parser = argparse.ArgumentParser(epilog=__doc__)
parser.add_argument('cs_bulk',
type=float,
help="bulk salt concentration [1/sigma^3], e.g. 1e-3")
args = parser.parse_args()
# System parameters
#############################################################
cs_bulk = args.cs_bulk
N0 = 70
box_l = (N0 / cs_bulk)**(1.0 / 3.0)
# Integration parameters
#############################################################
system = espressomd.System(box_l=[box_l, box_l, box_l])
np.random.seed(seed=42)
system.time_step = 0.01
system.cell_system.skin = 0.4
temperature = 1.0
#############################################################
# Setup System #
#############################################################
# Particle setup
#############################################################
# type 0 = HA
# type 1 = A-
# type 2 = H+
args = parser.parse_args()
output_path = "output/sim" + str(args.sim)
if not os.path.isdir(output_path):
os.makedirs(output_path)
print('Saving data to ' + output_path)
else:
warnings.warn("Folder {} already exists, files will be overwritten".format(
output_path))
boxX = 22.0
boxY = 14.0
boxZ = 15.0
time_step = 0.1
system = espressomd.System(box_l=(boxX, boxY, boxZ))
system.time_step = time_step
system.cell_system.skin = 0.2
# creating the template for RBCs
cell_type = oif.OifCellType(nodes_file="input/rbc374nodes.dat",
triangles_file="input/rbc374triangles.dat",
system=system,
ks=0.04,
kb=0.016,
kal=0.02,
kag=0.9,
kv=1.0,
check_orientation=False,
resize=(2.0, 2.0, 2.0))
class InteractionsBondedTest(ut.TestCase):
system = espressomd.System(box_l=[17.0, 9.0, 8.0])
np.random.seed(seed=system.seed)
box_l = 10.
start_pos = np.random.rand(3) * box_l
axis = np.random.rand(3)
axis /= np.linalg.norm(axis)
steps = 10
def setUp(self):
self.system.box_l = [self.box_l] * 3
self.system.cell_system.skin = 0.4
self.system.time_step = .2
self.system.part.add(id=0, pos=self.start_pos, type=0)
self.system.part.add(id=1, pos=self.start_pos, type=0)
def tearDown(self):
self.system.part.clear()
# Test Harmonic Bond
def test_harmonic(self):
hb_k = 5
hb_r_0 = 1.5
hb_r_cut = 3.355
hb = espressomd.interactions.HarmonicBond(k=hb_k,
r_0=hb_r_0,
r_cut=hb_r_cut)
self.run_test(
hb, lambda r: tests_common.harmonic_force(
scalar_r=r, k=hb_k, r_0=hb_r_0, r_cut=hb_r_cut),
lambda r: tests_common.harmonic_potential(
scalar_r=r, k=hb_k, r_0=hb_r_0, r_cut=hb_r_cut), 0.01,
hb_r_cut, True)
# Test Fene Bond
def test_fene(self):
fene_k = 23.15
fene_d_r_max = 3.355
fene_r_0 = 1.1
fene = espressomd.interactions.FeneBond(k=fene_k,
d_r_max=fene_d_r_max,
r_0=fene_r_0)
self.run_test(
fene, lambda r: tests_common.fene_force(
scalar_r=r, k=fene_k, d_r_max=fene_d_r_max, r_0=fene_r_0),
lambda r: tests_common.fene_potential(
scalar_r=r, k=fene_k, d_r_max=fene_d_r_max, r_0=fene_r_0),
0.01, fene_r_0 + fene_d_r_max, True)
@ut.skipIf(
not espressomd.has_features(["ELECTROSTATICS"]),
"ELECTROSTATICS feature is not available, skipping coulomb test.")
def test_coulomb(self):
coulomb_k = 1
q1 = 1
q2 = -1
self.system.part[0].q = q1
self.system.part[1].q = q2
self.run_test(
espressomd.interactions.BondedCoulomb(prefactor=coulomb_k),
lambda r: tests_common.coulomb_force(r, coulomb_k, q1, q2),
lambda r: tests_common.coulomb_potential(r, coulomb_k, q1, q2),
0.01, self.system.box_l[0] / 3)
@ut.skipIf(not espressomd.has_features(
["ELECTROSTATICS"]
), "ELECTROSTATICS feature is not available, skipping coulomb short range test."
)
def test_coulomb_sr(self):
# with negated actual charges and only short range int: cancels out all
# interactions
q1 = 1.2
q2 = -q1
self.system.part[0].q = q1
self.system.part[1].q = q2
r_cut = 2
sr_solver = espressomd.electrostatics.DH(prefactor=2,
kappa=0.8,
r_cut=r_cut)
self.system.actors.add(sr_solver)
coulomb_sr = espressomd.interactions.BondedCoulombSRBond(q1q2=-q1 * q2)
# no break test, bond can't break. it extends as far as the short range
# part of the electrostatics actor
self.run_test(coulomb_sr,
lambda r: [0., 0., 0.],
lambda r: 0,
0.01,
r_cut,
test_breakage=False)
def test_quartic(self):
"""Tests the Quartic bonded interaction by comparing the potential and force against the analytic values"""
quartic_k0 = 2.
quartic_k1 = 5.
quartic_r = 0.5
quartic_r_cut = self.system.box_l[0] / 3.
quartic = espressomd.interactions.QuarticBond(k0=quartic_k0,
k1=quartic_k1,
r=quartic_r,
r_cut=quartic_r_cut)
self.run_test(
quartic, lambda r: tests_common.quartic_force(k0=quartic_k0,
k1=quartic_k1,
r=quartic_r,
r_cut=quartic_r_cut,
scalar_r=r),
lambda r: tests_common.quartic_potential(k0=quartic_k0,
k1=quartic_k1,
r=quartic_r,
r_cut=quartic_r_cut,
scalar_r=r), 0.01,
quartic_r_cut, True)
def run_test(self,
bond_instance,
force_func,
energy_func,
min_dist,
cutoff,
test_breakage=False):
self.system.bonded_inter.add(bond_instance)
self.system.part[0].bonds = ((bond_instance, 1), )
# n+1 steps from min_dist to cut, then we remove the cut, because that
# may break the bond due to rounding errors
for dist in np.linspace(min_dist, cutoff, self.steps + 1)[:-1]:
self.system.part[
1].pos = self.system.part[0].pos + self.axis * dist
self.system.integrator.run(recalc_forces=True, steps=0)
# Calculate energies
E_sim = self.system.analysis.energy()["total"]
E_ref = energy_func(dist)
# Calculate forces
f0_sim = np.copy(self.system.part[0].f)
f1_sim = np.copy(self.system.part[1].f)
f1_ref = self.axis * force_func(dist)
# Check that energies match, ...
self.assertAlmostEqual(E_sim, E_ref)
# force equals minus the counter-force ...
np.testing.assert_allclose(f0_sim, -f1_sim, 1E-12)
# and has correct value.
np.testing.assert_almost_equal(f1_sim, f1_ref)
# Pressure
# Isotropic pressure =1/3 Trace Stress tensor
# =1/(3V) sum_i f_i r_i
# where F is the force between the particles and r their distance
p_expected = 1. / 3. * \
np.dot(f1_sim, self.axis * dist) / self.system.volume()
p_sim = self.system.analysis.pressure()["total"]
self.assertAlmostEqual(p_sim, p_expected, delta=1E-12)
# Pressure tensor
# P_ij = 1/V F_i r_j
p_tensor_expected = np.outer(
f1_sim, self.axis * dist) / self.system.volume()
p_tensor_sim = self.system.analysis.stress_tensor()["total"]
np.testing.assert_allclose(p_tensor_sim,
p_tensor_expected,
atol=1E-12)
if test_breakage:
self.system.part[
1].pos = self.system.part[0].pos + self.axis * cutoff * (1.01)
with self.assertRaisesRegexp(
Exception, "Encountered errors during integrate"):
self.system.integrator.run(recalc_forces=True, steps=0)
class Exclusions(ut.TestCase):
s = espressomd.System(box_l=[1.0, 1.0, 1.0])
s.seed = s.cell_system.get_state()['n_nodes'] * [1234]
def setUp(self):
self.s.part.clear()
self.s.box_l = 3 * [10]
self.s.cell_system.skin = 0.4
self.s.time_step = 0.01
def test_add_remove(self):
self.s.part.add(id=0, pos=[0, 0, 0])
self.s.part.add(id=1, pos=[0, 0, 0])
self.s.part.add(id=2, pos=[0, 0, 0])
self.s.part[0].add_exclusion(1)
self.s.part[0].add_exclusion(2)
self.assertTrue((self.s.part[0].exclusions == [1, 2]).all())
self.s.part[0].delete_exclusion(1)
self.assertEqual(self.s.part[0].exclusions, [2])
self.s.part[0].delete_exclusion(2)
self.assertEqual(list(self.s.part[0].exclusions), [])
def test_transfer(self):
self.s.part.add(id=0, pos=[0, 0, 0], v=[1., 1., 1])
self.s.part.add(id=1, pos=[0, 0, 0])
self.s.part.add(id=2, pos=[0, 0, 0])
self.s.part.add(id=3, pos=[0, 0, 0])
self.s.part[0].exclusions = [1, 2, 3]
for i in range(15):
self.s.integrator.run(100)
self.assertTrue((self.s.part[0].exclusions == [1, 2, 3]).all())
@ut.skipIf(not espressomd.has_features(['LENNARD_JONES']), "Skipping test")
def test_particle_property(self):
self.s.non_bonded_inter[0, 0].lennard_jones.set_params(epsilon=1.,
sigma=2.,
cutoff=1.5,
shift=0.0)
self.s.part.add(id=0, pos=[0, 0, 0], type=0)
self.s.part.add(id=1, pos=[1, 0, 0], type=0)
pair_energy = self.s.analysis.energy()['total']
self.assertGreater(pair_energy, 0.)
pair_pressure = self.s.analysis.pressure()['total']
self.assertGreater(pair_pressure, 0.)
self.s.integrator.run(0)
pair_force = self.s.part[0].f[0]
self.assertGreater(abs(pair_force), 0.)
self.assertAlmostEqual(self.s.part[1].f[0], -pair_force, places=7)
self.s.part.add(id=2, pos=[2, 0, 0], type=0)
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.analysis.energy()['total'],
2 * pair_energy)
self.assertAlmostEqual(self.s.analysis.pressure()['total'],
2 * pair_pressure)
self.assertAlmostEqual(self.s.part[2].f[0], -pair_force, places=7)
self.s.part[1].exclusions = [0, 2]
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.analysis.energy()['total'], 0)
self.assertAlmostEqual(self.s.analysis.pressure()['total'], 0)
self.assertAlmostEqual(self.s.part[0].f[0], 0, places=7)
self.assertAlmostEqual(self.s.part[1].f[0], 0, places=7)
self.assertAlmostEqual(self.s.part[2].f[0], 0, places=7)
self.s.part[1].exclusions = [0]
self.assertAlmostEqual(self.s.analysis.energy()['total'], pair_energy)
self.assertAlmostEqual(self.s.analysis.pressure()['total'],
pair_pressure)
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.part[0].f[0], 0, places=7)
self.assertAlmostEqual(self.s.part[1].f[0], pair_force, places=7)
self.assertAlmostEqual(self.s.part[2].f[0], -pair_force, places=7)
self.s.part[1].exclusions = []
self.assertAlmostEqual(self.s.analysis.energy()['total'],
2 * pair_energy)
self.assertAlmostEqual(self.s.analysis.pressure()['total'],
2 * pair_pressure)
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.part[0].f[0], pair_force, places=7)
self.assertAlmostEqual(self.s.part[1].f[0], 0, places=7)
self.assertAlmostEqual(self.s.part[2].f[0], -pair_force, places=7)
self.s.part[1].exclusions = [0]
self.assertAlmostEqual(self.s.analysis.energy()['total'], pair_energy)
self.assertAlmostEqual(self.s.analysis.pressure()['total'],
pair_pressure)
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.part[0].f[0], 0, places=7)
self.assertAlmostEqual(self.s.part[1].f[0], pair_force, places=7)
self.assertAlmostEqual(self.s.part[2].f[0], -pair_force, places=7)
@ut.skipIf(not espressomd.has_features(['P3M']), "Skipping test")
def test_electrostatics_not_excluded(self):
from espressomd.electrostatics import P3M
self.s.part.add(id=0, pos=[0, 0, 0], type=0, q=+1.)
self.s.part.add(id=1, pos=[1, 0, 0], type=0, q=-1.)
# Small alpha means large short-range contribution
self.s.actors.add(
P3M(prefactor=1,
r_cut=3.0,
accuracy=1e-3,
mesh=32,
cao=7,
alpha=0.1,
tune=False))
# Only short-range part of the coulomb energy
pair_energy = self.s.analysis.energy()[('coulomb', 0)]
self.assertGreater(abs(pair_energy), 0.)
self.s.integrator.run(0)
pair_force = self.s.part[0].f[0]
self.assertGreater(abs(pair_force), 0.)
self.assertAlmostEqual(self.s.part[1].f[0], -pair_force, places=7)
pair_pressure = self.s.analysis.pressure()[('coulomb', 0)]
self.assertGreater(abs(pair_pressure), 0.)
self.s.part[0].exclusions = [1]
# Force and energy should not be changed by the exclusion
self.s.integrator.run(0)
self.assertAlmostEqual(self.s.part[0].f[0], pair_force, places=7)
self.assertAlmostEqual(self.s.part[1].f[0], -pair_force, places=7)
self.assertAlmostEqual(self.s.analysis.energy()[('coulomb', 0)],
pair_energy,
places=7)
self.assertAlmostEqual(self.s.analysis.pressure()[('coulomb', 0)],
pair_pressure,
places=7)
class TabulatedTest(ut.TestCase):
s = espressomd.System(box_l=[1.0, 1.0, 1.0])
s.seed = s.cell_system.get_state()['n_nodes'] * [1234]
s.box_l = 3 * [10]
s.time_step = 0.01
s.cell_system.skin = 0.4
def setUp(self):
self.force = np.zeros((100,))
self.energy = np.zeros((100,))
self.min_ = 1.
self.max_ = 2.
self.dx = (self.max_ - self.min_) / 99.
for i in range(0, 100):
self.force[i] = 5 + i * 2.3 * self.dx
self.energy[i] = 5 - i * 2.3 * self.dx
self.s.part.clear()
self.s.part.add(id=0, type=0, pos=[5., 5., 5.0])
self.s.part.add(id=1, type=0, pos=[5., 5., 5.5])
def check(self):
# Below cutoff
np.testing.assert_allclose(np.copy(self.s.part[:].f), 0.0)
for z in np.linspace(0, self.max_ - self.min_, 200, endpoint=False):
self.s.part[1].pos = [5., 5., 6. + z]
self.s.integrator.run(0)
np.testing.assert_allclose(
np.copy(self.s.part[0].f), [0., 0., -(5. + z * 2.3)])
np.testing.assert_allclose(
np.copy(self.s.part[0].f), -np.copy(self.s.part[1].f))
self.assertAlmostEqual(
self.s.analysis.energy()['total'], 5. - z * 2.3)
@utx.skipIfMissingFeatures("TABULATED")
def test_non_bonded(self):
self.s.non_bonded_inter[0, 0].tabulated.set_params(
min=self.min_, max=self.max_, energy=self.energy, force=self.force)
np.testing.assert_allclose(
self.force, self.s.non_bonded_inter[0, 0].tabulated.get_params()['force'])
np.testing.assert_allclose(
self.energy, self.s.non_bonded_inter[0, 0].tabulated.get_params()['energy'])
self.assertAlmostEqual(
self.min_, self.s.non_bonded_inter[0, 0].tabulated.get_params()['min'])
self.assertAlmostEqual(
self.max_, self.s.non_bonded_inter[0, 0].tabulated.get_params()['max'])
self.check()
self.s.non_bonded_inter[0, 0].tabulated.set_params(
min=-1, max=-1, energy=[], force=[])
def test_bonded(self):
from espressomd.interactions import TabulatedDistance
tb = TabulatedDistance(min=self.min_, max=self.max_,
energy=self.energy, force=self.force)
self.s.bonded_inter.add(tb)
np.testing.assert_allclose(self.force, tb.params['force'])
np.testing.assert_allclose(self.energy, tb.params['energy'])
self.assertAlmostEqual(self.min_, tb.params['min'])
self.assertAlmostEqual(self.max_, tb.params['max'])
self.s.part[0].add_bond((tb, 1))
self.check()
self.s.part[0].delete_bond((tb, 1))
return stress
def stress_nonbonded_intra(particle_pairs):
stress = np.zeros([3, 3])
for p1, p2 in particle_pairs:
if p1.type == 0 and p2.type == 0 and p1.mol_id == p2.mol_id:
r = p1.pos - p2.pos
d = np.sqrt(np.sum(r**2))
r_hat = r / d
f = (24.0 * 1.0 * (2.0 * 1.0**12 / d**13 - 1.0**6 / d**7)) * r_hat
stress += np.einsum('i,j', f, r) / np.prod(system.box_l)
return stress
system = espressomd.System(box_l=[1.0, 1.0, 1.0])
@utx.skipIfMissingFeatures(['LENNARD_JONES'])
class Stress(ut.TestCase):
def test(self):
# system parameters
system.box_l = 3 * [10.0]
skin = 0.4
time_step = 0.01
system.time_step = time_step
# thermostat and cell system
system.thermostat.set_langevin(kT=0.0, gamma=1.0, seed=41)
system.cell_system.skin = skin
system.periodicity = [1, 1, 1]
class DDSGPUTest(ut.TestCase):
# Handle for espresso system
system = espressomd.System(box_l=[1.0, 1.0, 1.0])
@ut.skipIf(system.cell_system.get_state()["n_nodes"] > 1,
"Skipping test: only runs for n_nodes == 1")
def test(self):
pf_dds_gpu = 2.34
pf_dawaanr = 3.524
ratio_dawaanr_dds_gpu = pf_dawaanr / pf_dds_gpu
self.system.box_l = 3 * [15]
self.system.periodicity = [0, 0, 0]
self.system.time_step = 1E-4
self.system.cell_system.skin = 0.1
for n in [128, 541]:
dipole_modulus = 1.3
part_dip = dipole_modulus * tests_common.random_dipoles(n)
part_pos = np.random.random((n, 3)) * self.system.box_l[0]
self.system.part.add(pos=part_pos, dip=part_dip)
self.system.non_bonded_inter[0, 0].lennard_jones.set_params(
epsilon=10.0, sigma=0.5, cutoff=0.55, shift="auto")
self.system.thermostat.turn_off()
self.system.integrator.set_steepest_descent(f_max=0.0,
gamma=0.1,
max_displacement=0.1)
self.system.integrator.run(500)
g = espressomd.galilei.GalileiTransform()
g.kill_particle_motion(rotation=True)
self.system.integrator.set_vv()
self.system.non_bonded_inter[0, 0].lennard_jones.set_params(
epsilon=0.0, sigma=0.0, cutoff=0.0, shift=0.0)
self.system.cell_system.skin = 0.0
self.system.time_step = 0.01
self.system.thermostat.turn_off()
# gamma should be zero in order to avoid the noise term in force
# and torque
self.system.thermostat.set_langevin(kT=1.297, gamma=0.0, seed=42)
dds_cpu = espressomd.magnetostatics.DipolarDirectSumCpu(
prefactor=pf_dawaanr)
self.system.actors.add(dds_cpu)
self.system.integrator.run(steps=0, recalc_forces=True)
dawaanr_f = np.copy(self.system.part.all().f)
dawaanr_t = np.copy(self.system.part.all().torque_lab)
dawaanr_e = self.system.analysis.energy()["total"]
del dds_cpu
for i in range(len(self.system.actors.active_actors)):
self.system.actors.remove(self.system.actors.active_actors[i])
self.system.integrator.run(steps=0, recalc_forces=True)
dds_gpu = espressomd.magnetostatics.DipolarDirectSumGpu(
prefactor=pf_dds_gpu)
self.system.actors.add(dds_gpu)
self.system.integrator.run(steps=0, recalc_forces=True)
ddsgpu_f = np.copy(self.system.part.all().f)
ddsgpu_t = np.copy(self.system.part.all().torque_lab)
ddsgpu_e = self.system.analysis.energy()["total"]
# compare
for i in range(n):
np.testing.assert_allclose(
np.array(dawaanr_t[i]),
ratio_dawaanr_dds_gpu * np.array(ddsgpu_t[i]),
err_msg=f'Torques do not match for particle {i}',
atol=3e-3)
np.testing.assert_allclose(
np.array(dawaanr_f[i]),
ratio_dawaanr_dds_gpu * np.array(ddsgpu_f[i]),
err_msg=f'Forces do not match for particle {i}',
atol=3e-3)
self.assertAlmostEqual(
dawaanr_e,
ddsgpu_e * ratio_dawaanr_dds_gpu,
places=2,
msg='Energies for dawaanr {0} and dds_gpu {1} do not match.'.
format(dawaanr_e, ratio_dawaanr_dds_gpu * ddsgpu_e))
self.system.integrator.run(steps=0, recalc_forces=True)
del dds_gpu
self.system.actors.clear()
self.system.part.clear()
class InteractionsBondedTest(ut.TestCase):
system = espressomd.System(box_l=[1.0, 1.0, 1.0])
np.random.seed(seed=system.seed)
box_l = 10.
start_pos = [5., 5., 5.]
axis = np.array([1., 0., 0.])
axis /= np.linalg.norm(axis)
rel_pos_1 = np.array([0., 1., 0.])
rel_pos_2 = np.array([0., 0., 1.])
def setUp(self):
self.system.box_l = [self.box_l] * 3
self.system.cell_system.skin = 0.4
self.system.time_step = .1
self.system.part.add(id=0, pos=self.start_pos, type=0)
self.system.part.add(id=1, pos=self.start_pos, type=0)
self.system.part.add(id=2, pos=self.start_pos, type=0)
self.system.part.add(id=3, pos=self.start_pos, type=0)
def tearDown(self):
self.system.part.clear()
# Analytical Expression
def dihedral_angle(self, p1, p2, p3, p4):
"""
Calculate the dihedral angle phi based on particles' position p1, p2, p3, p4.
"""
v12 = p2 - p1
v23 = p3 - p2
v34 = p4 - p3
v12Xv23 = np.cross(v12, v23)
l_v12Xv23 = np.linalg.norm(v12Xv23)
v23Xv34 = np.cross(v23, v34)
l_v23Xv34 = np.linalg.norm(v23Xv34)
# if dihedral angle is not defined, phi := -1.
if l_v12Xv23 <= 1e-8 or l_v23Xv34 <= 1e-8:
return -1
else:
cosphi = np.abs(np.dot(v12Xv23, v23Xv34)) / (l_v12Xv23 * l_v23Xv34)
return np.arccos(cosphi)
# Test Dihedral Angle
def test_dihedral(self):
dh_k = 1
dh_phase = np.pi / 6
dh_n = 1
dh = espressomd.interactions.Dihedral(bend=dh_k,
mult=dh_n,
phase=dh_phase)
self.system.bonded_inter.add(dh)
self.system.part[1].add_bond((dh, 0, 2, 3))
self.system.part[2].pos = self.system.part[1].pos + [1, 0, 0]
N = 111
d_phi = np.pi / (N * 4)
for i in range(N):
self.system.part[0].pos = self.system.part[1].pos + \
rotate_vector(self.rel_pos_1, self.axis, i * d_phi)
self.system.part[3].pos = self.system.part[2].pos + \
rotate_vector(self.rel_pos_2, self.axis, -i * d_phi)
self.system.integrator.run(recalc_forces=True, steps=0)
# Calculate energies
E_sim = self.system.analysis.energy()["bonded"]
phi = self.dihedral_angle(self.system.part[0].pos,
self.system.part[1].pos,
self.system.part[2].pos,
self.system.part[3].pos)
E_ref = dihedral_potential(dh_k, phi, dh_n, dh_phase)
# Calculate forces
f2_sim = self.system.part[1].f
_, f2_ref, _ = dihedral_force(dh_k, dh_n, dh_phase,
self.system.part[0].pos,
self.system.part[1].pos,
self.system.part[2].pos,
self.system.part[3].pos)
# Check that energies match, ...
np.testing.assert_almost_equal(E_sim, E_ref)
# and has correct value.
f2_sim_copy = np.copy(f2_sim)
np.testing.assert_almost_equal(f2_sim_copy, f2_ref)
# Test Tabulated Dihedral Angle
@utx.skipIfMissingFeatures(["TABULATED"])
def test_tabulated_dihedral(self):
N = 111
d_phi = 2 * np.pi / N
# tabulated values for the range [0, 2*pi]
tab_phi = [i * d_phi for i in range(N + 1)]
tab_energy = [np.cos(i * d_phi) for i in range(N + 1)]
tab_force = [np.cos(i * d_phi) for i in range(N + 1)]
dihedral_tabulated = espressomd.interactions.Tabulated(
type='dihedral',
energy=tab_energy,
force=tab_force,
min=0.,
max=2 * np.pi)
self.system.bonded_inter.add(dihedral_tabulated)
self.system.part[1].add_bond((dihedral_tabulated, 0, 2, 3))
self.system.part[2].pos = self.system.part[1].pos + [1, 0, 0]
# check stored parameters
interaction_id = len(self.system.bonded_inter) - 1
tabulated = self.system.bonded_inter[interaction_id]
np.testing.assert_allclose(tabulated.params['force'], tab_force)
np.testing.assert_allclose(tabulated.params['energy'], tab_energy)
np.testing.assert_almost_equal(tabulated.params['min'], 0.)
np.testing.assert_almost_equal(tabulated.params['max'], 2 * np.pi)
# measure at half the angular resolution to observe interpolation
for i in range(2 * N - 1):
# increase dihedral angle by d_phi (phi ~ 0 at i = 0)
self.system.part[0].pos = self.system.part[1].pos + \
rotate_vector(self.rel_pos_1, self.axis, -i * d_phi / 4)
self.system.part[3].pos = self.system.part[2].pos + \
rotate_vector(self.rel_pos_1, self.axis, i * d_phi / 4)
self.system.integrator.run(recalc_forces=True, steps=0)
# Calculate energies
E_sim = self.system.analysis.energy()["bonded"]
# Get tabulated values
j = i // 2
if i % 2 == 0:
E_ref = tab_energy[j]
else:
E_ref = (tab_energy[j] + tab_energy[j + 1]) / 2.0
# Check that energies match, ...
np.testing.assert_almost_equal(E_sim, E_ref)
class AnalyzeDistributions(ut.TestCase):
system = espressomd.System(box_l=[1.0, 1.0, 1.0])
np.random.seed(1234)
num_part = 10
@classmethod
def setUpClass(cls):
box_l = 20.0
# start with a small box
cls.system.box_l = np.array([box_l, box_l, box_l])
cls.system.cell_system.set_n_square(use_verlet_lists=False)
for p in range(cls.num_part):
cls.system.part.add(id=p,
pos=np.random.random() * cls.system.box_l)
def calc_rdf(self, r, bins):
# this generates indices for all i<j combinations
ij = np.triu_indices(len(r), k=1)
r_ij = r[ij[0]] - r[ij[1]]
dist = np.sqrt(np.sum(r_ij**2, axis=1))
hist = np.histogram(dist, bins=bins, density=False)[0]
return hist
def calc_min_distribution(self, bins):
dist = []
for i in range(self.num_part):
dist.append(self.system.analysis.dist_to(id=i))
hist = np.histogram(dist, bins=bins, density=False)[0]
return hist / (float(np.sum(hist)))
# test system.analysis.rdf()
def test_rdf(self):
# increase PBC for remove mirror images
old_pos = self.system.part[:].pos.copy()
self.system.box_l = self.system.box_l * 2.
self.system.part[:].pos = old_pos
r_min = 0.0
r_max = 100.0
r_bins = 10
bin_width = (r_max - r_min) / r_bins
bins = np.arange(r_min, r_max + bin_width, bin_width)
bin_volume = 4. / 3. * np.pi * (bins[1:]**3 - bins[:-1]**3)
box_volume = np.prod(self.system.box_l)
# all the same type
core_rdf = self.system.analysis.rdf(rdf_type='rdf',
type_list_a=[0],
type_list_b=[0],
r_min=r_min,
r_max=r_max,
r_bins=r_bins)
num_pair = 0.5 * (self.num_part) * (self.num_part - 1)
r = self.system.part[:].pos
# bins
self.assertTrue(np.allclose(core_rdf[0], (bins[1:] + bins[:-1]) * 0.5))
# rdf
self.assertTrue(
np.allclose(core_rdf[1] * bin_volume * num_pair / box_volume,
self.calc_rdf(r, bins)))
# change one type
self.system.part[0].type = 1
r = self.system.part[1:].pos
core_rdf = self.system.analysis.rdf(rdf_type='rdf',
type_list_a=[0],
type_list_b=[0],
r_min=r_min,
r_max=r_max,
r_bins=r_bins)
num_pair = 0.5 * (self.num_part - 1) * (self.num_part - 2)
self.assertTrue(
np.allclose(core_rdf[1] * bin_volume * num_pair / box_volume,
self.calc_rdf(r, bins)))
# compare with type
core_rdf = self.system.analysis.rdf(rdf_type='rdf',
type_list_a=[1],
type_list_b=[0],
r_min=r_min,
r_max=r_max,
r_bins=r_bins)
num_pair = (self.num_part - 1)
dist = np.sqrt(
np.sum((self.system.part[1:].pos - self.system.part[0].pos)**2,
axis=1))
hist = np.histogram(dist, bins=bins, density=False)[0]
self.assertTrue(
np.allclose(core_rdf[1] * bin_volume * num_pair / box_volume,
hist))
# restore PBC
self.system.box_l = self.system.box_l / 2.
self.system.part[:].pos = old_pos
# test system.analysis.distribution(), all the same particle types
def test_distribution_lin(self):
# increase PBC for remove mirror images
old_pos = self.system.part[:].pos.copy()
self.system.box_l = self.system.box_l * 2.
self.system.part[:].pos = old_pos
r_min = 0.0
r_max = 100.0
r_bins = 100
bins = np.linspace(r_min, r_max, num=r_bins + 1, endpoint=True)
# no int flag
core_rdf = self.system.analysis.distribution(type_list_a=[0],
type_list_b=[0],
r_min=r_min,
r_max=r_max,
r_bins=r_bins,
log_flag=0,
int_flag=0)
# bins
self.assertTrue(np.allclose(core_rdf[0], (bins[1:] + bins[:-1]) * 0.5))
# rdf
self.assertTrue(
np.allclose(core_rdf[1], self.calc_min_distribution(bins)))
# with int flag
core_rdf = self.system.analysis.distribution(type_list_a=[0],
type_list_b=[0],
r_min=r_min,
r_max=r_max,
r_bins=r_bins,
log_flag=0,
int_flag=1)
self.assertTrue(
np.allclose(core_rdf[1],
np.cumsum(self.calc_min_distribution(bins))))
class Rotation(ut.TestCase):
s = espressomd.System(box_l=[1.0, 1.0, 1.0])
s.seed = s.cell_system.get_state()['n_nodes'] * [1234]
s.cell_system.skin = 0
s.time_step = 0.01
def test_langevin(self):
"""Applies langevin thermostat and checks that correct axes get
thermalized"""
s = self.s
s.thermostat.set_langevin(gamma=1, kT=1, seed=42)
for x in 0, 1:
for y in 0, 1:
for z in 0, 1:
s.part.clear()
s.part.add(id=0,
pos=(0, 0, 0),
rotation=(x, y, z),
quat=(1, 0, 0, 0),
omega_body=(0, 0, 0),
torque_lab=(0, 0, 0))
s.integrator.run(500)
self.validate(x, 0)
self.validate(y, 1)
self.validate(z, 2)
def validate(self, rotate, coord):
if rotate:
# self.assertNotEqual(self.s.part[0].torque_body[coord],0)
self.assertNotEqual(self.s.part[0].omega_body[coord], 0)
else:
# self.assertEqual(self.s.part[0].torque_body[coord],0)
self.assertEqual(self.s.part[0].omega_body[coord], 0)
@utx.skipIfMissingFeatures("EXTERNAL_FORCES")
def test_axes_changes(self):
"""Verifies that rotation axes in body and space frame stay the same
and other axes don't"""
s = self.s
s.part.clear()
s.part.add(id=0, pos=(0.9, 0.9, 0.9), ext_torque=(1, 1, 1))
s.thermostat.turn_off()
for dir in 0, 1, 2:
# Reset orientation
s.part[0].quat = [1, 0, 0, 0]
# Enable rotation in a single direction
rot = [0, 0, 0]
rot[dir] = 1
s.part[0].rotation = rot
s.integrator.run(30)
s.integrator.run(100)
# Check other axes:
for axis in [1, 0, 0], [0, 1, 0], [0, 0, 1]:
if rot == axis:
# The axis for which rotation is on should coincide in body
# and space frame
self.assertAlmostEqual(np.dot(
rot, s.part[0].convert_vector_body_to_space(rot)),
1,
places=8)
else:
# For non-rotation axis, body and space frame should differ
self.assertLess(
np.dot(axis,
s.part[0].convert_vector_body_to_space(axis)),
0.95)
def test_frame_conversion_and_rotation(self):
s = self.s
s.part.clear()
p = s.part.add(pos=np.random.random(3), rotation=(1, 1, 1))
# Space and body frame co-incide?
np.testing.assert_allclose(np.copy(p.director),
p.convert_vector_body_to_space((0, 0, 1)),
atol=1E-10)
# Random vector should still co-incide
v = (1., 5.5, 17)
np.testing.assert_allclose(v,
p.convert_vector_space_to_body(v),
atol=1E-10)
np.testing.assert_allclose(v,
p.convert_vector_body_to_space(v),
atol=1E-10)
# Particle rotation
p.rotate((1, 2, 0), np.pi / 4)
# Check angle for director
self.assertAlmostEqual(np.arccos(np.dot(p.director, (0, 0, 1))),
np.pi / 4,
delta=1E-10)
# Check other vector
v = (5, -7, 3)
v_r = p.convert_vector_body_to_space(v)
self.assertAlmostEqual(np.dot(v, v), np.dot(v_r, v_r), delta=1e-10)
np.testing.assert_allclose(p.convert_vector_space_to_body(v_r),
v,
atol=1E-10)
# Rotation axis should co-incide
np.testing.assert_allclose((1, 2, 0),
p.convert_vector_body_to_space((1, 2, 0)))
# Check rotation axis with all elements set
p.rotate(axis=(-5, 2, 17), angle=1.)
v = (5, -7, 3)
v_r = p.convert_vector_body_to_space(v)
self.assertAlmostEqual(np.dot(v, v), np.dot(v_r, v_r), delta=1e-10)
np.testing.assert_allclose(p.convert_vector_space_to_body(v_r),
v,
atol=1E-10)
class TestLBPressureACF:
"""Tests that the thermalized LB pressure auto correlation function
is consistent with the chosen viscosity
"""
system = espressomd.System(box_l=[AGRID * N_CELLS] * 3)
system.time_step = TAU
system.cell_system.skin = 0
def tearDown(self):
self.system.actors.clear()
self.system.thermostat.turn_off()
def test(self):
# setup
system = self.system
lb = self.lb_class(agrid=AGRID,
dens=DENS,
visc=VISC,
tau=TAU,
kT=KT,
seed=SEED)
system.actors.add(lb)
system.thermostat.set_lb(LB_fluid=lb, seed=2)
# Warmup
system.integrator.run(500)
# sampling
steps = 50000
p_global = np.zeros((steps, 3, 3))
p_node = np.zeros((steps, 3, 3))
node = lb[0, 0, 0]
for i in range(steps):
p_node[i] = node.pressure_tensor
p_global[i] = lb.pressure_tensor
system.integrator.run(2)
# Test that <sigma_[i!=j]> ~=0 and sigma_[ij]=sigma_[ji]
tol_global = 4 / np.sqrt(steps)
tol_node = tol_global * np.sqrt(N_CELLS**3)
# check single node
for i in range(3):
for j in range(i + 1, 3):
avg_ij = np.average(p_node[:, i, j])
avg_ji = np.average(p_node[:, i, j])
self.assertEqual(avg_ij, avg_ji)
self.assertLess(avg_ij, tol_node)
# check system-wide pressure
for i in range(3):
for j in range(i + 1, 3):
avg_ij = np.average(p_global[:, i, j])
avg_ji = np.average(p_global[:, i, j])
self.assertEqual(avg_ij, avg_ji)
self.assertLess(avg_ij, tol_global)
# Check that stress auto correlatin matches dynamic viscosity
# eta = V/kT integral(stress acf)
all_viscs = []
for i in range(3):
for j in range(i + 1, 3):
# Calculate acf
tmp = np.correlate(p_global[:, i, j],
p_global[:, i, j],
mode="full")
acf = tmp[len(tmp) // 2:] / steps
# integrate first part numerically, fit exponential to tail
t_max_fit = 50 * TAU
ts = np.arange(0, t_max_fit, 2 * TAU)
numeric_integral = np.trapz(acf[:len(ts)], dx=2 * TAU)
# fit tail
def f(x, a, b):
return a * np.exp(-b * x)
(a, b), _ = curve_fit(f, acf[:len(ts)], ts)
tail = f(ts[-1], a, b) / b
integral = numeric_integral + tail
measured_visc = integral * system.volume() / KT
self.assertAlmostEqual(measured_visc,
VISC * DENS,
delta=VISC * DENS * .15)
all_viscs.append(measured_visc)
# Check average over xy, xz and yz against tighter limit
self.assertAlmostEqual(np.average(all_viscs),
VISC * DENS,
delta=VISC * DENS * .07)
class ObservableTests(ut.TestCase):
n_tries = 50
n_parts = 5
box_l = 5.
system = espressomd.System(box_l=3 * [box_l])
system.periodicity = [1, 1, 1]
system.time_step = 0.01
system.cell_system.skin = 0.2 * box_l
def setUp(self):
for i in range(self.n_parts):
self.system.part.add(pos=[1 + i, 1 + i, 1 + i], id=i)
self.partcls = self.system.part.all()
def tearDown(self):
self.system.part.clear()
def test_ParticleDistances(self):
"""
Check ParticleDistances, for a particle pair and for a chain.
"""
pids = list(range(self.n_parts))
obs_single = espressomd.observables.ParticleDistances(ids=[0, 1])
obs_chain = espressomd.observables.ParticleDistances(ids=pids)
# take periodic boundaries into account: bond length cannot exceed
# half the box size along the smallest axis
min_dim = np.min(self.system.box_l)
max_bond_length = min_dim / 2.01
for _ in range(self.n_tries):
# build polymer
pos = np.zeros((self.n_parts, 3), dtype=float)
pos[0] = np.random.uniform(low=0, high=min_dim, size=3)
for i in range(1, self.n_parts):
pos[i] = pos[i - 1] + np.random.uniform(
low=0, high=max_bond_length, size=3)
self.partcls.pos = pos
# expected values
distances = np.linalg.norm(pos[1:] - pos[:-1], axis=1)
# observed values
self.system.integrator.run(0)
res_obs_single = obs_single.calculate()
res_obs_chain = obs_chain.calculate()
# checks
self.assertEqual(np.prod(res_obs_single.shape), 1)
self.assertEqual(np.prod(res_obs_chain.shape), self.n_parts - 1)
self.assertAlmostEqual(res_obs_single[0], distances[0], places=9)
np.testing.assert_array_almost_equal(
res_obs_chain, distances, decimal=9,
err_msg="Data did not agree for observable ParticleDistances")
# check exceptions
for i in range(2):
with self.assertRaises(RuntimeError):
espressomd.observables.ParticleDistances(ids=np.arange(i))
def test_BondAngles(self):
"""
Check BondAngles, for a particle triple and for a chain.
"""
pids = list(range(self.n_parts))
obs_single = espressomd.observables.BondAngles(ids=[0, 1, 2])
obs_chain = espressomd.observables.BondAngles(ids=pids)
# take periodic boundaries into account: bond length cannot exceed
# half the box size along the smallest axis
min_dim = np.min(self.system.box_l)
max_bond_length = min_dim / 2.01
for _ in range(self.n_tries):
# build polymer
pos = np.zeros((self.n_parts, 3), dtype=float)
pos[0] = np.random.uniform(low=0, high=min_dim, size=3)
for i in range(1, self.n_parts):
pos[i] = pos[i - 1] + np.random.uniform(
low=0, high=max_bond_length, size=3)
self.partcls.pos = pos
# expected values
v1 = pos[:-2] - pos[1:-1]
v2 = pos[2:] - pos[1:-1]
l1 = np.linalg.norm(v1, axis=1)
l2 = np.linalg.norm(v2, axis=1)
angles = np.arccos((v1 * v2).sum(1) / l1 / l2)
# observed values
self.system.integrator.run(0)
res_obs_single = obs_single.calculate()
res_obs_chain = obs_chain.calculate()
# checks
self.assertEqual(np.prod(res_obs_single.shape), 1)
self.assertEqual(np.prod(res_obs_chain.shape), self.n_parts - 2)
self.assertAlmostEqual(res_obs_single[0], angles[0], places=9)
np.testing.assert_array_almost_equal(
res_obs_chain, angles, decimal=9,
err_msg="Data did not agree for observable BondAngles")
# check exceptions
for i in range(3):
with self.assertRaises(RuntimeError):
espressomd.observables.BondAngles(ids=np.arange(i))
def test_BondDihedrals(self):
"""
Check BondDihedrals, for a particle quadruple and for a chain.
"""
def rotate_vector(v, k, phi):
"""Rotates vector v around unit vector k by angle phi.
Uses Rodrigues' rotation formula."""
vrot = v * np.cos(phi) + np.cross(k, v) * \
np.sin(phi) + k * np.dot(k, v) * (1.0 - np.cos(phi))
return vrot
def rotate_particle(p2, p3, p4, phi):
"""Rotates particle p4 around the axis formed by the bond
between p2 and p3."""
k = p3 - p2
k /= np.linalg.norm(k)
return p3 + rotate_vector(p4 - p3, k, phi)
def calculate_dihedral(a, b, c, d):
v1 = b - a
v2 = c - b
v3 = d - c
b1 = np.cross(v1, v2)
b2 = np.cross(v2, v3)
u2 = v2 / np.linalg.norm(v2)
return np.arctan2(np.dot(np.cross(b1, b2), u2), np.dot(b1, b2))
def place_particles(bl, offset):
"""Place 5 particles in the XY plane with bond length `bl` and
bond angle = 120 degrees. The chain is then shifted by `offset`."""
phi = 2 * np.pi / 3
pos = np.zeros((self.n_parts, 3), dtype=float)
pos[0] = [bl * np.cos(phi), bl * np.sin(phi), 0.]
pos[1] = [0., 0., 0.]
pos[2] = [bl, 0., 0.]
pos[3] = pos[2] + [bl * np.cos(np.pi - phi), bl * np.sin(phi), 0.]
pos[4] = pos[3] + [bl, 0., 0.]
pos += offset
self.partcls.pos = pos
return pos
pids = list(range(self.n_parts))
obs_single = espressomd.observables.BondDihedrals(ids=pids[:4])
obs_chain = espressomd.observables.BondDihedrals(ids=pids)
# test multiple angles, take periodic boundaries into account
p0, p4 = self.system.part.by_ids([0, 4])
for bond_length in [0.1, self.box_l / 2.0]:
for offset in [1.0, self.box_l / 2.0]:
for phi in np.arange(0, np.pi, np.pi / 6):
# place particles and keep list of unfolded positions
pos = place_particles(bond_length, 3 * [offset])
# rotate the 1st particle
p0.pos = pos[0] = rotate_particle(*pos[1:4, :][::-1],
phi=phi)
# rotate the 5th particle
p4.pos = pos[4] = rotate_particle(*pos[2:5, :], phi=phi)
# expected values
dih1 = calculate_dihedral(*pos[0:4, :][::-1])
dih2 = calculate_dihedral(*pos[1:5, :])
# observed values
self.system.integrator.run(0)
res_obs_single = obs_single.calculate()
res_obs_chain = obs_chain.calculate()
# checks
self.assertEqual(np.prod(res_obs_single.shape), 1)
self.assertEqual(
np.prod(res_obs_chain.shape),
self.n_parts - 3)
self.assertAlmostEqual(res_obs_single[0], dih1, places=9)
np.testing.assert_array_almost_equal(
res_obs_chain, [dih1, dih2], decimal=9,
err_msg="Data did not agree for observable BondDihedrals")
# check exceptions
for i in range(4):
with self.assertRaises(RuntimeError):
espressomd.observables.BondDihedrals(ids=np.arange(i))
def test_CosPersistenceAngles(self):
# First test: compare with python implementation
self.system.part.clear()
partcls = self.system.part.add(pos=np.array(
[np.linspace(0, self.system.box_l[0], 20)] * 3).T + np.random.random((20, 3)))
obs = espressomd.observables.CosPersistenceAngles(
ids=partcls.id)
np.testing.assert_allclose(
obs.calculate(), cos_persistence_angles(partcls.pos))
self.system.part.clear()
# Second test: place particles with fixed angles and check that the
# result of PersistenceAngle.calculate()[i] is i*phi
delta_phi = np.radians(4)
for i in range(10):
pos = [np.cos(i * delta_phi), np.sin(i * delta_phi), 0.0]
self.system.part.add(pos=pos)
new_partcls = self.system.part.all()
obs = espressomd.observables.CosPersistenceAngles(
ids=new_partcls.id)
expected = np.arange(1, 9) * delta_phi
np.testing.assert_allclose(obs.calculate(), np.cos(expected))
# check exceptions
for i in range(3):
with self.assertRaises(RuntimeError):
espressomd.observables.CosPersistenceAngles(ids=np.arange(i))
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
"""
Set up a linear polymer.
"""
import espressomd
espressomd.assert_features(["WCA"])
from espressomd import interactions
from espressomd import polymer
from espressomd.io.writer import vtf # pylint: disable=import-error
import numpy as np
# System parameters
#############################################################
system = espressomd.System(box_l=[100, 100, 100])
system.set_random_state_PRNG()
#system.seed = system.cell_system.get_state()['n_nodes'] * [1234]
np.random.seed(seed=system.seed)
system.time_step = 0.01
system.cell_system.skin = 0.4
system.cell_system.set_n_square(use_verlet_lists=False)
outfile = open('polymer.vtf', 'w')
system.non_bonded_inter[0, 0].wca.set_params(epsilon=1, sigma=1)
fene = interactions.FeneBond(k=10, d_r_max=2)
system.bonded_inter.add(fene)
positions = polymer.positions(n_polymers=1,