def metric_tensor_cog(self, p):
"""calculate the metric tensor when for w_i != m_i
Note: js850> why is x not used in this function?
"""
R, R1, R2, R3 = rot_mat_derivatives(p, True)
g = np.zeros([6, 6])
# the com part
g[0:3, 0:3] = self.W * np.identity(3)
# the rotational part
g[3, 3] = np.trace(np.dot(R1, np.dot(self.Sm, R1.transpose())))
g[3, 4] = np.trace(np.dot(R1, np.dot(self.Sm, R2.transpose())))
g[3, 5] = np.trace(np.dot(R1, np.dot(self.Sm, R3.transpose())))
g[4, 4] = np.trace(np.dot(R2, np.dot(self.Sm, R2.transpose())))
g[4, 5] = np.trace(np.dot(R2, np.dot(self.Sm, R3.transpose())))
g[5, 5] = np.trace(np.dot(R3, np.dot(self.Sm, R3.transpose())))
g[4, 3] = g[3, 4]
g[5, 4] = g[4, 5]
g[5, 3] = g[3, 5]
# the mixing part
# g[0:3,3] = 2.*self.W * np.dot(R1, self.cog)
# g[0:3,4] = 2.*self.W * np.dot(R2, self.cog)
# g[0:3,5] = 2.*self.W * np.dot(R3, self.cog)
# #g[0:3,3:] = g[0:3,3:].transpose()
#
# g[3,0:3] = g[0:3,3]
# g[4,0:3] = g[0:3,4]
# g[5,0:3] = g[0:3,5]
return g
def metric_tensor_cog(self, p):
"""calculate the metric tensor when for w_i != m_i
Note: js850> why is x not used in this function?
"""
R, R1, R2, R3 = rot_mat_derivatives(p, True)
g = np.zeros([6, 6])
# the com part
g[0:3, 0:3] = self.W * np.identity(3)
# the rotational part
g[3, 3] = np.trace(np.dot(R1, np.dot(self.Sm, R1.transpose())))
g[3, 4] = np.trace(np.dot(R1, np.dot(self.Sm, R2.transpose())))
g[3, 5] = np.trace(np.dot(R1, np.dot(self.Sm, R3.transpose())))
g[4, 4] = np.trace(np.dot(R2, np.dot(self.Sm, R2.transpose())))
g[4, 5] = np.trace(np.dot(R2, np.dot(self.Sm, R3.transpose())))
g[5, 5] = np.trace(np.dot(R3, np.dot(self.Sm, R3.transpose())))
g[4, 3] = g[3, 4]
g[5, 4] = g[4, 5]
g[5, 3] = g[3, 5]
# the mixing part
# g[0:3,3] = 2.*self.W * np.dot(R1, self.cog)
# g[0:3,4] = 2.*self.W * np.dot(R2, self.cog)
# g[0:3,5] = 2.*self.W * np.dot(R3, self.cog)
# #g[0:3,3:] = g[0:3,3:].transpose()
#
# g[3,0:3] = g[0:3,3]
# g[4,0:3] = g[0:3,4]
# g[5,0:3] = g[0:3,5]
return g
def test(): # pragma: no cover
from math import sin, cos, pi
from copy import deepcopy
water = RigidFragment()
rho = 0.9572
theta = 104.52/180.0*pi
water.add_atom("O", np.array([0., -1., 0.]), 1.)
water.add_atom("O", np.array([0., 1., 0.]), 1.)
#water.add_atom("H", rho*np.array([0.0, sin(0.5*theta), cos(0.5*theta)]), 1.)
#water.add_atom("H", rho*np.array([0.0, -sin(0.5*theta), cos(0.5*theta)]), 1.)
water.finalize_setup()
# define the whole water system
system = RBTopology()
nrigid = 1
system.add_sites([deepcopy(water) for i in xrange(nrigid)])
from pele.utils import rotations
rbcoords=np.zeros(6)
rbcoords[3:]= rotations.random_aa()
coords = system.to_atomistic(rbcoords)
print "rb coords\n", rbcoords
print "coords\n", coords
grad = (np.random.random(coords.shape) -0.5)
v = coords[1] - coords[0]
v/=np.linalg.norm(v)
grad[0] -= np.dot(grad[0], v)*v
grad[1] -= np.dot(grad[1], v)*v
grad -= np.average(grad, axis=0)
grad /= np.linalg.norm(grad)
print "torque", np.linalg.norm(np.cross(grad, v))
rbgrad = system.transform_gradient(rbcoords, grad)
p = rbcoords[3:]
x = rbcoords[0:3]
gp = rbgrad[3:]
gx = rbgrad[:3]
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
print "test1", np.linalg.norm(R1*gp[0])
print "test2", np.linalg.norm(R2*gp[1])
print "test3", np.linalg.norm(R3*gp[2])
print "test4", np.linalg.norm(R1*gp[0]) + np.linalg.norm(R2*gp[1]) + np.linalg.norm(R3*gp[2])
dR = R1*gp[0] + R2*gp[1] + R3*gp[2]
print "test", np.linalg.norm(R1*gp[0] + R2*gp[1] + R3*gp[2])
print np.trace(np.dot(dR, dR.transpose()))
G = water.metric_tensor_aa(p)
print np.dot(p, np.dot(G, p))
exit()
gnew = system.redistribute_forces(rbcoords, rbgrad)
print gnew
print system.transform_grad(rbcoords, gnew)
def transform_grad(self, p, g):
g_com = np.sum(g, axis=0)
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
g_p = np.zeros_like(g_com)
for ga, x in zip(g, self.atom_positions):
g_p[0] += np.dot(ga, np.dot(R1, x))
g_p[1] += np.dot(ga, np.dot(R2, x))
g_p[2] += np.dot(ga, np.dot(R3, x))
return g_com, g_p
def transform_grad(self, p, g):
g_com = np.sum(g, axis=0)
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
g_p = np.zeros_like(g_com)
for ga, x in zip(g, self.atom_positions):
g_p[0] += np.dot(ga, np.dot(R1, x))
g_p[1] += np.dot(ga, np.dot(R2, x))
g_p[2] += np.dot(ga, np.dot(R3, x))
return g_com, g_p
def redistribute_forces(self, p, grad_com, grad_p):
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
grad = np.dot(R1, np.transpose(self.atom_positions)).transpose()*grad_p[0]
grad += np.dot(R2, np.transpose(self.atom_positions)).transpose()*grad_p[1]
grad += np.dot(R3, np.transpose(self.atom_positions)).transpose()*grad_p[2]
grad += grad_com
grad = (self.atom_masses * grad.transpose()).transpose()/self.M
return grad
def test(): # pragma: no cover
from math import pi
from copy import deepcopy
water = RigidFragment()
rho = 0.9572
theta = 104.52 / 180.0 * pi
water.add_atom("O", np.array([0., -1., 0.]), 1.)
water.add_atom("O", np.array([0., 1., 0.]), 1.)
# water.add_atom("H", rho*np.array([0.0, sin(0.5*theta), cos(0.5*theta)]), 1.)
#water.add_atom("H", rho*np.array([0.0, -sin(0.5*theta), cos(0.5*theta)]), 1.)
water.finalize_setup()
# define the whole water system
system = RBTopology()
nrigid = 1
system.add_sites([deepcopy(water) for i in xrange(nrigid)])
from pele.utils import rotations
rbcoords = np.zeros(6)
rbcoords[3:] = rotations.random_aa()
coords = system.to_atomistic(rbcoords)
print "rb coords\n", rbcoords
print "coords\n", coords
grad = (np.random.random(coords.shape) - 0.5)
v = coords[1] - coords[0]
v /= np.linalg.norm(v)
grad[0] -= np.dot(grad[0], v) * v
grad[1] -= np.dot(grad[1], v) * v
grad -= np.average(grad, axis=0)
grad /= np.linalg.norm(grad)
print "torque", np.linalg.norm(np.cross(grad, v))
rbgrad = system.transform_gradient(rbcoords, grad)
p = rbcoords[3:]
x = rbcoords[0:3]
gp = rbgrad[3:]
gx = rbgrad[:3]
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
print "test1", np.linalg.norm(R1 * gp[0])
print "test2", np.linalg.norm(R2 * gp[1])
print "test3", np.linalg.norm(R3 * gp[2])
print "test4", np.linalg.norm(R1 * gp[0]) + np.linalg.norm(
R2 * gp[1]) + np.linalg.norm(R3 * gp[2])
dR = R1 * gp[0] + R2 * gp[1] + R3 * gp[2]
print "test", np.linalg.norm(R1 * gp[0] + R2 * gp[1] + R3 * gp[2])
print np.trace(np.dot(dR, dR.transpose()))
def redistribute_forces(self, p, grad_com, grad_p):
# js850> as far as I can tell this is never used. Maybe we should remove it?
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
grad = np.dot(R1, np.transpose(self.atom_positions)).transpose() * grad_p[0]
grad += np.dot(R2, np.transpose(self.atom_positions)).transpose() * grad_p[1]
grad += np.dot(R3, np.transpose(self.atom_positions)).transpose() * grad_p[2]
grad += grad_com
grad = (self.atom_masses * grad.transpose()).transpose() / self.M
return grad
def redistribute_forces(self, p, grad_com, grad_p):
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
grad = np.dot(R1, np.transpose(
self.atom_positions)).transpose() * grad_p[0]
grad += np.dot(R2, np.transpose(
self.atom_positions)).transpose() * grad_p[1]
grad += np.dot(R3, np.transpose(
self.atom_positions)).transpose() * grad_p[2]
grad += grad_com
grad = (self.atom_masses * grad.transpose()).transpose() / self.M
return grad
def metric_tensor(self, p):
"""calculate the mass weighted metric tensor """
R, R1, R2, R3 = rot_mat_derivatives(p, True)
g = np.zeros([3, 3])
g[0, 0] = np.trace(np.dot(R1, np.dot(self.Sm, R1.transpose())))
g[0, 1] = np.trace(np.dot(R1, np.dot(self.Sm, R2.transpose())))
g[0, 2] = np.trace(np.dot(R1, np.dot(self.Sm, R3.transpose())))
g[1, 1] = np.trace(np.dot(R2, np.dot(self.Sm, R2.transpose())))
g[1, 2] = np.trace(np.dot(R2, np.dot(self.Sm, R3.transpose())))
g[2, 2] = np.trace(np.dot(R3, np.dot(self.Sm, R3.transpose())))
g[1, 0] = g[0, 1]
g[2, 1] = g[1, 2]
g[2, 0] = g[0, 2]
gx = np.identity(3) * self.M
return gx, g
def metric_tensor(self, p):
"""calculate the mass weighted metric tensor """
R, R1, R2, R3 = rot_mat_derivatives(p, True)
g = np.zeros([3, 3])
g[0, 0] = np.trace(np.dot(R1, np.dot(self.Sm, R1.transpose())))
g[0, 1] = np.trace(np.dot(R1, np.dot(self.Sm, R2.transpose())))
g[0, 2] = np.trace(np.dot(R1, np.dot(self.Sm, R3.transpose())))
g[1, 1] = np.trace(np.dot(R2, np.dot(self.Sm, R2.transpose())))
g[1, 2] = np.trace(np.dot(R2, np.dot(self.Sm, R3.transpose())))
g[2, 2] = np.trace(np.dot(R3, np.dot(self.Sm, R3.transpose())))
g[1, 0] = g[0, 1]
g[2, 1] = g[1, 2]
g[2, 0] = g[0, 2]
gx = np.identity(3) * self.M
return gx, g