def updateRotation(self, x0, E0, grad0_):
iter_rot = 0
# get the zero eigenvalues
zev = []
if(self.zeroEigenVecs):
zev = self.zeroEigenVecs(x0)
# remove zero eigenvalues from gradient
grad0 = grad0_.copy()
evecs = gramm_schmidt(zev + [v[0] for v in self.tau_ignore])
self.orthogonalize(grad0, evecs)
#print u
#print np.dot(u[3],u[4]),np.dot(u[3],u[5]),np.dot(u[5],u[4])
#print self.potential.getEnergy(x0) - self.potential.getEnergy(x0 + 1e-8*u[3]/1e-8),\
#self.potential.getEnergy(x0) - self.potential.getEnergy(x0 + 1e-8*u[4]/1e-8),\
#self.potential.getEnergy(x0) - self.potential.getEnergy(x0 + 1e-8*u[5]/1e-8)
#print gramm_schmidt(zev)
# update ignore list for eigenvalues
for t in self.tau_ignore:
E,grad1 = self.potential.getEnergyGradient(x0 + t[0]*self.delta)
#grad1 = self.getOrthogonalGradient(x0 + t[1]*self.delta, zev)
t[1] = np.dot((grad1 - grad0), t[0])/self.delta
while iter_rot < self.max_rotsteps:
#self.tau = self.tau/np.linalg.norm(self.tau)
# construct dimer image and get energy + gradient
# remove zero eigenvalues from tau
self.orthogonalize(self.tau, evecs)
self.tau /= np.linalg.norm(self.tau)
x1 = x0 + self.tau*self.delta
grad1 = self.getOrthogonalGradient(x1, evecs)
# calculate the rotational force of dimer
F_rot = -2.*(grad1 - grad0) + 2.*np.dot(grad1 - grad0, self.tau)*self.tau
# For now just use steepest descent search direction for rotation.
# Replace this by LBFGS
Theta = F_rot / np.linalg.norm(F_rot)
# calculate curvature C and derivative of curvature
C = np.dot((grad1 - grad0), self.tau)/self.delta
dC = 2.*np.dot((grad1 - grad0), Theta)/self.delta
#print C,self.tau
# calculate estimated rotation angle
theta1=-0.5*np.arctan(dC/(2.*np.abs(C)))
# do we need to rotate or already smaller than cutoff?
if np.abs(theta1) < self.theta_cut:
return
# create rotated trial dimer
taup = self.rotate(self.tau, Theta, theta1)
# remove zero eigenvalues from tau
self.orthogonalize(taup, evecs)
taup /= np.linalg.norm(taup)
x1p = x0 + self.delta * taup
# get the new energy and gradient at trial conviguration
grad1p = self.getOrthogonalGradient(x1p, evecs)
#grad1p = -grad1p
# get curvature for trial point
Cp = np.dot((grad1p - grad0), taup)/self.delta
# calculate optimum rotation angle theta_min and taumin
b1 = 0.5*dC
a1 = (C - Cp + b1*np.sin(2.*theta1))/(1. - np.cos(2.*theta1))
theta_min=0.5*np.arctan(b1/a1)
self.tau = self.rotate(self.tau, Theta, theta_min)
# remove zero eigenvalues from tau
self.orthogonalize(self.tau, evecs)
self.tau /= np.linalg.norm(self.tau)
if np.abs(theta_min) < self.theta_cut:
return
iter_rot+=1
natoms = 1000
system = LJCluster(natoms)
#system.params.structural_quench_params.debug = True
#system.params.structural_quench_params.iprint = 100
db = system.create_database()
bh = system.get_basinhopping(db)
bh.run(1)
m = db.minima()[0]
coords = m.coords
potential = system.get_potential()
energy, gradient, hessian = potential.getEnergyGradientHessian(coords)
dummy_vec = ts.gramm_schmidt(ts.zeroEV_cluster(coords))
shifted_hess = hessian.copy()
for i in range(6):
shifted_hess += np.outer(dummy_vec[i], dummy_vec[i])
shifted_eval, shifted_evec = get_sorted_eig(shifted_hess)
print "First log sum: ", np.sum(np.log(shifted_eval[6:]))
sparse_hess = scipy.sparse.csc_matrix(shifted_hess)
factor = cholmod.cholesky(sparse_hess)
diagonal = np.diagonal(factor.L().todense())
def get_eigenvecs(self, x0):
zev = []
if(self.zeroEigenVecs):
zev = self.zeroEigenVecs(x0)
# print "lenzev", len(zev)
return gramm_schmidt(zev + [v[0] for v in self.tau_ignore])
natoms = 1000
system = LJCluster(natoms)
#system.params.structural_quench_params.debug = True
#system.params.structural_quench_params.iprint = 100
db = system.create_database()
bh = system.get_basinhopping(db)
bh.run(1)
m = db.minima()[0]
coords = m.coords
potential = system.get_potential()
energy, gradient, hessian = potential.getEnergyGradientHessian(coords)
dummy_vec = ts.gramm_schmidt(ts.zeroEV_cluster(coords))
shifted_hess = hessian.copy()
for i in range(6):
shifted_hess += np.outer(dummy_vec[i], dummy_vec[i])
shifted_eval, shifted_evec = get_sorted_eig(shifted_hess)
print("First log sum: ", np.sum(np.log(shifted_eval[6:])))
sparse_hess = scipy.sparse.csc_matrix(shifted_hess)
factor = cholmod.cholesky(sparse_hess)
diagonal = np.diagonal(factor.L().todense())