mirror of
https://github.com/TREX-CoE/irpjast.git
synced 2024-12-24 21:34:04 +01:00
272 lines
8.1 KiB
Python
272 lines
8.1 KiB
Python
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
|
|
def get_sphere_distribution(n, dmin, Ls, maxiter=1e4, allow_wall=True):
|
|
"""Get random points in a box with given dimensions and minimum separation.
|
|
|
|
Parameters:
|
|
|
|
- n: number of points
|
|
- dmin: minimum distance
|
|
- Ls: dimensions of box, shape (3,) array
|
|
- maxiter: maximum number of iterations.
|
|
- allow_wall: whether to allow points on wall;
|
|
(if False: points need to keep distance dmin/2 from the walls.)
|
|
|
|
Return:
|
|
|
|
- ps: array (n, 3) of point positions,
|
|
with 0 <= ps[:, i] < Ls[i]
|
|
- n_iter: number of iterations
|
|
- dratio: average nearest-neighbor distance, divided by dmin.
|
|
|
|
Note: with a fill density (sphere volume divided by box volume) above about
|
|
0.53, it takes very long. (Random close-packed spheres have a fill density
|
|
of 0.64).
|
|
|
|
Author: Han-Kwang Nienhuys (2020)
|
|
Copying: BSD, GPL, LGPL, CC-BY, CC-BY-SA
|
|
See Stackoverflow: https://stackoverflow.com/a/62895898/6228891
|
|
"""
|
|
Ls = np.array(Ls).reshape(3)
|
|
if not allow_wall:
|
|
Ls -= dmin
|
|
|
|
# filling factor; 0.64 is for random close-packed spheres
|
|
# This is an estimate because close packing is complicated near the walls.
|
|
# It doesn't work well for small L/dmin ratios.
|
|
sphere_vol = np.pi/6*dmin**3
|
|
box_vol = np.prod(Ls + 0.5*dmin)
|
|
fill_dens = n*sphere_vol/box_vol
|
|
if fill_dens > 0.64:
|
|
msg = f'Too many to fit in the volume, density {fill_dens:.3g}>0.64'
|
|
raise ValueError(msg)
|
|
|
|
# initial try
|
|
ps = np.random.uniform(size=(n, 3)) * Ls
|
|
|
|
# distance-squared matrix (diagonal is self-distance, don't count)
|
|
dsq = ((ps - ps.reshape(n, 1, 3))**2).sum(axis=2)
|
|
dsq[np.arange(n), np.arange(n)] = np.infty
|
|
|
|
for iter_no in range(int(maxiter)):
|
|
# find points that have too close neighbors
|
|
close_counts = np.sum(dsq < dmin**2, axis=1) # shape (n,)
|
|
n_close = np.count_nonzero(close_counts)
|
|
if n_close == 0:
|
|
break
|
|
|
|
# Move the one with the largest number of too-close neighbors
|
|
imv = np.argmax(close_counts)
|
|
|
|
# new positions
|
|
newp = np.random.uniform(size=3)*Ls
|
|
ps[imv]= newp
|
|
|
|
# update distance matrix
|
|
new_dsq_row = ((ps - newp.reshape(1, 3))**2).sum(axis=-1)
|
|
dsq[imv, :] = dsq[:, imv] = new_dsq_row
|
|
dsq[imv, imv] = np.inf
|
|
else:
|
|
raise RuntimeError(f'Failed after {iter_no+1} iterations.')
|
|
|
|
if not allow_wall:
|
|
ps += dmin/2
|
|
|
|
dratio = (np.sqrt(dsq.min(axis=1))/dmin).mean()
|
|
return ps, iter_no+1, dratio
|
|
|
|
def generateElsAroundPoints(n,LS,dmin):
|
|
"""
|
|
Parameters:
|
|
|
|
- n: number of points
|
|
- LS: list of position of all atoms
|
|
- dmin: minimum intra block distance
|
|
- shift: inter block distance
|
|
|
|
Return:
|
|
|
|
- r: array (n, 3) of point positions,
|
|
|
|
"""
|
|
|
|
xs = None
|
|
for Ls in LS:
|
|
|
|
# Get list of random points around Ls
|
|
distrib,a,b = get_sphere_distribution(n,dmin,Ls)
|
|
|
|
if xs is None:
|
|
xs = distrib[:,0]
|
|
ys = distrib[:,1]
|
|
zs = distrib[:,2]
|
|
else:
|
|
xs = np.concatenate((xs,distrib[:,0]))
|
|
ys = np.concatenate((ys,distrib[:,1]))
|
|
zs = np.concatenate((zs,distrib[:,2]))
|
|
|
|
return((np.array((xs,ys,zs))).T)
|
|
|
|
def getCoefList(Nord,Natom):
|
|
assert(Nord < 11)
|
|
dict = {
|
|
0 : lambda x,y:x-y-2,
|
|
1 : lambda x,y:x-y,
|
|
2 : lambda x,y:x-y,
|
|
3 : lambda x,y:x-y,
|
|
4 : lambda x,y:x-y,
|
|
5 : lambda x,y:x-y,
|
|
6 : lambda x,y:x-y,
|
|
7 : lambda x,y:x-y,
|
|
8 : lambda x,y:x-y,
|
|
9 : lambda x,y:x-y,
|
|
10 : lambda x,y:x-y,
|
|
11 : lambda x,y:x-y,
|
|
}
|
|
count = 0
|
|
for p in range(2,Nord+1):
|
|
for k in range(p-1,-1,-1):
|
|
lmax = dict[k](p,k)
|
|
for l in range(lmax,-1,-1):
|
|
if (p-k-l) & 1 is 0:
|
|
count += 1
|
|
coeflista = np.random.rand(Nord+1,Natom)
|
|
coeflistb = np.random.rand(Nord+1)
|
|
coeflistc = np.random.rand(count,Natom)
|
|
return (coeflista.reshape((Nord+1)*Natom),coeflistb,coeflistc.reshape(count*Natom))
|
|
#return (coeflista,coeflistb,coeflistc)
|
|
|
|
def get_sphere_distribution(n, dmin, Ls, maxiter=1e4, allow_wall=True):
|
|
"""Get random points in a box with given dimensions and minimum separation.
|
|
|
|
Parameters:
|
|
|
|
- n: number of points
|
|
- dmin: minimum distance
|
|
- Ls: dimensions of box, shape (3,) array
|
|
- maxiter: maximum number of iterations.
|
|
- allow_wall: whether to allow points on wall;
|
|
(if False: points need to keep distance dmin/2 from the walls.)
|
|
|
|
Return:
|
|
|
|
- ps: array (n, 3) of point positions,
|
|
with 0 <= ps[:, i] < Ls[i]
|
|
- n_iter: number of iterations
|
|
- dratio: average nearest-neighbor distance, divided by dmin.
|
|
|
|
Note: with a fill density (sphere volume divided by box volume) above about
|
|
0.53, it takes very long. (Random close-packed spheres have a fill density
|
|
of 0.64).
|
|
|
|
Author: Han-Kwang Nienhuys (2020)
|
|
Copying: BSD, GPL, LGPL, CC-BY, CC-BY-SA
|
|
See Stackoverflow: https://stackoverflow.com/a/62895898/6228891
|
|
"""
|
|
Ls = np.array(Ls).reshape(3)
|
|
if not allow_wall:
|
|
Ls -= dmin
|
|
|
|
# filling factor; 0.64 is for random close-packed spheres
|
|
# This is an estimate because close packing is complicated near the walls.
|
|
# It doesn't work well for small L/dmin ratios.
|
|
sphere_vol = np.pi/6*dmin**3
|
|
box_vol = np.prod(Ls + 0.5*dmin)
|
|
fill_dens = n*sphere_vol/box_vol
|
|
if fill_dens > 0.64:
|
|
msg = f'Too many to fit in the volume, density {fill_dens:.3g}>0.64'
|
|
raise ValueError(msg)
|
|
|
|
# initial try
|
|
ps = np.random.uniform(size=(n, 3)) * Ls
|
|
|
|
# distance-squared matrix (diagonal is self-distance, don't count)
|
|
dsq = ((ps - ps.reshape(n, 1, 3))**2).sum(axis=2)
|
|
dsq[np.arange(n), np.arange(n)] = np.infty
|
|
|
|
for iter_no in range(int(maxiter)):
|
|
# find points that have too close neighbors
|
|
close_counts = np.sum(dsq < dmin**2, axis=1) # shape (n,)
|
|
n_close = np.count_nonzero(close_counts)
|
|
if n_close == 0:
|
|
break
|
|
|
|
# Move the one with the largest number of too-close neighbors
|
|
imv = np.argmax(close_counts)
|
|
|
|
# new positions
|
|
newp = np.random.uniform(size=3)*Ls
|
|
ps[imv]= newp
|
|
|
|
# update distance matrix
|
|
new_dsq_row = ((ps - newp.reshape(1, 3))**2).sum(axis=-1)
|
|
dsq[imv, :] = dsq[:, imv] = new_dsq_row
|
|
dsq[imv, imv] = np.inf
|
|
else:
|
|
raise RuntimeError(f'Failed after {iter_no+1} iterations.')
|
|
|
|
if not allow_wall:
|
|
ps += dmin/2
|
|
|
|
dratio = (np.sqrt(dsq.min(axis=1))/dmin).mean()
|
|
return ps, iter_no+1, dratio
|
|
|
|
|
|
def scalingee(r,kappa=1.0):
|
|
return (numpy.ones_like(r) - numpy.exp(-kappa*r))/kappa
|
|
|
|
def scalingen(r,kappa=1.0):
|
|
return numpy.exp(-kappa*r)
|
|
|
|
if False:
|
|
Nord = 5
|
|
L1 = 2.0
|
|
n = 2 # number of points
|
|
dmin = 0.1 # min dist between points
|
|
Ls = np.array([L1,L1,L1]) # lengths of the box
|
|
shift = -10.0
|
|
kappa = 2.0
|
|
filename_atom = str(n) + "_geometry.txt"
|
|
filename_elec = str(n)
|
|
filename_coeffs = str(n) + "_jast_coeffs.txt"
|
|
(coeffsa, coeffsb, coeffsc) = getCoefList(Nord,n)
|
|
coeffsall = np.concatenate((coeffsa,coeffsb,coeffsc))
|
|
print(coeffsa.shape,coeffsb.shape,coeffsc.shape)
|
|
|
|
atomList,_,_ = get_sphere_distribution(n, dmin, Ls, maxiter=1e4, allow_wall=True)
|
|
#print(atomList)
|
|
|
|
L1 = 5.0
|
|
n = 5 # number of points
|
|
dmin = 0.1 # min dist between points
|
|
Ls = np.array([L1,L1,L1]) # lengths of the box
|
|
shift = -10.0
|
|
kappa = 2.0
|
|
filename_elec = filename_elec + "_" + str(n) + "_elec_coord.txt"
|
|
|
|
#rlist = generateBlockRandomPointsAtShftApart(n,L1,dmin,shift)
|
|
rlist = generateElsAroundPoints(n,atomList,dmin)
|
|
|
|
|
|
# Save file
|
|
np.savetxt(filename_elec,rlist)
|
|
np.savetxt(filename_atom,atomList)
|
|
np.savetxt(filename_coeffs,coeffsall)
|
|
|
|
fig = plt.figure()
|
|
ax = fig.add_subplot(111, projection='3d')
|
|
|
|
xs = rlist.T[0]
|
|
ys = rlist.T[1]
|
|
zs = rlist.T[2]
|
|
ax.scatter(xs, ys, zs, marker='o')
|
|
|
|
plt.show()
|
|
|
|
rijScaled = np.array([[(lambda xval, yval: np.linalg.norm(xval-yval))(xval,yval) for yval in rlist] for xval in rlist])
|
|
|
|
plt.imshow(rijScaled)
|
|
plt.colorbar()
|
|
plt.show()
|