def superpositionFit(confs):
"""
:param confs: the weight, reference position, and alternate
position for each atom
:type confs: sequence of (float, Vector, Vector)
:returns: the quaternion representing the rotation,
the center of mass in the reference configuration,
the center of mass in the alternate configuraton,
and the RMS distance after the optimal superposition
"""
w_sum = 0.
wr_sum = N.zeros((3,), N.Float)
for w, r_ref, r in confs:
w_sum += w
wr_sum += w*r_ref.array
ref_cms = wr_sum/w_sum
pos = N.zeros((3,), N.Float)
possq = 0.
cross = N.zeros((3, 3), N.Float)
for w, r_ref, r in confs:
w = w/w_sum
r_ref = r_ref.array-ref_cms
r = r.array
pos = pos + w*r
possq = possq + w*N.add.reduce(r*r) \
+ w*N.add.reduce(r_ref*r_ref)
cross = cross + w*r[:, N.NewAxis]*r_ref[N.NewAxis, :]
k = N.zeros((4, 4), N.Float)
k[0, 0] = -cross[0, 0]-cross[1, 1]-cross[2, 2]
k[0, 1] = cross[1, 2]-cross[2, 1]
k[0, 2] = cross[2, 0]-cross[0, 2]
k[0, 3] = cross[0, 1]-cross[1, 0]
k[1, 1] = -cross[0, 0]+cross[1, 1]+cross[2, 2]
k[1, 2] = -cross[0, 1]-cross[1, 0]
k[1, 3] = -cross[0, 2]-cross[2, 0]
k[2, 2] = cross[0, 0]-cross[1, 1]+cross[2, 2]
k[2, 3] = -cross[1, 2]-cross[2, 1]
k[3, 3] = cross[0, 0]+cross[1, 1]-cross[2, 2]
for i in range(1, 4):
for j in range(i):
k[i, j] = k[j, i]
k = 2.*k
for i in range(4):
k[i, i] = k[i, i] + possq - N.add.reduce(pos*pos)
from Scientific import LA
e, v = LA.eigenvectors(k)
i = N.argmin(e)
v = v[i]
if v[0] < 0: v = -v
if e[i] <= 0.:
rms = 0.
else:
rms = N.sqrt(e[i])
from Scientific.Geometry import Quaternion
return Quaternion.Quaternion(v), Vector(ref_cms), \
Vector(pos), rms
def superpositionFit(confs):
"""
:param confs: the weight, reference position, and alternate
position for each atom
:type confs: sequence of (float, Vector, Vector)
:returns: the quaternion representing the rotation,
the center of mass in the reference configuration,
the center of mass in the alternate configuraton,
and the RMS distance after the optimal superposition
"""
w_sum = 0.
wr_sum = N.zeros((3, ), N.Float)
for w, r_ref, r in confs:
w_sum += w
wr_sum += w * r_ref.array
ref_cms = wr_sum / w_sum
pos = N.zeros((3, ), N.Float)
possq = 0.
cross = N.zeros((3, 3), N.Float)
for w, r_ref, r in confs:
w = w / w_sum
r_ref = r_ref.array - ref_cms
r = r.array
pos = pos + w * r
possq = possq + w*N.add.reduce(r*r) \
+ w*N.add.reduce(r_ref*r_ref)
cross = cross + w * r[:, N.NewAxis] * r_ref[N.NewAxis, :]
k = N.zeros((4, 4), N.Float)
k[0, 0] = -cross[0, 0] - cross[1, 1] - cross[2, 2]
k[0, 1] = cross[1, 2] - cross[2, 1]
k[0, 2] = cross[2, 0] - cross[0, 2]
k[0, 3] = cross[0, 1] - cross[1, 0]
k[1, 1] = -cross[0, 0] + cross[1, 1] + cross[2, 2]
k[1, 2] = -cross[0, 1] - cross[1, 0]
k[1, 3] = -cross[0, 2] - cross[2, 0]
k[2, 2] = cross[0, 0] - cross[1, 1] + cross[2, 2]
k[2, 3] = -cross[1, 2] - cross[2, 1]
k[3, 3] = cross[0, 0] + cross[1, 1] - cross[2, 2]
for i in range(1, 4):
for j in range(i):
k[i, j] = k[j, i]
k = 2. * k
for i in range(4):
k[i, i] = k[i, i] + possq - N.add.reduce(pos * pos)
from Scientific import LA
e, v = LA.eigenvectors(k)
i = N.argmin(e)
v = v[i]
if v[0] < 0: v = -v
if e[i] <= 0.:
rms = 0.
else:
rms = N.sqrt(e[i])
from Scientific.Geometry import Quaternion
return Quaternion.Quaternion(v), Vector(ref_cms), \
Vector(pos), rms
def findTransformationAsQuaternion(self, conf1, conf2=None):
universe = self.universe()
if conf1.universe != universe:
raise ValueError("conformation is for a different universe")
if conf2 is None:
conf1, conf2 = conf2, conf1
else:
if conf2.universe != universe:
raise ValueError("conformation is for a different universe")
ref = conf1
conf = conf2
weights = universe.masses()
weights = weights / self.mass()
ref_cms = self.centerOfMass(ref).array
pos = Numeric.zeros((3, ), Numeric.Float)
possq = 0.
cross = Numeric.zeros((3, 3), Numeric.Float)
for a in self.atomList():
r = a.position(conf).array
r_ref = a.position(ref).array - ref_cms
w = weights[a]
pos = pos + w * r
possq = possq + w*Numeric.add.reduce(r*r) \
+ w*Numeric.add.reduce(r_ref*r_ref)
cross = cross + w * r[:,
Numeric.NewAxis] * r_ref[Numeric.NewAxis, :]
k = Numeric.zeros((4, 4), Numeric.Float)
k[0, 0] = -cross[0, 0] - cross[1, 1] - cross[2, 2]
k[0, 1] = cross[1, 2] - cross[2, 1]
k[0, 2] = cross[2, 0] - cross[0, 2]
k[0, 3] = cross[0, 1] - cross[1, 0]
k[1, 1] = -cross[0, 0] + cross[1, 1] + cross[2, 2]
k[1, 2] = -cross[0, 1] - cross[1, 0]
k[1, 3] = -cross[0, 2] - cross[2, 0]
k[2, 2] = cross[0, 0] - cross[1, 1] + cross[2, 2]
k[2, 3] = -cross[1, 2] - cross[2, 1]
k[3, 3] = cross[0, 0] + cross[1, 1] - cross[2, 2]
for i in range(1, 4):
for j in range(i):
k[i, j] = k[j, i]
k = 2. * k
for i in range(4):
k[i, i] = k[i, i] + possq - Numeric.add.reduce(pos * pos)
from Scientific import LA
e, v = LA.eigenvectors(k)
i = Numeric.argmin(e)
v = v[i]
if v[0] < 0: v = -v
if e[i] <= 0.:
rms = 0.
else:
rms = Numeric.sqrt(e[i])
return Quaternion.Quaternion(v), Vector(ref_cms), \
Vector(pos), rms
def findTransformationAsQuaternion(self, conf1, conf2 = None):
universe = self.universe()
if conf1.universe != universe:
raise ValueError("conformation is for a different universe")
if conf2 is None:
conf1, conf2 = conf2, conf1
else:
if conf2.universe != universe:
raise ValueError("conformation is for a different universe")
ref = conf1
conf = conf2
weights = universe.masses()
weights = weights/self.mass()
ref_cms = self.centerOfMass(ref).array
pos = Numeric.zeros((3,), Numeric.Float)
possq = 0.
cross = Numeric.zeros((3, 3), Numeric.Float)
for a in self.atomList():
r = a.position(conf).array
r_ref = a.position(ref).array-ref_cms
w = weights[a]
pos = pos + w*r
possq = possq + w*Numeric.add.reduce(r*r) \
+ w*Numeric.add.reduce(r_ref*r_ref)
cross = cross + w*r[:, Numeric.NewAxis]*r_ref[Numeric.NewAxis, :]
k = Numeric.zeros((4, 4), Numeric.Float)
k[0, 0] = -cross[0, 0]-cross[1, 1]-cross[2, 2]
k[0, 1] = cross[1, 2]-cross[2, 1]
k[0, 2] = cross[2, 0]-cross[0, 2]
k[0, 3] = cross[0, 1]-cross[1, 0]
k[1, 1] = -cross[0, 0]+cross[1, 1]+cross[2, 2]
k[1, 2] = -cross[0, 1]-cross[1, 0]
k[1, 3] = -cross[0, 2]-cross[2, 0]
k[2, 2] = cross[0, 0]-cross[1, 1]+cross[2, 2]
k[2, 3] = -cross[1, 2]-cross[2, 1]
k[3, 3] = cross[0, 0]+cross[1, 1]-cross[2, 2]
for i in range(1, 4):
for j in range(i):
k[i, j] = k[j, i]
k = 2.*k
for i in range(4):
k[i, i] = k[i, i] + possq - Numeric.add.reduce(pos*pos)
from Scientific import LA
e, v = LA.eigenvectors(k)
i = Numeric.argmin(e)
v = v[i]
if v[0] < 0: v = -v
if e[i] <= 0.:
rms = 0.
else:
rms = Numeric.sqrt(e[i])
return Quaternion.Quaternion(v), Vector(ref_cms), \
Vector(pos), rms
def __init__(self, trajectory, object, first=0, last=None, skip=1,
reference = None):
self.trajectory = trajectory
universe = trajectory.universe
if last is None: last = len(trajectory)
first_conf = trajectory.configuration[first]
offset = universe.contiguousObjectOffset([object], first_conf, True)
if reference is None:
reference = first_conf
reference = universe.contiguousObjectConfiguration([object], reference)
steps = (last-first+skip-1)/skip
mass = object.mass()
ref_cms = object.centerOfMass(reference)
atoms = object.atomList()
possq = N.zeros((steps,), N.Float)
cross = N.zeros((steps, 3, 3), N.Float)
rcms = N.zeros((steps, 3), N.Float)
# cms of the CONTIGUOUS object made of CONTINUOUS atom trajectories
for a in atoms:
r = trajectory.readParticleTrajectory(a, first, last, skip,
"box_coordinates").array
w = a._mass/mass
N.add(rcms, w*r, rcms)
if offset is not None:
N.add(rcms, w*offset[a].array, rcms)
# relative coords of the CONTIGUOUS reference
r_ref = N.zeros((len(atoms), 3), N.Float)
for a in range(len(atoms)):
r_ref[a] = atoms[a].position(reference).array - ref_cms.array
# main loop: storing data needed to fill M matrix
for a in range(len(atoms)):
r = trajectory.readParticleTrajectory(atoms[a],
first, last, skip,
"box_coordinates").array
r = r - rcms # (a-b)**2 != a**2 - b**2
if offset is not None:
N.add(r, offset[atoms[a]].array,r)
trajectory._boxTransformation(r, r)
w = atoms[a]._mass/mass
N.add(possq, w*N.add.reduce(r*r, -1), possq)
N.add(possq, w*N.add.reduce(r_ref[a]*r_ref[a],-1),
possq)
N.add(cross, w*r[:,:,N.NewAxis]*r_ref[N.NewAxis,
a,:],cross)
self.trajectory._boxTransformation(rcms, rcms)
# filling matrix M (formula no 40)
k = N.zeros((steps, 4, 4), N.Float)
k[:, 0, 0] = -cross[:, 0, 0]-cross[:, 1, 1]-cross[:, 2, 2]
k[:, 0, 1] = cross[:, 1, 2]-cross[:, 2, 1]
k[:, 0, 2] = cross[:, 2, 0]-cross[:, 0, 2]
k[:, 0, 3] = cross[:, 0, 1]-cross[:, 1, 0]
k[:, 1, 1] = -cross[:, 0, 0]+cross[:, 1, 1]+cross[:, 2, 2]
k[:, 1, 2] = -cross[:, 0, 1]-cross[:, 1, 0]
k[:, 1, 3] = -cross[:, 0, 2]-cross[:, 2, 0]
k[:, 2, 2] = cross[:, 0, 0]-cross[:, 1, 1]+cross[:, 2, 2]
k[:, 2, 3] = -cross[:, 1, 2]-cross[:, 2, 1]
k[:, 3, 3] = cross[:, 0, 0]+cross[:, 1, 1]-cross[:, 2, 2]
del cross
for i in range(1, 4):
for j in range(i):
k[:, i, j] = k[:, j, i]
N.multiply(k, 2., k)
for i in range(4):
N.add(k[:,i,i], possq, k[:,i,i])
del possq
quaternions = N.zeros((steps, 4), N.Float)
fit = N.zeros((steps,), N.Float)
from Scientific.LA import eigenvectors
for i in range(steps):
e, v = eigenvectors(k[i])
j = N.argmin(e)
if e[j] < 0.:
fit[i] = 0.
else:
fit[i] = N.sqrt(e[j])
if v[j,0] < 0.: quaternions[i] = -v[j] # eliminate jumps
else: quaternions[i] = v[j]
self.fit = fit
self.cms = rcms
self.quaternions = quaternions