def b_vector_for_positions(cls, *args):
if sanity_checking_enabled:
if len(args) != 4:
raise TypeError
#--------------------------------------------------------------------------------#
# Check the cache first
cache_resp = SimpleInternalCoordinate._check_b_tensor_cache(cls, args)
if cache_resp:
return cache_resp
#--------------------------------------------------------------------------------#
# Not in the cache...so compute it
def e(j, k):
ev = LightVector.l_sub(args[k-1], args[j-1]); ev.normalize()
return ev
def r(j, k):
return LightVector.l_sub(args[k-1], args[j-1]).magnitude()
e12, e23, e43 = e(1,2), e(2,3), e(4,3)
e32 = -e23
r12, r23, r43 = r(1,2), r(2, 3), r(3, 4)
r32 = r23
sin2phi2 = sin(angle_between_vectors(e12, e32))**2
cosphi2 = cos(angle_between_vectors(e12, e32))
sin2phi3 = sin(angle_between_vectors(e23, e43))**2
cosphi3 = cos(angle_between_vectors(e23, e43))
ret_val = [0,0,0,0]
ret_val[0] = cross(e12, e23) * (-1.0 / (r12 * sin2phi2))
ret_val[1] = ((r23 - r12 * cosphi2)/(r23*r12*sin2phi2)) * cross(e12, e23)\
+ (cosphi3/(r23*sin2phi3)) * cross(e43, e32)
ret_val[2] = ((r32 - r43 * cosphi3)/(r32*r43*sin2phi3)) * cross(e43, e32)\
+ (cosphi2/(r32*sin2phi2)) * cross(e12, e23)
ret_val[3] = cross(e43, e32) * (-1.0 / (r43 * sin2phi3))
SimpleInternalCoordinate.b_tensor_cache[(cls,) + tuple(args)] = ret_val
return ret_val
def noncanonical_value_for_xyz(cls, xyz):
def e(j, k):
ev = LightVector.l_sub(xyz[k-1], xyz[j-1]); ev.normalize()
return ev
e12 = e(1,2)
e21 = -e12
e32 = e(3,2)
e23 = -e32
e34 = e(3,4)
phi2 = angle_between_vectors(e21, e23)
phi3 = angle_between_vectors(e32, e34)
sinphi2, sinphi3 = sin(phi2), sin(phi3)
sintau = e21.dot(cross(e32, e34)) / (sinphi2 * sinphi3)
tau_0 = safe_asin(sintau)
#----------------------------------------#
# Deal with the sign
sign_val = cross(e21, e23).dot(cross(e32, e34))
#zero_cutoff = 1e-10
zero_cutoff = 0
if sign_val < -zero_cutoff:
tau_e = math.pi - tau_0
#tau_e = - tau_0
elif sign_val > zero_cutoff:
tau_e = tau_0
else:
tau_e = math.pi / 2.0
#----------------------------------------#
return tau_e
def transform_tensor(self, tensor, to_representation):
"""
"""
self.freeze()
to_representation.freeze()
shape = (len(to_representation), ) * len(tensor.shape)
ret_val = RepresentationDependentTensor(
shape=shape, representation=to_representation)
#--------------------------------------------------------------------------------#
if isinstance(to_representation, CartesianRepresentation):
if len(self) != len(to_representation):
raise ValueError(
"incompatible representation sizes ({} != {})".format(
len(self), len(to_representation)))
if tensor.representation is not self:
raise ValueError(
"representation {} can only transform a tensor whose representation attribute is the same "
" as itself (tensor.representation was {} ".format(
self, tensor.representation))
if self.molecule.is_linear():
raise NotImplementedError(
"linear molecule cartesian-to-cartesian transformation is not"
" yet implemented. Shouldn't be too hard...")
if sanity_checking_enabled:
#TODO use a recentered version of the 'from' representation if it is not centered
pass
# Make sure things are centered
#if not self.molecule.is_centered(cartesian_representation=self):
# raise ValueError("CartesianRepresentation objects transformed from and to"
# " must be centered at the center of mass ({} was not)".format(
# self
# ))
#elif not self.molecule.is_centered(cartesian_representation=to_representation):
# raise ValueError("CartesianRepresentation objects transformed from and to"
# " must be centered at the center of mass ({} was not)".format(
# to_representation
# ))
#----------------------------------------#
old = self.value
new = to_representation.value
unitconv = self.units.to(to_representation.units)
oldmat = Matrix(old).reshape((len(self) / 3, 3))
newmat = Matrix(new).reshape((len(self) / 3, 3))
#----------------------------------------#
# Check to see if the molecule is planar. If so, append the cross product of any
# two atoms' positions not colinear with the origin
if any(norm(oldmat[:dir].view(Vector)) < 1e-12 \
or norm(newmat[:dir].view(Vector)) < 1e-12 \
for dir in [X, Y, Z]):
first_atom = None
# TODO unit concious cutoff (e.g. this would fail if the units of the position matrix were meters)
nonorigin_cutoff = 1e-2
for i, v in enumerate(grouper(3, old)):
if norm(LightVector(v)) > nonorigin_cutoff:
first_atom = i
break
second_atom = None
for i in range(first_atom + 1, len(self) // 3):
#TODO make sure this works with Molecule.linear_cutoff
if norm(oldmat[i]) > nonorigin_cutoff and norm(newmat[i]) > nonorigin_cutoff \
and abs(angle_between_vectors(oldmat[first_atom], oldmat[i])) > 1e-5 \
and abs(angle_between_vectors(newmat[first_atom], newmat[i])) > 1e-5:
second_atom = i
break
oldmat = Matrix(
list(oldmat.rows) +
[cross(oldmat[first_atom], oldmat[second_atom])])
newmat = Matrix(
list(newmat.rows) +
[cross(newmat[first_atom], newmat[second_atom])])
#----------------------------------------#
rot_mat = newmat.T * np.linalg.pinv(oldmat.T)
# Divide by unit conversion because the representation dependent tensor
# is [some units] *per* representation units
rot_mat /= unitconv
trans_mat = Matrix(shape=(len(self), len(self)))
for idx in xrange(len(self) // 3):
off = idx * 3
trans_mat[off:off + 3, off:off + 3] = rot_mat
order = len(tensor.shape)
# This is basically impossible to read what I'm doing here, but work it out
# looking at the numpy.einsum documentation and you'll see that this is correct.
# Basically, we want to contract the row indices of the transformation matrix
# with each axis of the tensor to be transformed.
einsumargs = sum(
([trans_mat, [2 * i, 2 * i + 1]] for i in xrange(order)), [])
einsumargs += [
tensor, [i for i in xrange(2 * order) if i % 2 != 0]
]
einsumargs += [[i for i in xrange(2 * order) if i % 2 == 0]]
np.einsum(*einsumargs, out=ret_val)
return ret_val
#--------------------------------------------------------------------------------#
elif isinstance(to_representation, InternalRepresentation):
if len(tensor.shape) == 1:
A = to_representation.a_matrix
ret_val[...] = A.T * tensor.view(Vector)
else:
raise NotImplementedError("use transform_forcefield instead")
return ret_val
#--------------------------------------------------------------------------------#
elif isinstance(to_representation, NormalRepresentation):
B = to_representation.b_matrix
ret_val[...] = tensor.linearly_transformed(B)
return ret_val
else:
raise NotImplementedError(
"Transformation of arbitrary tensors from representation of type '{}' to "
" representations of type '{}' is not implemented.".format(
self.__class__.__name__,
to_representation.__class__.__name__))
def is_perpendicular(cls, v1, v2):
return abs(math.pi / 2.0 -
angle_between_vectors(v1, v2)) < cls.perpendicular_tolerance
def value_for_xyz(cls, xyz):
v1 = LightVector.l_sub(xyz[0], xyz[1])
v2 = LightVector.l_sub(xyz[2], xyz[1])
return angle_between_vectors(v1, v2)
def is_perpendicular(cls, v1, v2):
return abs(math.pi / 2.0 - angle_between_vectors(v1, v2)) < cls.perpendicular_tolerance
def value_for_xyz(cls, xyz):
v1 = LightVector.l_sub(xyz[0], xyz[1])
v2 = LightVector.l_sub(xyz[2], xyz[1])
return angle_between_vectors(v1, v2)
def transform_tensor(self, tensor, to_representation):
"""
"""
self.freeze()
to_representation.freeze()
shape = (len(to_representation),) * len(tensor.shape)
ret_val = RepresentationDependentTensor(shape=shape, representation=to_representation)
# --------------------------------------------------------------------------------#
if isinstance(to_representation, CartesianRepresentation):
if len(self) != len(to_representation):
raise ValueError(
"incompatible representation sizes ({} != {})".format(len(self), len(to_representation))
)
if tensor.representation is not self:
raise ValueError(
"representation {} can only transform a tensor whose representation attribute is the same "
" as itself (tensor.representation was {} ".format(self, tensor.representation)
)
if self.molecule.is_linear():
raise NotImplementedError(
"linear molecule cartesian-to-cartesian transformation is not"
" yet implemented. Shouldn't be too hard..."
)
if sanity_checking_enabled:
# TODO use a recentered version of the 'from' representation if it is not centered
pass
# Make sure things are centered
# if not self.molecule.is_centered(cartesian_representation=self):
# raise ValueError("CartesianRepresentation objects transformed from and to"
# " must be centered at the center of mass ({} was not)".format(
# self
# ))
# elif not self.molecule.is_centered(cartesian_representation=to_representation):
# raise ValueError("CartesianRepresentation objects transformed from and to"
# " must be centered at the center of mass ({} was not)".format(
# to_representation
# ))
# ----------------------------------------#
old = self.value
new = to_representation.value
unitconv = self.units.to(to_representation.units)
oldmat = Matrix(old).reshape((len(self) / 3, 3))
newmat = Matrix(new).reshape((len(self) / 3, 3))
# ----------------------------------------#
# Check to see if the molecule is planar. If so, append the cross product of any
# two atoms' positions not colinear with the origin
if any(
norm(oldmat[:dir].view(Vector)) < 1e-12 or norm(newmat[:dir].view(Vector)) < 1e-12 for dir in [X, Y, Z]
):
first_atom = None
# TODO unit concious cutoff (e.g. this would fail if the units of the position matrix were meters)
nonorigin_cutoff = 1e-2
for i, v in enumerate(grouper(3, old)):
if norm(LightVector(v)) > nonorigin_cutoff:
first_atom = i
break
second_atom = None
for i in range(first_atom + 1, len(self) // 3):
# TODO make sure this works with Molecule.linear_cutoff
if (
norm(oldmat[i]) > nonorigin_cutoff
and norm(newmat[i]) > nonorigin_cutoff
and abs(angle_between_vectors(oldmat[first_atom], oldmat[i])) > 1e-5
and abs(angle_between_vectors(newmat[first_atom], newmat[i])) > 1e-5
):
second_atom = i
break
oldmat = Matrix(list(oldmat.rows) + [cross(oldmat[first_atom], oldmat[second_atom])])
newmat = Matrix(list(newmat.rows) + [cross(newmat[first_atom], newmat[second_atom])])
# ----------------------------------------#
rot_mat = newmat.T * np.linalg.pinv(oldmat.T)
# Divide by unit conversion because the representation dependent tensor
# is [some units] *per* representation units
rot_mat /= unitconv
trans_mat = Matrix(shape=(len(self), len(self)))
for idx in xrange(len(self) // 3):
off = idx * 3
trans_mat[off : off + 3, off : off + 3] = rot_mat
order = len(tensor.shape)
# This is basically impossible to read what I'm doing here, but work it out
# looking at the numpy.einsum documentation and you'll see that this is correct.
# Basically, we want to contract the row indices of the transformation matrix
# with each axis of the tensor to be transformed.
einsumargs = sum(([trans_mat, [2 * i, 2 * i + 1]] for i in xrange(order)), [])
einsumargs += [tensor, [i for i in xrange(2 * order) if i % 2 != 0]]
einsumargs += [[i for i in xrange(2 * order) if i % 2 == 0]]
np.einsum(*einsumargs, out=ret_val)
return ret_val
# --------------------------------------------------------------------------------#
elif isinstance(to_representation, InternalRepresentation):
if len(tensor.shape) == 1:
A = to_representation.a_matrix
ret_val[...] = A.T * tensor.view(Vector)
else:
raise NotImplementedError("use transform_forcefield instead")
return ret_val
# --------------------------------------------------------------------------------#
elif isinstance(to_representation, NormalRepresentation):
B = to_representation.b_matrix
ret_val[...] = tensor.linearly_transformed(B)
return ret_val
else:
raise NotImplementedError(
"Transformation of arbitrary tensors from representation of type '{}' to "
" representations of type '{}' is not implemented.".format(
self.__class__.__name__, to_representation.__class__.__name__
)
)
