HI!  i'm seeking to understand the various math and ways im calculating the multidimensionality scoring, can you explain it to me try to use simple explanations at first then layering on more intermediate or mildly complex explanations? And finally can you explain why the context_confidence usually defaults to 0.5 and cases and rationale when it will actually return a score? Below is my code for my scoring system as reference:

# confidence_scorer.py

from typing import Dict, Any, Tuple, List, Set
from rapidfuzz import fuzz
from nltk.corpus import wordnet
import nltk
import re
import logging
from functools import lru_cache
import json
import numpy as np  # Import Numpy for array handling
import warnings

# Ensure NLTK WordNet data is downloaded
try:
    nltk.data.find('corpora/wordnet')
except LookupError:
    nltk.download('wordnet', quiet=True)

# ----------------- Constants -----------------

# Confidence thresholds
HIGH_CONFIDENCE_THRESHOLD: float = 0.7
MEDIUM_CONFIDENCE_THRESHOLD: float = 0.55
LOW_CONFIDENCE_THRESHOLD: float = 0.3

# Relevant keywords for scope determination
RELEVANT_KEYWORDS: Set[str] = {
    'import', 'comment', 'print', 'file', 'global',
    'function', 'class', 'method', 'update', 'modify',
    'change', 'compute', 'calculate'
}

# Synonym mapping using WordNet


def initialize_synonym_map() -> Dict[str, Set[str]]:
    """
    Initializes a synonym map for relevant keywords using WordNet.

    Returns:
        Dict[str, Set[str]]: A dictionary mapping each keyword to a set of its synonyms.
    """
    synonym_map: Dict[str, Set[str]] = {}
    for keyword in RELEVANT_KEYWORDS:
        synonyms = {lemma.name().lower().replace('_', ' ') for syn in wordnet.synsets(keyword) for lemma in syn.lemmas()}
        synonym_map[keyword] = synonyms
    return synonym_map


SYNONYM_MAP = initialize_synonym_map()

# ----------------- Logging Configuration -----------------

logging.basicConfig(
    level=logging.DEBUG,  # Adjust as needed (DEBUG, INFO, WARNING, etc.)
    format='%(asctime)s - %(levelname)s - %(message)s'
)
logger = logging.getLogger(__name__)

# ----------------- ConfidenceScorer Class -------------------


class ConfidenceScorer:
    """
    Base class for calculating confidence scores for code edit operations.

    Attributes:
        efc (Dict[str, Any]): Enhanced File Context containing code structure.
        query (str): The edit instruction or query.
        model (SentenceTransformer): Pre-trained model for generating embeddings.
        query_embedding (np.ndarray): Embedding vector for the query.
    """

    def __init__(self, efc: Dict[str, Any], query: str, model_name: str = 'all-MiniLM-L6-v2'):
        """
        Initializes the ConfidenceScorer with the provided Enhanced File Context and query.

        Args:
            efc (Dict[str, Any]): Enhanced File Context.
            query (str): The edit instruction or query.
            model_name (str, optional): Pre-trained model name. Defaults to 'all-MiniLM-L6-v2'.
        """
        self.efc: Dict[str, Any] = efc
        self.query: str = query
        self.model = self._initialize_model(model_name)
        self.query_embedding: np.ndarray = self.get_embedding(self.query)

    @staticmethod
    def _initialize_model(model_name: str):
        """
        Initializes the SentenceTransformer model.

        Args:
            model_name (str): Name of the pre-trained model.

        Returns:
            SentenceTransformer: The initialized model.
        """
        try:
            from sentence_transformers import SentenceTransformer
            return SentenceTransformer(model_name)
        except ImportError:
            logger.error("Please install 'sentence-transformers' package.")
            raise

    @lru_cache(maxsize=128)
    def get_embedding(self, text: str) -> np.ndarray:
        """
        Generates an embedding for the given text using the pre-trained model.

        Args:
            text (str): Text to be embedded.

        Returns:
            np.ndarray: The embedding vector.
        """
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", FutureWarning)
            return self.model.encode(text, convert_to_tensor=False)

    def calculate_confidence(self) -> float:
        """
        Calculates the overall confidence score based on semantic similarity.

        Returns:
            float: Confidence score normalized between 0 and 1.
        """
        code_block_names = [block['name'] for block in self.efc.get('custom_tokens', [])]
        code_block_contents = [block['code'] for block in self.efc.get('custom_tokens', [])]

        name_embeddings = [self.get_embedding(name) for name in code_block_names]
        content_embeddings = [self.get_embedding(content) for content in code_block_contents]

        best_name_score = self._get_best_similarity(self.query_embedding, name_embeddings)
        best_content_score = self._get_best_similarity(self.query_embedding, content_embeddings)

        # Weighted confidence: name and content contribute equally
        confidence = (0.5 * best_name_score) + (0.5 * best_content_score)
        logger.debug(f"Calculated confidence - Name: {best_name_score}, Content: {best_content_score}, Combined: {confidence}")
        return confidence

    @staticmethod
    def _get_best_similarity(query_embedding: np.ndarray, embeddings: List[np.ndarray]) -> float:
        """
        Computes the highest cosine similarity score between the query embedding and a list of embeddings.

        Args:
            query_embedding (np.ndarray): Embedding vector for the query.
            embeddings (List[np.ndarray]): List of embedding vectors to compare against.

        Returns:
            float: The highest similarity score between 0 and 1.
        """
        if not embeddings:
            return 0.0
        similarities = [ConfidenceScorer._cosine_similarity(query_embedding, emb) for emb in embeddings]
        best_similarity = max(similarities)
        return best_similarity

    @staticmethod
    def _cosine_similarity(vec1: np.ndarray, vec2: np.ndarray) -> float:
        """
        Computes the cosine similarity between two vectors.

        Args:
            vec1 (np.ndarray): First vector.
            vec2 (np.ndarray): Second vector.

        Returns:
            float: Cosine similarity between 0 and 1.
        """
        if vec1.size == 0 or vec2.size == 0:
            return 0.0
        dot_product = np.dot(vec1, vec2)
        magnitude1 = np.linalg.norm(vec1)
        magnitude2 = np.linalg.norm(vec2)
        if magnitude1 == 0 or magnitude2 == 0:
            return 0.0
        return dot_product / (magnitude1 * magnitude2)

    def assess_complexity(self) -> float:
        """
        Assesses the complexity of the edit based on the length and keyword richness of the query.

        Returns:
            float: Complexity score normalized between 0 and 1.
        """
        query_length = len(self.query.split())
        keyword_count = len(set(self.query.lower().split()).intersection(RELEVANT_KEYWORDS))
        complexity = (query_length / 20) + (keyword_count / len(RELEVANT_KEYWORDS))
        normalized_complexity = min(complexity / 2, 1.0)  # Normalize to 0-1
        logger.debug(f"Assessed complexity: {normalized_complexity} (length: {query_length}, keywords: {keyword_count})")
        return normalized_complexity

    def determine_scope(self) -> Tuple[str, float]:
        """
        Determines the appropriate scope for the edit operation based on confidence and complexity.

        Returns:
            Tuple[str, float]: The determined scope and confidence score.
        """
        confidence: float = self.calculate_confidence()
        complexity: float = self.assess_complexity()

        has_relevant_keyword: bool = self._has_relevant_keyword()

        if not has_relevant_keyword:
            scope = "file-level edit"
        else:
            # Prioritize function scope if function keywords are present
            function_keywords = {'function', 'def', 'method', 'update', 'modify', 'change', 'compute', 'calculate'}
            query_words = set(re.findall(r'\w+', self.query.lower()))
            is_function_related = bool(query_words.intersection(function_keywords))

            if is_function_related and confidence > HIGH_CONFIDENCE_THRESHOLD and complexity < 0.3:
                scope = "function"
            elif confidence > MEDIUM_CONFIDENCE_THRESHOLD and complexity < 0.6:
                scope = "class"
            else:
                scope = "file-level edit"

        logger.debug(f"Determine Scope - Confidence: {confidence}, Complexity: {complexity}, Scope: {scope}")
        return scope, confidence

    def _has_relevant_keyword(self) -> bool:
        """
        Checks if the query contains any relevant keywords or their synonyms.

        Returns:
            bool: True if relevant keywords are present, False otherwise.
        """
        query_words = set(re.findall(r'\w+', self.query.lower()))
        for keyword, synonyms in SYNONYM_MAP.items():
            if query_words.intersection(synonyms.union({keyword})):
                logger.debug(f"Relevant keyword detected: {keyword}")
                return True
        return False


# ----------------- EnhancedConfidenceScorer Class -----------------

class EnhancedConfidenceScorer(ConfidenceScorer):
    """
    Advanced confidence scoring system for code edit operations.

    Extends ConfidenceScorer with multi-dimensional confidence scoring and enhanced keyword recognition.
    """

    def __init__(self, efc: Dict[str, Any], query: str, model_name: str = 'all-MiniLM-L6-v2'):
        super().__init__(efc, query, model_name)

    def calculate_confidence(self) -> Dict[str, float]:
        """
        Calculates multi-dimensional confidence scores:
        - overall: Combined confidence score
        - name: Confidence in identifying the correct code block
        - content: Confidence in understanding the required changes
        - context: Confidence in the surrounding code context

        Returns:
            Dict[str, float]: Dictionary containing confidence scores.
        """
        name_similarity = self._calculate_name_confidence()
        content_similarity = self._calculate_content_confidence()
        context_confidence = self._calculate_context_confidence()

        # Weighting factors
        NAME_WEIGHT: float = 0.35
        CONTENT_WEIGHT: float = 0.5
        CONTEXT_WEIGHT: float = 0.15

        base_confidence: float = (
            name_similarity * NAME_WEIGHT +
            content_similarity * CONTENT_WEIGHT +
            context_confidence * CONTEXT_WEIGHT
        )

        # Apply boosting based on operation type
        boosted_confidence: float = self._boost_confidence(base_confidence)

        # Apply graceful degradation for low confidence
        confidence_scores: Dict[str, float] = {
            "overall": round(float(boosted_confidence), 2),
            "name": round(float(name_similarity), 2),
            "content": round(float(content_similarity), 2),
            "context": round(float(context_confidence), 2)
        }
        confidence_scores = self._apply_graceful_degradation(confidence_scores)

        logger.debug(f"Calculated confidence scores: {json.dumps(confidence_scores, indent=2)}")
        return confidence_scores

    def determine_scope(self) -> Tuple[str, Dict[str, float]]:
        """
        Determines the edit scope based on multi-dimensional confidence scores.

        Returns:
            Tuple[str, Dict[str, float]]: The determined scope and confidence scores.
        """
        confidence_scores: Dict[str, float] = self.calculate_confidence()
        complexity: float = self.assess_complexity()

        logger.debug(f"Instruction: {self.query}")
        logger.debug(f"Confidence scores: {confidence_scores}")
        logger.debug(f"Complexity: {complexity}")

        if not self.query.strip():
            confidence_scores = {
                "overall": 0.0,
                "name": 0.0,
                "content": 0.0,
                "context": 0.5  # Retain default context confidence
            }
            logger.debug("Empty query detected. Defaulting to 'file-level edit' with zero confidence.")
            return "file-level edit", confidence_scores

        if self._is_file_level_operation():
            logger.debug("Scope determined: File-level edit (file-level operation detected)")
            return "file-level edit", confidence_scores

        # Prioritize class-level operations first
        if self._is_class_level_operation():
            if confidence_scores['overall'] > 0.6 and complexity < 0.6:
                scope = "class"
            else:
                scope = "file-level edit"
            logger.debug(f"Scope determined: {scope} (Class-level operation)")
            return scope, confidence_scores

        # Then check for function-level operations
        if self._is_function_level_operation():
            if confidence_scores['overall'] > 0.7 and complexity < 0.3:
                scope = "function"
            else:
                scope = "file-level edit"
            logger.debug(f"Scope determined: {scope} (Function-level operation)")
            return scope, confidence_scores

        # Existing logic for file-level or ambiguous scopes
        if not self._has_relevant_keyword():
            scope = "file-level edit"
            logger.debug("Scope determined: File-level edit (irrelevant or vague instruction)")
        elif confidence_scores['overall'] > HIGH_CONFIDENCE_THRESHOLD:
            scope = "function"
            logger.debug("Scope determined: Function (high confidence)")
        elif confidence_scores['overall'] > MEDIUM_CONFIDENCE_THRESHOLD:
            scope = "class"
            logger.debug("Scope determined: Class (medium confidence)")
        else:
            scope = "file-level edit"
            logger.debug("Scope determined: File-level edit (default case)")
        return scope, confidence_scores

    def _calculate_name_confidence(self) -> float:
        """
        Calculates confidence in identifying the correct code block based on names.

        Returns:
            float: Name confidence score between 0 and 1.
        """
        code_block_names = [block['name'] for block in self.efc.get('custom_tokens', [])]
        name_similarity = self._get_best_similarity(self.query_embedding, [self.get_embedding(name) for name in code_block_names])
        logger.debug(f"Name similarity score: {name_similarity}")
        return name_similarity

    def _calculate_content_confidence(self) -> float:
        """
        Calculates confidence in understanding the required changes based on code content.

        Returns:
            float: Content confidence score between 0 and 1.
        """
        code_block_contents = [block['code'] for block in self.efc.get('custom_tokens', [])]
        content_similarity = self._get_best_similarity(self.query_embedding, [self.get_embedding(content) for content in code_block_contents])
        logger.debug(f"Content similarity score: {content_similarity}")
        return content_similarity

    def _calculate_context_confidence(self) -> float:
        """
        Calculates confidence in the surrounding code context.

        Returns:
            float: Context confidence score between 0 and 1.
        """
        # Example: Higher confidence if the query mentions keywords related to context
        contextual_keywords: Set[str] = {'syntax', 'structure', 'format', 'refactor'}
        query_tags = set(re.findall(r'\w+', self.query.lower()))
        common_keywords = query_tags.intersection(contextual_keywords)
        context_confidence = 1.0 if common_keywords else 0.5
        logger.debug(f"Context confidence score: {context_confidence}")
        return context_confidence

    def _boost_confidence(self, base_confidence: float) -> float:
        """
        Boosts the confidence score based on the type of operation detected.

        Args:
            base_confidence (float): The initial confidence score.

        Returns:
            float: The boosted confidence score, capped at 0.95.
        """
        if self._is_file_level_operation():
            boosted = min(base_confidence * 1.2, 0.95)
            logger.debug(f"Boosted confidence for file-level operation: {boosted}")
            return boosted
        elif self._is_function_level_operation():
            boosted = min(base_confidence * 1.2, 0.95)  # Increased boost multiplier
            logger.debug(f"Boosted confidence for function-level operation: {boosted}")
            return boosted
        return base_confidence

    def _apply_graceful_degradation(self, confidence_scores: Dict[str, float]) -> Dict[str, float]:
        """
        Applies graceful degradation to confidence scores if overall confidence is low.

        Args:
            confidence_scores (Dict[str, float]): The current confidence scores.

        Returns:
            Dict[str, float]: The adjusted confidence scores.
        """
        if confidence_scores['overall'] < LOW_CONFIDENCE_THRESHOLD:
            degraded_scores = {
                k: min(v * 0.8, 0.4) if k != 'context' else 0.5
                for k, v in confidence_scores.items()
            }
            logger.debug(f"Applied graceful degradation: {degraded_scores}")
            return degraded_scores
        return confidence_scores

    def _is_file_level_operation(self) -> bool:
        """
        Determines if the operation is at the file level based on keywords.

        Returns:
            bool: True if file-level operation, False otherwise.
        """
        file_level_keywords = {'import', 'comment', 'print', 'file', 'global'}
        query_words = set(re.findall(r'\w+', self.query.lower()))
        is_file_level = bool(query_words.intersection(file_level_keywords))
        logger.debug(f"Is file-level operation: {is_file_level}")
        return is_file_level

    def _is_function_level_operation(self) -> bool:
        """
        Determines if the operation is at the function level based on keywords.

        Returns:
            bool: True if function-level operation, False otherwise.
        """
        function_keywords = {'function', 'def', 'method', 'update', 'modify'}
        query_words = set(re.findall(r'\w+', self.query.lower()))
        is_function_level = bool(query_words.intersection(function_keywords))
        logger.debug(f"Is function-level operation: {is_function_level}")
        return is_function_level

    def _is_class_level_operation(self) -> bool:
        """
        Determines if the operation is at the class level based on keywords.

        Returns:
            bool: True if class-level operation, False otherwise.
        """
        class_keywords = {'class'}
        query_words = set(re.findall(r'\w+', self.query.lower()))
        is_class_level = bool(query_words.intersection(class_keywords))
        logger.debug(f"Is class-level operation: {is_class_level}")
        return is_class_level