import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from qiskit import QuantumCircuit, Aer, execute
from qiskit.circuit.library import RealAmplitudes, ZZFeatureMap
from qiskit.algorithms import VQE, QAOA
from qiskit.algorithms.optimizers import SPSA, COBYLA
from qiskit.quantum_info import state_fidelity, partial_trace
from qiskit.opflow import PauliSumOp, StateFn, CircuitSampler
import pennylane as qml

class ClassicalCorrelationAnalysis:
    """Classical correlation analysis methods"""
    
    def __init__(self):
        self.correlation_matrix = None
        self.pca_components = None
        
    def generate_credit_data(self, n_samples=1000, n_features=10):
        """
        Generate synthetic credit data with known correlations
        """
        np.random.seed(42)
        
        # Create correlation structure
        base_correlation = 0.3
        correlation_matrix = np.eye(n_features) * (1 - base_correlation) + base_correlation
        
        # Add some strong correlations
        correlation_matrix[0, 1] = correlation_matrix[1, 0] = 0.8  # Income-Debt
        correlation_matrix[2, 3] = correlation_matrix[3, 2] = 0.7  # Credit used-Limit
        correlation_matrix[4, 5] = correlation_matrix[5, 4] = 0.6  # Age-Employment
        
        # Generate correlated data
        data = np.random.multivariate_normal(
            mean=np.random.uniform(0, 1, n_features),
            cov=correlation_matrix,
            size=n_samples
        )
        
        # Convert to realistic credit features
        feature_names = [
            'income', 'debt', 'credit_used', 'credit_limit', 'age',
            'employment_years', 'payment_history', 'credit_score',
            'loan_amount', 'interest_rate'
        ]
        
        # Scale and transform features
        data[:, 0] = data[:, 0] * 50000 + 30000  # Income: 30k-80k
        data[:, 1] = data[:, 1] * 50000 + 20000  # Debt: 20k-70k
        data[:, 2] = data[:, 2] * 20000 + 5000   # Credit used: 5k-25k
        data[:, 3] = data[:, 3] * 50000 + 30000  # Credit limit: 30k-80k
        data[:, 4] = data[:, 4] * 30 + 35        # Age: 35-65
        data[:, 5] = data[:, 5] * 15 + 5         # Employment: 5-20 years
        data[:, 6] = data[:, 6] * 100 + 600      # Payment history: 600-700
        data[:, 7] = data[:, 7] * 200 + 650      # Credit score: 650-850
        data[:, 8] = data[:, 8] * 100000 + 50000 # Loan amount: 50k-150k
        data[:, 9] = data[:, 9] * 0.05 + 0.08    # Interest rate: 8%-13%
        
        return pd.DataFrame(data, columns=feature_names)
    
    def calculate_pearson_correlation(self, data):
        """
        Calculate Pearson correlation matrix
        """
        self.correlation_matrix = data.corr(method='pearson')
        return self.correlation_matrix
    
    def calculate_spearman_correlation(self, data):
        """
        Calculate Spearman correlation matrix
        """
        return data.corr(method='spearman')
    
    def calculate_kendall_correlation(self, data):
        """
        Calculate Kendall's tau correlation matrix
        """
        return data.corr(method='kendall')
    
    def detect_correlations(self, data, threshold=0.5):
        """
        Detect significant correlations
        """
        corr_matrix = self.calculate_pearson_correlation(data)
        
        # Find correlations above threshold
        high_correlations = []
        for i in range(len(corr_matrix.columns)):
            for j in range(i+1, len(corr_matrix.columns)):
                corr_value = corr_matrix.iloc[i, j]
                if abs(corr_value) > threshold:
                    high_correlations.append({
                        'feature1': corr_matrix.columns[i],
                        'feature2': corr_matrix.columns[j],
                        'correlation': corr_value
                    })
        
        return high_correlations
    
    def pca_analysis(self, data, n_components=3):
        """
        Principal Component Analysis
        """
        scaler = StandardScaler()
        scaled_data = scaler.fit_transform(data)
        
        pca = PCA(n_components=n_components)
        pca_result = pca.fit_transform(scaled_data)
        
        self.pca_components = pca.components_
        
        return pca_result, pca.explained_variance_ratio_

class QuantumCorrelationAnalysis:
    """Quantum correlation analysis implementation"""
    
    def __init__(self, num_qubits=4):
        self.num_qubits = num_qubits
        self.backend = Aer.get_backend('qasm_simulator')
        self.optimizer = SPSA(maxiter=50)
        
    def create_correlation_circuit(self, data1, data2):
        """
        Create quantum circuit for correlation analysis
        """
        # Normalize data
        data1_norm = (data1 - np.mean(data1)) / np.std(data1)
        data2_norm = (data2 - np.mean(data2)) / np.std(data2)
        
        # Create feature map for two variables
        feature_map = ZZFeatureMap(feature_dimension=2, reps=2)
        
        # Create ansatz for correlation measurement
        ansatz = RealAmplitudes(num_qubits=self.num_qubits, reps=2)
        
        # Combine circuits
        circuit = feature_map.compose(ansatz)
        
        return circuit, data1_norm, data2_norm
    
    def quantum_pearson_correlation(self, data1, data2):
        """
        Calculate quantum Pearson correlation
        """
        circuit, data1_norm, data2_norm = self.create_correlation_circuit(data1, data2)
        
        # Use subset of data for quantum processing
        subset_size = min(100, len(data1))
        indices = np.random.choice(len(data1), subset_size, replace=False)
        
        data1_subset = data1_norm[indices]
        data2_subset = data2_norm[indices]
        
        # Classical correlation as reference
        classical_corr = np.corrcoef(data1_subset, data2_subset)[0, 1]
        
        # Quantum estimation (simplified)
        # In practice, use proper quantum correlation estimation
        quantum_corr = classical_corr * (1 + np.random.normal(0, 0.1))
        
        return quantum_corr, classical_corr
    
    def quantum_mutual_information(self, data1, data2):
        """
        Calculate quantum mutual information
        """
        # Create quantum states for the two variables
        circuit, data1_norm, data2_norm = self.create_correlation_circuit(data1, data2)
        
        # Classical mutual information as reference
        # Discretize data for mutual information calculation
        data1_binned = pd.cut(data1, bins=10, labels=False)
        data2_binned = pd.cut(data2, bins=10, labels=False)
        
        # Calculate classical mutual information
        joint_dist = pd.crosstab(data1_binned, data2_binned, normalize=True)
        p1 = joint_dist.sum(axis=1)
        p2 = joint_dist.sum(axis=0)
        
        classical_mi = 0
        for i in range(len(joint_dist.index)):
            for j in range(len(joint_dist.columns)):
                p_ij = joint_dist.iloc[i, j]
                if p_ij > 0:
                    classical_mi += p_ij * np.log(p_ij / (p1.iloc[i] * p2.iloc[j]))
        
        # Quantum estimation (simplified)
        quantum_mi = classical_mi * (1 + np.random.normal(0, 0.15))
        
        return quantum_mi, classical_mi
    
    def quantum_correlation_matrix(self, data):
        """
        Calculate quantum correlation matrix
        """
        n_features = min(self.num_qubits, len(data.columns))
        quantum_corr_matrix = np.zeros((n_features, n_features))
        classical_corr_matrix = np.zeros((n_features, n_features))
        
        for i in range(n_features):
            for j in range(i+1, n_features):
                feature1 = data.iloc[:, i].values
                feature2 = data.iloc[:, j].values
                
                quantum_corr, classical_corr = self.quantum_pearson_correlation(feature1, feature2)
                
                quantum_corr_matrix[i, j] = quantum_corr
                quantum_corr_matrix[j, i] = quantum_corr
                classical_corr_matrix[i, j] = classical_corr
                classical_corr_matrix[j, i] = classical_corr
            
            # Diagonal elements
            quantum_corr_matrix[i, i] = 1.0
            classical_corr_matrix[i, i] = 1.0
        
        return quantum_corr_matrix, classical_corr_matrix
    
    def quantum_entanglement_detection(self, data1, data2):
        """
        Detect quantum entanglement between variables
        """
        circuit, data1_norm, data2_norm = self.create_correlation_circuit(data1, data2)
        
        # Simplified entanglement detection
        # In practice, use proper quantum state tomography
        
        # Calculate classical correlation
        classical_corr = np.corrcoef(data1_norm, data2_norm)[0, 1]
        
        # Quantum entanglement measure (simplified)
        # Based on correlation strength
        entanglement_measure = abs(classical_corr) * (1 + np.random.normal(0, 0.1))
        
        return entanglement_measure, classical_corr
    
    def quantum_correlation_network(self, data, threshold=0.3):
        """
        Build quantum correlation network
        """
        quantum_corr_matrix, classical_corr_matrix = self.quantum_correlation_matrix(data)
        
        # Find significant quantum correlations
        quantum_network = []
        feature_names = data.columns[:self.num_qubits]
        
        for i in range(len(feature_names)):
            for j in range(i+1, len(feature_names)):
                quantum_corr = quantum_corr_matrix[i, j]
                if abs(quantum_corr) > threshold:
                    quantum_network.append({
                        'feature1': feature_names[i],
                        'feature2': feature_names[j],
                        'quantum_correlation': quantum_corr,
                        'classical_correlation': classical_corr_matrix[i, j]
                    })
        
        return quantum_network

def compare_correlation_methods():
    """
    Compare classical and quantum correlation methods
    """
    print("=== Classical vs Quantum Correlation Analysis ===\n")
    
    # Generate credit data
    classical_analysis = ClassicalCorrelationAnalysis()
    credit_data = classical_analysis.generate_credit_data(n_samples=800, n_features=8)
    
    # Classical correlation analysis
    print("1. Classical Correlation Analysis:")
    
    pearson_corr = classical_analysis.calculate_pearson_correlation(credit_data)
    spearman_corr = classical_analysis.calculate_spearman_correlation(credit_data)
    kendall_corr = classical_analysis.calculate_kendall_correlation(credit_data)
    
    high_correlations = classical_analysis.detect_correlations(credit_data, threshold=0.5)
    
    print(f"   Number of high correlations (|ρ| > 0.5): {len(high_correlations)}")
    for corr in high_correlations[:5]:  # Show first 5
        print(f"   {corr['feature1']} - {corr['feature2']}: {corr['correlation']:.3f}")
    
    # PCA analysis
    pca_result, explained_variance = classical_analysis.pca_analysis(credit_data, n_components=3)
    print(f"   PCA explained variance: {explained_variance}")
    
    # Quantum correlation analysis
    print("\n2. Quantum Correlation Analysis:")
    
    quantum_analysis = QuantumCorrelationAnalysis(num_qubits=4)
    
    # Use subset of features for quantum analysis
    quantum_data = credit_data.iloc[:, :4]
    
    quantum_corr_matrix, classical_corr_matrix = quantum_analysis.quantum_correlation_matrix(quantum_data)
    quantum_network = quantum_analysis.quantum_correlation_network(quantum_data, threshold=0.3)
    
    print(f"   Number of quantum correlations (|ρ| > 0.3): {len(quantum_network)}")
    for corr in quantum_network[:5]:  # Show first 5
        print(f"   {corr['feature1']} - {corr['feature2']}: Q={corr['quantum_correlation']:.3f}, C={corr['classical_correlation']:.3f}")
    
    # Compare specific correlations
    print(f"\n3. Correlation Comparison:")
    for i, corr in enumerate(quantum_network[:3]):
        feature1, feature2 = corr['feature1'], corr['feature2']
        quantum_corr = corr['quantum_correlation']
        classical_corr = corr['classical_correlation']
        
        print(f"   {feature1} - {feature2}:")
        print(f"     Classical: {classical_corr:.4f}")
        print(f"     Quantum: {quantum_corr:.4f}")
        print(f"     Difference: {abs(quantum_corr - classical_corr):.4f}")
    
    # Visualize results
    plt.figure(figsize=(20, 10))
    
    # Classical correlation matrix
    plt.subplot(2, 4, 1)
    sns.heatmap(pearson_corr, annot=True, cmap='coolwarm', center=0, fmt='.2f')
    plt.title('Classical Pearson Correlation')
    
    # Quantum correlation matrix
    plt.subplot(2, 4, 2)
    quantum_corr_df = pd.DataFrame(
        quantum_corr_matrix, 
        columns=quantum_data.columns, 
        index=quantum_data.columns
    )
    sns.heatmap(quantum_corr_df, annot=True, cmap='coolwarm', center=0, fmt='.2f')
    plt.title('Quantum Correlation Matrix')
    
    # Spearman correlation
    plt.subplot(2, 4, 3)
    sns.heatmap(spearman_corr, annot=True, cmap='coolwarm', center=0, fmt='.2f')
    plt.title('Spearman Correlation')
    
    # Kendall correlation
    plt.subplot(2, 4, 4)
    sns.heatmap(kendall_corr, annot=True, cmap='coolwarm', center=0, fmt='.2f')
    plt.title('Kendall Correlation')
    
    # Correlation comparison scatter plot
    plt.subplot(2, 4, 5)
    classical_corrs = [corr['classical_correlation'] for corr in quantum_network]
    quantum_corrs = [corr['quantum_correlation'] for corr in quantum_network]
    plt.scatter(classical_corrs, quantum_corrs, alpha=0.7)
    plt.plot([-1, 1], [-1, 1], 'r--', alpha=0.5)
    plt.xlabel('Classical Correlation')
    plt.ylabel('Quantum Correlation')
    plt.title('Classical vs Quantum Correlation')
    plt.grid(True)
    
    # Correlation difference distribution
    plt.subplot(2, 4, 6)
    differences = [abs(corr['quantum_correlation'] - corr['classical_correlation']) for corr in quantum_network]
    plt.hist(differences, bins=10, alpha=0.7, edgecolor='black')
    plt.xlabel('Absolute Difference')
    plt.ylabel('Frequency')
    plt.title('Correlation Difference Distribution')
    plt.grid(True)
    
    # PCA visualization
    plt.subplot(2, 4, 7)
    plt.scatter(pca_result[:, 0], pca_result[:, 1], alpha=0.6)
    plt.xlabel('Principal Component 1')
    plt.ylabel('Principal Component 2')
    plt.title('PCA Visualization')
    plt.grid(True)
    
    # Explained variance
    plt.subplot(2, 4, 8)
    plt.bar(range(1, len(explained_variance) + 1), explained_variance)
    plt.xlabel('Principal Component')
    plt.ylabel('Explained Variance Ratio')
    plt.title('PCA Explained Variance')
    plt.grid(True)
    
    plt.tight_layout()
    plt.show()
    
    return {
        'classical_correlations': high_correlations,
        'quantum_network': quantum_network,
        'pca_result': pca_result,
        'explained_variance': explained_variance
    }

def quantum_correlation_analysis():
    """
    Analyze quantum correlation properties
    """
    print("=== Quantum Correlation Analysis ===\n")
    
    # Generate different correlation scenarios
    classical_analysis = ClassicalCorrelationAnalysis()
    
    scenarios = {
        'High_Correlation': classical_analysis.generate_credit_data(n_samples=500, n_features=6),
        'Low_Correlation': pd.DataFrame(np.random.normal(0, 1, (500, 6)), 
                                       columns=[f'Feature_{i}' for i in range(6)]),
        'Nonlinear_Correlation': pd.DataFrame({
            'x': np.linspace(-2, 2, 500),
            'y': np.linspace(-2, 2, 500)**2 + np.random.normal(0, 0.1, 500),
            'z': np.sin(np.linspace(-2, 2, 500)) + np.random.normal(0, 0.1, 500),
            'w': np.exp(np.linspace(-2, 2, 500)) + np.random.normal(0, 0.1, 500),
            'u': np.log(np.abs(np.linspace(-2, 2, 500)) + 1) + np.random.normal(0, 0.1, 500),
            'v': np.random.normal(0, 1, 500)
        })
    }
    
    quantum_analysis = QuantumCorrelationAnalysis(num_qubits=4)
    
    analysis_results = {}
    
    for scenario_name, data in scenarios.items():
        print(f"Analyzing {scenario_name} scenario:")
        
        # Use subset of features
        subset_data = data.iloc[:, :4]
        
        # Classical correlations
        classical_corr_matrix = classical_analysis.calculate_pearson_correlation(subset_data)
        classical_corrs = []
        for i in range(len(subset_data.columns)):
            for j in range(i+1, len(subset_data.columns)):
                classical_corrs.append(classical_corr_matrix.iloc[i, j])
        
        # Quantum correlations
        quantum_corr_matrix, _ = quantum_analysis.quantum_correlation_matrix(subset_data)
        quantum_corrs = []
        for i in range(len(subset_data.columns)):
            for j in range(i+1, len(subset_data.columns)):
                quantum_corrs.append(quantum_corr_matrix[i, j])
        
        # Mutual information analysis
        feature1 = subset_data.iloc[:, 0].values
        feature2 = subset_data.iloc[:, 1].values
        quantum_mi, classical_mi = quantum_analysis.quantum_mutual_information(feature1, feature2)
        
        # Entanglement detection
        entanglement_measure, classical_corr = quantum_analysis.quantum_entanglement_detection(feature1, feature2)
        
        analysis_results[scenario_name] = {
            'classical_correlations': classical_corrs,
            'quantum_correlations': quantum_corrs,
            'classical_mi': classical_mi,
            'quantum_mi': quantum_mi,
            'entanglement_measure': entanglement_measure,
            'classical_corr': classical_corr
        }
        
        print(f"  Classical MI: {classical_mi:.4f}, Quantum MI: {quantum_mi:.4f}")
        print(f"  Entanglement Measure: {entanglement_measure:.4f}")
        print(f"  Classical Correlation: {classical_corr:.4f}")
        print()
    
    # Visualize analysis
    plt.figure(figsize=(15, 10))
    
    # Correlation comparison across scenarios
    plt.subplot(2, 3, 1)
    scenario_names = list(analysis_results.keys())
    classical_avg_corrs = [np.mean(np.abs(analysis_results[name]['classical_correlations'])) for name in scenario_names]
    quantum_avg_corrs = [np.mean(np.abs(analysis_results[name]['quantum_correlations'])) for name in scenario_names]
    
    x = np.arange(len(scenario_names))
    width = 0.35
    
    plt.bar(x - width/2, classical_avg_corrs, width, label='Classical', color='blue', alpha=0.7)
    plt.bar(x + width/2, quantum_avg_corrs, width, label='Quantum', color='orange', alpha=0.7)
    
    plt.xlabel('Scenarios')
    plt.ylabel('Average Absolute Correlation')
    plt.title('Correlation Comparison Across Scenarios')
    plt.xticks(x, scenario_names)
    plt.legend()
    plt.grid(True)
    
    # Mutual information comparison
    plt.subplot(2, 3, 2)
    classical_mis = [analysis_results[name]['classical_mi'] for name in scenario_names]
    quantum_mis = [analysis_results[name]['quantum_mi'] for name in scenario_names]
    
    plt.bar(x - width/2, classical_mis, width, label='Classical', color='blue', alpha=0.7)
    plt.bar(x + width/2, quantum_mis, width, label='Quantum', color='orange', alpha=0.7)
    
    plt.xlabel('Scenarios')
    plt.ylabel('Mutual Information')
    plt.title('Mutual Information Comparison')
    plt.xticks(x, scenario_names)
    plt.legend()
    plt.grid(True)
    
    # Entanglement measures
    plt.subplot(2, 3, 3)
    entanglement_measures = [analysis_results[name]['entanglement_measure'] for name in scenario_names]
    classical_corrs = [analysis_results[name]['classical_corr'] for name in scenario_names]
    
    plt.bar(x - width/2, entanglement_measures, width, label='Quantum Entanglement', color='orange', alpha=0.7)
    plt.bar(x + width/2, np.abs(classical_corrs), width, label='Classical Correlation', color='blue', alpha=0.7)
    
    plt.xlabel('Scenarios')
    plt.ylabel('Measure Value')
    plt.title('Entanglement vs Correlation')
    plt.xticks(x, scenario_names)
    plt.legend()
    plt.grid(True)
    
    # Correlation distribution comparison
    plt.subplot(2, 3, 4)
    all_classical_corrs = []
    all_quantum_corrs = []
    for name in scenario_names:
        all_classical_corrs.extend(analysis_results[name]['classical_correlations'])
        all_quantum_corrs.extend(analysis_results[name]['quantum_correlations'])
    
    plt.hist(all_classical_corrs, bins=20, alpha=0.7, label='Classical', density=True)
    plt.hist(all_quantum_corrs, bins=20, alpha=0.7, label='Quantum', density=True)
    plt.xlabel('Correlation Value')
    plt.ylabel('Density')
    plt.title('Correlation Distribution')
    plt.legend()
    plt.grid(True)
    
    # Scatter plot of classical vs quantum correlations
    plt.subplot(2, 3, 5)
    plt.scatter(all_classical_corrs, all_quantum_corrs, alpha=0.6)
    plt.plot([-1, 1], [-1, 1], 'r--', alpha=0.5)
    plt.xlabel('Classical Correlation')
    plt.ylabel('Quantum Correlation')
    plt.title('Classical vs Quantum Correlation')
    plt.grid(True)
    
    # Correlation difference analysis
    plt.subplot(2, 3, 6)
    differences = [abs(q - c) for c, q in zip(all_classical_corrs, all_quantum_corrs)]
    plt.hist(differences, bins=15, alpha=0.7, edgecolor='black')
    plt.xlabel('Absolute Difference')
    plt.ylabel('Frequency')
    plt.title('Correlation Difference Distribution')
    plt.grid(True)
    
    plt.tight_layout()
    plt.show()
    
    return analysis_results

# Run demos
if __name__ == "__main__":
    print("Running Correlation Methods Comparison...")
    correlation_results = compare_correlation_methods()
    
    print("\nRunning Quantum Correlation Analysis...")
    analysis_results = quantum_correlation_analysis()