import numpy as np
import scipy.interpolate as interp
from scipy.integrate import odeint

def calc_null_curves(times, spatial_coords, gXX, gXt, gtt):
    """
    Compute null curves along a given axis.

    Shoot a null ray from each point in spatial_coords, in the positive and
    negative direction and compute its trajectory.

    :param array_like times: 1D array of coordinate times at which the spacetime
                             curvature is provided
    :param array_like spatial_coords: 1D array of spatial coordinates
    :param array_like gXX: 2D array containing the values of the XX component
                           of the spacetime metric, where X is the spatial
                           coordinate along which the rays are traced.
                           gXX[i, j] is the value at spacetime point
                           (t=times[i], X=spatial_coords[j]).
    :param array_like gXt: same as gXX, but for the Xt component of the metric
    :param array_like gtt: same as gXX, but for the tt component of the metric
    :return: tuple containing two 2D arrays with, respectively, the positive and
             negative-direction rays. rays[i, j] contains the X-coordinate of
             the ray shot from (t=times[0], X=spatial_coords[i]) at time
             t=times[j]
    """

    gXX_interp      = interp.RectBivariateSpline(times, spatial_coords, gXX)
    gXt_interp      = interp.RectBivariateSpline(times, spatial_coords, gXt)
    gtt_interp      = interp.RectBivariateSpline(times, spatial_coords, gtt)

    def _dXdt(coord, t, sign,
              coord_min = spatial_coords[0], coord_max = spatial_coords[-1],
              gXX = gXX_interp, gtt = gtt_interp, gXt = gXt_interp):
        if coord <= coord_min or coord >= coord_max:
            return float('nan')
        gXt_val = gXt(t, coord)
        gXX_val = gXX(t, coord)
        gtt_val = gtt(t, coord)
        return ((-gXt_val + sign * np.sqrt((gXt_val ** 2) - gtt_val * gXX_val)) / gXX_val).flatten()[0]

    rays_pos = np.empty((spatial_coords.shape[0], times.shape[0]))
    rays_neg = np.empty_like(rays_pos)
    for j, X0 in enumerate(spatial_coords):
        for tgt, sign in ((rays_pos, 1.0), (rays_neg, -1.0)):
            ray = odeint(_dXdt, X0, times, (sign,))[:, 0]

            # clip the rays to the integration area
            k = 0
            while np.isnan(ray[k]):
                k += 1
            while k > 0:
                ray[k - 1] = ray[k]
                k -= 1

            k = ray.shape[0] - 1
            while np.isnan(ray[k]):
                k -= 1
            while k < ray.shape[0] - 1:
                ray[k + 1] = ray[k]
                k += 1

            tgt[j] = ray

    return (rays_pos, rays_neg)

def calc_null_coordinates(times, spatial_coords, u_rays, v_rays,
                          gXX, gXt, gtt):
    """
    Compute double-null coordinates (u, v) as functions of
    position and time.

    :param array_like times: 1D array of coordinate times at which the spacetime
                             curvature is provided
    :param array_like spatial_coords: 1D array of spatial coordinates
    :param array_like u_rays: 1D array assigning the values of u on the initial
                              time slice. u_rays[i] is the value of u at
                              X=spatial_coords[i].
    :param array_like v_rays: same as u_rays, but for v.
    :param array_like gXX: 2D array containing the values of the XX component
                           of the spacetime metric, where X is the spatial
                           coordinate along which the rays are traced.
                           gXX[i, j] is the value at spacetime point
                           (t=times[i], X=spatial_coords[j]).
    :param array_like gXt: same as gXX, but for the Xt component of the metric
    :param array_like gtt: same as gXX, but for the tt component of the metric
    :return: tuple containing two 2D arrays with, respectively, values of u and
             v as functions of t and X. u/v[i, j] is the value of u/v at
             t=times[i], X=spatial_coords[j].
    """
    X_of_ut, X_of_vt = calc_null_curves(times, spatial_coords, gXX, gXt, gtt)

    u_of_tx = np.empty((times.shape[0], spatial_coords.shape[0]))
    v_of_tx = np.empty_like(u_of_tx)
    for i, t in enumerate(times):
        Xu = X_of_ut[:, i]
        Xv = X_of_vt[:, i]
        u_of_tx[i] = interp.interp1d(Xu, u_rays)(spatial_coords)
        v_of_tx[i] = interp.interp1d(Xv, v_rays)(spatial_coords)

    return (u_of_tx, v_of_tx)