def do_no_stepsearch(self, obj, one, two, orb, **kwargs):
'''Scale step size with factor self.alpha
**Arguments:**
obj
A class instance containing the objective function.
one, two
One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky
instances)
orb
An Expansion instance. Contains the MO coefficients
**Keywords:**
:kappa: Initial step size (OneIndex instance)
'''
kappa = kwargs.get('kappa')
#
# Scale current optimization step, rotate orbitals
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
rotate_orbitals(orb, rotation)
#
# Solve for wfn/population model
#
try:
obj.solve_model(one, two, orb, **kwargs)
except:
pass
def do_no_stepsearch(self, obj, one, two, orb, **kwargs):
'''Scale step size with factor self.alpha
**Arguments:**
obj
A class instance containing the objective function.
one, two
One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky
instances)
orb
An Expansion instance. Contains the MO coefficients
**Keywords:**
:kappa: Initial step size (OneIndex instance)
'''
kappa = kwargs.get('kappa')
#
# Scale current optimization step, rotate orbitals
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
rotate_orbitals(orb, rotation)
#
# Solve for wfn/population model
#
try:
obj.solve_model(one, two, orb, **kwargs)
except:
pass
def do_trust_region(self, obj, one, two, orb, **kwargs):
'''Do trust-region optimization.
**Arguments:**
obj
A class instance containing the objective function.
one/two
One and Two-body Hamiltonian (TwoIndex and FourIndex/Cholesky
instances)
orb
(Expansion instance) An MO expansion
**Keywords:**
:kappa: Initial step size (OneIndex instance)
:gradient: Orbital gradient (OneIndex instance)
:hessian: Orbital Hessian (OneIndex instance)
'''
kappa = kwargs.get('kappa')
gradient = kwargs.get('gradient')
hessian = kwargs.get('hessian')
iteri = 1
ofun_ref = obj.compute_objective_function()
De = 0.0
stepn = kappa.copy()
while True:
norm = stepn.norm()
#
# If ||kappa||_2 is outside the trust region, find a new Newton
# step inside the trust region:
#
if norm > self.trustradius:
#
# Preconditioned conjugate gradient
#
if self.optimizer == 'pcg':
optimizer = TruncatedCG(self.lf, gradient, hessian, self.trustradius)
optimizer(**{'niter': self.maxiterinner, 'abstol': self.threshold})
stepn = optimizer.step
#
# Powell's dogleg optimization:
#
elif self.optimizer == 'dogleg':
optimizer = Dogleg(kappa, gradient, hessian, self.trustradius)
optimizer()
stepn = optimizer.step
#
# Powell's double dogleg optimization:
#
elif self.optimizer == 'ddl':
optimizer = DoubleDogleg(kappa, gradient, hessian, self.trustradius)
optimizer()
stepn = optimizer.step
#
# New rotation
#
rotation = obj.compute_rotation_matrix(stepn)
orb_ = orb.copy()
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function after rotation
#
ofun = obj.compute_objective_function()
#
# Determine ratio for a given step:
#
hstep = hessian.new()
hessian.mult(stepn, hstep)
Destimate = gradient.dot(stepn)+0.5*stepn.dot(hstep)
De = ofun-ofun_ref
rho = De/Destimate
#
# For a given ratio, adjust trust radius and accept or reject
# Newton step:
#
if rho > self.maxeta and De <= 0.0:
#
# Enlarge trust radius:
#
new = min(self.upscale*self.trustradius,self.maxtrustradius)
self.update_trustradius(new)
orb.assign(orb_)
break
elif rho >= self.mineta and rho <= self.maxeta and De <= 0.0:
#
# Do nothing with trust radius:
#
orb.assign(orb_)
break
elif rho > 0 and rho < self.mineta and De <= 0.0:
#
# Decrease trust radius:
#
self.update_trustradius(self.downscale*self.trustradius)
orb.assign(orb_)
break
else:
#
# Bad step! Reject Newton step and repeat with smaller trust
# radius
#
self.update_trustradius(self.downscale*self.trustradius)
iteri = iteri+1
if iteri > self.maxiterouter:
log('Warning: Trust region search not converged after %i iterations. Trust region search aborted.' %self.maxiterouter)
orb.assign(orb_)
break
def do_backtracking(self, obj, one, two, orb, **kwargs):
'''Backtracking line search.
**Arguments:**
obj
A class instance containing the objctive function.
one, two
One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky
instances)
orb
An Expansion instance. Contains the MO coefficients
**Keywords:**
:kappa: Initial step size (OneIndex instance)
:gradient: Orbital gradient (OneIndex instance)
'''
kappa = kwargs.get('kappa')
gradient = kwargs.get('gradient')
#
# Update scaling factor to initial value
#
self.update_alpha(self.alpha0)
#
# Calculate objective function
#
ofun_ref = obj.compute_objective_function()
#
# Copy current orbitals
#
orb_ = orb.copy()
#
# Initial rotation
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function for rotated orbitals
#
ofun = obj.compute_objective_function()
#
# reduce step size until line search condition is satisfied
#
while self.check_line_search_condition(ofun, ofun_ref, kappa, gradient):
self.update_alpha(self.alpha*self.downscale)
#
# New rotation
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
orb_ = orb.copy()
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function for scaled rotation
#
ofun = obj.compute_objective_function()
#
# Abort if scaling factor falls below threshold
#
if self.alpha < self.minalpha:
break
orb.assign(orb_)
def do_trust_region(self, obj, one, two, orb, **kwargs):
'''Do trust-region optimization.
**Arguments:**
obj
A class instance containing the objective function.
one/two
One and Two-body Hamiltonian (TwoIndex and FourIndex/Cholesky
instances)
orb
(Expansion instance) An MO expansion
**Keywords:**
:kappa: Initial step size (OneIndex instance)
:gradient: Orbital gradient (OneIndex instance)
:hessian: Orbital Hessian (OneIndex instance)
'''
kappa = kwargs.get('kappa')
gradient = kwargs.get('gradient')
hessian = kwargs.get('hessian')
iteri = 1
ofun_ref = obj.compute_objective_function()
De = 0.0
stepn = kappa.copy()
while True:
norm = stepn.norm()
#
# If ||kappa||_2 is outside the trust region, find a new Newton
# step inside the trust region:
#
if norm > self.trustradius:
#
# Preconditioned conjugate gradient
#
if self.optimizer == 'pcg':
optimizer = TruncatedCG(self.lf, gradient, hessian,
self.trustradius)
optimizer(**{
'niter': self.maxiterinner,
'abstol': self.threshold
})
stepn = optimizer.step
#
# Powell's dogleg optimization:
#
elif self.optimizer == 'dogleg':
optimizer = Dogleg(kappa, gradient, hessian,
self.trustradius)
optimizer()
stepn = optimizer.step
#
# Powell's double dogleg optimization:
#
elif self.optimizer == 'ddl':
optimizer = DoubleDogleg(kappa, gradient, hessian,
self.trustradius)
optimizer()
stepn = optimizer.step
#
# New rotation
#
rotation = obj.compute_rotation_matrix(stepn)
orb_ = orb.copy()
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function after rotation
#
ofun = obj.compute_objective_function()
#
# Determine ratio for a given step:
#
hstep = hessian.new()
hessian.mult(stepn, hstep)
Destimate = gradient.dot(stepn) + 0.5 * stepn.dot(hstep)
De = ofun - ofun_ref
rho = De / Destimate
#
# For a given ratio, adjust trust radius and accept or reject
# Newton step:
#
if rho > self.maxeta and De <= 0.0:
#
# Enlarge trust radius:
#
new = min(self.upscale * self.trustradius, self.maxtrustradius)
self.update_trustradius(new)
orb.assign(orb_)
break
elif rho >= self.mineta and rho <= self.maxeta and De <= 0.0:
#
# Do nothing with trust radius:
#
orb.assign(orb_)
break
elif rho > 0 and rho < self.mineta and De <= 0.0:
#
# Decrease trust radius:
#
self.update_trustradius(self.downscale * self.trustradius)
orb.assign(orb_)
break
else:
#
# Bad step! Reject Newton step and repeat with smaller trust
# radius
#
self.update_trustradius(self.downscale * self.trustradius)
iteri = iteri + 1
if iteri > self.maxiterouter:
log('Warning: Trust region search not converged after %i iterations. Trust region search aborted.'
% self.maxiterouter)
orb.assign(orb_)
break
def do_backtracking(self, obj, one, two, orb, **kwargs):
'''Backtracking line search.
**Arguments:**
obj
A class instance containing the objctive function.
one, two
One- and Two-electron integrals (TwoIndex and FourIndex/Cholesky
instances)
orb
An Expansion instance. Contains the MO coefficients
**Keywords:**
:kappa: Initial step size (OneIndex instance)
:gradient: Orbital gradient (OneIndex instance)
'''
kappa = kwargs.get('kappa')
gradient = kwargs.get('gradient')
#
# Update scaling factor to initial value
#
self.update_alpha(self.alpha0)
#
# Calculate objective function
#
ofun_ref = obj.compute_objective_function()
#
# Copy current orbitals
#
orb_ = orb.copy()
#
# Initial rotation
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function for rotated orbitals
#
ofun = obj.compute_objective_function()
#
# reduce step size until line search condition is satisfied
#
while self.check_line_search_condition(ofun, ofun_ref, kappa,
gradient):
self.update_alpha(self.alpha * self.downscale)
#
# New rotation
#
kappa.iscale(self.alpha)
rotation = obj.compute_rotation_matrix(kappa)
orb_ = orb.copy()
rotate_orbitals(orb_, rotation)
#
# Solve for wfn/population model if required
#
try:
obj.solve_model(one, two, orb_, **kwargs)
except:
pass
#
# Calculate objective function for scaled rotation
#
ofun = obj.compute_objective_function()
#
# Abort if scaling factor falls below threshold
#
if self.alpha < self.minalpha:
break
orb.assign(orb_)