NSSC/Exercise_02/state.py

from dataclasses import dataclass
from math import e
from typing import List
import numpy as np
from constants import alpha, D_e, r_e
from scipy.optimize import minimize, Bounds
from scipy.spatial import distance_matrix as dm
from datetime import datetime
from jax import numpy as jnp

@dataclass
class State:
  count: int = 0
  size: float = 1.0
  molecules: np.matrix = np.zeros((0,6))
  temperature: float = 0

  def energy(self) -> float:
    return energy(self.positions())

  def minimize(self) -> None:
    # report with jax gradient
    res = minimize(energy, self.positions(), method='CG', jac='3-point')
    min = res.x
    min = np.matrix(min)
    min.shape = (self.count,3)
    self.molecules[:,0:3] = min

  @staticmethod
  def deserialize(lines: List[str]) -> None:
    #  disregard comment line
    lines.pop(1)

    count = int(lines.pop(0))
    size = float(lines.pop(0))
    lines = (line.strip() for line in lines)
    lines = (line.split() for line in lines if line)
    molecules = np.matrix([[float(f) for f in line] for line in lines])

    return State(count, size, molecules)

  def serialize(self) -> str:
    serialized = ''
    serialized += f'{self.count}\n'
    serialized += f'Written at {datetime.now()}\n'
    serialized += f'{self.size}\n'
    
    m = np.asmatrix(self.molecules)
    for i in range(m.shape[0]):
      serialized += '\t'.join(['{:+10.8f}'.format(f) for f in m[i,:].tolist()[0]]) + '\n'

    return serialized

  def positions(self) -> List[float]:
    return self.molecules[:,0:3].ravel()

def energy (p: np.matrix):
  P = jnp.reshape(p, (-1,3))
  V = _morse(distances(P))
  return jnp.nansum(jnp.tril(V, k=-1))

@jnp.vectorize
def _morse(r: float):
  return D_e * (e**(-2*alpha*(r-r_e)) - 2*e**(-alpha*(r - r_e)))

def distances(P):
  P = jnp.asarray(P)

  XYZ = jnp.asarray([
    # insert new axis with None to get an outer difference matrix for each dimension
    P[:, 0, None] - P[None, :, 0],
    P[:, 1, None] - P[None, :, 1],
    P[:, 2, None] - P[None, :, 2]
  ])

  XYZ = abs(XYZ)
  
  # nearest image convention
  # replace with modulo
  XYZ = XYZ.at[XYZ > 0.5].add(-0.5)
  XYZ = XYZ**2
  
  D = jnp.sum(XYZ, axis=0)
  D = D.at[D <= 0].set(0.0001)
  return jnp.sqrt(D)