n_samples=100, scale=10, k=6, seed=5, return_extra=False, model=None, use_predicted_laplacian=False, k_feat=4, device=None):
    """
    Generate a sphere dataset with a weighted graph and compute its Laplacian.
    Optionally use a model to predict the Laplacian instead of computing it directly.
    
    This function uses the sphere manifold (via gen_random_data with type 'sphere') and then applies
    a series of random transformations. Note that unlike the swiss roll version, here we:
      - Do not add an extra fixed z-dimension (since the data is already 3D)
      - Apply a uniform scaling to all dimensions (to preserve the spherical shape)
      - Use the same random rotation and translation (on x and y) as in the original code.
      
    Labels are assigned based on the geodesic distance on the sphere.
    
    Args:
        n_samples (int): Number of samples in the sphere
        scale (float): Scale parameter for the RBF kernel
        k (int): Number of nearest neighbors for graph construction
        seed (int): Random seed for reproducibility
        return_extra (bool): Whether to return additional data for visualization
        model: Optional model to predict the Laplacian
        use_predicted_laplacian (bool): Whether to use the model to predict Laplacian
        k_feat (int): Number of eigenvector features to select
        device: Device to create tensors on
        
    Returns:
        Multiple tensors depending on return_extra:
        - Always: adjacency, normalized Laplacian, eigenvalues, eigenvectors
        - If return_extra=True: Also t, a_translated (raw data)
    """
    if device is None:
        device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
        
    # Set seeds for reproducibility
    torch.manual_seed(seed)
    np.random.seed(seed)

    # Generate sphere data
    t, a = gen_random_data(1, n_samples, type='sphere')
    a = a.to(device)  # shape [1, n_samples, 3]

    # Apply random scaling uniformly to all dimensions to mimic randomness in the swiss roll.
    scale_factor = np.random.uniform(0.02, 0.1)
    a_translated = a * scale_factor

    # Apply random rotation (using the same rotation around the z-axis as before)
    theta = np.random.uniform(0, 2 * np.pi)
    rotation_matrix = torch.tensor([
        [np.cos(theta), -np.sin(theta), 0],
        [np.sin(theta),  np.cos(theta), 0],
        [0,             0,              1]
    ], dtype=torch.float32, device=device)
    a_rotated = torch.matmul(a_translated, rotation_matrix)

    # Apply random translation (only on x and y; leave z unchanged)
    translation_x = np.random.uniform(-1, 1)
    translation_y = np.random.uniform(-1, 1)
    translation = torch.tensor([[[translation_x, translation_y, 0]]], dtype=torch.float32, device=device)
    a_translated = a_rotated + translation

    # Compute RBF similarities.
    # For the sphere version, we use all three coordinates.
    inv_distances = random_data_to_adjacency(a_translated, scale=scale)

    # Construct k-NN adjacency matrix.
    knn_indices = smallest_k_indices(inv_distances[0, :, :], k)
    adj = torch.zeros((n_samples, n_samples), dtype=torch.float32, device=device)
    for i in range(knn_indices.shape[0]):
        for j in knn_indices[i, :]:
            if j < n_samples:
                weight = inv_distances[0, i, j].item()
                adj[i, j] = weight
                adj[j, i] = weight  # Ensure symmetry

    # Either compute or predict the Laplacian.
    if use_predicted_laplacian and model is not None:
        # Prepare input for the model
        Z_input_for_model = torch.zeros(1, n_samples, 2 * n_samples + k_feat, device=device)
        for row_idx in range(n_samples):
            Z_input_for_model[0, row_idx, 0:3] = a_translated[0, row_idx, :]  # Store (x, y, z)

        # Predict Laplacian rows using the model.
        model.eval()
        with torch.no_grad():
            predicted_output = model(Z_input_for_model)
            predicted_laplacian_rows = predicted_output[:, :, n_samples:2*n_samples]  # [1, n, n]
            L_test = predicted_laplacian_rows[0].to(device)  # [n, n]
    else:
        # Compute normalized Laplacian directly.
        degree = torch.sum(adj, dim=1)
        degree[degree == 0] = 1.0  # Avoid division by zero
        D_inv_sqrt = torch.diag(degree.pow(-0.5))
        L_test = torch.eye(adj.size(0), device=device) - D_inv_sqrt @ adj @ D_inv_sqrt

    # Compute eigenvalues and eigenvectors.
    target_eigenvals, target_ev_torch = torch.linalg.eigh(L_test)
    target_ev = target_ev_torch.cpu().numpy()

    if return_extra:
        # Additional plotting and visualization data.
        data = a_translated[0].cpu().numpy()
        # Assign labels based on geodesic distance on the sphere.
        chosen_idx = np.random.randint(0, n_samples)
        chosen_point = a_translated[0, chosen_idx]
        dots = torch.clamp(torch.matmul(a_translated[0], chosen_point), -1.0, 1.0)
        geodesic_distances = torch.acos(dots)
        labels = np.where(geodesic_distances.cpu().numpy() < 0.5, 1, -1)
        
        return t, a_translated, adj, L_test, target_eigenvals, target_ev
    else:
        return adj, L_test, target_eigenvals, target_ev


def cache_or_compute_test_data(n_samples, scale_rbf, k_nn, test_seed, cache_dir="./cache", force_recompute=False, device=None):
    """
    Cache test data to disk or retrieve it if it exists.
    
    Args:
        n_samples (int): Number of samples
        scale_rbf (float): Scale parameter for RBF kernel
        k_nn (int): Number of nearest neighbors
        test_seed (int): Random seed for test data
        cache_dir (str): Directory to store cached data
        force_recompute (bool): Whether to force recomputation even if cache exists
        device: Device to create tensors on
        
    Returns:
        tuple: (L_test, xyz_test, labels_test, adjacency)
    """
    # Create cache directory if it doesn't exist
    os.makedirs(cache_dir, exist_ok=True)
    
    # Create a unique filename based on parameters (note "sphere" in the filename)
    cache_filename = f"{cache_dir}/sphere_n{n_samples}_s{scale_rbf}_k{k_nn}_seed{test_seed}.pt"
    
    if os.path.exists(cache_filename) and not force_recompute:
        # Load cached data
        print(f"Loading cached test data from {cache_filename}")
        cached_data = torch.load(cache_filename)
        
        L_test = cached_data["L_test"]
        xyz_test = cached_data["xyz_test"]
        labels_test = cached_data["labels_test"]
        adjacency = cached_data["adjacency"]
        
        if device is not None:
            L_test = L_test.to(device)

        return L_test, xyz_test, labels_test, adjacency
    else:
        # Generate new data
        print(f"Generating new test data with seed {test_seed}")
        L_test, xyz_test, labels_test, adjacency = generate_small_sphere_in_3d(
            n_samples=n_samples,
            scale_rbf=scale_rbf,
            k_nn=k_nn,
            seed=test_seed,
            device=device
        )
        
        # Cache the data
        cached_data = {
            "L_test": L_test.cpu(),
            "xyz_test": xyz_test,
            "labels_test": labels_test,
            "adjacency": adjacency
        }
        
        torch.save(cached_data, cache_filename)
        print(f"Cached test data to {cache_filename}")
        
        return L_test, xyz_test, labels_test, adjacency


def visualize_adjacency_matrix(adjacency_matrix, title="Adjacency Matrix"):
    """
    Visualize an adjacency matrix as a heatmap.
    
    Args:
        adjacency_matrix: 2D tensor or array representing the adjacency matrix
        title (str): Title for the plot
    """
    plt.figure(figsize=(8, 6))
    plt.imshow(adjacency_matrix, cmap='viridis', interpolation='nearest')
    plt.colorbar(label="Edge Weight")
    plt.title(title)
    plt.xlabel("Node Index")
    plt.ylabel("Node Index")
    plt.grid(False)
    plt.show()


def visualize_3d_points(xyz, labels=None, title="3D Points"):
    """
    Visualize points in 3D space.
    
    Args:
        xyz: Array of shape [n_samples, 3] containing 3D coordinates
        labels: Optional array of labels for coloring the points
        title (str): Title for the plot
    """
    fig = plt.figure(figsize=(10, 8))
    ax = fig.add_subplot(111, projection='3d')
    
    if labels is not None:
        scatter = ax.scatter(xyz[:, 0], xyz[:, 1], xyz[:, 2], c=labels, cmap='bwr', s=40, alpha=0.8)
        legend = ax.legend(*scatter.legend_elements(), title="Classes")
        ax.add_artist(legend)
    else:
        ax.scatter(xyz[:, 0], xyz[:, 1], xyz[:, 2], s=40, alpha=0.8)
    
    ax.set_xlabel("X")
    ax.set_ylabel("Y")
    ax.set_zlabel("Z")
    ax.set_title(title)
    
    plt.tight_layout()
    plt.show()