/
LJ_bug.py
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/
LJ_bug.py
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from pyxtal.crystal import random_cluster
from copy import deepcopy
from optparse import OptionParser
from random import randint, choice
from scipy.optimize import minimize
from scipy.spatial.distance import pdist, cdist
from pyxtal.molecule import PointGroupAnalyzer
from pymatgen import Molecule
from pyxtal.database.collection import Collection
from time import time
import numpy as np
import matplotlib.pyplot as plt
import warnings
import sys
plt.style.use("bmh")
warnings.filterwarnings("ignore")
"""
This is a script to
1, generate random clusters
2, perform optimization
"""
def LJ(pos, dim, method=1, mu=0.1):
"""
Calculate the total energy
Args:
pos: 1D array with N*dim numbers representing the atomic positions
dim: dimension of the hyper/normal space
output
E: the total energy with punishing function
"""
N_atom = int(len(pos) / dim)
pos = np.reshape(pos, (N_atom, dim))
distance = pdist(pos)
r6 = np.power(distance, 6)
r12 = np.multiply(r6, r6)
Eng = np.sum(4 * (1 / r12 - 1 / r6))
if dim > 3:
norm = 0
for i in range(3, dim):
if method == 1:
diff = pos[:, i]
else:
diff = pos[:, i] - np.mean(pos[:, i])
norm += np.sum(np.multiply(diff, diff))
Eng += 0.5 * mu * norm
return Eng
def LJ_force(pos, dim, method=1, mu=0.1):
N_atom = int(len(pos) / dim)
pos = np.reshape(pos, [N_atom, dim])
force = np.zeros([N_atom, dim])
for i, pos0 in enumerate(pos):
pos1 = deepcopy(pos)
pos1 = np.delete(pos1, i, 0)
distance = cdist([pos0], pos1)
r = pos1 - pos0
r2 = np.power(distance, 2)
r6 = np.power(r2, 3)
r12 = np.power(r6, 2)
force[i] = np.dot((48 / r12 - 24 / r6) / r2, r)
# force from the punish function mu*sum([x-mean(x)]^2)
if dim > 3:
for j in range(3, dim):
if method == 1:
force[i, j] += mu * pos[i, j] # - np.mean(pos[:, j]))
else:
force[i, j] += mu * (pos[i, j] - np.mean(pos[:, j]))
return force.flatten()
def single_optimize(pos, dim=3, method=1, mu=0.1):
"""
perform optimization for a given cluster
Args:
pos: N*dim0 array representing the atomic positions
dim: dimension of the hyper/normal space
kt: perturbation factors
output:
energy: optmized energy
pos: optimized positions
"""
N_atom = len(pos)
diff = dim - np.shape(pos)[1]
# if the input pos has less dimensions, we insert a random array for the extra dimension
# if the input pos has more dimensions, we delete the array for the extra dimension
if diff > 0:
# pos = np.hstack((pos, 0.5*(np.random.random([N_atom, diff])-0.5) ))
pos = np.hstack((pos, np.random.uniform(-1, 1, (N_atom, diff))))
elif diff < 0:
pos = pos[:, :dim]
pos = pos.flatten()
res = minimize(LJ, pos, args=(dim, method, mu), jac=LJ_force, method="CG", tol=1e-3)
pos = np.reshape(res.x, (N_atom, dim))
energy = res.fun
return energy, pos
def hyper_optimize(pos, dim, method=1, mu=0.1):
"""
hyperspatial optimization
"""
[energy1, pos1] = single_optimize(pos, dim)
while True:
if dim == len(pos1[0]):
disp = np.random.uniform(-1.0, 1, (len(pos), dim))
pos2 = pos1 + disp
[energy3, pos3] = single_optimize(pos2, dim)
else:
[energy2, pos2] = single_optimize(pos1, dim, method, mu)
[energy3, pos3] = single_optimize(pos2, 3)
if energy3 - energy1 > 1e-4:
pos = pos1
energy = energy1
break
else:
pos1 = pos3
energy1 = energy3
return energy1, pos1
def parse_symmetry(pos):
mol = Molecule(["C"] * len(pos), pos)
try:
symbol = PointGroupAnalyzer(mol, tolerance=0.1).sch_symbol
except:
symbol = "N/A"
return symbol
class LJ_prediction:
"""
A class to perform global optimization on LJ clusters
Args:
Attributes:
"""
def __init__(self, numIons):
self.numIons = numIons
ref = Collection("clusters")[str(numIons)]
print(
"\nReference for LJ {0:3d} is {1:12.3f} eV, PG: {2:4s}".format(
numIons, ref["energy"], ref["pointgroup"]
)
)
self.reference = ref
self.time0 = time()
def generate_cluster(self, pgs=range(2, 33)):
run = True
while run:
pg = choice(pgs)
cluster = random_cluster(pg, ["Mo"], [self.numIons], 1.0)
if cluster.valid:
run = False
return cluster.cart_coords
def predict(self, dim=3, maxN=100, ncpu=2, pgs=range(2, 33), method=1):
print("\nPerforming random search at {0:d}D space\n".format(dim))
cycle = range(maxN)
if ncpu > 1:
from multiprocessing import Pool
from functools import partial
with Pool(ncpu) as p:
func = partial(self.relaxation, dim, pgs, method)
res = p.map(func, cycle)
p.close()
p.join()
else:
res = []
for i in cycle:
res.append(self.relaxation(dim, pgs, method, i))
N_success = 0
for dct in res:
if dct["ground"]:
N_success += 1
print(
"\nHit the ground state {0:4d} times out of {1:4d} attempts\n".format(
N_success, maxN
)
)
return res
def relaxation(self, dim, pgs, method, ind):
pos = self.generate_cluster(pgs)
pg1 = parse_symmetry(pos)
print("initial geometry:")
print(pos)
print("initial energy: ", LJ(pos.flatten(), 3))
if dim == 3:
[energy, pos] = single_optimize(pos, 3)
energy = [energy]
else:
[energy1, pos1] = single_optimize(pos, 3)
[energy2, pos2] = hyper_optimize(pos1, 3)
# [energy2, pos2] = hyper_optimize(pos1, dim, method=1, mu=0.1)
# [energy3, pos3] = hyper_optimize(pos1, dim, method=1, mu=0.2)
# [energy4, pos4] = hyper_optimize(pos1, dim, method=2, mu=0.1)
# [energy5, pos5] = hyper_optimize(pos1, dim, method=2, mu=0.2)
# [energy6, pos6] = hyper_optimize(pos1, 3)
energy = [energy1, energy2] # , energy3, energy4, energy5, energy6]
pos = [pos1, pos2] # , pos3, pos4, pos5, pos6]
if min(energy) - self.reference["energy"] < 1e-3:
ground = True
elif min(energy) > -10:
print("high energy" + str(energy) + " after relaxation")
print(pos1)
sys.exit()
else:
ground = False
pg2 = parse_symmetry(pos)
res = {
"pos_init": pos,
"energy": energy,
"pg_init": pg1,
"pg_finial": pg2,
"ground": ground,
"id": ind,
}
if ground:
print(
"ID: {0:4d} PG initial: {1:4s} relaxed: {2:4s} Energy: {3:12.3f} Time: {4:6.1f} ++++++".format(
ind, pg1, pg2, energy[-1], (time() - self.time0) / 60
)
)
elif ind % 2 == 0:
print(
"ID: {0:4d} PG initial: {1:4s} relaxed: {2:4s} Energy: {3:12.3f} Time: {4:6.1f} ".format(
ind, pg1, pg2, energy[-1], (time() - self.time0) / 60
)
)
return res
if __name__ == "__main__":
# -------------------------------- Options -------------------------
parser = OptionParser()
parser.add_option(
"-d",
"--dimension",
dest="dim",
metavar="dim",
default=3,
type=int,
help="dimension, 3 or higher",
)
parser.add_option(
"-n",
"--numIons",
dest="numIons",
default=16,
type=int,
help="desired numbers of atoms: 16",
)
parser.add_option(
"-m",
"--max",
dest="max",
default=100,
type=int,
help="maximum number of attempts",
)
parser.add_option(
"-p",
"--proc",
dest="proc",
default=1,
type=int,
help="number of processors, default 1",
)
parser.add_option(
"-f",
"--func",
dest="func",
default=1,
type=int,
help="penalty function, default 1: mu*r^2",
)
(options, args) = parser.parse_args()
N = options.numIons # 38
maxN = options.max # 1000
dim = options.dim # 4
ncpu = options.proc
method = options.func
lj_run = LJ_prediction(N)
eng_min = lj_run.reference["energy"]
t0 = time()
results1 = lj_run.predict(dim=4, maxN=maxN, ncpu=ncpu, pgs=[1])
print("time: {0:6.2f} seconds".format(time() - t0))
engs = []
for dct in results1:
engs.append(dct["energy"])
engs = np.array(engs)
for i in range(1, len(engs[0])):
print("method " + str(i), np.mean(engs[:, i] - engs[:, 0]))
grounds = []
for i in range(len(engs[0])):
eng_tmp = engs[:, i]
grounds.append(len(eng_tmp[eng_tmp < (eng_min + 1e-3)]))