def metric_tensor_cog(self, x, p):
''' calculate the metric tensor when for w_i != m_i '''
R, R1, R2, R3 = rotMatDeriv(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(self, p):
''' calculate the mass weighted metric tensor '''
R, R1, R2, R3 = rotMatDeriv(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 distance_squared_grad(self, com1, p1, com2, p2):
'''
calculate spring force between 2 sites
Parameters
----------
com1:
center of mass of 1st site
p1:
angle axis vector of 1st site
com2:
center of mass of 2nd site
p2:
angle axis vector of 2nd site
sitetype: AASiteType, optional
amgle axis site type with mass and moment of inertia tensor
returns: tuple
spring cart, spring rot
'''
return _aadist.sitedist_grad(self.get_smallest_rij(com1, com2), p1, p2, self.S, self.W, self.cog)
R1, R11, R12, R13 = rotMatDeriv(p1, True)
R2 = rotations.aa2mx(p2)
dR = R2 - R1
dR = dR
g_M = -2.*self.W*(com2-com1)
# dR_kl S_lm dR_km
g_P = np.zeros(3)
g_P[0] = -2.*np.trace(np.dot(R11, np.dot(self.S, dR.transpose())))
g_P[1] = -2.*np.trace(np.dot(R12, np.dot(self.S, dR.transpose())))
g_P[2] = -2.*np.trace(np.dot(R13, np.dot(self.S, dR.transpose())))
g_M -= 2.*self.W * np.dot(dR, self.cog)
g_P[0] -= 2.*self.W * np.dot((com2-com1), np.dot(R11, self.cog))
g_P[1] -= 2.*self.W * np.dot((com2-com1), np.dot(R12, self.cog))
g_P[2] -= 2.*self.W * np.dot((com2-com1), np.dot(R13, self.cog))
return g_M, g_P
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]
from pygmin.potentials.fortran.rmdrvt import rmdrvt as rotMatDeriv
R, R1, R2, R3 = rotMatDeriv(p, True)
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)
def update_rot_mat(self, aa, do_derivatives=True):
self.rotation_mat, self.drmat[0, :, :], self.drmat[
1, :, :], self.drmat[2, :, :] = rotMatDeriv(aa, do_derivatives)
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]
from pygmin.potentials.fortran.rmdrvt import rmdrvt as rotMatDeriv
R, R1, R2, R3 = rotMatDeriv(p, True)
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)
def update_rot_mat(self, aa, do_derivatives = True):
self.rotation_mat, self.drmat[0,:,:], self.drmat[1,:,:], self.drmat[2,:,:] = rotMatDeriv(aa, do_derivatives)