def convergence_error_commutator(ham, lf, overlap, *dms):
'''Compute the commutator error
**Arguments:**
ham
A Hamiltonian instance.
lf
The linalg factory to be used.
overlap
The overlap operator.
dm1, dm2, ...
A list of density matrices. The numbers of dms must match ham.ndm.
**Returns:** The commutator error. This measure (not this function) is
also used in some SCF algorithms to check for convergence.
'''
if len(dms) != ham.ndm:
raise TypeError('Expecting %i density matrices, got %i.' %
(ham.ndm, len(dms)))
ham.reset(*dms)
focks = [lf.create_two_index() for i in xrange(ham.ndm)]
ham.compute_fock(*focks)
error = 0.0
work = lf.create_two_index()
commutator = lf.create_two_index()
errorsq = 0.0
for i in xrange(ham.ndm):
compute_commutator(dms[i], focks[i], overlap, work, commutator)
errorsq += commutator.contract_two('ab,ab', commutator)
return errorsq**0.5
def convergence_error_commutator(ham, lf, overlap, *dms):
'''Compute the commutator error
**Arguments:**
ham
A Hamiltonian instance.
lf
The linalg factory to be used.
overlap
The overlap operator.
dm1, dm2, ...
A list of density matrices. The numbers of dms must match ham.ndm.
**Returns:** The commutator error. This measure (not this function) is
also used in some SCF algorithms to check for convergence.
'''
if len(dms) != ham.ndm:
raise TypeError('Expecting %i density matrices, got %i.' % (ham.ndm, len(dms)))
ham.reset(*dms)
focks = [lf.create_two_index() for i in xrange(ham.ndm)]
ham.compute_fock(*focks)
error = 0.0
work = lf.create_two_index()
commutator = lf.create_two_index()
errorsq = 0.0
for i in xrange(ham.ndm):
compute_commutator(dms[i], focks[i], overlap, work, commutator)
errorsq += commutator.contract_two('ab,ab', commutator)
return errorsq**0.5
def _build_combinations(self, coeffs, dms_output, focks_output):
'''Construct a linear combination of density/fock matrices
**Arguments:**
coeffs
The linear mixing coefficients for the previous SCF states.
dms_output
A list of output density matrices. (Ignored if None)
focks_output
A list of output density matrices. (Ignored if None)
**Returns:** the commutator error, only when both dms_output and
focks_output are given.
'''
if dms_output is not None:
if len(dms_output) != self.ndm:
raise TypeError('The number of density matrices must match the ndm parameter.')
for i in xrange(self.ndm):
dms_stack = [self.stack[j].dms[i] for j in xrange(self.nused)]
self._linear_combination(coeffs, dms_stack, dms_output[i])
if focks_output is not None:
if len(focks_output) != self.ndm:
raise TypeError('The number of Fock matrices must match the ndm parameter.')
for i in xrange(self.ndm):
focks_stack = [self.stack[j].focks[i] for j in xrange(self.nused)]
self._linear_combination(coeffs, focks_stack, focks_output[i])
if not (dms_output is None or focks_output is None):
errorsq = 0.0
for i in xrange(self.ndm):
compute_commutator(dms_output[i], focks_output[i], self.overlap, self.work, self.commutator)
errorsq += self.commutator.contract_two('ab,ab', self.commutator)
return errorsq**0.5
def assign(self, identity, energy, dms, focks):
'''Assign a new state.
**Arguments:**
identity
A unique id for the new state.
energy
The energy of the new state.
dm
The density matrix of the new state.
fock
The Fock matrix of the new state.
'''
self.identity = identity
self.energy = energy
self.normsq = 0.0
for i in xrange(self.ndm):
self.dms[i].assign(dms[i])
self.focks[i].assign(focks[i])
compute_commutator(dms[i], focks[i], self.overlap, self.work, self.commutators[i])
self.normsq += self.commutators[i].contract_two('ab,ab', self.commutators[i])
def convergence_error_commutator(ham, overlap, *dms):
'''Compute the commutator error
Parameters
----------
ham
A Hamiltonian instance.
overlap
The overlap operator.
dm1, dm2, ...
A list of density matrices. The numbers of dms must match ham.ndm.
Returns
-------
error: float
The commutator error. This measure (not this function) is also used in some SCF
algorithms to check for convergence.
'''
if len(dms) != ham.ndm:
raise TypeError('Expecting %i density matrices, got %i.' %
(ham.ndm, len(dms)))
ham.reset(*dms)
focks = [np.zeros(dms[0].shape) for i in xrange(ham.ndm)]
ham.compute_fock(*focks)
error = 0.0
errorsq = 0.0
for i in xrange(ham.ndm):
commutator = compute_commutator(dms[i], focks[i], overlap)
errorsq += np.einsum('ab,ab', commutator, commutator)
return errorsq**0.5
def convergence_error_commutator(ham, overlap, *dms):
'''Compute the commutator error
Parameters
----------
ham
A Hamiltonian instance.
overlap
The overlap operator.
dm1, dm2, ...
A list of density matrices. The numbers of dms must match ham.ndm.
Returns
-------
error: float
The commutator error. This measure (not this function) is also used in some SCF
algorithms to check for convergence.
'''
if len(dms) != ham.ndm:
raise TypeError('Expecting %i density matrices, got %i.' % (ham.ndm, len(dms)))
ham.reset(*dms)
focks = [np.zeros(dms[0].shape) for i in xrange(ham.ndm)]
ham.compute_fock(*focks)
error = 0.0
errorsq = 0.0
for i in xrange(ham.ndm):
commutator = compute_commutator(dms[i], focks[i], overlap)
errorsq += np.einsum('ab,ab', commutator, commutator)
return errorsq**0.5
def assign(self, identity, energy, dms, focks):
'''Assign a new state.
**Arguments:**
identity
A unique id for the new state.
energy
The energy of the new state.
dm
The density matrix of the new state.
fock
The Fock matrix of the new state.
'''
self.identity = identity
self.energy = energy
self.normsq = 0.0
for i in xrange(self.ndm):
self.dms[i][:] = dms[i]
self.focks[i][:] = focks[i]
self.commutators[i][:] = compute_commutator(
dms[i], focks[i], self.overlap)
self.normsq += np.einsum('ab,ab', self.commutators[i],
self.commutators[i])
def assign(self, identity, energy, dms, focks):
'''Assign a new state.
**Arguments:**
identity
A unique id for the new state.
energy
The energy of the new state.
dm
The density matrix of the new state.
fock
The Fock matrix of the new state.
'''
self.identity = identity
self.energy = energy
self.normsq = 0.0
for i in xrange(self.ndm):
self.dms[i][:] = dms[i]
self.focks[i][:] = focks[i]
self.commutators[i][:] = compute_commutator(dms[i], focks[i], self.overlap)
self.normsq += np.einsum('ab,ab', self.commutators[i], self.commutators[i])
def __call__(self, ham, overlap, occ_model, *dm0s):
'''Find a self-consistent set of density matrices.
**Arguments:**
ham
An effective Hamiltonian.
overlap
The overlap operator.
occ_model
Model for the orbital occupations.
dm1, dm2, ...
The initial density matrices. The number of dms must match
ham.ndm.
'''
# Some type checking
if ham.ndm != len(dm0s):
raise TypeError(
'The number of initial density matrices does not match the Hamiltonian.'
)
# Check input density matrices.
for i in xrange(ham.ndm):
check_dm(dm0s[i], overlap)
occ_model.check_dms(overlap, *dm0s)
if log.do_medium:
log('Starting SCF with optimal damping. ham.ndm=%i' % ham.ndm)
log.hline()
log(' Iter Energy Error Mixing')
log.hline()
fock0s = [np.zeros(overlap.shape) for i in xrange(ham.ndm)]
fock1s = [np.zeros(overlap.shape) for i in xrange(ham.ndm)]
dm1s = [np.zeros(overlap.shape) for i in xrange(ham.ndm)]
orbs = [Orbitals(overlap.shape[0]) for i in xrange(ham.ndm)]
work = np.zeros(dm0s[0].shape)
commutator = np.zeros(dm0s[0].shape)
converged = False
counter = 0
mixing = None
error = None
while self.maxiter is None or counter < self.maxiter:
# feed the latest density matrices in the hamiltonian
ham.reset(*dm0s)
# Construct the Fock operators in point 0
ham.compute_fock(*fock0s)
# Compute the energy in point 0
energy0 = ham.compute_energy()
if log.do_medium:
if mixing is None:
log('%5i %20.13f' % (counter, energy0))
else:
log('%5i %20.13f %12.5e %10.5f' %
(counter, energy0, error, mixing))
# go to point 1 by diagonalizing the fock matrices
for i in xrange(ham.ndm):
orbs[i].from_fock(fock0s[i], overlap)
# Assign new occupation numbers.
occ_model.assign(*orbs)
# Construct the density matrices
for i in xrange(ham.ndm):
dm1s[i][:] = orbs[i].to_dm()
# feed the latest density matrices in the hamiltonian
ham.reset(*dm1s)
# Compute the fock matrices in point 1
ham.compute_fock(*fock1s)
# Compute the energy in point 1
energy1 = ham.compute_energy()
# Compute the derivatives of the energy at point 0 and 1 for a
# linear interpolation of the density matrices
deriv0 = 0.0
deriv1 = 0.0
for i in xrange(ham.ndm):
deriv0 += np.einsum('ab,ab', fock0s[i], dm1s[i])
deriv0 -= np.einsum('ab,ab', fock0s[i], dm0s[i])
deriv1 += np.einsum('ab,ab', fock1s[i], dm1s[i])
deriv1 -= np.einsum('ab,ab', fock1s[i], dm0s[i])
deriv0 *= ham.deriv_scale
deriv1 *= ham.deriv_scale
# find the lambda that minimizes the cubic polynomial in the range [0,1]
if log.do_high:
log(' E0: % 10.5e D0: % 10.5e' %
(energy0, deriv0))
log(' E1-E0: % 10.5e D1: % 10.5e' %
(energy1 - energy0, deriv1))
mixing = find_min_cubic(energy0, energy1, deriv0, deriv1)
if self.debug:
check_cubic(ham, dm0s, dm1s, energy0, energy1, deriv0, deriv1)
# compute the mixed density and fock matrices (in-place in dm0s and fock0s)
for i in xrange(ham.ndm):
dm0s[i][:] *= 1 - mixing
dm0s[i][:] += dm1s[i] * mixing
fock0s[i][:] *= 1 - mixing
fock0s[i][:] += fock1s[i] * mixing
# Compute the convergence criterion.
errorsq = 0.0
for i in xrange(ham.ndm):
commutator = compute_commutator(dm0s[i], fock0s[i], overlap)
errorsq += np.einsum('ab,ab', commutator, commutator)
error = errorsq**0.5
if error < self.threshold:
converged = True
break
elif mixing == 0.0:
raise NoSCFConvergence(
'The ODA algorithm made a zero step without reaching convergence.'
)
# counter
counter += 1
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
def __call__(self, ham, lf, overlap, occ_model, *dm0s):
'''Find a self-consistent set of density matrices.
**Arguments:**
ham
An effective Hamiltonian.
lf
The linalg factory to be used.
overlap
The overlap operator.
occ_model
Model for the orbital occupations.
dm1, dm2, ...
The initial density matrices. The number of dms must match
ham.ndm.
'''
# Some type checking
if ham.ndm != len(dm0s):
raise TypeError('The number of initial density matrices does not match the Hamiltonian.')
# Check input density matrices.
for i in xrange(ham.ndm):
check_dm(dm0s[i], overlap, lf)
occ_model.check_dms(overlap, *dm0s)
if log.do_medium:
log('Starting SCF with optimal damping. ham.ndm=%i' % ham.ndm)
log.hline()
log(' Iter Energy Error Mixing')
log.hline()
fock0s = [lf.create_two_index() for i in xrange(ham.ndm)]
fock1s = [lf.create_two_index() for i in xrange(ham.ndm)]
dm1s = [lf.create_two_index() for i in xrange(ham.ndm)]
exps = [lf.create_expansion() for i in xrange(ham.ndm)]
work = dm0s[0].new()
commutator = dm0s[0].new()
converged = False
counter = 0
mixing = None
error = None
while self.maxiter is None or counter < self.maxiter:
# feed the latest density matrices in the hamiltonian
ham.reset(*dm0s)
# Construct the Fock operators in point 0
ham.compute_fock(*fock0s)
# Compute the energy in point 0
energy0 = ham.compute_energy()
if log.do_medium:
if mixing is None:
log('%5i %20.13f' % (counter, energy0))
else:
log('%5i %20.13f %12.5e %10.5f' % (counter, energy0, error, mixing))
# go to point 1 by diagonalizing the fock matrices
for i in xrange(ham.ndm):
exps[i].from_fock(fock0s[i], overlap)
# Assign new occupation numbers.
occ_model.assign(*exps)
# Construct the density matrices
for i in xrange(ham.ndm):
exps[i].to_dm(dm1s[i])
# feed the latest density matrices in the hamiltonian
ham.reset(*dm1s)
# Compute the fock matrices in point 1
ham.compute_fock(*fock1s)
# Compute the energy in point 1
energy1 = ham.compute_energy()
# Compute the derivatives of the energy at point 0 and 1 for a
# linear interpolation of the density matrices
deriv0 = 0.0
deriv1 = 0.0
for i in xrange(ham.ndm):
deriv0 += fock0s[i].contract_two('ab,ab', dm1s[i])
deriv0 -= fock0s[i].contract_two('ab,ab', dm0s[i])
deriv1 += fock1s[i].contract_two('ab,ab', dm1s[i])
deriv1 -= fock1s[i].contract_two('ab,ab', dm0s[i])
deriv0 *= ham.deriv_scale
deriv1 *= ham.deriv_scale
# find the lambda that minimizes the cubic polynomial in the range [0,1]
if log.do_high:
log(' E0: % 10.5e D0: % 10.5e' % (energy0, deriv0))
log(' E1-E0: % 10.5e D1: % 10.5e' % (energy1-energy0, deriv1))
mixing = find_min_cubic(energy0, energy1, deriv0, deriv1)
if self.debug:
check_cubic(ham, dm0s, dm1s, energy0, energy1, deriv0, deriv1)
# compute the mixed density and fock matrices (in-place in dm0s and fock0s)
for i in xrange(ham.ndm):
dm0s[i].iscale(1-mixing)
dm0s[i].iadd(dm1s[i], mixing)
fock0s[i].iscale(1-mixing)
fock0s[i].iadd(fock1s[i], mixing)
# Compute the convergence criterion.
errorsq = 0.0
for i in xrange(ham.ndm):
compute_commutator(dm0s[i], fock0s[i], overlap, work, commutator)
errorsq += commutator.contract_two('ab,ab', commutator)
error = errorsq**0.5
if error < self.threshold:
converged = True
break
elif mixing == 0.0:
raise NoSCFConvergence('The ODA algorithm made a zero step without reaching convergence.')
# counter
counter += 1
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter