def __init__(self, boxdim=2, nr_particles=100, hard_phi=0.4,
nr_steps=1e6, epsilon=1, alpha=0.1, verbose=False):
# Settings.
np.random.seed(42)
# Input parameters.
self.boxdim = boxdim
self.nr_particles = nr_particles
self.hard_phi = hard_phi
self.nr_steps = nr_steps
self.epsilon = epsilon
self.alpha = alpha
self.verbose = verbose
# Derived quantities.
self.hard_radii = np.ones(self.nr_particles)
def volume_nball(radius, n):
return np.power(np.pi, n / 2) * np.power(radius, n) / gamma(n / 2 + 1)
self.box_length = np.power(np.sum(np.asarray([volume_nball(r, self.boxdim) for r in self.hard_radii])) / self.hard_phi, 1 / self.boxdim)
self.box_vector = np.ones(self.boxdim) * self.box_length
# HS-WCA potential.
self.potential = HS_WCA(use_periodic=True, use_cell_lists=True,
ndim=self.boxdim, eps=self.epsilon,
sca=self.alpha, radii=self.hard_radii,
boxvec=self.box_vector)
# Initial configuration by minimization.
self.nr_dof = self.boxdim * self.nr_particles
self.x = np.random.uniform(-0.5 * self.box_length, 0.5 * self.box_length, self.nr_dof)
optimizer = LBFGS_CPP(self.x, self.potential)
optimizer.run()
if not optimizer.get_result().success:
print ("warning: minimization has not converged")
self.x = optimizer.get_result().coords.copy()
# Potential and MC rules.
self.temperature = 1
self.mc = MC(self.potential, self.x, self.temperature, self.nr_steps)
self.step = RandomCoordsDisplacement(42, 1, single=True, nparticles=self.nr_particles, bdim=self.boxdim)
if self.verbose:
print ("initial MC stepsize")
print self.step.get_stepsize()
self.mc.set_takestep(self.step)
self.eq_steps = self.nr_steps / 2
self.mc.set_report_steps(self.eq_steps)
self.gr_quench = RecordPairDistHistogram(self.box_vector, 50, self.eq_steps, self.nr_particles, optimizer=optimizer)
self.gr = RecordPairDistHistogram(self.box_vector, 50, self.eq_steps, self.nr_particles)
self.mc.add_action(self.gr_quench)
self.mc.add_action(self.gr)
self.test = MetropolisTest(44)
self.mc.add_accept_test(self.test)
def quench_LBFGS(x0, pot, steps=2000, **kwargs):
""" \"Subroutine\" for quenching LBFGS, add subtract yada yada
to control how information gets returned, basically simply passing
pot, x0 with these default parameters should give identical results
between different pieces.
"""
lbfgs = LBFGS_CPP(x0, pot, steps=2000, **kwargs)
lbfgs.run(nsteps)
res = LBFGS_CPP.get_result()
return res
class MinimizeUniformHardsSpheres(object):
def __init__(self, nr_particles=42, hard_volume_fraction=0.5, epsilon=1, alpha=0.2):
np.random.seed(42)
self.nr_particles = nr_particles
self.hard_volume_fraction = hard_volume_fraction
self.epsilon = epsilon
self.alpha = alpha
self.hard_radii = np.random.normal(loc=1, scale=0.1, size=self.nr_particles)
self.box_length = np.power(np.sum(np.asarray([4 * np.pi * r**3 / 3 for r in self.hard_radii])) / self.hard_volume_fraction, 1/3)
self.nr_dof = 3 * self.nr_particles
self.x = np.random.uniform(-0.5 * self.box_length, 0.5 * self.box_length, self.nr_dof)
self.box_vector = np.ones(3) * self.box_length
self.rcut = 2 * (1 + alpha) * np.amax(self.hard_radii)
self.potential = HS_WCA(use_periodic=True, use_cell_lists=False, eps=self.epsilon, sca=self.alpha, radii=self.hard_radii, boxvec=self.box_vector, rcut=self.rcut)
self.optimizer = LBFGS_CPP(self.x, self.potential)
print "energy before:", self.potential.getEnergy(self.x)
self.optimizer.run()
print "minimization converged", self.optimizer.get_result().success
print "energy after:", self.potential.getEnergy(self.optimizer.get_result().coords)
def test_reset(self):
lbfgs1 = LBFGS_CPP(self.x0, self.pot)
lbfgs1.run()
res1 = lbfgs1.get_result()
x2 = self.x0.copy()
x2[1] = 2.
lbfgs2 = LBFGS_CPP(x2, self.pot)
H0 = lbfgs2.get_result()["H0"]
lbfgs2.run()
lbfgs2.reset(self.x0)
lbfgs2.set_H0(H0)
lbfgs2.run()
res2 = lbfgs2.get_result()
self.assertEqual(res1.rms, res2.rms)
self.assertEqual(res1.H0, res2.H0)
self.assertEqual(res1.nfev, res2.nfev)
self.assertEqual(res1.nsteps, res2.nsteps)
self.assertTrue(np.all(res1.coords == res2.coords))
def test_reset(self):
lbfgs1 = LBFGS_CPP(self.x0, self.pot)
lbfgs1.run()
res1 = lbfgs1.get_result()
x2 = self.x0.copy()
x2[1] = 2.
lbfgs2 = LBFGS_CPP(x2, self.pot)
H0 = lbfgs2.get_result()["H0"]
lbfgs2.run()
lbfgs2.reset(self.x0)
lbfgs2.set_H0(H0)
lbfgs2.run()
res2 = lbfgs2.get_result()
self.assertEqual(res1.rms, res2.rms)
self.assertEqual(res1.H0, res2.H0)
self.assertEqual(res1.nfev, res2.nfev)
self.assertEqual(res1.nsteps, res2.nsteps)
self.assertTrue(np.all(res1.coords == res2.coords))
class MinimizeUniformHardsSpheres(object):
def __init__(self,
nr_particles=42,
hard_volume_fraction=0.5,
epsilon=1,
alpha=0.2,
use_hswca=False):
np.random.seed(42)
self.nr_particles = nr_particles
self.hard_volume_fraction = hard_volume_fraction
self.epsilon = epsilon
self.alpha = alpha
self.use_hswca = use_hswca
self.hard_radii = np.random.normal(loc=1,
scale=0.1,
size=self.nr_particles)
self.box_length = np.power(
np.sum(np.asarray([4 * np.pi * r**3 / 3
for r in self.hard_radii])) /
self.hard_volume_fraction, 1 / 3)
self.nr_dof = 3 * self.nr_particles
self.x = np.random.uniform(-0.5 * self.box_length,
0.5 * self.box_length, self.nr_dof)
self.box_vector = np.ones(3) * self.box_length
self.rcut = 2 * (1 + alpha) * np.amax(self.hard_radii)
if self.use_hswca:
self.potential = HS_WCA(use_periodic=True,
use_cell_lists=False,
eps=self.epsilon,
sca=self.alpha,
radii=self.hard_radii,
boxvec=self.box_vector,
rcut=self.rcut)
else:
self.potential = InversePowerStillinger(8, boxvec=self.box_vector)
self.optimizer = LBFGS_CPP(self.x, self.potential)
print "energy before:", self.potential.getEnergy(self.x)
self.optimizer.run()
print "minimization converged", self.optimizer.get_result().success
print "energy after:", self.potential.getEnergy(
self.optimizer.get_result().coords)
class Config2D(object):
def __init__(self, nparticles_x, amplitude):
self.ndim = 2
self.LX = nparticles_x
self.LY = self.LX
self.nparticles_x = nparticles_x
self.N = self.nparticles_x ** self.ndim
self.dof = self.ndim * self.N
self.amplitude = amplitude
self.x = np.zeros(self.dof)
for particle in xrange(self.N):
pid = self.ndim * particle
self.x[pid] = particle % self.LX
self.x[pid + 1] = int(particle / self.LX)
self.x_initial = np.asarray([xi + np.random.uniform(- self.amplitude, self.amplitude) for xi in self.x])
self.x_initial = np.reshape(self.x_initial, (self.N,2))
self.x_initial[:,0] -= np.mean(self.x_initial[:,0])
self.x_initial[:,1] -= np.mean(self.x_initial[:,1])
self.x_initial = self.x_initial.flatten()
#self.radius = 0.3
#self.sca = 1.5
self.radius = 0.25
self.sca = 1.8
self.radii = np.ones(self.N) * self.radius
self.eps = 1.0
self.boxvec = np.array([self.LX, self.LY])
self.potential = HS_WCA(use_periodic=use_periodic, eps=self.eps,
sca=self.sca, radii=self.radii.copy(), ndim=self.ndim, boxvec=self.boxvec.copy())
self.potential_ = HS_WCA(use_periodic=use_periodic, eps=self.eps,
sca=self.sca, radii=self.radii.copy(), ndim=self.ndim, boxvec=self.boxvec.copy())
self.rcut = 2 * (1 + self.sca) * self.radius
self.ncellx_scale = 1
self.potential_cells = HS_WCA(use_periodic=use_periodic,
use_cell_lists=True, eps=self.eps,
sca=self.sca, radii=self.radii.copy(),
boxvec=self.boxvec.copy(),
rcut=self.rcut, ndim=self.ndim,
ncellx_scale=self.ncellx_scale)
self.potential_cells_ = HS_WCA(use_periodic=use_periodic,
use_cell_lists=True, eps=self.eps,
sca=self.sca, radii=self.radii.copy(),
boxvec=self.boxvec.copy(),
rcut=self.rcut, ndim=self.ndim,
ncellx_scale=self.ncellx_scale)
self.tol = 1e-7
self.maxstep = np.amax(self.radii)
self.nstepsmax = int(1e6)
assert(self.boxvec[0]==self.boxvec[1])
print "x_initial energy:", self.potential.getEnergy(self.x_initial)
print "x_initial cells energy:", self.potential_cells.getEnergy(self.x_initial)
assert(self.potential.getEnergy(self.x_initial) == self.potential_.getEnergy(self.x_initial))
assert(self.potential_cells.getEnergy(self.x_initial) == self.potential_cells_.getEnergy(self.x_initial))
#assert abs(self.potential.getEnergy(self.x_initial) - self.potential_cells.getEnergy(self.x_initial)) < 1e-10
assert np.allclose(self.potential.getEnergy(self.x_initial), self.potential_cells.getEnergy(self.x_initial), rtol=1e-10)
print self.boxvec
#plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
def optimize(self, nr_samples = 1):
self.optimizer = ModifiedFireCPP(self.x_initial.copy(), self.potential,
dtmax=1, maxstep=self.maxstep,
tol=self.tol, nsteps=1e8, verbosity=-1, iprint=-1)
self.optimizer_ = LBFGS_CPP(self.x_initial.copy(), self.potential_)
self.optimizer_cells = ModifiedFireCPP(self.x_initial.copy(), self.potential_cells,
dtmax=1, maxstep=self.maxstep,
tol=self.tol, nsteps=1e8, verbosity=-1, iprint=-1)
self.optimizer_cells_ = LBFGS_CPP(self.x_initial.copy(), self.potential_cells_)
print "initial E, x:", self.potential.getEnergy(self.x_initial.copy())
print "initial E, x_:", self.potential_cells.getEnergy(self.x_initial.copy())
t0 = time.time()
print "self.optimizer.run(self.nstepsmax)", self.nstepsmax
self.optimizer.run(self.nstepsmax)
self.res_x_final = self.optimizer.get_result()
t1 = time.time()
self.optimizer_cells.run(self.nstepsmax)
self.res_x_final_cells = self.optimizer_cells.get_result()
t2 = time.time()
self.x_final = self.res_x_final.coords
self.x_final_cells = self.res_x_final_cells.coords
print "fire final E, x:", self.optimizer.get_result().energy
print "fire final E, x_cells:", self.optimizer_cells.get_result().energy
print "fire final E, plain: ", self.potential.getEnergy(self.x_final)
print "fire final E, cell: ", self.potential_cells.getEnergy(self.x_final_cells)
print "fire number of particles:", self.N
print "fire time no cell lists:", t1 - t0, "sec"
print "fire time cell lists:", t2 - t1, "sec"
print "fire ratio:", (t1 - t0) / (t2 - t1)
if not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final.rms:", self.res_x_final.rms
print "res_x_final.nfev:", self.res_x_final.nfev
print "res_x_final_cells.rms:", self.res_x_final_cells.rms
print "res_x_final_cells.nfev:", self.res_x_final_cells.nfev
print "self.res_x_final.success", self.res_x_final.success
print "self.res_x_final_cells.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells, self.radii, self.boxvec, sca=self.sca)
self.optimizer_.run(self.nstepsmax)
self.res_x_final_ = self.optimizer_.get_result()
t3 = time.time()
self.optimizer_cells_.run(self.nstepsmax)
self.res_x_final_cells_ = self.optimizer_cells_.get_result()
t4 = time.time()
self.x_final_ = self.res_x_final_.coords
self.x_final_cells_ = self.res_x_final_cells_.coords
print "lbfgs final E, x:", self.optimizer_.get_result().energy
print "lbfgs final E, x_cells:", self.optimizer_cells_.get_result().energy
print "lbfgs final E, plain: ", self.potential_.getEnergy(self.x_final_)
print "lbfgs final E, cell: ", self.potential_cells_.getEnergy(self.x_final_cells_)
print "lbfgs number of particles:", self.N
print "lbfgs time no cell lists:", t3 - t2, "sec"
print "lbfgs time cell lists:", t4 - t3, "sec"
print "lbfgs ratio:", (t3 - t2) / (t4 - t3)
if not self.res_x_final_.success or not self.res_x_final_cells_.success or not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final_.rms:", self.res_x_final_.rms
print "res_x_final_.nfev:", self.res_x_final_.nfev
print "res_x_final_cells_.rms:", self.res_x_final_cells_.rms
print "res_x_final_cells_.nfev:", self.res_x_final_cells_.nfev
print "self.res_x_final_.success", self.res_x_final.success
print "self.res_x_final_cells_.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells_, self.radii, self.boxvec, sca=self.sca)
assert(self.res_x_final.success)
assert(self.res_x_final_cells.success)
assert(self.res_x_final_.success)
assert(self.res_x_final_cells_.success)
for (xci, xi) in zip(self.x_final_cells, self.x_final):
passed = (np.abs(xci - xi) < 1e-10)
if (passed is False):
print "xci", xci
print "xi", xi
assert(passed)
print "energy no cell lists:", self.res_x_final.energy
print "energy cell lists:", self.res_x_final_cells.energy
self.t_ratio = (t1 - t0) / (t2 - t1)
self.t_ratio_lbfgs = (t3 - t2) / (t4 - t3)
class Config2DFrozenBoundary(object):
def __init__(self, nparticles_x, amplitude):
self.ndim = 2
self.LX = nparticles_x
self.LY = self.LX
self.nparticles_x = nparticles_x
self.N = self.nparticles_x ** self.ndim
self.amplitude = amplitude
self.dof = self.ndim * self.N
self.x = np.zeros(self.dof)
self.frozen_atoms = []
for particle in xrange(self.N):
pid = self.ndim * particle
xcoor = particle % self.LX
ycoor = int(particle / self.LX)
self.x[pid] = xcoor
self.x[pid + 1] = ycoor
if xcoor == 0 or xcoor == self.LX - 1 or ycoor == 0 or ycoor == self.LY - 1:
self.frozen_atoms.append(particle)
self.x_initial = copy.copy(self.x)
for particle in xrange(self.N):
if particle not in self.frozen_atoms:
pid = self.ndim * particle
self.x_initial[pid] += np.random.uniform(- self.amplitude, self.amplitude)
self.x_initial[pid + 1] += np.random.uniform(- self.amplitude, self.amplitude)
self.x_initial = np.reshape(self.x_initial, (self.N,2))
self.x_initial[:,0] -= np.mean(self.x_initial[:,0])
self.x_initial[:,1] -= np.mean(self.x_initial[:,1])
self.x_initial = self.x_initial.flatten()
min_x = np.amin(self.x_initial)
if min_x < 0:
self.x_initial -= min_x
#self.radius = 0.3
#self.sca = 1.5
self.radius = 0.25
self.sca = 1.8
self.radii = np.ones(self.N) * self.radius
self.eps = 1.0
max_edge = np.amax([np.amax(self.x_initial), np.abs(np.amin(self.x_initial))]) + 2 * self.amplitude + (1 + self.sca) * self.radius
self.boxvec = np.array([max_edge, max_edge])
self.frozen_atoms1 = np.array(self.frozen_atoms)
self.frozen_atoms2 = np.array(self.frozen_atoms)
print "self.frozen_atoms1", self.frozen_atoms1
self.potential = HS_WCA(use_frozen=True, use_periodic=use_periodic_frozen,
reference_coords=self.x_initial,
frozen_atoms=self.frozen_atoms1,
eps=self.eps, sca=self.sca, radii=self.radii,
ndim=self.ndim, boxvec=self.boxvec)
self.rcut = 2 * (1 + self.sca) * self.radius
self.ncellx_scale = 1.0
self.potential_cells = HS_WCA(use_frozen=True,
use_periodic=use_periodic_frozen, use_cell_lists=True,
eps=self.eps, sca=self.sca,
radii=self.radii, boxvec=self.boxvec,
reference_coords=self.x_initial,
rcut=self.rcut, ndim=self.ndim,
ncellx_scale=self.ncellx_scale,
frozen_atoms=self.frozen_atoms2)
self.tol = 1e-7
self.maxstep = np.amax(self.radii)
self.nstepsmax = int(1e6)
assert(self.boxvec[0]==self.boxvec[1])
self.x_initial_red = reduce_coordinates(self.x_initial,self.frozen_atoms,self.ndim)
print "x_initial energy:", self.potential.getEnergy(self.x_initial_red)
print "x_initial cells energy:", self.potential_cells.getEnergy(self.x_initial_red)
#assert abs(self.potential.getEnergy(self.x_initial_red) - self.potential_cells.getEnergy(self.x_initial_red)) < 1e-10
assert np.allclose(self.potential.getEnergy(self.x_initial_red), self.potential_cells.getEnergy(self.x_initial_red), rtol=1e-10)
print self.boxvec
def optimize(self, nr_samples=1):
self.x_initial_red = reduce_coordinates(self.x_initial,self.frozen_atoms,self.ndim)
self.optimizer = ModifiedFireCPP(self.x_initial_red.copy(), self.potential, tol = self.tol, maxstep = self.maxstep)
self.optimizer_ = LBFGS_CPP(self.x_initial_red.copy(), self.potential)
self.optimizer_cells = ModifiedFireCPP(self.x_initial_red.copy(), self.potential_cells, tol = self.tol, maxstep = self.maxstep)
self.optimizer_cells_ = LBFGS_CPP(self.x_initial_red.copy(), self.potential_cells)
t0 = time.time()
print "self.optimizer.run(self.nstepsmax)", self.nstepsmax
self.optimizer.run(self.nstepsmax)
self.res_x_final = self.optimizer.get_result()
t1 = time.time()
self.optimizer_cells.run(self.nstepsmax)
self.res_x_final_cells = self.optimizer_cells.get_result()
t2 = time.time()
self.x_final = self.res_x_final.coords
self.x_final_cells = self.res_x_final_cells.coords
print "fire final E, x:", self.optimizer.get_result().energy
print "fire final E, x_cells:", self.optimizer_cells.get_result().energy
print "fire final E, plain: ", self.potential.getEnergy(self.x_final)
print "fire final E, cell: ", self.potential_cells.getEnergy(self.x_final_cells)
print "fire number of particles:", self.N
print "fire time no cell lists:", t1 - t0, "sec"
print "fire time cell lists:", t2 - t1, "sec"
print "fire ratio:", (t1 - t0) / (t2 - t1)
if not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final.rms:", self.res_x_final.rms
print "res_x_final.nfev:", self.res_x_final.nfev
print "res_x_final_cells.rms:", self.res_x_final_cells.rms
print "res_x_final_cells.nfev:", self.res_x_final_cells.nfev
print "self.res_x_final.success", self.res_x_final.success
print "self.res_x_final_cells.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells, self.radii, self.boxvec, sca=self.sca)
self.optimizer_.run(self.nstepsmax)
self.res_x_final_ = self.optimizer_.get_result()
t3 = time.time()
self.optimizer_cells_.run(self.nstepsmax)
self.res_x_final_cells_ = self.optimizer_cells_.get_result()
t4 = time.time()
self.x_final_ = self.res_x_final_.coords
self.x_final_cells_ = self.res_x_final_cells_.coords
print "lbfgs final E, x:", self.optimizer_.get_result().energy
print "lbfgs final E, x_cells:", self.optimizer_cells_.get_result().energy
print "lbfgs final E, plain: ", self.potential.getEnergy(self.x_final_)
print "lbfgs final E, cell: ", self.potential_cells.getEnergy(self.x_final_cells_)
print "lbfgs number of particles:", self.N
print "lbfgs time no cell lists:", t3 - t2, "sec"
print "lbfgs time cell lists:", t4 - t3, "sec"
print "lbfgs ratio:", (t3 - t2) / (t4 - t3)
if not self.res_x_final_.success or not self.res_x_final_cells_.success or not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final_.rms:", self.res_x_final_.rms
print "res_x_final_.nfev:", self.res_x_final_.nfev
print "res_x_final_cells_.rms:", self.res_x_final_cells_.rms
print "res_x_final_cells_.nfev:", self.res_x_final_cells_.nfev
print "self.res_x_final_.success", self.res_x_final.success
print "self.res_x_final_cells_.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells_, self.radii, self.boxvec, sca=self.sca)
assert(self.res_x_final.success)
assert(self.res_x_final_cells.success)
assert(self.res_x_final_.success)
assert(self.res_x_final_cells_.success)
for (xci, xi) in zip(self.x_final_cells, self.x_final):
passed = (np.abs(xci - xi) < 1e-10)
if (passed is False):
print "xci", xci
print "xi", xi
assert(passed)
print "energy no cell lists:", self.res_x_final.energy
print "energy cell lists:", self.res_x_final_cells.energy
self.t_ratio = (t1 - t0) / (t2 - t1)
self.t_ratio_lbfgs = (t3 - t2) / (t4 - t3)
class Config2D(object):
def __init__(self, nparticles_x, amplitude):
self.ndim = 2
self.LX = nparticles_x
self.LY = self.LX
self.nparticles_x = nparticles_x
self.N = self.nparticles_x**self.ndim
self.dof = self.ndim * self.N
self.amplitude = amplitude
self.x = np.zeros(self.dof)
for particle in xrange(self.N):
pid = self.ndim * particle
self.x[pid] = particle % self.LX
self.x[pid + 1] = int(particle / self.LX)
self.x_initial = np.asarray([
xi + np.random.uniform(-self.amplitude, self.amplitude)
for xi in self.x
])
self.x_initial = np.reshape(self.x_initial, (self.N, 2))
self.x_initial[:, 0] -= np.mean(self.x_initial[:, 0])
self.x_initial[:, 1] -= np.mean(self.x_initial[:, 1])
self.x_initial = self.x_initial.flatten()
#self.radius = 0.3
#self.sca = 1.5
self.radius = 0.25
self.sca = 1.8
self.radii = np.ones(self.N) * self.radius
self.eps = 1.0
self.boxvec = np.array([self.LX, self.LY])
self.potential = HS_WCA(use_periodic=use_periodic,
eps=self.eps,
sca=self.sca,
radii=self.radii.copy(),
ndim=self.ndim,
boxvec=self.boxvec.copy())
self.potential_ = HS_WCA(use_periodic=use_periodic,
eps=self.eps,
sca=self.sca,
radii=self.radii.copy(),
ndim=self.ndim,
boxvec=self.boxvec.copy())
self.rcut = 2 * (1 + self.sca) * self.radius
self.ncellx_scale = 1
self.potential_cells = HS_WCA(use_periodic=use_periodic,
use_cell_lists=True,
eps=self.eps,
sca=self.sca,
radii=self.radii.copy(),
boxvec=self.boxvec.copy(),
rcut=self.rcut,
ndim=self.ndim,
ncellx_scale=self.ncellx_scale)
self.potential_cells_ = HS_WCA(use_periodic=use_periodic,
use_cell_lists=True,
eps=self.eps,
sca=self.sca,
radii=self.radii.copy(),
boxvec=self.boxvec.copy(),
rcut=self.rcut,
ndim=self.ndim,
ncellx_scale=self.ncellx_scale)
self.tol = 1e-7
self.maxstep = np.amax(self.radii)
self.nstepsmax = int(1e6)
assert (self.boxvec[0] == self.boxvec[1])
print "x_initial energy:", self.potential.getEnergy(self.x_initial)
print "x_initial cells energy:", self.potential_cells.getEnergy(
self.x_initial)
assert (self.potential.getEnergy(
self.x_initial) == self.potential_.getEnergy(self.x_initial))
assert (self.potential_cells.getEnergy(
self.x_initial) == self.potential_cells_.getEnergy(self.x_initial))
#assert abs(self.potential.getEnergy(self.x_initial) - self.potential_cells.getEnergy(self.x_initial)) < 1e-10
assert np.allclose(self.potential.getEnergy(self.x_initial),
self.potential_cells.getEnergy(self.x_initial),
rtol=1e-10)
print self.boxvec
#plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
def optimize(self, nr_samples=1):
self.optimizer = ModifiedFireCPP(self.x_initial.copy(),
self.potential,
dtmax=1,
maxstep=self.maxstep,
tol=self.tol,
nsteps=1e8,
verbosity=-1,
iprint=-1)
self.optimizer_ = LBFGS_CPP(self.x_initial.copy(), self.potential_)
self.optimizer_cells = ModifiedFireCPP(self.x_initial.copy(),
self.potential_cells,
dtmax=1,
maxstep=self.maxstep,
tol=self.tol,
nsteps=1e8,
verbosity=-1,
iprint=-1)
self.optimizer_cells_ = LBFGS_CPP(self.x_initial.copy(),
self.potential_cells_)
print "initial E, x:", self.potential.getEnergy(self.x_initial.copy())
print "initial E, x_:", self.potential_cells.getEnergy(
self.x_initial.copy())
t0 = time.time()
print "self.optimizer.run(self.nstepsmax)", self.nstepsmax
self.optimizer.run(self.nstepsmax)
self.res_x_final = self.optimizer.get_result()
t1 = time.time()
self.optimizer_cells.run(self.nstepsmax)
self.res_x_final_cells = self.optimizer_cells.get_result()
t2 = time.time()
self.x_final = self.res_x_final.coords
self.x_final_cells = self.res_x_final_cells.coords
print "fire final E, x:", self.optimizer.get_result().energy
print "fire final E, x_cells:", self.optimizer_cells.get_result(
).energy
print "fire final E, plain: ", self.potential.getEnergy(self.x_final)
print "fire final E, cell: ", self.potential_cells.getEnergy(
self.x_final_cells)
print "fire number of particles:", self.N
print "fire time no cell lists:", t1 - t0, "sec"
print "fire time cell lists:", t2 - t1, "sec"
print "fire ratio:", (t1 - t0) / (t2 - t1)
if not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final.rms:", self.res_x_final.rms
print "res_x_final.nfev:", self.res_x_final.nfev
print "res_x_final_cells.rms:", self.res_x_final_cells.rms
print "res_x_final_cells.nfev:", self.res_x_final_cells.nfev
print "self.res_x_final.success", self.res_x_final.success
print "self.res_x_final_cells.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells,
self.radii,
self.boxvec,
sca=self.sca)
self.optimizer_.run(self.nstepsmax)
self.res_x_final_ = self.optimizer_.get_result()
t3 = time.time()
self.optimizer_cells_.run(self.nstepsmax)
self.res_x_final_cells_ = self.optimizer_cells_.get_result()
t4 = time.time()
self.x_final_ = self.res_x_final_.coords
self.x_final_cells_ = self.res_x_final_cells_.coords
print "lbfgs final E, x:", self.optimizer_.get_result().energy
print "lbfgs final E, x_cells:", self.optimizer_cells_.get_result(
).energy
print "lbfgs final E, plain: ", self.potential_.getEnergy(
self.x_final_)
print "lbfgs final E, cell: ", self.potential_cells_.getEnergy(
self.x_final_cells_)
print "lbfgs number of particles:", self.N
print "lbfgs time no cell lists:", t3 - t2, "sec"
print "lbfgs time cell lists:", t4 - t3, "sec"
print "lbfgs ratio:", (t3 - t2) / (t4 - t3)
if not self.res_x_final_.success or not self.res_x_final_cells_.success or not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final_.rms:", self.res_x_final_.rms
print "res_x_final_.nfev:", self.res_x_final_.nfev
print "res_x_final_cells_.rms:", self.res_x_final_cells_.rms
print "res_x_final_cells_.nfev:", self.res_x_final_cells_.nfev
print "self.res_x_final_.success", self.res_x_final.success
print "self.res_x_final_cells_.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells_,
self.radii,
self.boxvec,
sca=self.sca)
assert (self.res_x_final.success)
assert (self.res_x_final_cells.success)
assert (self.res_x_final_.success)
assert (self.res_x_final_cells_.success)
for (xci, xi) in zip(self.x_final_cells, self.x_final):
passed = (np.abs(xci - xi) < 1e-10)
if (passed is False):
print "xci", xci
print "xi", xi
assert (passed)
print "energy no cell lists:", self.res_x_final.energy
print "energy cell lists:", self.res_x_final_cells.energy
self.t_ratio = (t1 - t0) / (t2 - t1)
self.t_ratio_lbfgs = (t3 - t2) / (t4 - t3)
class Config2DFrozenBoundary(object):
def __init__(self, nparticles_x, amplitude):
self.ndim = 2
self.LX = nparticles_x
self.LY = self.LX
self.nparticles_x = nparticles_x
self.N = self.nparticles_x**self.ndim
self.amplitude = amplitude
self.dof = self.ndim * self.N
self.x = np.zeros(self.dof)
self.frozen_atoms = []
for particle in xrange(self.N):
pid = self.ndim * particle
xcoor = particle % self.LX
ycoor = int(particle / self.LX)
self.x[pid] = xcoor
self.x[pid + 1] = ycoor
if xcoor == 0 or xcoor == self.LX - 1 or ycoor == 0 or ycoor == self.LY - 1:
self.frozen_atoms.append(particle)
self.x_initial = copy.copy(self.x)
for particle in xrange(self.N):
if particle not in self.frozen_atoms:
pid = self.ndim * particle
self.x_initial[pid] += np.random.uniform(
-self.amplitude, self.amplitude)
self.x_initial[pid + 1] += np.random.uniform(
-self.amplitude, self.amplitude)
self.x_initial = np.reshape(self.x_initial, (self.N, 2))
self.x_initial[:, 0] -= np.mean(self.x_initial[:, 0])
self.x_initial[:, 1] -= np.mean(self.x_initial[:, 1])
self.x_initial = self.x_initial.flatten()
min_x = np.amin(self.x_initial)
if min_x < 0:
self.x_initial -= min_x
#self.radius = 0.3
#self.sca = 1.5
self.radius = 0.25
self.sca = 1.8
self.radii = np.ones(self.N) * self.radius
self.eps = 1.0
max_edge = np.amax([
np.amax(self.x_initial),
np.abs(np.amin(self.x_initial))
]) + 2 * self.amplitude + (1 + self.sca) * self.radius
self.boxvec = np.array([max_edge, max_edge])
self.frozen_atoms1 = np.array(self.frozen_atoms)
self.frozen_atoms2 = np.array(self.frozen_atoms)
print "self.frozen_atoms1", self.frozen_atoms1
self.potential = HS_WCA(use_frozen=True,
use_periodic=use_periodic_frozen,
reference_coords=self.x_initial,
frozen_atoms=self.frozen_atoms1,
eps=self.eps,
sca=self.sca,
radii=self.radii,
ndim=self.ndim,
boxvec=self.boxvec)
self.rcut = 2 * (1 + self.sca) * self.radius
self.ncellx_scale = 1.0
self.potential_cells = HS_WCA(use_frozen=True,
use_periodic=use_periodic_frozen,
use_cell_lists=True,
eps=self.eps,
sca=self.sca,
radii=self.radii,
boxvec=self.boxvec,
reference_coords=self.x_initial,
rcut=self.rcut,
ndim=self.ndim,
ncellx_scale=self.ncellx_scale,
frozen_atoms=self.frozen_atoms2)
self.tol = 1e-7
self.maxstep = np.amax(self.radii)
self.nstepsmax = int(1e6)
assert (self.boxvec[0] == self.boxvec[1])
self.x_initial_red = reduce_coordinates(self.x_initial,
self.frozen_atoms, self.ndim)
print "x_initial energy:", self.potential.getEnergy(self.x_initial_red)
print "x_initial cells energy:", self.potential_cells.getEnergy(
self.x_initial_red)
#assert abs(self.potential.getEnergy(self.x_initial_red) - self.potential_cells.getEnergy(self.x_initial_red)) < 1e-10
assert np.allclose(self.potential.getEnergy(self.x_initial_red),
self.potential_cells.getEnergy(self.x_initial_red),
rtol=1e-10)
print self.boxvec
def optimize(self, nr_samples=1):
self.x_initial_red = reduce_coordinates(self.x_initial,
self.frozen_atoms, self.ndim)
self.optimizer = ModifiedFireCPP(self.x_initial_red.copy(),
self.potential,
tol=self.tol,
maxstep=self.maxstep)
self.optimizer_ = LBFGS_CPP(self.x_initial_red.copy(), self.potential)
self.optimizer_cells = ModifiedFireCPP(self.x_initial_red.copy(),
self.potential_cells,
tol=self.tol,
maxstep=self.maxstep)
self.optimizer_cells_ = LBFGS_CPP(self.x_initial_red.copy(),
self.potential_cells)
t0 = time.time()
print "self.optimizer.run(self.nstepsmax)", self.nstepsmax
self.optimizer.run(self.nstepsmax)
self.res_x_final = self.optimizer.get_result()
t1 = time.time()
self.optimizer_cells.run(self.nstepsmax)
self.res_x_final_cells = self.optimizer_cells.get_result()
t2 = time.time()
self.x_final = self.res_x_final.coords
self.x_final_cells = self.res_x_final_cells.coords
print "fire final E, x:", self.optimizer.get_result().energy
print "fire final E, x_cells:", self.optimizer_cells.get_result(
).energy
print "fire final E, plain: ", self.potential.getEnergy(self.x_final)
print "fire final E, cell: ", self.potential_cells.getEnergy(
self.x_final_cells)
print "fire number of particles:", self.N
print "fire time no cell lists:", t1 - t0, "sec"
print "fire time cell lists:", t2 - t1, "sec"
print "fire ratio:", (t1 - t0) / (t2 - t1)
if not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final.rms:", self.res_x_final.rms
print "res_x_final.nfev:", self.res_x_final.nfev
print "res_x_final_cells.rms:", self.res_x_final_cells.rms
print "res_x_final_cells.nfev:", self.res_x_final_cells.nfev
print "self.res_x_final.success", self.res_x_final.success
print "self.res_x_final_cells.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells,
self.radii,
self.boxvec,
sca=self.sca)
self.optimizer_.run(self.nstepsmax)
self.res_x_final_ = self.optimizer_.get_result()
t3 = time.time()
self.optimizer_cells_.run(self.nstepsmax)
self.res_x_final_cells_ = self.optimizer_cells_.get_result()
t4 = time.time()
self.x_final_ = self.res_x_final_.coords
self.x_final_cells_ = self.res_x_final_cells_.coords
print "lbfgs final E, x:", self.optimizer_.get_result().energy
print "lbfgs final E, x_cells:", self.optimizer_cells_.get_result(
).energy
print "lbfgs final E, plain: ", self.potential.getEnergy(self.x_final_)
print "lbfgs final E, cell: ", self.potential_cells.getEnergy(
self.x_final_cells_)
print "lbfgs number of particles:", self.N
print "lbfgs time no cell lists:", t3 - t2, "sec"
print "lbfgs time cell lists:", t4 - t3, "sec"
print "lbfgs ratio:", (t3 - t2) / (t4 - t3)
if not self.res_x_final_.success or not self.res_x_final_cells_.success or not self.res_x_final.success or not self.res_x_final_cells.success:
print "-------------"
print "res_x_final_.rms:", self.res_x_final_.rms
print "res_x_final_.nfev:", self.res_x_final_.nfev
print "res_x_final_cells_.rms:", self.res_x_final_cells_.rms
print "res_x_final_cells_.nfev:", self.res_x_final_cells_.nfev
print "self.res_x_final_.success", self.res_x_final.success
print "self.res_x_final_cells_.success", self.res_x_final_cells.success
print "-------------"
plot_disks(self.x_initial, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_, self.radii, self.boxvec, sca=self.sca)
plot_disks(self.x_final_cells_,
self.radii,
self.boxvec,
sca=self.sca)
assert (self.res_x_final.success)
assert (self.res_x_final_cells.success)
assert (self.res_x_final_.success)
assert (self.res_x_final_cells_.success)
for (xci, xi) in zip(self.x_final_cells, self.x_final):
passed = (np.abs(xci - xi) < 1e-10)
if (passed is False):
print "xci", xci
print "xi", xi
assert (passed)
print "energy no cell lists:", self.res_x_final.energy
print "energy cell lists:", self.res_x_final_cells.energy
self.t_ratio = (t1 - t0) / (t2 - t1)
self.t_ratio_lbfgs = (t3 - t2) / (t4 - t3)
def __init__(self,
boxdim=2,
nr_particles=100,
hard_phi=0.4,
nr_steps=1e6,
epsilon=1,
alpha=0.1,
verbose=False):
# Settings.
np.random.seed(42)
# Input parameters.
self.boxdim = boxdim
self.nr_particles = nr_particles
self.hard_phi = hard_phi
self.nr_steps = nr_steps
self.epsilon = epsilon
self.alpha = alpha
self.verbose = verbose
# Derived quantities.
self.hard_radii = np.ones(self.nr_particles)
def volume_nball(radius, n):
return np.power(np.pi, n / 2) * np.power(radius,
n) / gamma(n / 2 + 1)
self.box_length = np.power(
np.sum(
np.asarray(
[volume_nball(r, self.boxdim)
for r in self.hard_radii])) / self.hard_phi,
1 / self.boxdim)
self.box_vector = np.ones(self.boxdim) * self.box_length
# HS-WCA potential.
self.potential = HS_WCA(use_periodic=True,
use_cell_lists=True,
ndim=self.boxdim,
eps=self.epsilon,
sca=self.alpha,
radii=self.hard_radii,
boxvec=self.box_vector)
# Initial configuration by minimization.
self.nr_dof = self.boxdim * self.nr_particles
self.x = np.random.uniform(-0.5 * self.box_length,
0.5 * self.box_length, self.nr_dof)
optimizer = LBFGS_CPP(self.x, self.potential)
optimizer.run()
if not optimizer.get_result().success:
print("warning: minimization has not converged")
self.x = optimizer.get_result().coords.copy()
# Potential and MC rules.
self.temperature = 1
self.mc = MC(self.potential, self.x, self.temperature, self.nr_steps)
self.step = RandomCoordsDisplacement(42,
1,
single=True,
nparticles=self.nr_particles,
bdim=self.boxdim)
if self.verbose:
print("initial MC stepsize")
print self.step.get_stepsize()
self.mc.set_takestep(self.step)
self.eq_steps = self.nr_steps / 2
self.mc.set_report_steps(self.eq_steps)
self.gr_quench = RecordPairDistHistogram(self.box_vector,
50,
self.eq_steps,
self.nr_particles,
optimizer=optimizer)
self.gr = RecordPairDistHistogram(self.box_vector, 50, self.eq_steps,
self.nr_particles)
self.mc.add_action(self.gr_quench)
self.mc.add_action(self.gr)
self.test = MetropolisTest(44)
self.mc.add_accept_test(self.test)
