# The implementation is adopted from FairMOT,
# made publicly available under the MIT License at https://github.com/ifzhang/FairMOT
import numpy as np
import scipy.linalg

chi2inv95 = {
    1: 3.8415,
    2: 5.9915,
    3: 7.8147,
    4: 9.4877,
    5: 11.070,
    6: 12.592,
    7: 14.067,
    8: 15.507,
    9: 16.919
}


class KalmanFilter(object):
    """
    A simple Kalman filter for tracking bounding boxes in image space.

    The 8-dimensional state space

        x, y, a, h, vx, vy, va, vh

    contains the bounding box center position (x, y), aspect ratio a, height h,
    and their respective velocities.

    Object motion follows a constant velocity model. The bounding box location
    (x, y, a, h) is taken as direct observation of the state space (linear
    observation model).

    """

    def __init__(self):
        ndim, dt = 4, 1.

        # Create Kalman filter model matrices.
        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
        for i in range(ndim):
            self._motion_mat[i, ndim + i] = dt
        self._update_mat = np.eye(ndim, 2 * ndim)

        # Motion and observation uncertainty are chosen relative to the current
        # state estimate. These weights control the amount of uncertainty in
        # the model. This is a bit hacky.
        self._std_weight_position = 1. / 20
        self._std_weight_velocity = 1. / 160

    def initiate(self, measurement):
        """Create track from unassociated measurement.

        Args:
        measurement : ndarray
            Bounding box coordinates (x, y, a, h) with center position (x, y),
            aspect ratio a, and height h.

        Returns:
            (ndarray, ndarray): Returns the mean vector (8 dimensional) and covariance matrix
            (8x8 dimensional) of the new track. Unobserved velocities are initialized
            to 0 mean.

        """
        mean_pos = measurement
        mean_vel = np.zeros_like(mean_pos)
        mean = np.r_[mean_pos, mean_vel]

        std = [
            2 * self._std_weight_position * measurement[3],
            2 * self._std_weight_position * measurement[3], 1e-2,
            2 * self._std_weight_position * measurement[3],
            10 * self._std_weight_velocity * measurement[3],
            10 * self._std_weight_velocity * measurement[3], 1e-5,
            10 * self._std_weight_velocity * measurement[3]
        ]
        covariance = np.diag(np.square(std))
        return mean, covariance

    def predict(self, mean, covariance):
        """Run Kalman filter prediction step.

        Args:
            mean : ndarray
                The 8 dimensional mean vector of the object state at the previous
                time step.
            covariance : ndarray
                The 8x8 dimensional covariance matrix of the object state at the
                previous time step.

        Returns:
            (ndarray, ndarray)
                Returns the mean vector and covariance matrix of the predicted
                state. Unobserved velocities are initialized to 0 mean.

        """
        std_pos = [
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[3], 1e-2,
            self._std_weight_position * mean[3]
        ]
        std_vel = [
            self._std_weight_velocity * mean[3],
            self._std_weight_velocity * mean[3], 1e-5,
            self._std_weight_velocity * mean[3]
        ]
        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

        mean = np.dot(mean, self._motion_mat.T)
        covariance = np.linalg.multi_dot(
            (self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

        return mean, covariance

    def project(self, mean, covariance):
        """Project state distribution to measurement space.

        Args:
            mean : ndarray
                The state's mean vector (8 dimensional array).
            covariance : ndarray
                The state's covariance matrix (8x8 dimensional).

        Returns:
            (ndarray, ndarray)
                Returns the projected mean and covariance matrix of the given state
                estimate.

        """
        std = [
            self._std_weight_position * mean[3],
            self._std_weight_position * mean[3], 1e-1,
            self._std_weight_position * mean[3]
        ]
        innovation_cov = np.diag(np.square(std))

        mean = np.dot(self._update_mat, mean)
        covariance = np.linalg.multi_dot(
            (self._update_mat, covariance, self._update_mat.T))
        return mean, covariance + innovation_cov

    def multi_predict(self, mean, covariance):
        """Run Kalman filter prediction step (Vectorized version).

        Args:
            mean : ndarray
                The Nx8 dimensional mean matrix of the object states at the previous
                time step.
            covariance : ndarray
                The Nx8x8 dimensional covariance matrics of the object states at the
                previous time step.

        Returns:
            (ndarray, ndarray)
                Returns the mean vector and covariance matrix of the predicted
                state. Unobserved velocities are initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[:, 3],
            self._std_weight_position * mean[:, 3],
            1e-2 * np.ones_like(mean[:, 3]),
            self._std_weight_position * mean[:, 3]
        ]
        std_vel = [
            self._std_weight_velocity * mean[:, 3],
            self._std_weight_velocity * mean[:, 3],
            1e-5 * np.ones_like(mean[:, 3]),
            self._std_weight_velocity * mean[:, 3]
        ]
        sqr = np.square(np.r_[std_pos, std_vel]).T

        motion_cov = []
        for i in range(len(mean)):
            motion_cov.append(np.diag(sqr[i]))
        motion_cov = np.asarray(motion_cov)

        mean = np.dot(mean, self._motion_mat.T)
        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
        covariance = np.dot(left, self._motion_mat.T) + motion_cov

        return mean, covariance

    def update(self, mean, covariance, measurement):
        """Run Kalman filter correction step.

        Args:
            mean : ndarray
                The predicted state's mean vector (8 dimensional).
            covariance : ndarray
                The state's covariance matrix (8x8 dimensional).
            measurement : ndarray
                The 4 dimensional measurement vector (x, y, a, h), where (x, y)
                is the center position, a the aspect ratio, and h the height of the
                bounding box.

        Returns:
            (ndarray, ndarray)
                Returns the measurement-corrected state distribution.

        """
        projected_mean, projected_cov = self.project(mean, covariance)

        chol_factor, lower = scipy.linalg.cho_factor(
            projected_cov, lower=True, check_finite=False)
        kalman_gain = scipy.linalg.cho_solve((chol_factor, lower),
                                             np.dot(covariance,
                                                    self._update_mat.T).T,
                                             check_finite=False).T
        innovation = measurement - projected_mean

        new_mean = mean + np.dot(innovation, kalman_gain.T)
        new_covariance = covariance - np.linalg.multi_dot(
            (kalman_gain, projected_cov, kalman_gain.T))
        return new_mean, new_covariance

    def gating_distance(self,
                        mean,
                        covariance,
                        measurements,
                        only_position=False,
                        metric='maha'):
        """Compute gating distance between state distribution and measurements.
        A suitable distance threshold can be obtained from `chi2inv95`. If
        `only_position` is False, the chi-square distribution has 4 degrees of
        freedom, otherwise 2.

        Args:
            mean : ndarray
                Mean vector over the state distribution (8 dimensional).
            covariance : ndarray
                Covariance of the state distribution (8x8 dimensional).
            measurements : ndarray
                An Nx4 dimensional matrix of N measurements, each in
                format (x, y, a, h) where (x, y) is the bounding box center
                position, a the aspect ratio, and h the height.
            only_position : Optional[bool]
                If True, distance computation is done with respect to the bounding
                box center position only.

        Returns:
            an array of length N, where the i-th element contains the
            squared Mahalanobis distance between (mean, covariance) and
            `measurements[i]`.
        """
        mean, covariance = self.project(mean, covariance)
        if only_position:
            mean, covariance = mean[:2], covariance[:2, :2]
            measurements = measurements[:, :2]

        d = measurements - mean
        if metric == 'gaussian':
            return np.sum(d * d, axis=1)
        elif metric == 'maha':
            cholesky_factor = np.linalg.cholesky(covariance)
            z = scipy.linalg.solve_triangular(
                cholesky_factor,
                d.T,
                lower=True,
                check_finite=False,
                overwrite_b=True)
            squared_maha = np.sum(z * z, axis=0)
            return squared_maha
        else:
            raise ValueError('invalid distance metric')
