def _align_pythonic(self, coords1, coords2):
"""the slow pythonic version of align"""
# note: this minimizes the angle-distance, but it might be better to
# minimize the atomistic distance. These are not always the same
c1 = self.topology.coords_adapter(coords1)
c2 = self.topology.coords_adapter(coords2)
# now account for inner-molecular symmetry
for p1, p2, site in izip(c1.rotRigid,c2.rotRigid, self.topology.sites):
theta_min = 10.
mx2 = rotations.aa2mx(p2)
mx1 = rotations.aa2mx(p1).transpose()
mx = np.dot(mx1, mx2)
# find the symmetry operation which puts p2 into best alignment with p1
for rot in site.symmetries:
mx_diff = np.dot(mx, rot)
# theta is the rotation angle between p1 and p2 after
# applying the symmetry operation rot to site2
theta = np.linalg.norm(rotations.mx2aa(mx_diff))
# remove any extra factors of 2*pi
theta -= int(theta / (2.*pi)) * 2.*pi
if theta < theta_min:
theta_min = theta
rot_best = rot
p2[:] = rotations.rotate_aa(rotations.mx2aa(rot_best), p2)
def _align_pythonic(self, coords1, coords2):
"""the slow pythonic version of align"""
# note: this minimizes the angle-distance, but it might be better to
# minimize the atomistic distance. These are not always the same
c1 = self.topology.coords_adapter(coords1)
c2 = self.topology.coords_adapter(coords2)
# now account for inner-molecular symmetry
for p1, p2, site in zip(c1.rotRigid, c2.rotRigid, self.topology.sites):
theta_min = 10.
mx2 = rotations.aa2mx(p2)
mx1 = rotations.aa2mx(p1).transpose()
mx = np.dot(mx1, mx2)
# find the symmetry operation which puts p2 into best alignment with p1
for rot in site.symmetries:
mx_diff = np.dot(mx, rot)
# theta is the rotation angle between p1 and p2 after
# applying the symmetry operation rot to site2
theta = np.linalg.norm(rotations.mx2aa(mx_diff))
# remove any extra factors of 2*pi
theta -= int(old_div(theta, (2. * pi))) * 2. * pi
if theta < theta_min:
theta_min = theta
rot_best = rot
p2[:] = rotations.rotate_aa(rotations.mx2aa(rot_best), p2)
def align(system, coords1, coords2):
c1 = system.coords_adapter(coords1)
c2 = system.coords_adapter(coords2)
R = findrotation_kabsch(c2.posRigid, c1.posRigid).transpose()
#R = rotations.aa2mx(p)
for x, p in zip(c2.posRigid, c2.rotRigid):
x[:] = np.dot(R, x)
p[:] = rotations.rotate_aa(p, rotations.mx2aa(R))
# now account for symmetry in water
for p1, p2 in zip(c1.rotRigid,c2.rotRigid):
theta1 = np.linalg.norm(rotations.rotate_aa(p2,-p1))
p2n = rotations.rotate_aa(np.array([0., 0., pi]), p2)
theta2 = np.linalg.norm(rotations.rotate_aa(p2n,-p1))
theta1 -= int(theta1/2./pi)*2.*pi
theta2 -= int(theta2/2./pi)*2.*pi
if(theta2 < theta1):
p2[:]=p2n
def align(system, coords1, coords2):
c1 = system.coords_adapter(coords1)
c2 = system.coords_adapter(coords2)
R = findrotation_kabsch(c2.posRigid, c1.posRigid).transpose()
#R = rotations.aa2mx(p)
for x, p in zip(c2.posRigid, c2.rotRigid):
x[:] = np.dot(R, x)
p[:] = rotations.rotate_aa(p, rotations.mx2aa(R))
# now account for symmetry in water
for p1, p2 in zip(c1.rotRigid, c2.rotRigid):
theta1 = np.linalg.norm(rotations.rotate_aa(p2, -p1))
p2n = rotations.rotate_aa(np.array([0., 0., pi]), p2)
theta2 = np.linalg.norm(rotations.rotate_aa(p2n, -p1))
theta1 -= int(theta1 / 2. / pi) * 2. * pi
theta2 -= int(theta2 / 2. / pi) * 2. * pi
if (theta2 < theta1):
p2[:] = p2n
def test_rotate_aa(self):
print "\ntest rotate_aa"
p1 = np.array(range(1,4), dtype=float)
p2 = p1 + 1
p3 = rotations.rotate_aa(p1, p2)
print repr(p3)
ptrue = np.array([ 0.74050324, 1.64950785, 2.20282887])
for v1, v2 in izip(p3, ptrue):
self.assertAlmostEqual(v1, v2, 4)
def test_align_exact(self):
x1 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
x2 = x1.copy()
tet = create_tetrahedron()
mx = tet.symmetries[2].copy()
p = x2[-3:].copy()
x2[-3:] = rotations.rotate_aa(rotations.mx2aa(mx), p)
self.measure._align_pythonic(x1, x2)
assert_arrays_almost_equal(self, x1, x2)
def test_align_exact(self):
x1 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
x2 = x1.copy()
tet = create_tetrahedron()
mx = tet.symmetries[2].copy()
p = x2[-3:].copy()
x2[-3:] = rotations.rotate_aa(rotations.mx2aa(mx), p)
self.measure._align_pythonic(x1, x2)
assert_arrays_almost_equal(self, x1, x2)
def rotate(self, X, mx):
ca = self.topology.coords_adapter(X)
if(ca.nrigid > 0):
ca.posRigid[:] = np.dot(mx, ca.posRigid.transpose()).transpose()
dp = rotations.mx2aa(mx)
for p in ca.rotRigid:
p[:] = rotations.rotate_aa(p, dp)
if(ca.natoms > 0):
ca.posAtom[:] = np.dot(mx, ca.posAtom.transpose()).transpose()
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=old_div(coords.size, 6), coords=coords)
for i in range(ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
a *= 2. * (np.random.random() - 0.5) * self.rotate_base
ca.rotRigid[i] = rotations.rotate_aa(ca.rotRigid[i], a)
# random rotation for angle-axis vectors
if self.rotate_backbone != 0.:
for j in range(self.ntorsionmoves):
# choose bond to rotate around, index is first bead that changes
index = choose_bond(ca.nrigid - 1, self.P_mid) + 1
# determine backbone beads
a1 = np.dot(rotations.aa2mx(ca.rotRigid[index - 1]),
np.array([1., 0., 0.]))
a2 = np.dot(rotations.aa2mx(ca.rotRigid[index]),
np.array([1., 0., 0.]))
x1 = ca.posRigid[index - 1] - 0.4 * a1 # backbone bead
x2 = ca.posRigid[index] - 0.4 * a2 # backbone bead
# get bond vector as axis of rotation + random magnitude
p = x2 - x1
p /= np.linalg.norm(p)
p *= 2. * (np.random.random() - 0.5) * self.rotate_backbone
# convert random rotation to a matrix
mx = rotations.aa2mx(p)
# center of rotation is in middle of backbone bond
center = 0.5 * (x1 + x2)
# apply rotation to positions and orientations
for i in range(index, ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]),
np.array([1., 0., 0.]))
ca.rotRigid[i] = rotations.rotate_aa(ca.rotRigid[i], p)
x = ca.posRigid[i] - 0.4 * a
ca.posRigid[i] = np.dot(mx, x - center) + center
a = np.dot(rotations.aa2mx(ca.rotRigid[i]),
np.array([1., 0., 0.]))
ca.posRigid[i] += 0.4 * a
def coordsApplyRotation(coordsin, aa):
coords = coordsin.copy()
nmol = len(coords) / 3 / 2
rmat = rot.aa2mx(aa)
# rotate center of mass coords
for imol in range(nmol):
k = imol * 3
coords[k : k + 3] = np.dot(rmat, coords[k : k + 3])
# update aa coords
for imol in range(nmol):
k = nmol * 3 + imol * 3
coords[k : k + 3] = rot.rotate_aa(coords[k : k + 3], aa)
return coords
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
for i in xrange(ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
a *= 2. * (np.random.random() - 0.5) * self.rotate_base
ca.rotRigid[i] = rotations.rotate_aa(ca.rotRigid[i], a)
# random rotation for angle-axis vectors
if self.rotate_backbone != 0.:
for j in xrange(self.ntorsionmoves):
# choose bond to rotate around, index is first bead that changes
index = choose_bond(ca.nrigid - 1, self.P_mid) + 1
# determine backbone beads
a1 = np.dot(rotations.aa2mx(ca.rotRigid[index - 1]), np.array([1., 0., 0.]))
a2 = np.dot(rotations.aa2mx(ca.rotRigid[index]), np.array([1., 0., 0.]))
x1 = ca.posRigid[index - 1] - 0.4 * a1 # backbone bead
x2 = ca.posRigid[index] - 0.4 * a2 # backbone bead
# get bond vector as axis of rotation + random magnitude
p = x2 - x1
p /= np.linalg.norm(p)
p *= 2. * (np.random.random() - 0.5) * self.rotate_backbone
# convert random rotation to a matrix
mx = rotations.aa2mx(p)
# center of rotation is in middle of backbone bond
center = 0.5 * (x1 + x2)
# apply rotation to positions and orientations
for i in xrange(index, ca.nrigid):
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
ca.rotRigid[i] = rotations.rotate_aa(ca.rotRigid[i], p)
x = ca.posRigid[i] - 0.4 * a
ca.posRigid[i] = np.dot(mx, x - center) + center
a = np.dot(rotations.aa2mx(ca.rotRigid[i]), np.array([1., 0., 0.]))
ca.posRigid[i] += 0.4 * a
def _rotate_python(self, X, mx):
"""the slow pythonic version of rotate"""
ca = self.topology.coords_adapter(X)
if ca.nrigid > 0:
# rotate the center of mass positions
ca.posRigid[:] = np.dot(ca.posRigid, mx.transpose())
# rotate the angle axis rotations
dp = rotations.mx2aa(mx)
for p in ca.rotRigid:
p[:] = rotations.rotate_aa(p, dp)
if ca.natoms > 0:
ca.posAtom[:] = np.dot(mx, ca.posAtom.transpose()).transpose()
def _rotate_python(self, X, mx):
"""the slow pythonic version of rotate"""
ca = self.topology.coords_adapter(X)
if ca.nrigid > 0:
# rotate the center of mass positions
ca.posRigid[:] = np.dot(ca.posRigid, mx.transpose())
# rotate the angle axis rotations
dp = rotations.mx2aa(mx)
for p in ca.rotRigid:
p[:] = rotations.rotate_aa(p, dp)
if ca.natoms > 0:
ca.posAtom[:] = np.dot(mx, ca.posAtom.transpose()).transpose()
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
# random displacement for positions
ca.posRigid[:] += 2. * self.displace * (np.random.random(ca.posRigid.shape) - 0.5)
# determine backbone beads
for com, p in zip(ca.posRigid, ca.rotRigid):
p_rnd = rotations.small_random_aa(self.rotate)
# adjust center of mass
if self.rotate_around_backbone:
a1 = np.dot(rotations.aa2mx(p), np.array([1., 0., 0.]))
x1 = com - 0.4 * a1
mx = rotations.aa2mx(p_rnd)
com[:] = np.dot(mx, com - x1) + x1
# random rotation for angle-axis vectors
p[:] = rotations.rotate_aa(p, p_rnd)
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
# random displacement for positions
ca.posRigid[:] += 2. * self.displace * (np.random.random(ca.posRigid.shape) - 0.5)
# determine backbone beads
for com, p in zip(ca.posRigid, ca.rotRigid):
p_rnd = rotations.small_random_aa(self.rotate)
# adjust center of mass
if self.rotate_around_backbone:
a1 = np.dot(rotations.aa2mx(p), np.array([1., 0., 0.]))
x1 = com - 0.4 * a1
mx = rotations.aa2mx(p_rnd)
com[:] = np.dot(mx, com - x1) + x1
# random rotation for angle-axis vectors
p[:] = rotations.rotate_aa(p, p_rnd)
def rotate(self, X, mx):
"""rotate the com + angle-axis position X by the rotation matrix mx
"""
try:
return self.cpp_transform.rotate(X, mx)
except AttributeError:
pass
ca = self.topology.coords_adapter(X)
if ca.nrigid > 0:
# rotate the center of mass positions
ca.posRigid[:] = np.dot(ca.posRigid, mx.transpose())
# rotate the angle axis rotations
dp = rotations.mx2aa(mx)
for p in ca.rotRigid:
p[:] = rotations.rotate_aa(p, dp)
if ca.natoms > 0:
ca.posAtom[:] = np.dot(mx, ca.posAtom.transpose()).transpose()
def rotate(self, X, mx):
"""rotate the com + angle-axis position X by the rotation matrix mx
"""
try:
return self.cpp_transform.rotate(X, mx)
except AttributeError:
pass
ca = self.topology.coords_adapter(X)
if(ca.nrigid > 0):
# rotate the center of mass positions
ca.posRigid[:] = np.dot(ca.posRigid, mx.transpose())
# rotate the angle axis rotations
dp = rotations.mx2aa(mx)
for p in ca.rotRigid:
p[:] = rotations.rotate_aa(p, dp)
if(ca.natoms > 0):
ca.posAtom[:] = np.dot(mx, ca.posAtom.transpose()).transpose()
def align(self, coords1, coords2):
c1 = self.topology.coords_adapter(coords1)
c2 = self.topology.coords_adapter(coords2)
# now account for symmetry in water
for p1, p2, site in zip(c1.rotRigid,c2.rotRigid, self.topology.sites):
theta_min = 10.
mx2 = rotations.aa2mx(p2)
mx1 = rotations.aa2mx(p1).transpose()
mx = np.dot(mx1, mx2)
for rot in site.symmetries:
mx_diff = np.dot(mx, rot)
theta = np.linalg.norm(rotations.mx2aa(mx_diff))
theta -= int(theta/2./pi)*2.*pi
if(theta < theta_min):
theta_min = theta
rot_best = rot
p2[:] = rotations.rotate_aa(rotations.mx2aa(rot_best), p2)
def getSymmetries(self, com, aa ):
"""
a generator which iteratively returns the absolute xyz coordinates
of the molecule subject to it's symmetries
com: the center of mass coords of the molecule
aa: the orientation of the molecule in angle-axis
"""
com = np.array(com)
rmat = rot.aa2mx(aa) #rotation matrix
#first yield the unaltered molecule
xyz = self.getxyz_rmat(rmat, com=com)
yield xyz, aa
#now loop through the symmetries
for p in self.symmetrylist_rot:
#combine the two rotations into one
rmat_comb = np.dot( rmat, rot.aa2mx(p) )
xyz = self.getxyz_rmat(rmat_comb, com=com)
newaa = rot.rotate_aa(p, aa)
#print rmat_comb
#print rot.aa2mx( newaa)
yield xyz, newaa
def align(self, coords1, coords2):
"""align the rotations so that the atomistic coordinates will be in best alignment"""
try:
return self.cpp_measure.align(coords1, coords2)
except AttributeError:
pass
c1 = self.topology.coords_adapter(coords1)
c2 = self.topology.coords_adapter(coords2)
# now account for inner-molecular symmetry
for p1, p2, site in zip(c1.rotRigid, c2.rotRigid, self.topology.sites):
theta_min = 10.
mx2 = rotations.aa2mx(p2)
mx1 = rotations.aa2mx(p1).transpose()
mx = np.dot(mx1, mx2)
for rot in site.symmetries:
mx_diff = np.dot(mx, rot)
theta = np.linalg.norm(rotations.mx2aa(mx_diff))
theta -= int(theta / 2. / pi) * 2. * pi
if theta < theta_min:
theta_min = theta
rot_best = rot
p2[:] = rotations.rotate_aa(rotations.mx2aa(rot_best), p2)
def align(self, coords1, coords2):
"""align the rotations so that the atomistic coordinates will be in best alignment"""
try:
return self.cpp_measure.align(coords1, coords2)
except AttributeError:
pass
c1 = self.topology.coords_adapter(coords1)
c2 = self.topology.coords_adapter(coords2)
# now account for symmetry in water
for p1, p2, site in zip(c1.rotRigid,c2.rotRigid, self.topology.sites):
theta_min = 10.
mx2 = rotations.aa2mx(p2)
mx1 = rotations.aa2mx(p1).transpose()
mx = np.dot(mx1, mx2)
for rot in site.symmetries:
mx_diff = np.dot(mx, rot)
theta = np.linalg.norm(rotations.mx2aa(mx_diff))
theta -= int(theta/2./pi)*2.*pi
if(theta < theta_min):
theta_min = theta
rot_best = rot
p2[:] = rotations.rotate_aa(rotations.mx2aa(rot_best), p2)
def invert(self, X):
"""invert the structure"""
ca = self.topology.coords_adapter(X)
ca.posRigid[:] = -ca.posRigid
for p, site in zip(ca.rotRigid, self.topology.sites):
p[:] = rotations.rotate_aa(rotations.mx2aa(site.inversion), p)
def test_rotate_aa(self):
p1 = random_aa()
p2 = random_aa()
p3 = rotate_aa(p1, p2)
p4 = rotations.rotate_aa(p1, p2)
self.arrays_equal(p3, p4)
def test_rotate_aa(self):
p1 = random_aa()
p2 = random_aa()
p3 = rotate_aa(p1, p2)
p4 = rotations.rotate_aa(p1, p2)
self.arrays_equal(p3, p4)
def invert(self, X):
"""invert the structure"""
ca = self.topology.coords_adapter(X)
ca.posRigid[:] = - ca.posRigid
for p, site in zip(ca.rotRigid, self.topology.sites):
p[:] = rotations.rotate_aa(rotations.mx2aa(site.inversion), p)
e2.append(pot.getEnergy(path[0]))
#for i in xrange(1):
for i in range(len(path) - 1):
e1.append(pot.getEnergy(path[i + 1]))
c1 = CoordsAdapter(nrigid=13, coords=path[i])
c2 = CoordsAdapter(nrigid=13, coords=path[i + 1])
com1 = np.sum(c1.posRigid, axis=0) / float(13)
com2 = np.sum(c1.posRigid, axis=0) / float(13)
c1.posRigid -= com1
c2.posRigid -= com2
mx = findrotation_kabsch(c2.posRigid, c1.posRigid).transpose()
# print mx
c2.posRigid[:] = np.dot(mx, c2.posRigid.transpose()).transpose()
for p in c2.rotRigid:
p[:] = rotations.rotate_aa(p, rotations.mx2aa(mx))
e2.append(pot.getEnergy(path[i + 1]))
for p1, p2 in zip(c1.rotRigid, c2.rotRigid):
n2 = old_div(p2, np.linalg.norm(p2) * 2. * pi)
while True:
p2n = p2 + n2
if (np.linalg.norm(p2n - p1) > np.linalg.norm(p2 - p1)):
break
p2[:] = p2n
while True:
p2n = p2 - n2
if (np.linalg.norm(p2n - p1) > np.linalg.norm(p2 - p1)):
break
xyz = otp.getxyz()
from pele.printing.print_atoms_xyz import printAtomsXYZ as printxyz
import sys
#with open("out.xyz", "w") as fout:
printxyz(sys.stdout, xyz)
aa = np.array([.2, .3, .4])
for xyz, aanew in otp.getSymmetries( np.zeros(3), aa):
printxyz(sys.stdout, xyz, line2="symmetry")
xyz = otp.getxyz(aa = aanew)
printxyz(sys.stdout, xyz, line2="symmetry from returned aa")
if __name__ == "__main__":
test_molecule()
aa1 = rot.random_aa()
aa2 = rot.random_aa()
rmat1 = rot.aa2mx(aa1)
rmat2 = rot.aa2mx(aa2)
rmat21 = np.dot(rmat2, rmat1)
aa21 = rot.rotate_aa(aa1, aa2)
rmat21aa = rot.aa2mx(aa21)
print rmat21
print rmat21aa
print abs(rmat21 - rmat21aa) < 1e-12
e2.append(pot.getEnergy(path[0]))
#for i in xrange(1):
for i in xrange(len(path) - 1):
e1.append(pot.getEnergy(path[i + 1]))
c1 = CoordsAdapter(nrigid=13, coords=path[i])
c2 = CoordsAdapter(nrigid=13, coords=path[i + 1])
com1 = np.sum(c1.posRigid, axis=0) / float(13)
com2 = np.sum(c1.posRigid, axis=0) / float(13)
c1.posRigid -= com1
c2.posRigid -= com2
mx = findrotation_kabsch(c2.posRigid, c1.posRigid).transpose()
# print mx
c2.posRigid[:] = np.dot(mx, c2.posRigid.transpose()).transpose()
for p in c2.rotRigid:
p[:] = rotations.rotate_aa(p, rotations.mx2aa(mx))
e2.append(pot.getEnergy(path[i + 1]))
for p1, p2 in zip(c1.rotRigid, c2.rotRigid):
n2 = p2 / np.linalg.norm(p2) * 2. * pi
while True:
p2n = p2 + n2
if (np.linalg.norm(p2n - p1) > np.linalg.norm(p2 - p1)):
break
p2[:] = p2n
while True:
p2n = p2 - n2
if (np.linalg.norm(p2n - p1) > np.linalg.norm(p2 - p1)):
break