#!/usr/bin/env python

from optparse import OptionParser   # to parse script parameters
import scipy
import numpy as np                  # static objects like constants (and outside functions)
from jax import numpy as jnp        # tracable objects like particle positions
from jax import jit, grad, vmap

# Parte script parameters
arg_parser = OptionParser()
arg_parser.add_option("-M", "--particles", action = "store", type = int,
    dest = "nr_particles", help = "Nr. of particles", default = 1000)
arg_parser.add_option("-L", "--box_size", action = "store", type = float,
    dest = "box_size", help = "side box_size [A (angstrom)] of the simulation cube",
    default = 15.0)
arg_parser.add_option("-T", "--temp", action = "store", type = float,
    dest = "temp", help = "temperature [K] to generate initial conditions",
    default = 300.0)
arg_parser.add_option("-f", "--file", action = "store", type = str,
    dest = "path", help = "output file path",
    default = "task02.xyz")
arg_parser.add_option("-p", "--plot", action = "store", type = str,
    dest = "plot", help = "output file path for a plot of the configuration " \
                          "(default: no plot generated)",
    default = None)
arg_parser.add_option("-v", action = "store_true", dest = "verbose",
    default = False, help = "turn verbosity mode on (default: off a.k.a. silent)")
# Parse command line arguments (as def. above) or store defaults to `config`
config, args = arg_parser.parse_args()

# toy moleculat dynamic system parameters
De = 1.6                            # [eV (electronvolt)]
alpha = 3.028                       # [A^-1]
re = 1.411                          # [A]
mass = 18.998403                    # atomic mass of a single particle

def dump(position, velocity, box_size = config.box_size, \
         path = config.path, mode = "w", comment = ""):
    """
    Dumps `position` and `velocity` to `path` with meta data.

    First writes a header to `path` in `mode` file write mode defines as three
    lines.
    `<nr of particles [int]>`
    `<comment (ignored)>`
    `<box side lenght [float]>`
    then each line (nr of particles many) have the form `x y z vx vy vx`.
    """
    with open(path, mode) as file:
        # write headers
        print(position.shape[0], comment, box_size, sep = "\n", file = file)
        # store position and velocity for with `x y z vx vy vz` entries per line`
        for (x, y, z), (vx, vy, vz) in zip(position, velocity):
            print(x, y, z, vx, vy, vz, file = file)

@jit
def energy(position):
    """
    Computes the potential energy of a system of particles with `position` using
    Morses potential.
    """
    # enforce expected shape
    # (`scipy.optimize.minimize` drops shape information)
    position = position.reshape((config.nr_particles, 3))
    # compute all pairwise position differences (all!)
    diff = position[:, jnp.newaxis, :] - position
    # extract only one of two distance combinations of non-equal particles
    lower_tri = jnp.tril_indices(config.nr_particles, k = -1)
    diff = diff[lower_tri[0], lower_tri[1], :]
    # fold space in all directions. The `max_dist` is the maximum distance
    # in the folded space untill the distance through the folded space
    # border is smaller than inside the box. 3-axis parallel fold
    max_dist = config.box_size / 2
    diff = jnp.mod(diff + max_dist, 2 * max_dist) - max_dist
    # Compute distances
    dist = jnp.linalg.norm(diff, axis = 1)
    # calc inbetween exp(.) expression
    ex = jnp.exp(-alpha * (dist - re))
    # evaluate Morse potential
    return De * jnp.sum(ex * (ex - 2.0))

@jit
def force(position):
    """
    Computes the forces acting on each particle in `position` as the gradient of
    the potential energy. (a.k.a. the derivative (gradient) of `energy`)
    """
    return grad(energy)(position)

# Sample random positions in a 3D cube (TODO: make this not just uniform :-})
position = np.random.uniform(0.0, config.box_size, (config.nr_particles, 3))

# Sample particle velocities
sd = np.sqrt(scipy.constants.Boltzmann * config.temp / mass)
velocity = np.random.normal(0.0, sd, (config.nr_particles, 3))
# center velocities
velocity -= velocity.mean(axis = 0)

# remember energy before optimizing for a low energy state
initial_energy = energy(position)

# optimize energy to find low energy system state using Conjugate-Gradients
optim = scipy.optimize.minimize(energy, x0 = position, jac = force, method = "CG")
# extract (and reshape) optimization result
position = optim.x.reshape((config.nr_particles, 3))

# recompute stats after optimizing for low energy state
final_energy = energy(position)
mean_forces = force(position).mean(axis = 0)

# store state snapshot to file (default target file defined by script args)
dump(position, velocity)

# report stats (if requested by `-v` script argument)
if config.verbose:
    print("Initial Energy: {:.4e}".format(initial_energy))
    print("Final Energy:   {:.4e}".format(final_energy))
    print("Mean Forces:    {:.4e} {:.4e} {:.4e}".format(*mean_forces))

# if a plot path is provided
if not config.plot is None:
    from mpl_toolkits import mplot3d
    import matplotlib.pyplot as plt
    # new plot with 3D axis
    plt.figure()
    ax = plt.axes(projection = "3d")
    # create 3D position scatter plot
    ax.scatter(position[:, 0], position[:, 1], position[:, 2])
    # and save to file
    plt.savefig(config.plot)