import warnings

#from typing import Optional

import numpy as np

import networkx as nx

class Inferer(object):

    '''

    The class for doing inference based on posterior estimations.

    '''

    def __init__(self, n_states: int):

        '''

        Parameters

        ----------

        n_states : int

            The number of vertices in the latent space.

        '''        

        self.n_states = n_states

        self.n_categories = int(n_states*(n_states+1)/2)

      #  self.A, self.B = np.nonzero(np.triu(np.ones(n_states)))

       ## indicator of the catagories

        self.C = np.triu(np.ones(n_states))

        self.C[self.C>0] = np.arange(self.n_categories)

        self.C = self.C.astype(int)

    def build_graphs(self, w_tilde, pc_x, method: str = 'mean', thres: float = 0.5, no_loop: bool = False, 

            cutoff = 0):

        '''Build the backbone.

        Parameters

        ----------

        pc_x : np.array

            \([N, K]\) The estimated \(p(c_i|Y_i,X_i)\).        

        method : string, optional 

            'mean', 'modified_mean', 'map', or 'modified_map'.

        thres : float, optional 

            The threshold used for filtering edges \(e_{ij}\) that \((n_{i}+n_{j}+e_{ij})/N<thres\), only applied to mean method.

        Retruns

        ----------

        G : nx.Graph

            The graph of edge scores.

        '''

        self.no_loop = no_loop

    #    self.w_tilde = w_tilde

        graph = np.zeros((self.n_states,self.n_states))

        if method=='mean':

            for i in range(self.n_states-1):

                for j in range(i+1,self.n_states):

                    idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)>=thres

                    if np.sum(idx)>0:

                        graph[i,j] = np.mean(pc_x[idx,self.C[i,j]]/np.sum(pc_x[idx][:,self.C[[i,i,j],[i,j,j]]], axis=-1))

        elif method=='modified_mean':

            for i in range(self.n_states-1):

                for j in range(i+1,self.n_states):

                    idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)>=thres

                    if np.sum(idx)>0:

                        graph[i,j] = np.sum(pc_x[idx,self.C[i,j]])/np.sum(pc_x[idx][:,self.C[[i,i,j],[i,j,j]]])

        elif method=='map':

            c = np.argmax(pc_x, axis=-1)

            for i in range(self.n_states-1):

                for j in range(i+1,self.n_states):

                    if np.sum(c==self.C[i,j])>0:

                        graph[i,j] = np.sum(c==self.C[i,j])/np.sum((c==self.C[i,j])|(c==self.C[i,i])|(c==self.C[j,j]))

        elif method=='modified_map':

            c = np.argmax(pc_x, axis=-1)

            for i in range(self.n_states-1):

                for j in range(i+1,self.n_states):

                    graph[i,j] = np.sum(c==self.C[i,j])/(np.sum((w_tilde[:,i]>0.5)|(w_tilde[:,j]>0.5))+1e-16)

        elif method=='raw_map':

            c = np.argmax(pc_x, axis=-1)

            for i in range(self.n_states-1):

                for j in range(i+1,self.n_states):

                    if np.sum(c==self.C[i,j])>0:

                        graph[i,j] = np.sum(c==self.C[i,j])/np.sum(np.isin(c, np.diagonal(self.C)) == False)

        elif method == "w_base":

            for i in range(self.n_states):

                for j in range(i+1,self.n_states):

                    two_vertice_max_w = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j),:]

                    num_two_vertice = two_vertice_max_w.shape[0]

                    if num_two_vertice > 0:

                        graph[i, j] = np.sum(

                            np.abs(two_vertice_max_w[:, i] - two_vertice_max_w[:, j]) < 0.1) / num_two_vertice

        elif method == "modified_w_base":

            top2_idx = np.argpartition(w_tilde, -2, axis=1)[:, -2:]

            for i in range(self.n_states):

                for j in range(i + 1, self.n_states):

                    two_vertice_max_w = np.all(top2_idx == [i, j], axis=1) | np.all(top2_idx == [j, i], axis=1)

                    two_vertice_max_w = w_tilde[two_vertice_max_w, :]

                    vertice_count = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j), :]

                    vertice_count = vertice_count.shape[0]

                    if vertice_count > 0:

                        edge_count = \

                            np.max((two_vertice_max_w[:, i], two_vertice_max_w[:, j]), axis=0) \

                            / (two_vertice_max_w[:, i] + two_vertice_max_w[:, j])

                        edge_count = np.sum(edge_count < 0.55)

                        graph[i, j] = edge_count / vertice_count

        else:

            raise ValueError("Invalid method, must be one of 'mean', 'modified_mean', 'map', 'modified_map','raw_map','w_base', and 'modified_w_base'.")

        graph[graph<=cutoff] = 0

        G = nx.from_numpy_array(graph)

        if self.no_loop and not nx.is_tree(G):

            # prune if there are no loops

            G = nx.maximum_spanning_tree(G)

        return G

    def modify_wtilde(self, w_tilde, edges):

        '''Project \(\\tilde{w}\) to the estimated backbone.

        Parameters

        ----------

        w_tilde : np.array

            \([N, k]\) The estimated \(\\tilde{w}\).        

        edges : np.array

            \([|\\mathcal{E}(\\widehat{\\mathcal{B}})|, 2]\).

        Retruns

        ----------

        w : np.array

            The projected \(\\tilde{w}\).

        '''

        w = np.zeros_like(w_tilde)

        # projection on nodes

        best_proj_err_node = np.sum(w_tilde**2, axis=-1) - 2*np.max(w_tilde, axis=-1) +1

        best_proj_err_node_ind = np.argmax(w_tilde, axis=-1)

        if len(edges)>0:

            # projection on edges

            idc = np.tile(np.arange(w.shape[0]), (2,1)).T

            ide = edges[np.argmax(np.sum(w_tilde[:,edges], axis=-1)**2 -

                                  4 * np.prod(w_tilde[:,edges], axis=-1) +

                                  2 * np.sum(w_tilde[:,edges], axis=-1), axis=-1)]

            w[idc, ide] = w_tilde[idc, ide] + (1-np.sum(w_tilde[idc, ide], axis=-1, keepdims=True))/2

            best_proj_err_edge = np.sum(w_tilde**2, axis=-1) - np.sum(w_tilde[idc, ide]**2, axis=-1) + (1-np.sum(w_tilde[idc, ide], axis=-1))**2/2

            idc = (best_proj_err_node<best_proj_err_edge)

            w[idc,:] = np.eye(w_tilde.shape[-1])[best_proj_err_node_ind[idc]]

        else:

            idc = np.arange(w.shape[0])

            w[idc, best_proj_err_node_ind] = 1

        return w

    def build_milestone_net(self, subgraph, init_node: int):

        '''Build the milestone network.

        Parameters

        ----------

        subgraph : nx.Graph

            The connected component of the backbone given the root vertex.

        init_node : int

            The root vertex.

        Returns

        ----------

        df_subgraph : pd.DataFrame 

            The milestone network.

        '''

        if len(subgraph)==1:

            warnings.warn('Singular node.')

            return []

        elif nx.is_directed_acyclic_graph(subgraph):

            milestone_net = []

            for edge in list(subgraph.edges):

                if edge[0]==init_node:

                    dist = 1

                elif edge[1]==init_node:

                    paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0])

                    dist = - (np.max([len(p) for p in paths_1]) - 1)

                else:

                    paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0])

                    paths_1 = nx.all_simple_paths(subgraph, source=init_node, target=edge[1])

                    dist = np.max([len(p) for p in paths_1]) - np.max([len(p) for p in paths_0])

                milestone_net.append([edge[0], edge[1], dist])

        else:

            # Dijkstra's Algorithm to find the shortest path

            unvisited = {node: {'parent':None,

                                'score':np.inf,

                                'distance':np.inf} for node in subgraph.nodes}

            current = init_node

            currentScore = 0

            currentDistance = 0

            unvisited[current]['score'] = currentScore

            milestone_net = []

            while True:

                for neighbour in subgraph.neighbors(current):

                    if neighbour not in unvisited: continue

                    newScore = currentScore + subgraph[current][neighbour]['weight']

                    if unvisited[neighbour]['score'] > newScore:

                        unvisited[neighbour]['score'] = newScore

                        unvisited[neighbour]['parent'] = current

                        unvisited[neighbour]['distance'] = currentDistance+1

                if len(unvisited)<len(subgraph):

                    milestone_net.append([unvisited[current]['parent'],

                                          current,

                                          unvisited[current]['distance']])

                del unvisited[current]

                if not unvisited: break

                current, currentScore, currentDistance = \

                    sorted([(i[0],i[1]['score'],i[1]['distance']) for i in unvisited.items()],

                            key = lambda x: x[1])[0]

            return np.array(milestone_net)

    def comp_pseudotime(self, milestone_net, init_node: int, w):

        '''Compute pseudotime.

        Parameters

        ----------

        milestone_net : pd.DataFrame

            The milestone network.

        init_node : int

            The root vertex.

        w : np.array

            \([N, k]\) The projected \(\\tilde{w}\).

        Returns

        ----------

        pseudotime : np.array

            \([N, k]\) The estimated pseudtotime.

        '''

        pseudotime = np.empty(w.shape[0])

        pseudotime.fill(np.nan)

        pseudotime[w[:,init_node]==1] = 0

        if len(milestone_net)>0:

            for i in range(len(milestone_net)):

                _from, _to = milestone_net[i,:2]

                _from, _to = int(_from), int(_to)

                idc = ((w[:,_from]>0)&(w[:,_to]>0)) | (w[:,_to]==1)

                pseudotime[idc] = w[idc,_to] + milestone_net[i,-1] - 1

        return pseudotime