#!/usr/bin/env python
# coding: utf-8

# <div class="alert alert-info">For executing this notebook you will need to use the branch `iod-numba` of the poliastro repository: https://github.com/Pybonacci/poliastro/tree/iod-numba</div>

# In[1]:


import numpy as np

from astropy import units as u

from poliastro.bodies import Earth
from poliastro.iod import lambert
from poliastro.math import dot
from poliastro.stumpff import c2, c3


# In[2]:


k = Earth.k
r0 = [15945.34, 0.0, 0.0] * u.km
r = [12214.83399, 10249.46731, 0.0] * u.km
tof = 76.0 * u.min


# In[3]:


lambert(k.to(u.km ** 3 / u.s ** 2).value,
        r0.value, r.value,
        tof.to(u.s).value)


# Prepare inputs to measure performance:

# In[4]:


k_ = k.to(u.km ** 3 / u.s ** 2).value
r0_ = r0.to(u.km).value
r_ = r.to(u.km).value
tof_ = tof.to(u.s).value


# In[5]:


get_ipython().run_line_magic('timeit', 'lambert(k_, r0_, r_, tof_)')


# Let's implement the simplest one: Bate-Mueller-White universal variable approach, with a bisection method as suggested by Vallado.

# In[6]:


def lambert_py(k, r0, r, tof, short=True, numiter=35, rtol=1e-6):
    if short:
        t_m = +1
    else:
        t_m = -1

    norm_r0 = np.dot(r0, r0)**.5
    norm_r = np.dot(r, r)**.5
    cos_dnu = np.dot(r0, r) / (norm_r0 * norm_r)
    sin_dnu = t_m * (1 - cos_dnu ** 2)**.5

    A = t_m * (norm_r * norm_r0 * (1 + cos_dnu))**.5

    if A == 0.0:
        raise RuntimeError("Cannot compute orbit")

    psi = 0.0
    psi_low = -4 * np.pi
    psi_up = 4 * np.pi

    count = 0
    while count < numiter:
        y = norm_r0 + norm_r + A * (psi * c3(psi) - 1) / c2(psi)**.5
        if A > 0.0 and y < 0.0:
            # Readjust xi_low until y > 0.0 (?)
            pass
        xi = np.sqrt(y / c2(psi))
        tof_new = (xi**3 * c3(psi) + A * np.sqrt(y)) / np.sqrt(k)

        # Convergence check
        if np.abs((tof_new - tof) / tof) < rtol:
            break
        else:
            count += 1
            # Bisection check
            if tof_new <= tof:
                psi_low = psi
            else:
                psi_up = psi
            psi = (psi_up + psi_low) / 2
    else:
        raise RuntimeError("Convergence could not be achieved under "
                           "%d iterations" % numiter)

    f = 1 - y / norm_r0
    g = A * np.sqrt(y / k)

    gdot = 1 - y / norm_r

    v0 = (r - f * r0) / g
    v = (gdot * r - r0) / g

    return v0, v


# In[7]:


lambert_py(k_, r0_, r_, tof_)


# In[8]:


get_ipython().run_line_magic('timeit', 'lambert_py(k_, r0_, r_, tof_)')


# In[9]:


import numba

def lambert_numba(k, r0, r, tof, short=True, numiter=35, rtol=1e-8):
    try:
        f, g, fdot, gdot = _lambert(k, r0, r, tof, short, numiter, rtol)
    except RuntimeError as e:
        raise e

    v0 = (r - f * r0) / g
    v = (gdot * r - r0) / g

    return v0, v

@numba.njit
def _lambert(k, r0, r, tof, short, numiter, rtol):
    if short:
        t_m = +1
    else:
        t_m = -1

    norm_r0 = dot(r0, r0)**.5
    norm_r = dot(r, r)**.5
    cos_dnu = dot(r0, r) / (norm_r0 * norm_r)
    sin_dnu = t_m * (1 - cos_dnu ** 2)**.5

    A = t_m * (norm_r * norm_r0 * (1 + cos_dnu))**.5

    if A == 0.0:
        raise RuntimeError

    psi = 0.0
    psi_low = -4 * np.pi
    psi_up = 4 * np.pi

    count = 0
    while count < numiter:
        y = norm_r0 + norm_r + A * (psi * c3(psi) - 1) / c2(psi)**.5
        if A > 0.0 and y < 0.0:
            # Readjust xi_low until y > 0.0
            # Translated directly from Vallado
            while y < 0.0:
                psi_low = psi
                psi = 0.8 * (1.0 / c3(psi)) * (1.0 - (norm_r0 + norm_r) * np.sqrt(c2(psi)) / A)
                y = norm_r0 + norm_r + A * (psi * c3(psi) - 1) / c2(psi)**.5

        xi = np.sqrt(y / c2(psi))
        tof_new = (xi**3 * c3(psi) + A * np.sqrt(y)) / np.sqrt(k)

        # Convergence check
        if np.abs((tof_new - tof) / tof) < rtol:
            break
        else:
            count += 1
            # Bisection check
            if tof_new <= tof:
                psi_low = psi
            else:
                psi_up = psi
            psi = (psi_up + psi_low) / 2
    else:
        raise RuntimeError

    f = 1 - y / norm_r0
    g = A * np.sqrt(y / k)

    gdot = 1 - y / norm_r

    return f, g, (f * gdot - 1) / g, gdot


# In[10]:


lambert_numba(k_, r0_, r_, tof_)


# In[11]:


get_ipython().run_line_magic('timeit', 'lambert_numba(k_, r0_, r_, tof_)')


# In[12]:


import poliastro
import poliastro.iod
poliastro.iod.lambert = lambert_numba

poliastro.test()