import numpy as np
from scipy.optimize import minimize
from scipy.linalg import solve
import time

def maxentdefaultparams(algorithm_params):
    """
    Fill in default parameters for the MaxEnt algorithm.
    """
    # Create default parameters.
    default_params = {
        'seed': 0,
        'laplace_prior': 0,
        'all_features': 1,
        'true_features': 0
    }
    # Set parameters.
    algorithm_params = filldefaultparams(algorithm_params, default_params)
    return algorithm_params

def filldefaultparams(algorithm_params, default_params):
    """
    Fill in default parameters for any missing parameters in algorithm_params.
    """
    if algorithm_params is None:
        algorithm_params = {}
    for key in default_params:
        if key not in algorithm_params:
            algorithm_params[key] = default_params[key]
    return algorithm_params

def maxentsoftmax(q):
    """
    Compute row-wise softmax of a matrix q.
    Returns v, where v(s) = log(sum_a exp(q(s,a)))
    """
    max_q = np.max(q, axis=1, keepdims=True)
    v = max_q + np.log(np.sum(np.exp(q - max_q), axis=1, keepdims=True))
    return v.ravel()  # Return as 1D array of length states

def linearvalueiteration(mdp_data, r_sa, max_iterations=1000, tolerance=1e-4):
    """
    Perform linear value iteration for MaxEnt IRL.

    mdp_data: dict containing MDP information
    r_sa: reward for each state-action pair (S x A)
    """
    states = mdp_data['states']
    actions = mdp_data['actions']
    gamma = mdp_data['discount']

    # Initialize V(s)
    V = np.zeros(states)

    # Precompute transition probabilities
    P = mdp_data['sa_p']    # shape (S, A, S)
    policy = np.full((states, actions), 1.0 / actions)  # Uniform policy initialization

    for iteration in range(max_iterations):
        V_old = V.copy()
        Q = np.zeros((states, actions))
        for a in range(actions):
            # For each action, compute Q(s,a)
            Q[:, a] = r_sa[:, a] + gamma * P[:, a, :].dot(V)
        # Update V(s)
        V = maxentsoftmax(Q)
        # Check for convergence
        if np.max(np.abs(V - V_old)) < tolerance:
            break

    # Compute policy
    log_policy = Q - V[:, np.newaxis]
    policy = np.exp(log_policy)
    # Normalize policy
    policy = policy / np.sum(policy, axis=1, keepdims=True)
    return policy, log_policy

def linearmdpfrequency(mdp_data, policy_data, initD):
    """
    Compute state visitation frequencies D for MaxEnt IRL.

    mdp_data: dict with MDP information
    policy_data: dict containing 'p', the policy (S x A)
    initD: initial state distribution (S x 1)
    Returns D: state visitation frequencies (S x 1)
    """
    states = mdp_data['states']
    gamma = mdp_data['discount']

    P = mdp_transition_matrix(mdp_data, policy_data['p'])

    # Compute D
    # D = (I - gamma * P.T)^{-1} * initD
    I = np.eye(states)
    A = I - gamma * P.T
    D = solve(A, initD)
    return D

def mdp_transition_matrix(mdp_data, policy):
    """
    Compute the transition matrix P_pi under a given policy.

    mdp_data: dict with MDP information
    policy: policy matrix (S x A)
    Returns P_pi: transition matrix (S x S)
    """
    states = mdp_data['states']
    actions = mdp_data['actions']

    P_pi = np.zeros((states, states))

    for s in range(states):
        for a in range(actions):
            P_pi[s, :] += policy[s, a] * mdp_data['sa_p'][s, a, :]
    return P_pi

def maxentdiscounted(r, F, muE, mu_sa, mdp_data, initD, laplace_prior=0):
    """
    Compute MaxEnt objective and gradient. Discounted infinite-horizon version.
    """
    actions = mdp_data['actions']

    # Convert to full reward
    wts = r.copy()
    r_full = F @ r

    # Compute policy and log policy
    r_sa = np.tile(r_full.reshape(-1,1), (1, actions))
    policy, log_policy = linearvalueiteration(mdp_data, r_sa)

    # Compute value by adding up log example probabilities
    val = np.sum(log_policy * mu_sa)

    # Add Laplace prior for regularization
    if laplace_prior:
        val -= laplace_prior * np.sum(np.abs(wts))

    # Invert for descent (since we are minimizing)
    val = -val

    # Compute gradient
    D = linearmdpfrequency(mdp_data, {'p': policy}, initD)

    # Compute gradient
    dr = muE - F.T @ D

    # Laplace prior
    if laplace_prior:
        dr -= laplace_prior * np.sign(wts)

    # Invert for descent
    dr = -dr

    return val, dr

def maxentrun(algorithm_params, mdp_data, mdp_model,
              feature_data, example_samples, true_features, verbosity):
    """
    Ziebart's Maximum Entropy IRL, with optional prior on reward values.

    Args:
        algorithm_params: parameters of the MaxEnt algorithm
        mdp_data: MDP definition
        mdp_model: MDP model (not used in this implementation)
        feature_data: feature data
        example_samples: list of example trajectories, each a list of (state, action) tuples
        true_features: true feature matrix (if available)
        verbosity: verbosity level

    Returns:
        irl_result: result of the IRL algorithm
    """
    # Fill in default parameters
    algorithm_params = maxentdefaultparams(algorithm_params)

    np.random.seed(algorithm_params['seed'])

    # Initialize variables
    sa_p = mdp_data['sa_p']  # Transition probabilities (S x A x S)
    states, actions, _ = sa_p.shape

    N = len(example_samples)
    T = len(example_samples[0])

    # Build feature membership matrix
    if algorithm_params['all_features']:
        F = feature_data['splittable']  # Assuming splittable is a numpy array
        # Add dummy feature
        F = np.hstack([F, np.ones((states, 1))])
    elif algorithm_params['true_features']:
        F = true_features
    else:
        F = np.eye(states)
    # Count features
    features = F.shape[1]

    # Compute feature expectations
    muE = np.zeros(features)
    mu_sa = np.zeros((states, actions))
    ex_s = np.zeros((N, T), dtype=int)
    ex_a = np.zeros((N, T), dtype=int)
    for i in range(N):
        for t in range(T):
            s = example_samples[i][t][0]
            a = example_samples[i][t][1]
            ex_s[i,t] = s
            ex_a[i,t] = a
            mu_sa[s,a] += 1
            muE += F[s]

    # Normalize mu_sa
    mu_sa /= N * T

    # Generate initial state distribution for infinite horizon
    initD = np.bincount(ex_s[:,0], minlength=states).astype(float)
    initD /= initD.sum()

    # Objective function
    def fun(r):
        val, grad = maxentdiscounted(r, F, muE, mu_sa, mdp_data, initD, algorithm_params['laplace_prior'])
        return val, grad

    # Optimization options
    if verbosity == 0:
        opt_options = {'disp': False, 'maxiter': 100}
    else:
        opt_options = {'disp': True, 'maxiter': 100}

    start_time = time.time()

    # Initialize reward parameters
    r0 = np.random.rand(features)

    # Run unconstrained minimization
    res = minimize(fun, r0, method='L-BFGS-B', jac=True, options=opt_options)

    # Get timing
    time_elapsed = time.time() - start_time
    if verbosity != 0:
        print('Optimization completed in {:.2f} seconds.'.format(time_elapsed))

    # Get final reward weights
    r = res.x

    # Convert to full tabulated reward
    wts = r.copy()
    r_full = F @ r

    # Return corresponding reward function
    r_sa = np.tile(r_full.reshape(-1,1), (1, actions))
    soln = mdp_solve(mdp_data, r_sa)
    v = soln['v']
    q = soln['q']
    p = soln['p']

    # Construct returned structure
    irl_result = {
        'r': r_sa,
        'v': v,
        'p': p,
        'q': q,
        'r_itr': [r_sa],
        'model_itr': [wts],
        'model_r_itr': [r_sa],
        'p_itr': [p],
        'model_p_itr': [p],
        'time': time_elapsed
    }

    return irl_result

def mdp_solve(mdp_data, r_sa, max_iterations=1000, tolerance=1e-4):
    """
    Solve the MDP given the reward r_sa (S x A).
    Returns solution containing 'v', 'q', 'p'.
    """
    states = mdp_data['states']
    actions = mdp_data['actions']
    gamma = mdp_data['discount']

    # Use standard value iteration
    V = np.zeros(states)
    P = mdp_data['sa_p']  # Transition probabilities (S x A x S)
    for iteration in range(max_iterations):
        V_old = V.copy()
        Q = np.zeros((states, actions))
        for a in range(actions):
            Q[:, a] = r_sa[:, a] + gamma * P[:, a, :].dot(V)
        V = np.max(Q, axis=1)
        if np.max(np.abs(V - V_old)) < tolerance:
            break

    # Compute policy
    policy = np.zeros((states, actions))
    for s in range(states):
        best_actions = np.argwhere(Q[s, :] == np.max(Q[s, :])).flatten()
        policy[s, best_actions] = 1.0 / len(best_actions)

    soln = {'v': V, 'q': Q, 'p': policy}
    return soln

def maxenttransfer(prev_result, mdp_data, mdp_model,
                   feature_data, true_feature_map, verbosity):
    """
    Transfer learned reward function to a new state space.

    Args:
        prev_result: previous IRL result containing learned weights
        mdp_data: new MDP data
        mdp_model: MDP model (not used in this implementation)
        feature_data: feature data
        true_feature_map: true feature mapping
        verbosity: verbosity level

    Returns:
        irl_result: IRL result for the new MDP
    """
    # Get weights
    wts = prev_result['model_itr'][-1]

    # Decide if we want true features
    if len(wts) == true_feature_map.shape[1]:
        # Use true features
        F = true_feature_map
    elif len(wts) == feature_data['splittable'].shape[1] + 1:
        # Use all features
        F = feature_data['splittable']
        # Add dummy feature
        F = np.hstack([F, np.ones((mdp_data['states'], 1))])
    else:
        # Use identity matrix
        F = np.eye(mdp_data['states'])

    # Compute reward
    r_sa = np.tile((F @ wts).reshape(-1,1), (1, mdp_data['actions']))

    # Solve MDP
    soln = mdp_solve(mdp_data, r_sa)
    v = soln['v']
    q = soln['q']
    p = soln['p']

    # Build IRL result
    irl_result = {
        'r': r_sa,
        'v': v,
        'p': p,
        'q': q,
        'model_itr': [wts],
        'r_itr': [r_sa],
        'model_r_itr': [r_sa],
        'p_itr': [p],
        'model_p_itr': [p],
        'time': 0,
        'score': 0
    }

    return irl_result

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