# Complex demo: Load Iris, perform linear algebra operations (matrix multiplication, eigenvalues), apply PCA, visualize with Matplotlib/Seaborn
import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt
from scipy.linalg import eig
import seaborn as sns

def advanced_iris_linear_demo():
    # Load and prep
    iris = load_iris()
    df = pd.DataFrame(iris.data, columns=iris.feature_names)
    df['Target'] = iris.target
    # Feature engineering
    df['Petal_Product'] = df['petal length (cm)'] * df['petal width (cm)']
    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 matrix approximation
    # Eigenvalues and eigenvectors
    eigenvalues, eigenvectors = eig(matrix_mult)
    print("Eigenvalues:\n", eigenvalues)
    print("Eigenvectors:\n", eigenvectors)
    # Apply PCA
    pca = PCA(n_components=2)
    X_pca = pca.fit_transform(X)
    df_pca = pd.DataFrame(X_pca, columns=['PC1', 'PC2'])
    df_pca['Target'] = y
    # Split and model
    X_train, X_test, y_train, y_test = train_test_split(X_pca, y, test_size=0.3, random_state=42)
    model = RandomForestClassifier(n_estimators=100, random_state=42)
    model.fit(X_train, y_train)
    y_pred = model.predict(X_test)
    acc = accuracy_score(y_test, y_pred)
    print(f"PCA-Integrated Accuracy: {acc:.2f}")
    # Visualize PCA with eigenvectors annotation
    plt.scatter(df_pca['PC1'], df_pca['PC2'], c=df_pca['Target'], cmap='viridis')
    plt.title('PCA for Iris with Linear Algebra Integration')
    plt.xlabel('Principal Component 1')
    plt.ylabel('Principal Component 2')
    plt.annotate('Eigenvector Dir', xy=(0, 0), xytext=(1, 1), arrowprops=dict(facecolor='black', shrink=0.05))
    plt.show()
    # Heatmap for covariance matrix
    sns.heatmap(matrix_mult, annot=False, cmap='coolwarm')
    plt.title('Covariance Matrix Heatmap for Iris')
    plt.show()

advanced_iris_linear_demo()