# Complex demo: Load California Housing, perform linear algebra operations (matrix multiplication, SVD), apply regression, evaluate, visualize with Matplotlib/Seaborn
import pandas as pd
import numpy as np
from sklearn.datasets import fetch_california_housing
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.decomposition import TruncatedSVD
import matplotlib.pyplot as plt
from scipy.linalg import svd
import seaborn as sns

def advanced_housing_linear_demo():
    # Load and prep
    housing = fetch_california_housing()
    df = pd.DataFrame(housing.data, columns=housing.feature_names)
    df['Target'] = housing.target
    # Feature engineering
    df['Rooms_Pop'] = df['AveRooms'] * df['Population']
    X = df.drop('Target', axis=1).values
    y = df['Target'].values
    # Linear algebra operations
    # Matrix multiplication
    X_transpose = X.T
    matrix_mult = np.dot(X_transpose, X)  # Covariance approximation
    # SVD
    U, S, Vt = svd(matrix_mult, full_matrices=True)
    print("Singular Values:\n", S)
    # Apply TruncatedSVD
    svd_model = TruncatedSVD(n_components=5)
    X_svd = svd_model.fit_transform(X)
    df_svd = pd.DataFrame(X_svd, columns=[f'SVD_{i}' for i in range(5)])
    df_svd['Target'] = y
    # Split and model
    X_train, X_test, y_train, y_test = train_test_split(X_svd, y, test_size=0.25, random_state=42)
    model = LinearRegression()
    model.fit(X_train, y_train)
    y_pred = model.predict(X_test)
    mse = mean_squared_error(y_test, y_pred)
    r2 = r2_score(y_test, y_pred)
    print(f"SVD-Integrated MSE: {mse:.2f}, R2: {r2:.2f}")
    # Visualize SVD components
    plt.scatter(df_svd['SVD_0'], df_svd['SVD_1'], c=df_svd['Target'], cmap='viridis')
    plt.title('SVD for Housing with Linear Algebra Integration')
    plt.xlabel('SVD Component 1')
    plt.ylabel('SVD Component 2')
    plt.annotate('Singular Dir', xy=(0, 0), xytext=(1, 1), arrowprops=dict(facecolor='black', shrink=0.05))
    plt.show()
    # Heatmap for U matrix
    sns.heatmap(U[:5, :5], annot=False, cmap='coolwarm')
    plt.title('U Matrix Heatmap from SVD for Housing')
    plt.show()

advanced_housing_linear_demo()