def test_transform_gradient(self):
tai, atom_indices = self.make_atom_indices_python_topology()
tnorm = self.make_normal_python_topology()
coords = self.get_random_rbcoords()
aai = tai.to_atomistic(coords.copy())
anorm = tnorm.to_atomistic(coords.copy())
lj = LJ()
# atomistic_coords = np.random.uniform(-1, 1, 3*len(atom_indices))
# e, atomistic_grad = lj.getEnergyGradient(atomistic_coords)
e1, gai = lj.getEnergyGradient(aai.ravel())
e2, gnorm = lj.getEnergyGradient(anorm.ravel())
self.assertAlmostEqual(e1, e2)
assert_arrays_almost_equal(self, gai.reshape(-1,3)[atom_indices], gnorm.reshape(-1,3))
rb_gai = tai.transform_gradient(coords.copy(), gai)
rb_gnorm = tnorm.transform_gradient(coords.copy(), gnorm)
assert_arrays_almost_equal(self, rb_gai, rb_gnorm)
def test2():
import numpy as np
from pele.potentials import LJ
from pele.utils.frozen_atoms import FrozenPotWrapper
from pele.optimize import mylbfgs
natoms = 4
pot = LJ()
reference_coords = np.random.uniform(-1, 1, [3 * natoms])
print reference_coords
# freeze the first two atoms (6 degrees of freedom)
frozen_dof = range(6)
fpot = FrozenPotWrapper(pot, reference_coords, frozen_dof)
reduced_coords = fpot.coords_converter.get_reduced_coords(reference_coords)
print "the energy in the full representation:"
print pot.getEnergy(reference_coords)
print "is the same as the energy in the reduced representation:"
print fpot.getEnergy(reduced_coords)
ret = mylbfgs(reduced_coords, fpot)
print "after a minimization the energy is ", ret.energy, "and the rms gradient is", ret.rms
print "the coordinates of the frozen degrees of freedom are unchanged"
print "starting coords:", reference_coords
print "minimized coords:", fpot.coords_converter.get_full_coords(ret.coords)
class ATLJ(BasePotential):
"""
Lennard Jones + three body Axilrod-Teller term
V = sum_ij VLJ_ij + sum_ijk Z * (1 + 3*cos(t1)*cos(t2)*cos(t3)) / (rij * rjk * rik)**3 )
where t1, t2, t3 are the internal angles of the triangle ijk
Z > 0 stabilizes linear vs. triangular geometries
"""
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
def getEnergySlow(self, coords):
Elj = self.lj.getEnergy(coords)
natoms = coords.size / 3
X = np.reshape(coords, [natoms, 3])
Z = self.Z
energy = 0.
for i in range(natoms):
for j in range(i):
for k in range(j):
drij = X[i, :] - X[j, :]
drik = X[i, :] - X[k, :]
drjk = X[j, :] - X[k, :]
rij = np.linalg.norm(drij)
rik = np.linalg.norm(drik)
rjk = np.linalg.norm(drjk)
energy += (Z * (1. + 3. *
np.dot(drij, -drjk) *
np.dot(-drij, -drik) *
np.dot(drik, drjk) / (rij * rik * rjk) ** 2)
/ (rij * rik * rjk) ** 3 )
energy += Elj
return energy
def getEnergyFortran(self, coords):
garbage, e = ATfort.axt(coords, False, self.Z)
Elj = self.lj.getEnergy(coords)
return e + Elj
def getEnergyGradientFortran(self, coords):
grad, e = ATfort.axt(coords, True, self.Z)
elj, gradlj = self.lj.getEnergyGradient(coords)
return e + elj, grad + gradlj
def getEnergy(self, coords):
return self.getEnergyFortran(coords)
def getEnergyGradient(self, coords):
return self.getEnergyGradientFortran(coords)
def test_to_atomistic2(self):
x0 = np.array(list(range(self.nrigid * 6)), dtype=float)
x2 = x0.reshape([-1,3])
for p in x2[self.nrigid:,:]:
p /= np.linalg.norm(p)
atomistic = self.topology.to_atomistic(x0).flatten()
from pele.potentials import LJ
lj = LJ()
e, g = lj.getEnergyGradient(atomistic.reshape(-1))
grb = self.topology.transform_gradient(x0, g)
rbpot = RBPotentialWrapper(self.topology, lj)
print(rbpot.getEnergy(x0))
class TestLJ_CPP(unittest.TestCase):
def setUp(self):
self.natoms = 18
self.pot = _lj.LJ()
self.pot_comp = LJ()
x = np.random.uniform(-1,1, 3*self.natoms)
ret = mylbfgs(x, self.pot_comp, tol=10.)
self.x = ret.coords
def test(self):
eonly = self.pot.getEnergy(self.x)
e, g = self.pot.getEnergyGradient(self.x)
self.assertAlmostEqual(e, eonly, delta=1e-6)
et, gt = self.pot_comp.getEnergyGradient(self.x)
self.assertAlmostEqual(e, et, delta=1e-6)
self.assertLess(np.max(np.abs(g - gt)), 1e-6)
def test_numerical_gradient(self):
e, g = self.pot.getEnergyGradient(self.x)
gnum = self.pot.NumericalDerivative(self.x)
gnum_old = self.pot_comp.NumericalDerivative(self.x)
self.assertLess(np.max(np.abs(gnum_old - gnum)), 1e-6)
self.assertLess(np.max(np.abs(g - gnum)), 1e-6)
def test_numerical_hessian(self):
# e, g = self.pot.getEnergyGradient(self.x)
h = self.pot.NumericalHessian(self.x)
h_old = self.pot_comp.NumericalHessian(self.x)
self.assertLess(np.max(np.abs(h_old - h)), 1e-6)
def setUp(self):
self.natoms = 18
self.pot = _lj.LJ()
self.pot_comp = LJ()
x = np.random.uniform(-1,1, 3*self.natoms)
ret = mylbfgs(x, self.pot_comp, tol=10.)
self.x = ret.coords
def setUp(self):
self.natoms = 18
self.ilist = np.array([(i,j) for i in xrange(self.natoms) for j in xrange(i+1,self.natoms)]).reshape(-1)
assert self.ilist.size == self.natoms*(self.natoms-1)
# print self.ilist
self.pot = _lj.LJInteractionList(self.ilist)
self.pot_comp = LJ()
x = np.random.uniform(-1,1, 3*self.natoms)
ret = mylbfgs(x, self.pot_comp, tol=10.)
self.x = ret.coords
def main():
natoms = 4
pot = LJ()
reference_coords = np.random.uniform(-1, 1, [3 * natoms])
print reference_coords
# freeze the first two atoms (6 degrees of freedom)
frozen_dof = range(6)
fpot = FrozenPotentialWrapper(pot, reference_coords, frozen_dof)
reduced_coords = fpot.get_reduced_coords(reference_coords)
print "the energy in the full representation:"
print pot.getEnergy(reference_coords)
print "is the same as the energy in the reduced representation:"
print fpot.getEnergy(reduced_coords)
ret = mylbfgs(reduced_coords, fpot)
print "after a minimization the energy is ", ret.energy, "and the rms gradient is", ret.rms
print "the coordinates of the frozen degrees of freedom are unchanged"
print "starting coords:", reference_coords
print "minimized coords:", fpot.get_full_coords(ret.coords)
def test_to_atomistic2(self):
x0 = np.array(range(self.nrigid * 6), dtype=float);
x2 = x0.reshape([-1,3])
for p in x2[self.nrigid:,:]:
p /= np.linalg.norm(p);
print x0
print "range to atomistic"
print x0
atomistic = self.topology.to_atomistic(x0).flatten()
print atomistic
print atomistic.size
print atomistic[14]
print atomistic[23]
from pele.potentials import LJ
lj = LJ()
e, g = lj.getEnergyGradient(atomistic.reshape(-1))
grb = self.topology.transform_gradient(x0, g);
print "transformed gradient"
print grb
print "rbpotential"
rbpot = RBPotentialWrapper(self.topology, lj);
print rbpot.getEnergy(x0);
class TestLJ_CPP_Ilist(unittest.TestCase):
def setUp(self):
self.natoms = 18
self.ilist = np.array([(i,j) for i in xrange(self.natoms) for j in xrange(i+1,self.natoms)]).reshape(-1)
assert self.ilist.size == self.natoms*(self.natoms-1)
# print self.ilist
self.pot = _lj.LJInteractionList(self.ilist)
self.pot_comp = LJ()
x = np.random.uniform(-1,1, 3*self.natoms)
ret = mylbfgs(x, self.pot_comp, tol=10.)
self.x = ret.coords
def test(self):
eonly = self.pot.getEnergy(self.x)
e, g = self.pot.getEnergyGradient(self.x)
self.assertAlmostEqual(e, eonly, delta=1e-6)
et, gt = self.pot_comp.getEnergyGradient(self.x)
self.assertAlmostEqual(e, et, delta=1e-6)
self.assertLess(np.max(np.abs(g - gt)), 1e-6)
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
def get_potential(self):
return LJ(self.natoms)
def getEnergyGradient(self, coords):
atom_coords = self.aatopology.to_atomistic(coords)
e, atom_grad = LJ.getEnergyGradient(self, atom_coords.flatten())
grad = self.aatopology.transform_gradient(coords, atom_grad)
return e, grad
In the above we used three imports. We used the `numpy` library to construct a random
one dimensional array. We used the Lennard-Jones potential :class:`.LJ`, and we used the minimization
routine :func:`.lbfgs_py` which is just a wrapper for the class :class:`.LBFGS`.
The return value is an optimization result, which is just a container (:class:`.Result`) that stores
the final energy, final coordinates, the number of function calls, etc.
If we want to then save the minimized coordinates in an xyz file we can use the function :func:`.write_xyz`
::
from pele.utils.xyz import write_xyz
with open("out.xyz", "w") as fout:
title = "energy = " + str(result.energy)
write_xyz(fout, result.coords, title=title)
"""
import numpy as np
from pele.potentials import LJ
from pele.optimize import lbfgs_py
natoms = 5
x = np.random.uniform(-2, 2, natoms * 3)
pot = LJ()
result = lbfgs_py(x, pot)
print result
from pele.utils.xyz import write_xyz
with open("out.xyz", "w") as fout:
title = "energy = " + str(result.energy)
write_xyz(fout, result.coords, title=title)
class ATLJ(BasePotential):
"""
Lennard Jones + three body Axilrod-Teller term
V = sum_ij VLJ_ij + sum_ijk Z * (1 + 3*cos(t1)*cos(t2)*cos(t3)) / (rij * rjk * rik)**3 )
where t1, t2, t3 are the internal angles of the triangle ijk
Z > 0 stabilizes linear vs. triangular geometries
"""
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
# def getEnergyWeave(self, coords):
# """
# use weave inline
# """
# Elj = self.lj.getEnergy(coords)
#
# natoms = coords.size/3
# coords = np.reshape(coords, [natoms,3])
# energy=0.
# Z = self.Z
# #support_code
# code = """
# double drij[3];
# double drik[3];
# double drjk[3];
# energy = 0.;
# for (int i=0; i < natoms; ++i){
# for (int j=0; j<i; ++j){
# for (int k=0; k<j; ++k){
#
# double rij = 0.;
# double rik = 0.;
# double rjk = 0.;
#
# for (int d=0; d<3; ++d){
# drij[d] = coords(i,d) - coords(j,d);
# rij += drij[d]*drij[d];
# }
# for (int d=0; d<3; ++d){
# drjk[d] = coords(j,d) - coords(k,d);
# rjk += drjk[d]*drjk[d];
# }
# for (int d=0; d<3; ++d){
# drik[d] = coords(i,d) - coords(k,d);
# rik += drik[d]*drik[d];
# }
#
# rij = sqrt(rij);
# rjk = sqrt(rjk);
# rik = sqrt(rik);
#
# double ctijk = ( -(drij[0]*drjk[0] + drij[1]*drjk[1] + drij[2]*drjk[2]) / (rij * rjk) );
# double ctjki = ( (drjk[0]*drik[0] + drjk[1]*drik[1] + drjk[2]*drik[2]) / (rjk * rik) );
# double ctkij = ( (drik[0]*drij[0] + drik[1]*drij[1] + drik[2]*drij[2]) / (rik * rij) );
#
# double r3 = rij*rjk*rik;
# energy += Z*(1. + 3. * ctijk * ctjki * ctkij) / (r3*r3*r3);
# }
# }
# }
# return_val= energy;
# """
# energy = weave.inline(code, ["coords", "energy", "Z", "natoms"], type_converters=converters.blitz, verbose=2)
# #print "fast energy", Elj, energy
# energy += Elj
# return energy
def getEnergySlow(self, coords):
Elj = self.lj.getEnergy(coords)
natoms = coords.size/3
X = np.reshape(coords, [natoms,3])
Z = self.Z
energy = 0.
for i in range(natoms):
for j in range(i):
for k in range(j):
#print i, j, k
drij = X[i,:] - X[j,:]
drik = X[i,:] - X[k,:]
drjk = X[j,:] - X[k,:]
rij = np.linalg.norm( drij )
rik = np.linalg.norm( drik )
rjk = np.linalg.norm( drjk )
energy += Z * (1. + 3.*\
np.dot( drij, -drjk ) * \
np.dot(-drij, -drik ) * \
np.dot( drik, drjk ) / (rij*rik*rjk)**2) \
/ (rij*rik*rjk)**3
#print "slow energy", Elj, energy
energy += Elj
return energy
def getEnergyFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords)/3
garbage, e = ATfort.axt(coords, False, self.Z)
Elj = self.lj.getEnergy(coords)
return e + Elj
def getEnergyGradientFortran(self, coords):
#grad,potel = axt(x,gradt,zstar,[n])
natoms = len(coords)/3
grad, e = ATfort.axt(coords, True, self.Z)
elj, gradlj = self.lj.getEnergyGradient(coords)
return e + elj, grad + gradlj
def getEnergy(self, coords):
return self.getEnergyFortran(coords)
def getEnergyGradient(self, coords):
#return self.getEnergyGradientNumerical(coords)
return self.getEnergyGradientFortran(coords)
def get_potential(self):
return LJ()
# finalize the rigid body setup
for rb in rb_sites:
rb.finalize_setup()
# define a new rigid body system
rbsystem = rigidbody.RBSystem()
rbsystem.add_sites(rb_sites)
print len(rbsystem.sites), len(rbsystem.indices)
rbcoords = rbsystem.coords_adapter(np.zeros(len(rbsystem.sites)*6))
for site, com in zip(rbsystem.sites, rbcoords.posRigid):
com[:] = ref.coords[site.indices[0]] - site.atom_positions[0]
# for simplicity just use a lj potential here
pot = LJ(sigma=2.)
# get the flattened coordinate array
print pot.getEnergy(ref.coords.flatten())
rbpot = rigidbody.RBPotentialWrapper(rbsystem, pot)
print rbpot.getEnergy(rbcoords.coords)
e, g = rbpot.getEnergyGradient(rbcoords.coords)
g_n = rbpot.NumericalDerivative(rbcoords.coords, eps=1e-4)
cg = rbsystem.coords_adapter(g-g_n)
print cg.posRigid
print cg.rotRigid
ret = lbfgs_py(rbcoords.coords, rbpot)
print ret.energy
xyz.write_xyz(open("quenched.xyz", "w"), rbsystem.to_atomistic(ret.coords), atomtypes=ref.atomtypes)
def get_potential(self, eps, sig, boxl=None):
# return LJ(self.natoms, sig=sig, boxl = boxl)
return LJ(eps, sig, boxl=boxl)
import _pele
import numpy as np
import time
import sys
import _lj
import _lbfgs
from pele.optimize import mylbfgs
N = 100
natoms = [
10, 13, 20, 30, 31, 38, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140,
150
]
print("benchmarking lennard jones potential, %d atoms, %d calls", natoms, N)
pot_old = LJ()
pot = _lj.LJ()
clbfgs = _lbfgs.LBFGS(pot)
res = open("results.txt", "w")
for na in natoms:
t0 = time.time()
for i in range(N):
x = np.random.random(3 * na) - 0.5
ret = clbfgs.run(x)
t1 = time.time()
for i in range(N):
x = np.random.random(3 * na) - 0.5
import _pele
import numpy as np
import time
import sys
import _lj
import _lbfgs
from pele.optimize import mylbfgs
from . import _lj_cython
import _pythonpotential
N = int(sys.argv[2])
natoms = int(sys.argv[1])
print("benchmarking lennard jones potential, %d atoms, %d calls" % (natoms, N))
pot_old = LJ()
pot = _lj.LJ()
t0 = time.time()
for i in range(N):
x = 1. * (np.random.random(3 * natoms) - 0.5)
clbfgs = _lbfgs.LBFGS_CPP(pot, x, tol=1e-4)
ret = clbfgs.run()
t1 = time.time()
for i in range(N):
x = 1. * (np.random.random(3 * natoms) - 0.5)
ret = mylbfgs(x, pot_old, tol=1e-4)
t2 = time.time()
def getEnergy(self, coords):
atom_coords = self.aatopology.to_atomistic(coords)
return LJ.getEnergy(self, atom_coords.flatten())
def __init__(self, eps=1.0, sig=1.0, Z=1.):
""" simple lennard jones potential"""
self.sig = sig
self.eps = eps
self.Z = Z
self.lj = LJ(self.sig, self.eps)
def setUp(self):
from pele.potentials import LJ
self.x0 = np.zeros(6)
self.x0[0] = 2.
self.pot = LJ()
def __init__(self, aatopology):
self.aatopology = aatopology
LJ.__init__(self)