import numpy as np
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.preprocessing import LabelEncoder
from sklearn.utils.validation import check_X_y, check_array, check_is_fitted
from sklearn.utils.multiclass import unique_labels
from scipy.linalg import sqrtm, logm, expm
from scipy.optimize import minimize


class QuantumGeometricClassifier(BaseEstimator, ClassifierMixin):
    """
    Quantum Geometric Classifier using Information Geometry on Probability Manifolds.
    
    This classifier optimizes quantum superposition states along geodesics of the
    Fisher information metric, implementing maximum compression principles for
    classification tasks.
    
    Parameters
    ----------
    n_qubits : int, default=4
        Number of qubits for quantum state representation
    max_iter : int, default=100
        Maximum number of optimization iterations
    learning_rate : float, default=0.01
        Learning rate for natural gradient descent
    compression_factor : float, default=0.5
        Compression factor for geodesic optimization (0 < factor <= 1)
    regularization : float, default=1e-6
        Regularization parameter for Fisher information matrix
    random_state : int, default=None
        Random seed for reproducibility
        
    Attributes
    ----------
    classes_ : ndarray of shape (n_classes,)
        The classes labels
    quantum_states_ : dict
        Quantum state parameters for each class
    fisher_metrics_ : dict
        Fisher information metrics for each class
    """
    
    def __init__(self, n_qubits=4, max_iter=100, learning_rate=0.01,
                 compression_factor=0.5, regularization=1e-6, random_state=None):
        self.n_qubits = n_qubits
        self.max_iter = max_iter
        self.learning_rate = learning_rate
        self.compression_factor = compression_factor
        self.regularization = regularization
        self.random_state = random_state
        
    def _initialize_quantum_state(self, dim):
        """Initialize quantum state parameters."""
        rng = np.random.RandomState(self.random_state)
        # Initialize as normalized random complex amplitudes
        real_part = rng.randn(dim)
        imag_part = rng.randn(dim)
        state = real_part + 1j * imag_part
        return state / np.linalg.norm(state)
    
    def _compute_density_matrix(self, state):
        """Compute density matrix from state vector."""
        state = state.reshape(-1, 1)
        return state @ state.conj().T
    
    def _compute_fisher_metric(self, density_matrix):
        """Compute Fisher information metric for quantum state."""
        dim = density_matrix.shape[0]
        # Quantum Fisher information metric
        # For pure states: g_ij = 4 * Re(<∂_i ψ|∂_j ψ> - <∂_i ψ|ψ><ψ|∂_j ψ>)
        # Approximated using density matrix formulation
        fisher = np.zeros((dim, dim), dtype=complex)
        
        for i in range(dim):
            for j in range(dim):
                # Symmetric logarithmic derivative approach
                fisher[i, j] = 2 * np.real(density_matrix[i, j])
        
        # Add regularization for numerical stability
        fisher = fisher + self.regularization * np.eye(dim)
        return fisher
    
    def _encode_classical_to_quantum(self, X):
        """Encode classical data into quantum probability amplitudes."""
        n_samples, n_features = X.shape
        dim = 2 ** self.n_qubits
        
        # Normalize and encode features into quantum amplitudes
        quantum_encoded = np.zeros((n_samples, dim), dtype=complex)
        
        for i in range(n_samples):
            # Feature embedding using angle encoding
            angles = np.zeros(dim)
            for j in range(min(n_features, dim)):
                angles[j] = X[i, j % n_features] * np.pi
            
            # Create superposition state
            state = np.exp(1j * angles)
            # Normalize
            quantum_encoded[i] = state / np.linalg.norm(state)
            
        return quantum_encoded
    
    def _geodesic_distance(self, state1, state2, metric):
        """Compute geodesic distance on quantum probability manifold."""
        # Fubini-Study metric for quantum states
        inner_product = np.abs(np.vdot(state1, state2))
        # Clip to avoid numerical issues with arccos
        inner_product = np.clip(inner_product, 0, 1)
        return np.arccos(inner_product)
    
    def _natural_gradient_step(self, state, gradient, fisher_metric):
        """Perform natural gradient descent step using Fisher metric."""
        # Compute natural gradient: G^{-1} * gradient
        try:
            fisher_inv = np.linalg.inv(fisher_metric)
            natural_grad = fisher_inv @ gradient
        except np.linalg.LinAlgError:
            # Fallback to pseudo-inverse
            natural_grad = np.linalg.pinv(fisher_metric) @ gradient
        
        # Update state along geodesic
        new_state = state - self.learning_rate * natural_grad
        # Normalize to maintain unit norm
        return new_state / np.linalg.norm(new_state)
    
    def _compress_along_geodesic(self, state, target_state, compression):
        """Move along geodesic with compression factor."""
        # Geodesic interpolation on quantum state manifold
        inner = np.vdot(state, target_state)
        
        if np.abs(inner) > 0.9999:  # States are very close
            return target_state
        
        # Compute geodesic path parameter
        theta = np.arccos(np.clip(np.abs(inner), 0, 1))
        
        if theta < 1e-10:
            return target_state
        
        # Interpolate along geodesic with compression
        t = compression
        compressed_state = (np.sin((1 - t) * theta) / np.sin(theta)) * state + \
                          (np.sin(t * theta) / np.sin(theta)) * target_state
        
        return compressed_state / np.linalg.norm(compressed_state)
    
    def _optimize_class_state(self, quantum_data, iterations):
        """Optimize quantum state for a class using information geometry."""
        dim = quantum_data.shape[1]
        
        # Initialize class prototype state
        class_state = np.mean(quantum_data, axis=0)
        class_state = class_state / np.linalg.norm(class_state)
        
        for iteration in range(iterations):
            # Compute density matrix
            rho = self._compute_density_matrix(class_state)
            
            # Compute Fisher information metric
            fisher = self._compute_fisher_metric(rho)
            
            # Compute gradient (maximize compression of class data)
            gradient = np.zeros(dim, dtype=complex)
            
            for sample in quantum_data:
                # Gradient of fidelity/distance
                diff = sample - class_state
                gradient += diff
            
            gradient = gradient / len(quantum_data)
            
            # Natural gradient step
            class_state = self._natural_gradient_step(
                class_state, gradient, fisher
            )
            
            # Apply compression along geodesic
            target = np.mean(quantum_data, axis=0)
            target = target / np.linalg.norm(target)
            class_state = self._compress_along_geodesic(
                class_state, target, self.compression_factor
            )
        
        return class_state, fisher
    
    def fit(self, X, y):
        """
        Fit the Quantum Geometric Classifier.
        
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training data
        y : array-like of shape (n_samples,)
            Target values
            
        Returns
        -------
        self : object
            Fitted estimator
        """
        # Validate input
        X, y = check_X_y(X, y)
        
        # Store classes
        self.classes_ = unique_labels(y)
        self.n_classes_ = len(self.classes_)
        
        # Encode labels
        self.label_encoder_ = LabelEncoder()
        y_encoded = self.label_encoder_.fit_transform(y)
        
        # Normalize features
        self.mean_ = np.mean(X, axis=0)
        self.std_ = np.std(X, axis=0) + 1e-10
        X_normalized = (X - self.mean_) / self.std_
        
        # Encode classical data to quantum states
        quantum_data = self._encode_classical_to_quantum(X_normalized)
        
        # Optimize quantum state for each class
        self.quantum_states_ = {}
        self.fisher_metrics_ = {}
        
        for class_idx in range(self.n_classes_):
            # Get samples for this class
            class_mask = (y_encoded == class_idx)
            class_quantum_data = quantum_data[class_mask]
            
            # Optimize class prototype state
            class_state, fisher_metric = self._optimize_class_state(
                class_quantum_data, self.max_iter
            )
            
            self.quantum_states_[class_idx] = class_state
            self.fisher_metrics_[class_idx] = fisher_metric
        
        self.is_fitted_ = True
        return self
    
    def _compute_class_probability(self, quantum_state, class_idx):
        """Compute probability of quantum state belonging to class."""
        class_state = self.quantum_states_[class_idx]
        
        # Compute fidelity (quantum overlap)
        fidelity = np.abs(np.vdot(quantum_state, class_state)) ** 2
        
        # Compute geodesic distance
        fisher_metric = self.fisher_metrics_[class_idx]
        distance = self._geodesic_distance(
            quantum_state, class_state, fisher_metric
        )
        
        # Convert distance to probability (using Gaussian-like kernel)
        probability = fidelity * np.exp(-distance ** 2)
        
        return probability
    
    def predict_proba(self, X):
        """
        Predict class probabilities for X.
        
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Test samples
            
        Returns
        -------
        proba : ndarray of shape (n_samples, n_classes)
            Class probabilities
        """
        check_is_fitted(self, 'is_fitted_')
        X = check_array(X)
        
        # Normalize features
        X_normalized = (X - self.mean_) / self.std_
        
        # Encode to quantum states
        quantum_data = self._encode_classical_to_quantum(X_normalized)
        
        # Compute probabilities for each class
        n_samples = X.shape[0]
        probabilities = np.zeros((n_samples, self.n_classes_))
        
        for i in range(n_samples):
            for class_idx in range(self.n_classes_):
                probabilities[i, class_idx] = self._compute_class_probability(
                    quantum_data[i], class_idx
                )
            
            # Normalize probabilities
            prob_sum = np.sum(probabilities[i])
            if prob_sum > 0:
                probabilities[i] /= prob_sum
            else:
                probabilities[i] = 1.0 / self.n_classes_
        
        return probabilities
    
    def predict(self, X):
        """
        Predict class labels for X.
        
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Test samples
            
        Returns
        -------
        y_pred : ndarray of shape (n_samples,)
            Predicted class labels
        """
        probabilities = self.predict_proba(X)
        class_indices = np.argmax(probabilities, axis=1)
        return self.label_encoder_.inverse_transform(class_indices)
    
    def score(self, X, y):
        """
        Return the mean accuracy on the given test data and labels.
        
        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Test samples
        y : array-like of shape (n_samples,)
            True labels
            
        Returns
        -------
        score : float
            Mean accuracy
        """
        from sklearn.metrics import accuracy_score
        return accuracy_score(y, self.predict(X))