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
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, *dms):
'''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(dms):
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(dms[i], overlap, lf)
occ_model.check_dms(overlap, *dms)
# keep local variables as attributes for inspection/debugging by caller
self._history = self.DIISHistoryClass(lf, self.nvector, ham.ndm, ham.deriv_scale, overlap)
self._focks = [lf.create_two_index() for i in xrange(ham.ndm)]
self._exps = [lf.create_expansion() for i in xrange(ham.ndm)]
if log.do_medium:
log('Starting restricted closed-shell %s-SCF' % self._history.name)
log.hline()
log('Iter Error CN Last nv Method Energy Change')
log.hline()
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# Construct the Fock operator from scratch if the history is empty:
if self._history.nused == 0:
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operators
ham.compute_fock(*self._focks)
# Compute the energy if needed by the history
energy = ham.compute_energy() if self._history.need_energy \
else None
# Add the current fock+dm pair to the history
error = self._history.add(energy, dms, self._focks)
# Screen logging
if log.do_high:
log(' DIIS add')
if error < self.threshold:
converged = True
break
if log.do_high:
log.blank()
if log.do_medium:
energy_str = ' '*20 if energy is None else '% 20.13f' % energy
log('%4i %12.5e %2i %20s' % (
counter, error, self._history.nused, energy_str
))
if log.do_high:
log.blank()
fock_interpolated = False
else:
energy = None
fock_interpolated = True
# Take a regular SCF step using the current fock matrix. Then
# construct a new density matrix and fock matrix.
for i in xrange(ham.ndm):
self._exps[i].from_fock(self._focks[i], overlap)
occ_model.assign(*self._exps)
for i in xrange(ham.ndm):
self._exps[i].to_dm(dms[i])
ham.reset(*dms)
energy = ham.compute_energy() if self._history.need_energy else None
ham.compute_fock(*self._focks)
# Add the current (dm, fock) pair to the history
if log.do_high:
log(' DIIS add')
error = self._history.add(energy, dms, self._focks)
# break when converged
if error < self.threshold:
converged = True
break
# Screen logging
if log.do_high:
log.blank()
if log.do_medium:
energy_str = ' '*20 if energy is None else '% 20.13f' % energy
log('%4i %12.5e %2i %20s' % (
counter, error, self._history.nused, energy_str
))
if log.do_high:
log.blank()
# get extra/intra-polated Fock matrix
while True:
# The following method writes the interpolated dms and focks
# in-place.
energy_approx, coeffs, cn, method, error = self._history.solve(dms, self._focks)
# if the error is small on the interpolated state, we have
# converged to a solution that may have fractional occupation
# numbers.
if error < self.threshold:
converged = True
break
#if coeffs[coeffs<0].sum() < -1:
# if log.do_high:
# log(' DIIS (coeffs too negative) -> drop %i and retry' % self._history.stack[0].identity)
# self._history.shrink()
if self._history.nused <= 2:
break
if coeffs[-1] == 0.0:
if log.do_high:
log(' DIIS (last coeff zero) -> drop %i and retry' % self._history.stack[0].identity)
self._history.shrink()
else:
break
if False and len(coeffs) == 2:
dms_tmp = [dm.copy() for dm in dms]
import matplotlib.pyplot as pt
xs = np.linspace(0.0, 1.0, 25)
a, b = self._history._setup_equations()
energies1 = []
energies2 = []
for x in xs:
x_coeffs = np.array([1-x, x])
energies1.append(np.dot(x_coeffs, 0.5*np.dot(a, x_coeffs) - b))
self._history._build_combinations(x_coeffs, dms_tmp, None)
ham.reset(*dms_tmp)
energies2.append(ham.compute_energy())
print x, energies1[-1], energies2[-1]
pt.clf()
pt.plot(xs, energies1, label='est')
pt.plot(xs, energies2, label='ref')
pt.axvline(coeffs[1], color='k')
pt.legend(loc=0)
pt.savefig('diis_test_%05i.png' % counter)
if energy_approx is not None:
energy_change = energy_approx - min(state.energy for state in self._history.stack)
else:
energy_change = None
# log
if log.do_high:
self._history.log(coeffs)
if log.do_medium:
change_str = ' '*10 if energy_change is None else '% 12.7f' % energy_change
log('%4i %10.3e %12.7f %2i %s %12s' % (
counter, cn, coeffs[-1], self._history.nused, method,
change_str
))
if log.do_high:
log.blank()
if self.prune_old_states:
# get rid of old states with zero coeff
for i in xrange(self._history.nused):
if coeffs[i] == 0.0:
if log.do_high:
log(' DIIS insignificant -> drop %i' % self._history.stack[0].identity)
self._history.shrink()
else:
break
# counter
counter += 1
if log.do_medium:
if converged:
log('%4i %12.5e (converged)' % (counter, error))
log.blank()
if not self.skip_energy or self._history.need_energy:
if not self._history.need_energy:
ham.compute_energy()
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
