from collections import OrderedDict
import numpy as np
import torch
from lietorch import SO3, SE3, Sim3
from .graph_utils import graph_to_edge_list
from .projective_ops import projective_transform


def pose_metrics(dE):
    """ Translation/Rotation/Scaling metrics from Sim3 """
    t, q, s = dE.data.split([3, 4, 1], -1)
    ang = SO3(q).log().norm(dim=-1)

    # convert radians to degrees
    r_err = (180 / np.pi) * ang
    t_err = t.norm(dim=-1)
    s_err = (s - 1.0).abs()
    return r_err, t_err, s_err


def fit_scale(Ps, Gs):
    b = Ps.shape[0]
    t1 = Ps.data[...,:3].detach().reshape(b, -1)
    t2 = Gs.data[...,:3].detach().reshape(b, -1)

    s = (t1*t2).sum(-1) / ((t2*t2).sum(-1) + 1e-8)
    return s


def geodesic_loss(Ps, Gs, graph, gamma=0.9, do_scale=True):
    """ Loss function for training network """

    # relative pose
    ii, jj, kk = graph_to_edge_list(graph)
    dP = Ps[:,jj] * Ps[:,ii].inv()

    n = len(Gs)
    geodesic_loss = 0.0

    for i in range(n):
        w = gamma ** (n - i - 1)
        dG = Gs[i][:,jj] * Gs[i][:,ii].inv()

        if do_scale:
            s = fit_scale(dP, dG)
            dG = dG.scale(s[:,None])
        
        # pose error
        d = (dG * dP.inv()).log()

        if isinstance(dG, SE3):
            tau, phi = d.split([3,3], dim=-1)
            geodesic_loss += w * (
                tau.norm(dim=-1).mean() + 
                phi.norm(dim=-1).mean())

        elif isinstance(dG, Sim3):
            tau, phi, sig = d.split([3,3,1], dim=-1)
            geodesic_loss += w * (
                tau.norm(dim=-1).mean() + 
                phi.norm(dim=-1).mean() + 
                0.05 * sig.norm(dim=-1).mean())
            
        dE = Sim3(dG * dP.inv()).detach()
        r_err, t_err, s_err = pose_metrics(dE)

    metrics = {
        'rot_error': r_err.mean().item(),
        'tr_error': t_err.mean().item(),
        'bad_rot': (r_err < .1).float().mean().item(),
        'bad_tr': (t_err < .01).float().mean().item(),
    }

    return geodesic_loss, metrics


def residual_loss(residuals, gamma=0.9):
    """ loss on system residuals """
    residual_loss = 0.0
    n = len(residuals)

    for i in range(n):
        w = gamma ** (n - i - 1)
        residual_loss += w * residuals[i].abs().mean()

    return residual_loss, {'residual': residual_loss.item()}


def flow_loss(Ps, disps, poses_est, disps_est, intrinsics, graph, gamma=0.9):
    """ optical flow loss """

    N = Ps.shape[1]
    graph = OrderedDict()
    for i in range(N):
        graph[i] = [j for j in range(N) if abs(i-j)==1]

    ii, jj, kk = graph_to_edge_list(graph)
    coords0, val0 = projective_transform(Ps, disps, intrinsics, ii, jj)
    val0 = val0 * (disps[:,ii] > 0).float().unsqueeze(dim=-1)

    n = len(poses_est)
    flow_loss = 0.0

    for i in range(n):
        w = gamma ** (n - i - 1)
        coords1, val1 = projective_transform(poses_est[i], disps_est[i], intrinsics, ii, jj)

        v = (val0 * val1).squeeze(dim=-1)
        epe = v * (coords1 - coords0).norm(dim=-1)
        flow_loss += w * epe.mean()

    epe = epe.reshape(-1)[v.reshape(-1) > 0.5]
    metrics = {
        'f_error': epe.mean().item(),
        '1px': (epe<1.0).float().mean().item(),
    }

    return flow_loss, metrics