def bondAngles(self):
"""
:returns: a list of all bond angles that can be formed from the
bonds in the list
:rtype: :class:`~MMTK.Bonds.BondAngleList`
"""
if self.bond_angles is None:
# find all atoms that are involved in more than one bond
bonds = {}
atom_list = []
for bond in self:
try:
bl = bonds[bond.a1]
except KeyError:
bl = []
bonds[bond.a1] = bl
atom_list.append(bond.a1)
bl.append(bond)
try:
bl = bonds[bond.a2]
except KeyError:
bl = []
bonds[bond.a2] = bl
atom_list.append(bond.a2)
bl.append(bond)
angles = []
for atom in atom_list:
# each pair of bonds at the same atom defines a bond angle
for p in Utility.pairs(bonds[atom]):
angles.append(BondAngle(p[0], p[1], atom))
self.bond_angles = BondAngleList(angles)
return self.bond_angles
def forceConstantTest(universe, atoms = None, delta = 0.0001):
"""
Test force constants by comparing to the numerical derivatives
of the gradients.
:param universe: the universe on which the test is performed
:type universe: :class:`~MMTK.Universe.Universe`
:param atoms: the atoms of the universe for which the gradient
is tested (default: all atoms)
:type atoms: list
:param delta: the step size used in calculating the numerical derivatives
:type delta: float
"""
e0, grad0, fc = universe.energyGradientsAndForceConstants()
if atoms is None:
atoms = universe.atomList()
for a1, a2 in itertools.chain(itertools.izip(atoms, atoms),
Utility.pairs(atoms)):
print a1, a2
print fc[a1, a2]
num_fc = []
for v in [ex, ey, ez]:
x = a1.position()
a1.setPosition(x+delta*v)
e_plus, grad_plus = universe.energyAndGradients()
a1.setPosition(x-delta*v)
e_minus, grad_minus = universe.energyAndGradients()
a1.setPosition(x)
num_fc.append(0.5*(grad_plus[a2]-grad_minus[a2])/delta)
print N.array(map(lambda a: a.array, num_fc))
def forceConstantTest(universe, atoms=None, delta=0.0001):
"""
Test force constants by comparing to the numerical derivatives
of the gradients.
:param universe: the universe on which the test is performed
:type universe: :class:`~MMTK.Universe.Universe`
:param atoms: the atoms of the universe for which the gradient
is tested (default: all atoms)
:type atoms: list
:param delta: the step size used in calculating the numerical derivatives
:type delta: float
"""
e0, grad0, fc = universe.energyGradientsAndForceConstants()
if atoms is None:
atoms = universe.atomList()
for a1, a2 in itertools.chain(itertools.izip(atoms, atoms),
Utility.pairs(atoms)):
print a1, a2
print fc[a1, a2]
num_fc = []
for v in [ex, ey, ez]:
x = a1.position()
a1.setPosition(x + delta * v)
e_plus, grad_plus = universe.energyAndGradients()
a1.setPosition(x - delta * v)
e_minus, grad_minus = universe.energyAndGradients()
a1.setPosition(x)
num_fc.append(0.5 * (grad_plus[a2] - grad_minus[a2]) / delta)
print N.array(map(lambda a: a.array, num_fc))
def dihedralAngles(self):
"""
:returns: a list of all dihedral angles that can be formed from the
bond angles in the list
:rtype: :class:`~MMTK.Bonds.DihedralAngleList`
"""
# find all bonds that are involved in more than one bond angle
angles = {}
bond_list = []
for angle in self.data:
try:
al = angles[angle.b1]
except KeyError:
al = []
angles[angle.b1] = al
bond_list.append(angle.b1)
al.append(angle)
try:
al = angles[angle.b2]
except KeyError:
al = []
angles[angle.b2] = al
bond_list.append(angle.b2)
al.append(angle)
dihedrals = []
for bond in bond_list:
# each pair of bond angles with a common bond defines a dihedral
for p in Utility.pairs(angles[bond]):
d = DihedralAngle(p[0], p[1], bond)
if d.normalized:
dihedrals.append(d)
return DihedralAngleList(dihedrals)
def pairsWithinCutoff(self, cutoff):
"""
:param cutoff: a cutoff for pair distances
:returns: a list containing all pairs of objects in the
collection whose center-of-mass distance is less than
the cutoff
:rtype: list
"""
pairs = []
positions = {}
for index, objects in self.partition.items():
pos = map(lambda o: o.position(), objects)
positions[index] = pos
for o1, o2 in Utility.pairs(zip(objects, pos)):
if (o2[1] - o1[1]).length() <= cutoff:
pairs.append((o1[0], o2[0]))
partition_cutoff = int(N.floor((cutoff / self.partition_size)**2))
ones = N.array([1, 1, 1])
zeros = N.array([0, 0, 0])
keys = self.partition.keys()
for i in range(len(keys)):
p1 = keys[i]
for j in range(i + 1, len(keys)):
p2 = keys[j]
d = N.maximum(abs(N.array(p2) - N.array(p1)) - ones, zeros)
if N.add.reduce(d * d) <= partition_cutoff:
for o1, pos1 in zip(self.partition[p1], positions[p1]):
for o2, pos2 in zip(self.partition[p2], positions[p2]):
if (pos2 - pos1).length() <= cutoff:
pairs.append((o1, o2))
return pairs
def pairsWithinCutoff(self, cutoff):
"""
:param cutoff: a cutoff for pair distances
:returns: a list containing all pairs of objects in the
collection whose center-of-mass distance is less than
the cutoff
:rtype: list
"""
pairs = []
positions = {}
for index, objects in self.partition.items():
pos = map(lambda o: o.position(), objects)
positions[index] = pos
for o1, o2 in Utility.pairs(zip(objects, pos)):
if (o2[1]-o1[1]).length() <= cutoff:
pairs.append((o1[0], o2[0]))
partition_cutoff = int(N.floor((cutoff/self.partition_size)**2))
ones = N.array([1,1,1])
zeros = N.array([0,0,0])
keys = self.partition.keys()
for i in range(len(keys)):
p1 = keys[i]
for j in range(i+1, len(keys)):
p2 = keys[j]
d = N.maximum(abs(N.array(p2)-N.array(p1)) -
ones, zeros)
if N.add.reduce(d*d) <= partition_cutoff:
for o1, pos1 in zip(self.partition[p1],
positions[p1]):
for o2, pos2 in zip(self.partition[p2],
positions[p2]):
if (pos2-pos1).length() <= cutoff:
pairs.append((o1, o2))
return pairs
def dihedralAngles(self):
"""
:returns: a list of all dihedral angles that can be formed from the
bond angles in the list
:rtype: :class:`~MMTK.Bonds.DihedralAngleList`
"""
# find all bonds that are involved in more than one bond angle
angles = {}
bond_list = []
for angle in self.data:
try:
al = angles[angle.b1]
except KeyError:
al = []
angles[angle.b1] = al
bond_list.append(angle.b1)
al.append(angle)
try:
al = angles[angle.b2]
except KeyError:
al = []
angles[angle.b2] = al
bond_list.append(angle.b2)
al.append(angle)
dihedrals = []
for bond in bond_list:
# each pair of bond angles with a common bond defines a dihedral
for p in Utility.pairs(angles[bond]):
d = DihedralAngle(p[0], p[1], bond)
if d.normalized:
dihedrals.append(d)
return DihedralAngleList(dihedrals)
def bondAngles(self):
"""
:returns: a list of all bond angles that can be formed from the
bonds in the list
:rtype: :class:`~MMTK.Bonds.BondAngleList`
"""
if self.bond_angles is None:
# find all atoms that are involved in more than one bond
bonds = {}
atom_list = []
for bond in self:
try:
bl = bonds[bond.a1]
except KeyError:
bl = []
bonds[bond.a1] = bl
atom_list.append(bond.a1)
bl.append(bond)
try:
bl = bonds[bond.a2]
except KeyError:
bl = []
bonds[bond.a2] = bl
atom_list.append(bond.a2)
bl.append(bond)
angles = []
for atom in atom_list:
# each pair of bonds at the same atom defines a bond angle
for p in Utility.pairs(bonds[atom]):
angles.append(BondAngle(p[0], p[1], atom))
self.bond_angles = BondAngleList(angles)
return self.bond_angles
def addToForceConstants(total_fc, indices, small_fc):
indices = zip(indices, range(len(indices)))
for i1, i2 in map(lambda i: (i, i), indices) + Utility.pairs(indices):
ii1, jj1 = i1
ii2, jj2 = i2
if ii1 > ii2:
ii1, ii2 = ii2, ii1
jj1, jj2 = jj2, jj1
jj1 = 3 * jj1
jj2 = 3 * jj2
total_fc[ii1,:,ii2,:] = total_fc[ii1,:,ii2,:] + \
small_fc[jj1:jj1+3, jj2:jj2+3]
def addToForceConstants(total_fc, indices, small_fc):
indices = map(None, indices, range(len(indices)))
for i1, i2 in map(lambda i: (i,i), indices) + Utility.pairs(indices):
ii1, jj1 = i1
ii2, jj2 = i2
if ii1 > ii2:
ii1, ii2 = ii2, ii1
jj1, jj2 = jj2, jj1
jj1 = 3*jj1
jj2 = 3*jj2
total_fc[ii1,:,ii2,:] = total_fc[ii1,:,ii2,:] + \
small_fc[jj1:jj1+3, jj2:jj2+3]
def addToForceConstants(total_fc, indices, small_fc):
indices = zip(indices, range(len(indices)))
for i1, i2 in itertools.chain(itertools.izip(indices, indices),
Utility.pairs(indices)):
ii1, jj1 = i1
ii2, jj2 = i2
if ii1 > ii2:
ii1, ii2 = ii2, ii1
jj1, jj2 = jj2, jj1
jj1 = 3*jj1
jj2 = 3*jj2
total_fc[ii1,:,ii2,:] += small_fc[jj1:jj1+3, jj2:jj2+3]
def __init__(self, universe, rigid_bodies):
"""
:param universe: the universe for which the subspace is created
:type universe: :class:~MMTK.Universe.Universe
:param rigid_bodies: a list or set of rigid bodies
with some common atoms
"""
ex_ey_ez = [Vector(1.,0.,0.), Vector(0.,1.,0.), Vector(0.,0.,1.)]
# Constructs
# 1) a list of vectors describing the rigid-body motions of each
# rigid body as if it were independent.
# 2) a list of pair-distance constraint vectors for all pairs of
# atoms inside a rigid body.
# The LRB subspace is constructed from the projections of the
# first set of vectors onto the orthogonal complement of the
# subspace generated by the second set of vectors.
vectors = []
c_vectors = []
for rb in rigid_bodies:
atoms = rb.atomList()
for d in ex_ey_ez:
v = ParticleProperties.ParticleVector(universe)
for a in atoms:
v[a] = d
vectors.append(v)
if len(atoms) > 1:
center = rb.centerOfMass()
iv = len(vectors)-3
for d in ex_ey_ez:
v = ParticleProperties.ParticleVector(universe)
for a in atoms:
v[a] = d.cross(a.position()-center)
for vt in vectors[iv:]:
v -= v.dotProduct(vt)*vt
if v.dotProduct(v) > 0.:
vectors.append(v)
for a1, a2 in Utility.pairs(atoms):
distance = universe.distanceVector(a1.position(),
a2.position())
v = ParticleProperties.ParticleVector(universe)
v[a1] = distance
v[a2] = -distance
c_vectors.append(v)
if c_vectors:
constraints = Subspace(universe, c_vectors)
vectors = [constraints.projectionComplementOf(v)
for v in vectors]
Subspace.__init__(self, universe, vectors)
def __init__(self, universe, rigid_bodies):
"""
:param universe: the universe for which the subspace is created
:type universe: :class:`~MMTK.Universe.Universe`
:param rigid_bodies: a list or set of rigid bodies
with some common atoms
"""
ex_ey_ez = [Vector(1.,0.,0.), Vector(0.,1.,0.), Vector(0.,0.,1.)]
# Constructs
# 1) a list of vectors describing the rigid-body motions of each
# rigid body as if it were independent.
# 2) a list of pair-distance constraint vectors for all pairs of
# atoms inside a rigid body.
# The LRB subspace is constructed from the projections of the
# first set of vectors onto the orthogonal complement of the
# subspace generated by the second set of vectors.
vectors = []
c_vectors = []
for rb in rigid_bodies:
atoms = rb.atomList()
for d in ex_ey_ez:
v = ParticleProperties.ParticleVector(universe)
for a in atoms:
v[a] = d
vectors.append(v)
if len(atoms) > 1:
center = rb.centerOfMass()
iv = len(vectors)-3
for d in ex_ey_ez:
v = ParticleProperties.ParticleVector(universe)
for a in atoms:
v[a] = d.cross(a.position()-center)
for vt in vectors[iv:]:
v -= v.dotProduct(vt)*vt
if v.dotProduct(v) > 0.:
vectors.append(v)
for a1, a2 in Utility.pairs(atoms):
distance = universe.distanceVector(a1.position(),
a2.position())
v = ParticleProperties.ParticleVector(universe)
v[a1] = distance
v[a2] = -distance
c_vectors.append(v)
if c_vectors:
constraints = Subspace(universe, c_vectors)
vectors = [constraints.projectionComplementOf(v)
for v in vectors]
Subspace.__init__(self, universe, vectors)
def forceConstantTest(universe, atoms=None, delta=0.0001):
e0, grad0, fc = universe.energyGradientsAndForceConstants()
if atoms is None:
atoms = universe.atomList()
for a1, a2 in map(lambda a: (a, a), atoms) + Utility.pairs(atoms):
print a1, a2
print fc[a1, a2]
num_fc = []
for v in [ex, ey, ez]:
x = a1.position()
a1.setPosition(x + delta * v)
e_plus, grad_plus = universe.energyAndGradients()
a1.setPosition(x - delta * v)
e_minus, grad_minus = universe.energyAndGradients()
a1.setPosition(x)
num_fc.append(0.5 * (grad_plus[a2] - grad_minus[a2]) / delta)
print Numeric.array(map(lambda a: a.array, num_fc))
def forceConstantTest(universe, atoms = None, delta = 0.0001):
e0, grad0, fc = universe.energyGradientsAndForceConstants()
if atoms is None:
atoms = universe.atomList()
for a1, a2 in map(lambda a: (a,a), atoms) + Utility.pairs(atoms):
print a1, a2
print fc[a1, a2]
num_fc = []
for v in [VectorModule.ex, VectorModule.ey, VectorModule.ez]:
x = a1.position()
a1.setPosition(x+delta*v)
e_plus, grad_plus = universe.energyAndGradients()
a1.setPosition(x-delta*v)
e_minus, grad_minus = universe.energyAndGradients()
a1.setPosition(x)
num_fc.append(0.5*(grad_plus[a2]-grad_minus[a2])/delta)
print Numeric.array(map(lambda a: a.array, num_fc))
def excludedPairs(self, subset1, subset2, global_data):
if 'excluded_pairs' not in global_data.get('initialized'):
excluded_pairs = global_data.get('excluded_pairs')
if subset1 is not None:
for s1, s2 in [(subset1, subset2), (subset2, subset1)]:
set = {}
for a in s1.atomList():
set[a.index] = None
for a in s2.atomList():
try:
del set[a.index]
except KeyError: pass
excluded_pairs = excluded_pairs + \
Utility.pairs(set.keys())
set = {}
for a in subset1.atomList():
set[a.index] = None
for a in subset2.atomList():
set[a.index] = None
atom_subset = set.keys()
atom_subset.sort()
else:
atom_subset = None
global_data.set('atom_subset', atom_subset)
excluded_pairs = map(_normalizePair, excluded_pairs)
excluded_pairs.sort(_cmpPair)
_makeUnique(excluded_pairs)
global_data.set('excluded_pairs', excluded_pairs)
one_four_pairs = map(_normalizePair,
global_data.get('1_4_pairs'))
one_four_pairs.sort(_cmpPair)
_makeUnique(one_four_pairs)
_eliminateExcluded(one_four_pairs, excluded_pairs)
global_data.set('1_4_pairs', one_four_pairs)
global_data.add('initialized', 'excluded_pairs')
return global_data.get('excluded_pairs'), \
global_data.get('1_4_pairs'), \
global_data.get('atom_subset')
