"""
RCAT (Reversed Compound Agent Theorem) model builder.

Converts a queueing network into a RCAT model for analysis of
non-product-form networks.

RCAT Model Structure:
- Active processes (A): one per class
- Passive processes (P): one per queue
- Actions: corresponding to network transitions
- Action rates: unknowns to be solved

Algorithm:
1. Extract network structure (stations, classes, routing)
2. Build state transition matrices for each process
3. Identify action-to-process mapping
4. Setup constraint system for rate solving

References:
    MATLAB: matlab/src/solvers/MAM/solver_mam_rcat.m (lines 252-636)
"""

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


class RCATModel:
    """RCAT model representation.

    Attributes:
        nprocesses: Number of processes (classes + queues)
        nactions: Number of actions
        processes: List of process transition matrices
        action_map: (nactions, 2) mapping actions to (process, transition)
        lb: Lower bounds for action rates
        ub: Upper bounds for action rates
    """

    def __init__(self, nprocesses: int, nactions: int):
        self.nprocesses = nprocesses
        self.nactions = nactions
        self.processes = []  # List of transition matrices
        self.action_map = {}  # action_id -> (process_id, trans_idx)
        self.lb = np.zeros(nactions)
        self.ub = np.ones(nactions) * np.inf
        self.rates = np.zeros(nactions)  # Unknown action rates


def build_rcat_model(sn, K: int, M: int) -> RCATModel:
    """Build RCAT model from network structure.

    Args:
        sn: NetworkStruct
        K: Number of classes
        M: Number of stations

    Returns:
        RCATModel instance
    """
    # Number of processes: K active + M passive
    nprocesses = K + M

    # Number of actions: class transitions + queue transitions
    # Simplified: assume one action per (class, routing choice)
    nactions = K * M  # Rough estimate

    model = RCATModel(nprocesses, nactions)

    # Build transition matrices for each process
    # Active processes (classes): state = which queue
    for k in range(K):
        # Transition matrix for class k (active process)
        # State = current queue, transitions = routing
        trans = np.zeros((M, M))
        # Routing: assume from routing matrix
        if hasattr(sn, 'rt') and sn.rt is not None:
            routing = np.asarray(sn.rt, dtype=np.float64)
            if routing.ndim == 3:
                trans = routing[:, :, k]
            elif routing.ndim == 2:
                trans = routing
        else:
            # Default: uniform routing
            trans = np.ones((M, M)) / M

        model.processes.append(trans)

    # Passive processes (queues): state = queue length
    # Simplified: just record that they exist
    for m in range(M):
        # For now, identity matrix (state independent)
        trans = np.eye(M)
        model.processes.append(trans)

    return model


class RCATSolver:
    """Base class for RCAT-based solvers."""

    def __init__(self, model: RCATModel):
        self.model = model

    def setup_constraints(self) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """Setup constraint system for rate solving.

        For each process equilibrium: π_p * Q_p = 0

        Returns:
            (A, b, bounds) for constraint system
        """
        nactions = self.model.nactions
        A = np.zeros((nactions, nactions))
        b = np.zeros(nactions)

        # Simplified: identity system
        # Full implementation would build equilibrium equations
        A = np.eye(nactions)

        return A, b, (self.model.lb, self.model.ub)

    def solve_rates(self) -> np.ndarray:
        """Solve for action rates.

        Returns:
            Action rate vector
        """
        A, b, bounds = self.setup_constraints()

        # Simple solver: assume uniform rates
        rates = np.ones(self.model.nactions)

        return rates
