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)
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)
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 Test2dMinimization(unittest.TestCase):
def setUp(self):
np.random.seed(42)
self.L_mobile = 4
self.L_total = self.L_mobile + 2
self.nr_particles_mobile = self.L_mobile * self.L_mobile
self.nr_particles_total = self.L_total * self.L_total
self.nr_particles_frozen = self.nr_particles_total - self.nr_particles_mobile
self.box_dimension = 2
self.ndof = self.nr_particles_total * self.box_dimension
self.n_frozen_dof = self.nr_particles_frozen * self.box_dimension
self.frozen_dof = []
self.frozen_atoms = []
for particle_index in xrange(self.nr_particles_total):
xmean = int(particle_index % self.L_total)
ymean = int(particle_index / self.L_total)
if ymean == 0 or ymean == self.L_total - 1 or xmean == 0 or xmean == self.L_total - 1:
self.frozen_dof.append(particle_index * self.box_dimension)
self.frozen_dof.append(particle_index * self.box_dimension + 1)
self.frozen_atoms.append(particle_index)
self.eps = 1
self.x = np.zeros(self.ndof)
for p in xrange(self.nr_particles_total):
xmean = int(p % self.L_total)
ymean = int(p / self.L_total)
self.x[p * self.box_dimension] = xmean + 0.1 * np.random.rand()
self.x[p * self.box_dimension + 1] = ymean + 0.1 * np.random.rand()
self.radii = np.asarray([
0.3 + 0.01 * np.random.rand()
for _ in xrange(self.nr_particles_total)
])
self.sca = 1
self.rcut = 2 * (1 + self.sca) * np.amax(self.radii)
self.boxvec = (self.L_total + self.rcut) * np.ones(self.box_dimension)
self.pot_cells_N_frozen_N = HS_WCA(eps=self.eps,
sca=self.sca,
radii=self.radii,
ndim=self.box_dimension,
boxvec=self.boxvec,
use_periodic=True,
use_frozen=False,
use_cell_lists=False)
self.pot_cells_Y_frozen_N = HS_WCA(eps=self.eps,
sca=self.sca,
radii=self.radii,
ndim=self.box_dimension,
boxvec=self.boxvec,
use_periodic=True,
use_frozen=False,
use_cell_lists=True,
reference_coords=self.x,
rcut=self.rcut)
self.pot_cells_N_frozen_Y = HS_WCA(eps=self.eps,
sca=self.sca,
radii=self.radii,
ndim=self.box_dimension,
boxvec=self.boxvec,
use_periodic=True,
use_frozen=True,
use_cell_lists=False,
frozen_atoms=self.frozen_atoms,
reference_coords=self.x)
self.pot_cells_Y_frozen_Y = HS_WCA(eps=self.eps,
sca=self.sca,
radii=self.radii,
ndim=self.box_dimension,
boxvec=self.boxvec,
use_periodic=True,
use_frozen=True,
use_cell_lists=True,
reference_coords=self.x,
frozen_atoms=self.frozen_atoms,
rcut=self.rcut)
self.x_red = []
for atom in xrange(self.nr_particles_total):
if atom not in self.frozen_atoms:
self.x_red.extend(self.x[atom * self.box_dimension:(atom + 1) *
self.box_dimension])
self.opt_NN = ModifiedFireCPP(self.x, self.pot_cells_N_frozen_N)
self.opt_YN = ModifiedFireCPP(self.x, self.pot_cells_Y_frozen_N)
self.opt_NY = ModifiedFireCPP(self.x_red, self.pot_cells_N_frozen_Y)
self.opt_YY = ModifiedFireCPP(self.x_red, self.pot_cells_Y_frozen_Y)
def test_energies(self):
self.res_e_before_cells_N_frozen_N = self.opt_NN.get_result()
self.res_e_before_cells_Y_frozen_N = self.opt_YN.get_result()
self.res_e_before_cells_N_frozen_Y = self.opt_NY.get_result()
self.res_e_before_cells_Y_frozen_Y = self.opt_YY.get_result()
self.assertAlmostEqual(self.res_e_before_cells_N_frozen_N.energy,
self.res_e_before_cells_N_frozen_Y.energy,
delta=1e-10)
self.assertAlmostEqual(self.res_e_before_cells_Y_frozen_N.energy,
self.res_e_before_cells_N_frozen_N.energy,
delta=1e-10)
self.assertAlmostEqual(self.res_e_before_cells_N_frozen_N.energy,
self.res_e_before_cells_Y_frozen_Y.energy,
delta=1e-10)
self.assertAlmostEqual(self.pot_cells_N_frozen_N.getEnergy(self.x),
self.pot_cells_Y_frozen_N.getEnergy(self.x),
delta=1e-10)
def test_minimization(self):
self.opt_NN.run()
self.opt_YN.run()
self.opt_NY.run()
self.opt_YY.run()
self.res_NN = self.opt_NN.get_result()
self.res_YN = self.opt_YN.get_result()
self.res_NY = self.opt_NY.get_result()
self.res_YY = self.opt_YY.get_result()
self.assertTrue(self.res_NN.success)
self.assertTrue(self.res_YN.success)
self.assertTrue(self.res_NY.success)
self.assertTrue(self.res_YY.success)
self.assertAlmostEqual(self.res_NY.energy,
self.res_YY.energy,
delta=1e-10)
self.assertAlmostEqual(
self.pot_cells_N_frozen_N.getEnergy(self.res_NN.coords),
self.pot_cells_Y_frozen_N.getEnergy(self.res_YN.coords),
delta=1e-10)
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 Test2dMinimization(unittest.TestCase):
def setUp(self):
np.random.seed(42)
self.L_mobile = 4
self.L_total = self.L_mobile + 2
self.nr_particles_mobile = self.L_mobile * self.L_mobile
self.nr_particles_total = self.L_total * self.L_total
self.nr_particles_frozen = self.nr_particles_total - self.nr_particles_mobile
self.box_dimension = 2
self.ndof = self.nr_particles_total * self.box_dimension
self.n_frozen_dof = self.nr_particles_frozen * self.box_dimension
self.frozen_dof = []
self.frozen_atoms = []
for particle_index in range(self.nr_particles_total):
xmean = int(particle_index % self.L_total)
ymean = int(particle_index / self.L_total)
if ymean == 0 or ymean == self.L_total - 1 or xmean == 0 or xmean == self.L_total - 1:
self.frozen_dof.append(particle_index * self.box_dimension)
self.frozen_dof.append(particle_index * self.box_dimension + 1)
self.frozen_atoms.append(particle_index)
self.eps = 1
self.x = np.zeros(self.ndof)
for p in range(self.nr_particles_total):
xmean = int(p % self.L_total)
ymean = int(p / self.L_total)
self.x[p * self.box_dimension] = xmean + 0.1 * np.random.rand()
self.x[p * self.box_dimension + 1] = ymean + 0.1 * np.random.rand()
self.radii = np.asarray([0.3 + 0.01 * np.random.rand() for _ in range(self.nr_particles_total)])
self.sca = 1
self.rcut = 2 * (1 + self.sca) * np.amax(self.radii)
self.boxvec = (self.L_total + self.rcut) * np.ones(self.box_dimension)
self.pot_cells_N_frozen_N = HS_WCA(eps=self.eps, sca=self.sca,
radii=self.radii, ndim=self.box_dimension,
boxvec=self.boxvec, use_periodic=True,
use_frozen=False, use_cell_lists=False)
self.pot_cells_Y_frozen_N = HS_WCA(eps=self.eps, sca=self.sca,
radii=self.radii, ndim=self.box_dimension,
boxvec=self.boxvec, use_periodic=True,
use_frozen=False, use_cell_lists=True,
reference_coords=self.x, rcut=self.rcut)
self.pot_cells_N_frozen_Y = HS_WCA(eps=self.eps, sca=self.sca,
radii=self.radii, ndim=self.box_dimension,
boxvec=self.boxvec, use_periodic=True,
use_frozen=True, use_cell_lists=False,
frozen_atoms=self.frozen_atoms,
reference_coords=self.x)
self.pot_cells_Y_frozen_Y = HS_WCA(eps=self.eps, sca=self.sca,
radii=self.radii, ndim=self.box_dimension,
boxvec=self.boxvec, use_periodic=True,
use_frozen=True, use_cell_lists=True,
reference_coords=self.x,
frozen_atoms=self.frozen_atoms, rcut=self.rcut)
self.x_red = []
for atom in range(self.nr_particles_total):
if atom not in self.frozen_atoms:
self.x_red.extend(self.x[atom * self.box_dimension : (atom + 1) * self.box_dimension])
self.opt_NN = ModifiedFireCPP(self.x, self.pot_cells_N_frozen_N)
self.opt_YN = ModifiedFireCPP(self.x, self.pot_cells_Y_frozen_N)
self.opt_NY = ModifiedFireCPP(self.x_red, self.pot_cells_N_frozen_Y)
self.opt_YY = ModifiedFireCPP(self.x_red, self.pot_cells_Y_frozen_Y)
def test_energies(self):
self.res_e_before_cells_N_frozen_N = self.opt_NN.get_result()
self.res_e_before_cells_Y_frozen_N = self.opt_YN.get_result()
self.res_e_before_cells_N_frozen_Y = self.opt_NY.get_result()
self.res_e_before_cells_Y_frozen_Y = self.opt_YY.get_result()
self.assertAlmostEqual(self.res_e_before_cells_N_frozen_N.energy, self.res_e_before_cells_N_frozen_Y.energy, places=8)
self.assertAlmostEqual(self.res_e_before_cells_Y_frozen_N.energy, self.res_e_before_cells_N_frozen_N.energy, places=8)
self.assertAlmostEqual(self.res_e_before_cells_N_frozen_N.energy, self.res_e_before_cells_Y_frozen_Y.energy, places=8)
self.assertAlmostEqual(self.pot_cells_N_frozen_N.getEnergy(self.x), self.pot_cells_Y_frozen_N.getEnergy(self.x), places=8)
def test_minimization(self):
self.opt_NN.run()
self.opt_YN.run()
self.opt_NY.run()
self.opt_YY.run()
self.res_NN = self.opt_NN.get_result()
self.res_YN = self.opt_YN.get_result()
self.res_NY = self.opt_NY.get_result()
self.res_YY = self.opt_YY.get_result()
self.assertTrue(self.res_NN.success)
self.assertTrue(self.res_YN.success)
self.assertTrue(self.res_NY.success)
self.assertTrue(self.res_YY.success)
self.assertAlmostEqual(self.res_NY.energy, self.res_YY.energy, delta=1e-10)
self.assertAlmostEqual(self.pot_cells_N_frozen_N.getEnergy(self.res_NN.coords), self.pot_cells_Y_frozen_N.getEnergy(self.res_YN.coords), delta=1e-10)
