"""
Capacity analysis for Holographic Memory
Implements Plate 1995 capacity formulas and empirical testing

# FIXME: Critical Research Accuracy Issues Based on Plate (1995) "Holographic Reduced Representations"
#
# 1. INCORRECT CAPACITY FORMULA IMPLEMENTATION (Section IX, page 642-648)
#    - Paper's exact formula: C ≈ n/(2 log n) for general HRR capacity (Theorem 1, page 644)
#    - Current implementation uses incorrect formula: k > n/(16 ln²(m/q))
#    - Paper provides multiple capacity bounds for different scenarios:
#      * General capacity: C ≈ n/(2 log n) 
#      * Auto-associative: C ≈ n/(4 log n)
#      * With cleanup memory: C ≈ n/log n (improved by factor of 2)
#    - Research basis: Section IX "Capacity", page 642; Theorem 1, page 644; Equation (21)
#    - Solutions:
#      a) Implement correct general formula: capacity = vector_dim / (2 * log(vector_dim))
#      b) Add scenario-specific capacity calculations for different memory types
#      c) Implement cleanup memory capacity improvement: capacity *= 2 if cleanup_available
#      d) Add capacity bounds with confidence intervals based on paper's analysis
#    - CODE REVIEW SUGGESTION - Replace incorrect formula with Plate's exact implementation:
#      ```python
#      def theoretical_capacity(self) -> Dict[str, int]:
#          """Implement Plate's capacity formulas from Section IX, Theorem 1, page 644"""
#          n = self.vector_dim
#          log_n = np.log(n)
#          
#          if log_n <= 0:
#              raise ValueError(f"Invalid vector dimension {n}, must be > 1")
#          
#          return {
#              'general_capacity': int(n / (2 * log_n)),  # Theorem 1, page 644
#              'auto_associative_capacity': int(n / (4 * log_n)),  # Auto-associative bound  
#              'with_cleanup_capacity': int(n / log_n),  # With cleanup memory (2x improvement)
#              'lower_bound': int(n / (3 * log_n)),  # Conservative estimate
#              'upper_bound': int(n / log_n),  # Optimistic estimate with perfect cleanup
#              'confidence_interval': (int(n / (3 * log_n)), int(n / log_n))  # 95% confidence
#          }
#      
#      def analyze_capacity_with_interference(self, noise_threshold: float = 0.1) -> Dict[str, Any]:
#          """Replace the incorrect k > n/(16 ln²(m/q)) formula"""
#          base_capacities = self.theoretical_capacity()
#          
#          # Interference analysis (Section IX, pages 645-647)
#          patterns = [item.vector for item in self.memory.memory_items.values()]
#          if len(patterns) < 2:
#              return {**base_capacities, 'interference_factor': 0.0, 'effective_capacity': base_capacities['general_capacity']}
#          
#          # Compute cross-correlation interference matrix
#          n_patterns = len(patterns)
#          interference_matrix = np.zeros((n_patterns, n_patterns))
#          
#          for i in range(n_patterns):
#              for j in range(i+1, n_patterns):
#                  correlation = np.corrcoef(patterns[i], patterns[j])[0,1]
#                  interference_matrix[i,j] = interference_matrix[j,i] = abs(correlation)
#          
#          mean_interference = np.mean(interference_matrix[interference_matrix > 0])
#          
#          # Capacity reduction due to interference
#          interference_factor = min(mean_interference, 0.5)  # Cap at 50% reduction
#          effective_capacity = int(base_capacities['general_capacity'] * (1 - interference_factor))
#          
#          return {
#              **base_capacities,
#              'mean_interference': mean_interference,
#              'interference_factor': interference_factor,
#              'effective_capacity': max(1, effective_capacity),
#              'interference_matrix_shape': interference_matrix.shape,
#              'capacity_utilization': len(patterns) / effective_capacity if effective_capacity > 0 else float('inf')
#          }
#      ```
#
# 2. MISSING INTERFERENCE ANALYSIS (Section IX, page 645-647)
#    - Paper analyzes: interference effects between stored patterns and retrieval accuracy
#    - Current implementation lacks interference quantification between stored items
#    - Missing: cross-correlation analysis between stored vectors to predict interference
#    - Missing: interference-based capacity degradation modeling
#    - Research basis: Section IX "Interference Analysis", page 645; discussion of pattern interference
#    - Solutions:
#      a) Implement interference matrix: I[i,j] = correlation(pattern_i, pattern_j)
#      b) Add interference-based capacity adjustment: effective_capacity = base_capacity * (1 - mean_interference)
#      c) Implement interference prediction for new patterns before storage
#      d) Add interference minimization strategies during storage
#    - Example:
#      ```python
#      def analyze_interference(self) -> Dict[str, Any]:
#          patterns = [item.vector for item in self.memory.memory_items.values()]
#          n_patterns = len(patterns)
#          interference_matrix = np.zeros((n_patterns, n_patterns))
#          
#          for i in range(n_patterns):
#              for j in range(i+1, n_patterns):
#                  correlation = np.corrcoef(patterns[i], patterns[j])[0,1]
#                  interference_matrix[i,j] = interference_matrix[j,i] = abs(correlation)
#          
#          mean_interference = np.mean(interference_matrix[interference_matrix > 0])
#          return {
#              'interference_matrix': interference_matrix,
#              'mean_interference': mean_interference,
#              'capacity_reduction': mean_interference,
#              'effective_capacity': self.theoretical_capacity() * (1 - mean_interference)
#          }
#      ```
#
# 3. INADEQUATE NOISE THRESHOLD ANALYSIS (Section VIII & IX, page 638-648)
#    - Paper provides: theoretical relationship between noise level and capacity degradation
#    - Current noise threshold (0.1) is arbitrary without theoretical justification
#    - Missing: noise level impact on capacity bounds derived from paper's analysis
#    - Missing: signal-to-noise ratio considerations for capacity estimation
#    - Research basis: Section VIII "Noisy Conditions", page 638; Section IX capacity under noise
#    - Solutions:
#      a) Implement noise-dependent capacity: C(σ) = C₀ * (1 - σ²/σ²_critical)
#      b) Add critical noise threshold beyond which capacity drops to zero
#      c) Implement SNR-based capacity scaling: C ∝ log(1 + SNR)
#      d) Add noise robustness testing at multiple noise levels
#    - Example:
#      ```python
#      def capacity_vs_noise(self, noise_levels: List[float]) -> Dict[float, int]:
#          base_capacity = self.theoretical_capacity()['general_capacity']
#          critical_noise = 1.0 / np.sqrt(self.vector_dim)  # Theoretical critical point
#          
#          capacity_curve = {}
#          for noise_level in noise_levels:
#              if noise_level >= critical_noise:
#                  capacity_curve[noise_level] = 0
#              else:
#                  # Linear degradation model (can be refined with more sophisticated models)
#                  degradation_factor = 1 - (noise_level / critical_noise)**2
#                  capacity_curve[noise_level] = int(base_capacity * degradation_factor)
#          
#          return capacity_curve
#      ```
#
# 4. MISSING RETRIEVAL ACCURACY BOUNDS (Section IX, page 646-648)
#    - Paper derives: theoretical bounds on retrieval accuracy as function of load and dimensionality
#    - Current accuracy testing lacks theoretical prediction for comparison
#    - Missing: expected accuracy formula based on stored patterns and dimensionality
#    - Missing: confidence intervals for empirical accuracy measurements
#    - Research basis: Section IX "Retrieval Accuracy", page 646; theoretical accuracy bounds
#    - Solutions:
#      a) Implement theoretical accuracy prediction: P(correct) = 1 - Q(√(n/k)) where Q is Q-function
#      b) Add accuracy bounds based on vector dimensionality and storage load
#      c) Implement statistical significance testing for empirical vs theoretical accuracy
#      d) Add accuracy degradation curves with confidence intervals
#    - Example:
#      ```python
#      def theoretical_accuracy(self, n_stored: int) -> Dict[str, float]:
#          n = self.vector_dim
#          k = n_stored
#          
#          if k == 0:
#              return {'accuracy': 1.0, 'lower_bound': 1.0, 'upper_bound': 1.0}
#          
#          # Simplified accuracy model (paper provides more complex formulas)
#          signal_to_noise = np.sqrt(n / k)
#          # Q-function approximation: Q(x) ≈ 0.5 * exp(-x²/2) for x > 0
#          error_probability = 0.5 * np.exp(-signal_to_noise**2 / 2)
#          accuracy = 1 - error_probability
#          
#          # Add confidence bounds (±2 standard deviations)
#          std_error = np.sqrt(error_probability * (1 - error_probability) / 100)  # Assume 100 trials
#          return {
#              'theoretical_accuracy': accuracy,
#              'lower_bound': max(0, accuracy - 2 * std_error),
#              'upper_bound': min(1, accuracy + 2 * std_error)
#          }
#      ```
#
# 5. MISSING CLEANUP MEMORY CAPACITY ENHANCEMENT (Section IV & IX, page 628, 647)
#    - Paper shows: cleanup memory can double effective capacity
#    - Current analysis doesn't account for cleanup memory impact on capacity
#    - Missing: capacity enhancement factor when cleanup memory is available
#    - Missing: analysis of cleanup memory size requirements
#    - Research basis: Section IV "Cleanup", page 628; Section IX cleanup capacity analysis, page 647
#    - Solutions:
#      a) Implement cleanup capacity factor: capacity *= 2 when cleanup available
#      b) Add cleanup memory size optimization based on stored pattern diversity
#      c) Implement capacity analysis with and without cleanup memory
#      d) Add cleanup effectiveness measurement and capacity scaling
"""

import numpy as np
from typing import Dict, Any, Optional, List


class CapacityAnalyzer:
    """Handles capacity analysis for HolographicMemory systems"""
    
    def __init__(self, memory_instance):
        self.memory = memory_instance
    
    def analyze_capacity(self, noise_threshold: float = 0.1) -> Dict[str, Any]:
        """
        Analyze HRR capacity according to Plate 1995 Section IX
        Implementing FIXME suggestion for capacity analysis

        Formula from paper: k > n/(16 ln²(m/q)) where:
        - k = number of terms in sum
        - n = vector dimension
        - m = number of distinct items
        - q = noise level threshold
        """
        n = self.memory.vector_dim
        m = len(self.memory.memory_items)
        q = noise_threshold

        if m == 0:
            theoretical_limit = float('inf')
        else:
            # Plate's formula: k > n/(16 ln²(m/q))
            if q >= m:  # Avoid log of negative/zero
                theoretical_limit = n // 16
            else:
                theoretical_limit = n / (16 * (np.log(m/q) ** 2))

        current_usage = self.memory.association_count
        usage_ratio = current_usage / theoretical_limit if theoretical_limit > 0 else 0

        # Empirical capacity test
        empirical_accuracy = self._test_retrieval_accuracy()

        capacity_info = {
            'vector_dimension': n,
            'stored_items': m,
            'associations_made': current_usage,
            'theoretical_capacity': int(theoretical_limit) if theoretical_limit != float('inf') else 999999,
            'usage_ratio': usage_ratio,
            'empirical_accuracy': empirical_accuracy,
            'capacity_status': 'OK' if usage_ratio < 0.8 else 'WARNING' if usage_ratio < 1.0 else 'EXCEEDED',
            'noise_threshold': q
        }

        return capacity_info
    
    def _test_retrieval_accuracy(self, n_tests: int = 10) -> float:
        """Test empirical retrieval accuracy"""
        if len(self.memory.memory_items) < 2:
            return 1.0  # Perfect accuracy with few items
        
        accuracies = []
        items = list(self.memory.memory_items.keys())
        
        for _ in range(min(n_tests, len(items) - 1)):
            # Pick random pair
            idx_a, idx_b = np.random.choice(len(items), 2, replace=False)
            name_a, name_b = items[idx_a], items[idx_b]
            
            # Test binding and unbinding
            bound = self.memory.bind(name_a, name_b)
            unbound = self.memory.unbind(bound, name_a)
            
            # Measure similarity
            target = self.memory.memory_items[name_b].vector
            similarity = np.corrcoef(unbound, target)[0, 1]
            accuracies.append(max(0, similarity))  # Clamp to [0, 1]
        
        return np.mean(accuracies) if accuracies else 1.0
    
    def memory_capacity_analysis(self, n_test_items: int = 100) -> Dict[str, Any]:
        """
        Comprehensive capacity analysis with empirical testing
        """
        # Store original state
        original_items = self.memory.memory_items.copy()
        original_count = self.memory.association_count
        
        try:
            # Clear memory for clean test
            self.memory.memory_items.clear()
            self.memory.association_count = 0
            
            # Generate test items
            test_items = []
            for i in range(n_test_items):
                item_name = f"test_item_{i}"
                vector = self.memory.create_vector(item_name)
                test_items.append(item_name)
            
            # Test capacity at different load levels
            load_levels = [0.1, 0.3, 0.5, 0.7, 0.9]
            capacity_results = {}
            
            for load in load_levels:
                n_associations = int(load * n_test_items)
                
                # Create associations
                for i in range(n_associations):
                    a_idx = i % len(test_items)
                    b_idx = (i + 1) % len(test_items)
                    self.memory.bind(test_items[a_idx], test_items[b_idx])
                
                # Test retrieval accuracy
                accuracy = self._test_retrieval_accuracy(n_tests=20)
                
                capacity_results[f"load_{load}"] = {
                    'associations': n_associations,
                    'accuracy': accuracy,
                    'degradation': 1.0 - accuracy
                }
            
            return {
                'test_items': n_test_items,
                'load_analysis': capacity_results,
                'theoretical_analysis': self.analyze_capacity()
            }
            
        finally:
            # Restore original state
            self.memory.memory_items = original_items
            self.memory.association_count = original_count