def __call__(self):
"""dumps single-orbital entropy and orbital-pair mututal information
see :py:meth:`horton.orbital_entanglement.orbital_entanglement.OrbitalEntanglement.dump_output` for more info
"""
if log.do_medium:
log(' ')
log('Calculating orbital entanglement measures')
log(' ')
#
# Compute single-orbital entropy and mutual information
#
if log.do_medium:
log(' Computing s(1) and I_ij')
self.compute_single_orbital_entropy()
self.compute_two_orbital_entropy()
self.compute_mutual_information()
#
# Dump output to file:
#
if log.do_medium:
log(' Dumping output files')
log(' ')
log.hline('=')
self.dump_output()
def __call__(self):
"""dumps single-orbital entropy and orbital-pair mututal information
see :py:meth:`horton.orbital_entanglement.orbital_entanglement.OrbitalEntanglement.dump_output` for more info
"""
if log.do_medium:
log(' ')
log('Calculating orbital entanglement measures')
log(' ')
#
# Compute single-orbital entropy and mutual information
#
if log.do_medium:
log(' Computing s(1) and I_ij')
self.compute_single_orbital_entropy()
self.compute_two_orbital_entropy()
self.compute_mutual_information()
#
# Dump output to file:
#
if log.do_medium:
log(' Dumping output files')
log(' ')
log.hline('=')
self.dump_output()
def normalize(self):
if log.do_medium:
log('Normalizing proatoms to integer populations')
log(' Z charge before after')
log.hline()
for number in self.get_numbers():
rgrid = self.get_rgrid(number)
for charge in self.get_charges(number):
r = self.get_record(number, charge)
nel_before = rgrid.integrate(r.rho)
nel_integer = r.pseudo_number - charge
r.rho[:] *= nel_integer / nel_before
nel_after = rgrid.integrate(r.rho)
if log.do_medium:
log('%4i %+3i %15.8e %15.8e' %
(number, charge, nel_before, nel_after))
def normalize(self):
if log.do_medium:
log('Normalizing proatoms to integer populations')
log(' Z charge before after')
log.hline()
for number in self.get_numbers():
rgrid = self.get_rgrid(number)
for charge in self.get_charges(number):
r = self.get_record(number, charge)
nel_before = rgrid.integrate(r.rho)
nel_integer = r.pseudo_number - charge
r.rho[:] *= nel_integer/nel_before
nel_after = rgrid.integrate(r.rho)
if log.do_medium:
log('%4i %+3i %15.8e %15.8e' % (
number, charge, nel_before, nel_after
))
def _init_log_memory(self):
if log.do_medium:
# precompute arrays sizes for certain grids
nbyte_global = self.grid.size*8
nbyte_locals = np.array([self.get_grid(i).size*8 for i in xrange(self.natom)])
# compute and report usage
estimates = self.get_memory_estimates()
nbyte_total = 0
log('Coarse estimate of memory usage for the partitioning:')
log(' Label Memory[GB]')
log.hline()
for label, nlocals, nglobal in estimates:
nbyte = np.dot(nlocals, nbyte_locals) + nglobal*nbyte_global
log('%30s %10.3f' % (label, nbyte/1024.0**3))
nbyte_total += nbyte
log('%30s %10.3f' % ('Total', nbyte_total/1024.0**3))
log.hline()
log.blank()
def _init_log_memory(self):
if log.do_medium:
# precompute arrays sizes for certain grids
nbyte_global = self.grid.size*8
nbyte_locals = np.array([self.get_grid(i).size*8 for i in xrange(self.natom)])
# compute and report usage
estimates = self.get_memory_estimates()
nbyte_total = 0
log('Coarse estimate of memory usage for the partitioning:')
log(' Label Memory[GB]')
log.hline()
for label, nlocals, nglobal in estimates:
nbyte = np.dot(nlocals, nbyte_locals) + nglobal*nbyte_global
log('%30s %10.3f' % (label, nbyte/1024.0**3))
nbyte_total += nbyte
log('%30s %10.3f' % ('Total', nbyte_total/1024.0**3))
log.hline()
log.blank()
def log(self):
log(' Nr Pop Chg Energy Ionization Affinity')
log.hline()
for number, cases in sorted(self.all.iteritems()):
for pop, energy in sorted(cases.iteritems()):
energy_prev = cases.get(pop-1)
if energy_prev is None:
ip_str = ''
else:
ip_str = '% 18.10f' % (energy_prev - energy)
energy_next = cases.get(pop+1)
if energy_next is None:
ea_str = ''
else:
ea_str = '% 18.10f' % (energy - energy_next)
log('%3i %3i %+3i % 18.10f %18s %18s' % (
number, pop, number-pop, energy, ip_str, ea_str
))
log.blank()
def log(self):
log(' Nr Pop Chg Energy Ionization Affinity'
)
log.hline()
for number, cases in sorted(self.all.iteritems()):
for pop, energy in sorted(cases.iteritems()):
energy_prev = cases.get(pop - 1)
if energy_prev is None:
ip_str = ''
else:
ip_str = '% 18.10f' % (energy_prev - energy)
energy_next = cases.get(pop + 1)
if energy_next is None:
ea_str = ''
else:
ea_str = '% 18.10f' % (energy - energy_next)
log('%3i %3i %+3i % 18.10f %18s %18s' %
(number, pop, number - pop, energy, ip_str, ea_str))
log.blank()
def do_partitioning(self):
# Perform one general check in the beginning to avoid recomputation
new = any(('at_weights', i) not in self.cache for i in xrange(self.natom))
new |= 'niter' not in self.cache
new |= 'change'not in self.cache
if new:
propars = self._init_propars()
if log.medium:
log.hline()
log('Iteration Change')
log.hline()
counter = 0
change = 1e100
while True:
counter += 1
# Update the parameters that determine the pro-atoms.
old_propars = propars.copy()
self._update_propars()
# Check for convergence
change = self.compute_change(propars, old_propars)
if log.medium:
log('%9i %10.5e' % (counter, change))
if change < self._threshold or counter >= self._maxiter:
break
if log.medium:
log.hline()
self._finalize_propars()
self.cache.dump('niter', counter, tags='o')
self.cache.dump('change', change, tags='o')
def compact(self, nel_lost):
'''Make the pro-atoms more compact
**Argument:**
nel_lost
This parameter controls the part of the tail that gets
neglected. This is the (maximym) number of electrons in the part
that gets discarded.
Note that only 'safe' atoms are considered to determine the cutoff
radius.
'''
if log.do_medium:
log('Reducing extents of the pro-atoms')
log(' Z npiont radius')
log.hline()
for number in self.get_numbers():
rgrid = self.get_rgrid(number)
npoint = 0
for charge in self.get_charges(number, safe=True):
r = self.get_record(number, charge)
nel = r.pseudo_number-charge
npoint = max(npoint, r.compute_radii([nel-nel_lost])[0][0]+1)
for charge in self.get_charges(number):
r = self.get_record(number, charge)
r.chop(npoint)
new_rgrid = self._rgrid_map[number].chop(npoint)
self._rgrid_map[number] = new_rgrid
if log.do_medium:
log('%4i %5i -> %5i %10.3e -> %10.3e' % (
number, rgrid.size, new_rgrid.size, rgrid.radii[-1],
new_rgrid.radii[-1]
))
if log.do_medium:
log.hline()
def compact(self, nel_lost):
'''Make the pro-atoms more compact
**Argument:**
nel_lost
This parameter controls the part of the tail that gets
neglected. This is the (maximym) number of electrons in the part
that gets discarded.
Note that only 'safe' atoms are considered to determine the cutoff
radius.
'''
if log.do_medium:
log('Reducing extents of the pro-atoms')
log(' Z npiont radius')
log.hline()
for number in self.get_numbers():
rgrid = self.get_rgrid(number)
npoint = 0
for charge in self.get_charges(number, safe=True):
r = self.get_record(number, charge)
nel = r.pseudo_number-charge
npoint = max(npoint, r.compute_radii([nel-nel_lost])[0][0]+1)
for charge in self.get_charges(number):
r = self.get_record(number, charge)
r.chop(npoint)
new_rgrid = self._rgrid_map[number].chop(npoint)
self._rgrid_map[number] = new_rgrid
if log.do_medium:
log('%4i %5i -> %5i %10.3e -> %10.3e' % (
number, rgrid.size, new_rgrid.size, rgrid.radii[-1],
new_rgrid.radii[-1]
))
if log.do_medium:
log.hline()
def log_energy(self):
'''Write an overview of the last energy computation on screen'''
log('Contributions to the energy:')
log.hline()
log(' Energy term Value')
log.hline()
for term in self.terms:
energy = self.system.extra['energy_%s' % term.label]
log('%50s %20.12f' % (term.label, energy))
log('%50s %20.12f' % ('nn', self.system.extra['energy_nn']))
log('%50s %20.12f' % ('total', self.system.extra['energy']))
log.hline()
log.blank()
def log(self):
"""Write an overview of the last computation on screen."""
log('Contributions to the energy:')
log.hline()
log(' term Value')
log.hline()
for term in self.terms:
energy = self.cache['energy_%s' % term.label]
log('%50s %20.12f' % (term.label, energy))
for key, energy in self.external.iteritems():
log('%50s %20.12f' % (key, energy))
log('%50s %20.12f' % ('total', self.cache['energy']))
log.hline()
log.blank()
def log_energy(self):
'''Write an overview of the last energy computation on screen'''
log('Contributions to the energy:')
log.hline()
log(' Energy term Value'
)
log.hline()
for term in self.terms:
energy = self.system.extra['energy_%s' % term.label]
log('%50s %20.12f' % (term.label, energy))
log('%50s %20.12f' % ('nn', self.system.extra['energy_nn']))
log('%50s %20.12f' % ('total', self.system.extra['energy']))
log.hline()
log.blank()
def __init__(self, numbers, proatomdb):
self.numbers = numbers
self.proatomdb = proatomdb
self.nbasis = 0
self.basis_specs = []
for i in xrange(len(numbers)):
number = numbers[i]
rgrid = proatomdb.get_rgrid(number)
licos = self._init_atom_licos(number, proatomdb)
#padb_charges = proatomdb.get_charges(number, safe=True)
#complete = proatomdb.get_record(number, padb_charges[0]).pseudo_population == 1
# remove redundant basis functions
for j in xrange(len(licos) - 1, -1, -1):
# test if this lico is redundant with respect to earlier ones
redundant = False
rho = self.proatomdb.get_rho(number, licos[j])
for earlier_lico in licos[:j]:
earlier_rho = self.proatomdb.get_rho(number, earlier_lico)
delta = rho - earlier_rho
rmsd = np.sqrt(rgrid.integrate(delta, delta))
if rmsd < 1e-8:
redundant = True
break
# remove if redundant
if redundant:
if log.do_medium:
log('Skipping redundant basis function for atom %i: %s'
% (i, licos[j]))
licos.pop(j)
self.basis_specs.append([self.nbasis, licos])
self.nbasis += len(licos)
if log.do_high:
log('Hirshfeld-E basis')
log.hline()
log('Atom Z k label')
log.hline()
for i in xrange(len(numbers)):
for j in xrange(self.get_atom_nbasis(i)):
label = self.get_basis_label(i, j)
log('%4i %3i %3i %s' % (i, numbers[i], j, label))
log.hline()
def __init__(self, numbers, proatomdb):
self.numbers = numbers
self.proatomdb = proatomdb
self.nbasis = 0
self.basis_specs = []
for i in xrange(len(numbers)):
number = numbers[i]
rgrid = proatomdb.get_rgrid(number)
licos = self._init_atom_licos(number, proatomdb)
#padb_charges = proatomdb.get_charges(number, safe=True)
#complete = proatomdb.get_record(number, padb_charges[0]).pseudo_population == 1
# remove redundant basis functions
for j in xrange(len(licos)-1, -1, -1):
# test if this lico is redundant with respect to earlier ones
redundant = False
rho = self.proatomdb.get_rho(number, licos[j])
for earlier_lico in licos[:j]:
earlier_rho = self.proatomdb.get_rho(number, earlier_lico)
delta = rho - earlier_rho
rmsd = np.sqrt(rgrid.integrate(delta, delta))
if rmsd < 1e-8:
redundant = True
break
# remove if redundant
if redundant:
if log.do_medium:
log('Skipping redundant basis function for atom %i: %s' % (i, licos[j]))
licos.pop(j)
self.basis_specs.append([self.nbasis, licos])
self.nbasis += len(licos)
if log.do_high:
log('Hirshfeld-E basis')
log.hline()
log('Atom Z k label')
log.hline()
for i in xrange(len(numbers)):
for j in xrange(self.get_atom_nbasis(i)):
label = self.get_basis_label(i, j)
log('%4i %3i %3i %s' % (i, numbers[i], j, label))
log.hline()
def converge_scf_oda_os(ham, maxiter=128, threshold=1e-6, debug=False):
'''Minimize the energy of the open-shell wavefunction with optimal damping
**Arguments:**
ham
A Hamiltonian instance.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction.
debug
Make debug plots with matplotlib of the linear interpolation
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
if log.do_medium:
log('Starting restricted closed-shell SCF with optimal damping')
log.hline()
log(' Iter Energy Error(alpha) Error(beta) Mixing')
log.hline()
# initialization of variables and datastructures
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
# suffixes
# 0 = current or initial state
# 1 = state after conventional SCF step
# 2 = state after optimal damping
# a = alpha
# b = beta
fock0a = lf.create_one_body()
fock1a = lf.create_one_body()
fock0b = lf.create_one_body()
fock1b = lf.create_one_body()
dm0a = lf.create_one_body()
dm2a = lf.create_one_body()
dm0b = lf.create_one_body()
dm2b = lf.create_one_body()
converged = False
mixing = None
errora = None
errorb = None
# Get rid of outdated stuff
ham.clear()
# If an input density matrix is present, check if it sensible. This avoids
# redundant testing of a density matrix that is derived here from the
# orbitals.
if 'dm_alpha' in wfn._cache:
check_dm(wfn.dm_alpha, overlap, lf, 'alpha')
if 'dm_beta' in wfn._cache:
check_dm(wfn.dm_beta, overlap, lf, 'beta')
counter = 0
while maxiter is None or counter < maxiter:
# A) Construct Fock operator, compute energy and keep dm at current/initial point
fock0a.clear()
fock0b.clear()
ham.compute_fock(fock0a, fock0b)
energy0 = ham.compute()
dm0a.assign(wfn.dm_alpha)
dm0b.assign(wfn.dm_beta)
if log.do_medium:
if mixing is None:
log('%5i %20.13f' % (counter, energy0))
else:
log('%5i %20.13f %12.5e %12.5e %10.5f' % (counter, energy0, errora, errorb, mixing))
# B) Diagonalize fock operator and go to state 1
wfn.clear()
wfn.update_exp(fock0a, fock0b, overlap)
# Let the hamiltonian know that the wavefunction has changed.
ham.clear()
# C) Compute Fock matrix at state 1
fock1a.clear()
fock1b.clear()
ham.compute_fock(fock1a, fock1b)
# Compute energy at new point
energy1 = ham.compute()
# take the density matrix
dm1a = wfn.dm_alpha
dm1b = wfn.dm_beta
# D) Find the optimal damping
# Compute the derivatives of the energy towards lambda at edges 0 and 1
ev_00 = fock0a.expectation_value(dm0a) + fock0b.expectation_value(dm0b)
ev_01 = fock0a.expectation_value(dm1a) + fock0b.expectation_value(dm1b)
ev_10 = fock1a.expectation_value(dm0a) + fock1b.expectation_value(dm0b)
ev_11 = fock1a.expectation_value(dm1a) + fock1b.expectation_value(dm1b)
energy0_deriv = (ev_01-ev_00)
energy1_deriv = (ev_11-ev_10)
# 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, energy0_deriv))
log(' E1-E0: % 10.5e D1: % 10.5e' % (energy1-energy0, energy1_deriv))
mixing = find_min_cubic(energy0, energy1, energy0_deriv, energy1_deriv)
if log.do_high:
log(' mixing: % 10.5f' % mixing)
if debug:
check_cubic_os(ham, dm0a, dm0b, dm1a, dm1b, energy0, energy1, energy0_deriv, energy1_deriv)
# E) Construct the new dm
# Put the mixed dm in dm_old, which is local in this routine.
dm2a.clear()
dm2a.iadd(dm1a, factor=mixing)
dm2a.iadd(dm0a, factor=1-mixing)
dm2b.clear()
dm2b.iadd(dm1b, factor=mixing)
dm2b.iadd(dm0b, factor=1-mixing)
# Wipe the caches and use the interpolated density matrix
wfn.clear()
wfn.update_dm('alpha', dm2a)
wfn.update_dm('beta', dm2b)
ham.clear()
errora = dm2a.distance(dm0a)
errorb = dm2b.distance(dm0b)
if errora < threshold and errorb < threshold:
if abs(energy0_deriv) > threshold:
raise RuntimeError('The ODA algorithm stopped a point with non-zero gradient.')
converged = True
break
# Write intermediate wfn to checkpoint.
ham.system.update_chk('wfn')
# counter
counter += 1
# compute orbitals, energies and occupation numbers
# Note: suffix 0 is used for final state here
dm0a.assign(wfn.dm_alpha)
dm0b.assign(wfn.dm_beta)
fock0a.clear()
fock0b.clear()
ham.compute_fock(fock0a, fock0b)
wfn.clear()
wfn.update_exp(fock0a, fock0b, overlap, dm0a, dm0b)
energy0 = ham.compute()
# Write final wfn to checkpoint.
ham.system.update_chk('wfn')
if log.do_medium:
log('%5i %20.13f %12.5e %12.5e %10.5f' % (counter+1, energy0, errora, errorb, mixing))
log.blank()
if log.do_medium:
ham.log_energy()
if not converged:
raise NoSCFConvergence
return counter
def __call__(self, ham, lf, overlap, occ_model, *exps):
'''Find a self-consistent set of orbitals.
**Arguments:**
ham
An effective Hamiltonian.
lf
The linalg factory to be used.
overlap
The overlap operator.
occ_model
Model for the orbital occupations.
exp1, exp2, ...
The initial orbitals. The number of dms must match ham.ndm.
'''
# Some type checking
if ham.ndm != len(exps):
raise TypeError(
'The number of initial orbital expansions does not match the Hamiltonian.'
)
# Impose the requested occupation numbers
occ_model.assign(*exps)
# Check the orthogonality of the orbitals
for exp in exps:
exp.check_normalization(overlap)
if log.do_medium:
log('Starting plain SCF solver. ndm=%i' % ham.ndm)
log.hline()
log('Iter Error')
log.hline()
focks = [lf.create_two_index() for i in xrange(ham.ndm)]
dms = [lf.create_two_index() for i in xrange(ham.ndm)]
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# convert the orbital expansions to density matrices
for i in xrange(ham.ndm):
exps[i].to_dm(dms[i])
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operator
ham.compute_fock(*focks)
# Check for convergence
error = 0.0
for i in xrange(ham.ndm):
error += exps[i].error_eigen(focks[i], overlap)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < self.threshold:
converged = True
break
# Diagonalize the fock operators to obtain new orbitals and
for i in xrange(ham.ndm):
exps[i].from_fock(focks[i], overlap)
# Assign new occupation numbers.
occ_model.assign(*exps)
# counter
counter += 1
if log.do_medium:
log.blank()
if not self.skip_energy:
ham.compute_energy()
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, *exps):
'''Find a self-consistent set of orbitals.
**Arguments:**
ham
An effective Hamiltonian.
lf
The linalg factory to be used.
overlap
The overlap operator.
occ_model
Model for the orbital occupations.
exp1, exp2, ...
The initial orbitals. The number of dms must match ham.ndm.
'''
# Some type checking
if ham.ndm != len(exps):
raise TypeError('The number of initial orbital expansions does not match the Hamiltonian.')
# Impose the requested occupation numbers
occ_model.assign(*exps)
# Check the orthogonality of the orbitals
for exp in exps:
exp.check_normalization(overlap)
if log.do_medium:
log('Starting plain SCF solver. ndm=%i' % ham.ndm)
log.hline()
log('Iter Error')
log.hline()
focks = [lf.create_two_index() for i in xrange(ham.ndm)]
dms = [lf.create_two_index() for i in xrange(ham.ndm)]
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# convert the orbital expansions to density matrices
for i in xrange(ham.ndm):
exps[i].to_dm(dms[i])
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operator
ham.compute_fock(*focks)
# Check for convergence
error = 0.0
for i in xrange(ham.ndm):
error += exps[i].error_eigen(focks[i], overlap)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < self.threshold:
converged = True
break
# Diagonalize the fock operators to obtain new orbitals and
for i in xrange(ham.ndm):
exps[i].from_fock(focks[i], overlap)
# Assign new occupation numbers.
occ_model.assign(*exps)
# counter
counter += 1
if log.do_medium:
log.blank()
if not self.skip_energy:
ham.compute_energy()
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
def converge_scf_diis_cs(ham,
DIISHistoryClass,
maxiter=128,
threshold=1e-6,
nvector=6,
prune_old_states=False,
skip_energy=False,
scf_step='regular'):
'''Minimize the energy of the closed-shell wavefunction with EDIIS
**Arguments:**
ham
A Hamiltonian instance.
DIISHistoryClass
A DIIS history class.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction
prune_old_states
When set to True, old states are pruned from the history when their
coefficient is zero. Pruning starts at the oldest state and stops
as soon as a state is encountered with a non-zero coefficient. Even
if some newer states have a zero coefficient.
skip_energy
When set to True, the final energy is not computed. Note that some
DIIS variants need to compute the energy anyway. for these methods
this option is irrelevant.
scf_step
The type of SCF step to take after the interpolated states was
create from the DIIS history. This can be 'regular', 'oda2' or
'oda3'.
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
# allocated and define some one body operators
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
history = DIISHistoryClass(lf, nvector, overlap)
fock = lf.create_one_body()
dm = lf.create_one_body()
# The scf step
if scf_step == 'regular':
cs_scf_step = CSSCFStep(ham)
elif scf_step == 'oda2':
cs_scf_step = CSQuadraticODAStep(ham)
elif scf_step == 'oda3':
cs_scf_step = CSCubicODAStep(ham)
else:
raise ValueError('scf_step argument not recognized: %s' % scf_step)
# Get rid of outdated stuff
ham.clear()
if log.do_medium:
log('Starting restricted closed-shell %s-SCF' % history.name)
log.hline()
log('Iter Error(alpha) CN(alpha) Last(alpha) nv Method Energy Change'
)
log.hline()
converged = False
counter = 0
while maxiter is None or counter < maxiter:
# Construct the Fock operator from scratch:
if history.nused == 0:
# Update the Fock matrix
fock.clear()
ham.compute_fock(fock, None)
# Put this state also in the history
energy = ham.compute() if history.need_energy else None
# Add the current fock+dm pair to the history
error = history.add(energy, wfn.dm_alpha, fock)
if log.do_high:
log(' DIIS add')
if error < 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, history.nused, energy_str))
if log.do_high:
log.blank()
fock_interpolated = False
else:
energy = None
fock_interpolated = True
# Construct a new density matrix and fock matrix (based on the current
# density matrix or fock matrix). The fock matrix is modified in-place
# while the density matrix is stored in ham.system.wfn
mixing = cs_scf_step(energy, fock, fock_interpolated)
if mixing == 0.0:
converged = True
break
energy = ham.compute() if history.need_energy else None
# Write intermediate results to checkpoint
ham.system.update_chk('wfn')
# Add the current (dm, fock) pair to the history
if log.do_high:
log(' DIIS add')
error = history.add(energy, wfn.dm_alpha, fock)
# break when converged
if error < 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, history.nused, energy_str))
if log.do_high:
log.blank()
# get extra/intra-polated Fock matrix
while True:
energy_approx, coeffs, cn, method = history.solve(dm, fock)
#if coeffs[coeffs<0].sum() < -1:
# if log.do_high:
# log(' DIIS (coeffs too negative) -> drop %i and retry' % history.stack[0].identity)
# history.shrink()
if history.nused <= 2:
break
if coeffs[-1] == 0.0:
if log.do_high:
log(' DIIS (last coeff zero) -> drop %i and retry'
% history.stack[0].identity)
history.shrink()
else:
break
if False and len(coeffs) == 2:
tmp = dm.copy()
import matplotlib.pyplot as pt
xs = np.linspace(0.0, 1.0, 25)
a, b = 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))
history._build_combinations(x_coeffs, tmp, None)
wfn.clear()
wfn.update_dm('alpha', tmp)
ham.clear()
energies2.append(ham.compute())
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('ediis2_test_%05i.png' % counter)
wfn.clear()
wfn.update_dm('alpha', dm)
ham.clear()
if energy_approx is not None:
energy_change = energy_approx - min(state.energy
for state in history.stack)
else:
energy_change = None
# log
if log.do_high:
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], history.nused, method, change_str))
if log.do_high:
log.blank()
if prune_old_states:
# get rid of old states with zero coeff
for i in xrange(history.nused):
if coeffs[i] == 0.0:
if log.do_high:
log(' DIIS insignificant -> drop %i' %
history.stack[0].identity)
history.shrink()
else:
break
# counter
counter += 1
if log.do_medium:
if converged:
log('%4i %12.5e (converged)' % (counter, error))
log.blank()
if not skip_energy or history.need_energy:
if not history.need_energy:
ham.compute()
if log.do_medium:
ham.log_energy()
if not converged:
raise NoSCFConvergence
return counter
def converge_scf_cs(ham, maxiter=128, threshold=1e-8, skip_energy=False):
'''Minimize the energy of the wavefunction with basic closed-shell SCF
**Arguments:**
ham
A Hamiltonian instance.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction.
skip_energy
When set to True, the final energy is not computed.
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
if log.do_medium:
log('Starting restricted closed-shell SCF')
log.hline()
log('Iter Error(alpha)')
log.hline()
# Get rid of outdated stuff
ham.clear()
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
fock = lf.create_one_body()
converged = False
counter = 0
while maxiter is None or counter < maxiter:
# Construct the Fock operator
fock.clear()
ham.compute_fock(fock, None)
# Check for convergence
error = lf.error_eigen(fock, overlap, wfn.exp_alpha)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < threshold:
converged = True
break
# Diagonalize the fock operator
wfn.clear() # discard previous wfn state
wfn.update_exp(fock, overlap)
# Let the hamiltonian know that the wavefunction has changed.
ham.clear()
# Write intermediate results to checkpoint
ham.system.update_chk('wfn')
# counter
counter += 1
if log.do_medium:
log.blank()
if not skip_energy:
ham.compute()
if log.do_medium:
ham.log_energy()
if not converged:
raise NoSCFConvergence
return counter
def __call__(self, ham, lf, overlap, occ_model, *exps):
"""Find a self-consistent set of orbitals.
Parameters
----------
ham : EffHam
An effective Hamiltonian.
lf : LinalgFactor
The linalg factory to be used.
overlap : TwoIndex
The overlap operator.
occ_model : OccModel
Model for the orbital occupations.
exp1, exp2, ... : Expansion
The initial orbitals. The number of dms must match ham.ndm.
"""
# Some type checking
if ham.ndm != len(exps):
raise TypeError('The number of initial orbital expansions does not match the Hamiltonian.')
# Impose the requested occupation numbers
occ_model.assign(*exps)
# Check the orthogonality of the orbitals
for exp in exps:
exp.check_normalization(overlap)
if log.do_medium:
log('Starting plain SCF solver. ndm=%i' % ham.ndm)
log.hline()
log('Iter Error')
log.hline()
focks = [lf.create_two_index() for i in xrange(ham.ndm)]
dms = [lf.create_two_index() for i in xrange(ham.ndm)]
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# convert the orbital expansions to density matrices
for i in xrange(ham.ndm):
exps[i].to_dm(dms[i])
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operator
ham.compute_fock(*focks)
# Check for convergence
error = 0.0
for i in xrange(ham.ndm):
error += exps[i].error_eigen(focks[i], overlap)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < self.threshold:
converged = True
break
# If requested, add the level shift to the Fock operator
if self.level_shift > 0:
for i in xrange(ham.ndm):
lshift = overlap.copy()
lshift.idot(dms[i])
lshift.idot(overlap)
# The normal behavior is to shift down the occupied levels.
lshift.iscale(-self.level_shift)
focks[i].iadd(lshift)
# Diagonalize the fock operators to obtain new orbitals and
for i in xrange(ham.ndm):
exps[i].from_fock(focks[i], overlap)
# If requested, compensate for level-shift. This compensation
# is only correct when the SCF has converged.
if self.level_shift > 0:
exps[i].energies[:] += self.level_shift*exps[i].occupations
# Assign new occupation numbers.
occ_model.assign(*exps)
# counter
counter += 1
if log.do_medium:
log.blank()
if not self.skip_energy:
ham.compute_energy()
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
def converge_scf_cs(ham, maxiter=128, threshold=1e-8, skip_energy=False):
'''Minimize the energy of the wavefunction with basic closed-shell SCF
**Arguments:**
ham
A Hamiltonian instance.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction.
skip_energy
When set to True, the final energy is not computed.
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
if log.do_medium:
log('Starting restricted closed-shell SCF')
log.hline()
log('Iter Error(alpha)')
log.hline()
# Get rid of outdated stuff
ham.clear()
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
fock = lf.create_one_body()
converged = False
counter = 0
while maxiter is None or counter < maxiter:
# Construct the Fock operator
fock.clear()
ham.compute_fock(fock, None)
# Check for convergence
error = lf.error_eigen(fock, overlap, wfn.exp_alpha)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < threshold:
converged = True
break
# Diagonalize the fock operator
wfn.clear() # discard previous wfn state
wfn.update_exp(fock, overlap)
# Let the hamiltonian know that the wavefunction has changed.
ham.clear()
# Write intermediate results to checkpoint
ham.system.update_chk('wfn')
# counter
counter += 1
if log.do_medium:
log.blank()
if not skip_energy:
ham.compute()
if log.do_medium:
ham.log_energy()
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
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
def converge_scf_oda_os(ham, maxiter=128, threshold=1e-6, debug=False):
'''Minimize the energy of the open-shell wavefunction with optimal damping
**Arguments:**
ham
A Hamiltonian instance.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction.
debug
Make debug plots with matplotlib of the linear interpolation
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
if log.do_medium:
log('Starting restricted closed-shell SCF with optimal damping')
log.hline()
log(' Iter Energy Error(alpha) Error(beta) Mixing')
log.hline()
# initialization of variables and datastructures
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
# suffixes
# 0 = current or initial state
# 1 = state after conventional SCF step
# 2 = state after optimal damping
# a = alpha
# b = beta
fock0a = lf.create_one_body()
fock1a = lf.create_one_body()
fock0b = lf.create_one_body()
fock1b = lf.create_one_body()
dm0a = lf.create_one_body()
dm2a = lf.create_one_body()
dm0b = lf.create_one_body()
dm2b = lf.create_one_body()
converged = False
mixing = None
errora = None
errorb = None
# Get rid of outdated stuff
ham.clear()
# If an input density matrix is present, check if it sensible. This avoids
# redundant testing of a density matrix that is derived here from the
# orbitals.
if 'dm_alpha' in wfn._cache:
check_dm(wfn.dm_alpha, overlap, lf, 'alpha')
if 'dm_beta' in wfn._cache:
check_dm(wfn.dm_beta, overlap, lf, 'beta')
counter = 0
while maxiter is None or counter < maxiter:
# A) Construct Fock operator, compute energy and keep dm at current/initial point
fock0a.clear()
fock0b.clear()
ham.compute_fock(fock0a, fock0b)
energy0 = ham.compute()
dm0a.assign(wfn.dm_alpha)
dm0b.assign(wfn.dm_beta)
if log.do_medium:
if mixing is None:
log('%5i %20.13f' % (counter, energy0))
else:
log('%5i %20.13f %12.5e %12.5e %10.5f' % (counter, energy0, errora, errorb, mixing))
# B) Diagonalize fock operator and go to state 1
wfn.clear()
wfn.update_exp(fock0a, fock0b, overlap)
# Let the hamiltonian know that the wavefunction has changed.
ham.clear()
# C) Compute Fock matrix at state 1
fock1a.clear()
fock1b.clear()
ham.compute_fock(fock1a, fock1b)
# Compute energy at new point
energy1 = ham.compute()
# take the density matrix
dm1a = wfn.dm_alpha
dm1b = wfn.dm_beta
# D) Find the optimal damping
# Compute the derivatives of the energy towards lambda at edges 0 and 1
ev_00 = fock0a.expectation_value(dm0a) + fock0b.expectation_value(dm0b)
ev_01 = fock0a.expectation_value(dm1a) + fock0b.expectation_value(dm1b)
ev_10 = fock1a.expectation_value(dm0a) + fock1b.expectation_value(dm0b)
ev_11 = fock1a.expectation_value(dm1a) + fock1b.expectation_value(dm1b)
energy0_deriv = (ev_01-ev_00)
energy1_deriv = (ev_11-ev_10)
# 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, energy0_deriv))
log(' E1-E0: % 10.5e D1: % 10.5e' % (energy1-energy0, energy1_deriv))
mixing = find_min_cubic(energy0, energy1, energy0_deriv, energy1_deriv)
if log.do_high:
log(' mixing: % 10.5f' % mixing)
if debug:
check_cubic_os(ham, dm0a, dm0b, dm1a, dm1b, energy0, energy1, energy0_deriv, energy1_deriv)
# E) Construct the new dm
# Put the mixed dm in dm_old, which is local in this routine.
dm2a.clear()
dm2a.iadd(dm1a, factor=mixing)
dm2a.iadd(dm0a, factor=1-mixing)
dm2b.clear()
dm2b.iadd(dm1b, factor=mixing)
dm2b.iadd(dm0b, factor=1-mixing)
# Wipe the caches and use the interpolated density matrix
wfn.clear()
wfn.update_dm('alpha', dm2a)
wfn.update_dm('beta', dm2b)
ham.clear()
errora = dm2a.distance(dm0a)
errorb = dm2b.distance(dm0b)
if errora < threshold and errorb < threshold:
if abs(energy0_deriv) > threshold:
raise RuntimeError('The ODA algorithm stopped a point with non-zero gradient.')
converged = True
break
# Write intermediate wfn to checkpoint.
ham.system.update_chk('wfn')
# counter
counter += 1
# compute orbitals, energies and occupation numbers
# Note: suffix 0 is used for final state here
dm0a.assign(wfn.dm_alpha)
dm0b.assign(wfn.dm_beta)
fock0a.clear()
fock0b.clear()
ham.compute_fock(fock0a, fock0b)
wfn.clear()
wfn.update_exp(fock0a, fock0b, overlap, dm0a, dm0b)
energy0 = ham.compute()
# Write final wfn to checkpoint.
ham.system.update_chk('wfn')
if log.do_medium:
log('%5i %20.13f %12.5e %12.5e %10.5f' % (counter+1, energy0, errora, errorb, mixing))
log.blank()
if log.do_medium:
ham.log_energy()
if not converged:
raise NoSCFConvergence
return counter
def __call__(self, ham, overlap, occ_model, *orbs):
"""Find a self-consistent set of orbitals.
Parameters
----------
ham : EffHam
An effective Hamiltonian.
overlap : np.ndarray, shape=(nbasis, nbasis)
The overlap operator.
occ_model : OccModel
Model for the orbital occupations.
orb1, orb2, ... : Orbitals
The initial orbitals. The number of dms must match ham.ndm.
"""
# Some type checking
if ham.ndm != len(orbs):
raise TypeError(
'The number of initial orbital expansions does not match the Hamiltonian.'
)
# Impose the requested occupation numbers
occ_model.assign(*orbs)
# Check the orthogonality of the orbitals
for orb in orbs:
orb.check_normalization(overlap)
if log.do_medium:
log('Starting plain SCF solver. ndm=%i' % ham.ndm)
log.hline()
log('Iter Error')
log.hline()
focks = [np.zeros(overlap.shape) for i in xrange(ham.ndm)]
dms = [None] * ham.ndm
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# convert the orbital expansions to density matrices
for i in xrange(ham.ndm):
dms[i] = orbs[i].to_dm()
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operator
ham.compute_fock(*focks)
# Check for convergence
error = 0.0
for i in xrange(ham.ndm):
error += orbs[i].error_eigen(focks[i], overlap)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < self.threshold:
converged = True
break
# If requested, add the level shift to the Fock operator
if self.level_shift > 0:
for i in xrange(ham.ndm):
# The normal behavior is to shift down the occupied levels.
focks[i] += -self.level_shift * get_level_shift(
dms[i], overlap)
# Diagonalize the fock operators to obtain new orbitals and
for i in xrange(ham.ndm):
orbs[i].from_fock(focks[i], overlap)
# If requested, compensate for level-shift. This compensation
# is only correct when the SCF has converged.
if self.level_shift > 0:
orbs[i].energies[:] += self.level_shift * orbs[
i].occupations
# Assign new occupation numbers.
occ_model.assign(*orbs)
# counter
counter += 1
if log.do_medium:
log.blank()
if not self.skip_energy:
ham.compute_energy()
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
def converge_scf_diis_cs(ham, DIISHistoryClass, maxiter=128, threshold=1e-6, nvector=6, prune_old_states=False, skip_energy=False, scf_step='regular'):
'''Minimize the energy of the closed-shell wavefunction with EDIIS
**Arguments:**
ham
A Hamiltonian instance.
DIISHistoryClass
A DIIS history class.
**Optional arguments:**
maxiter
The maximum number of iterations. When set to None, the SCF loop
will go one until convergence is reached.
threshold
The convergence threshold for the wavefunction
prune_old_states
When set to True, old states are pruned from the history when their
coefficient is zero. Pruning starts at the oldest state and stops
as soon as a state is encountered with a non-zero coefficient. Even
if some newer states have a zero coefficient.
skip_energy
When set to True, the final energy is not computed. Note that some
DIIS variants need to compute the energy anyway. for these methods
this option is irrelevant.
scf_step
The type of SCF step to take after the interpolated states was
create from the DIIS history. This can be 'regular', 'oda2' or
'oda3'.
**Raises:**
NoSCFConvergence
if the convergence criteria are not met within the specified number
of iterations.
**Returns:** the number of iterations
'''
# allocated and define some one body operators
lf = ham.system.lf
wfn = ham.system.wfn
overlap = ham.system.get_overlap()
history = DIISHistoryClass(lf, nvector, overlap)
fock = lf.create_one_body()
dm = lf.create_one_body()
# The scf step
if scf_step == 'regular':
cs_scf_step = CSSCFStep(ham)
elif scf_step == 'oda2':
cs_scf_step = CSQuadraticODAStep(ham)
elif scf_step == 'oda3':
cs_scf_step = CSCubicODAStep(ham)
else:
raise ValueError('scf_step argument not recognized: %s' % scf_step)
# Get rid of outdated stuff
ham.clear()
if log.do_medium:
log('Starting restricted closed-shell %s-SCF' % history.name)
log.hline()
log('Iter Error(alpha) CN(alpha) Last(alpha) nv Method Energy Change')
log.hline()
converged = False
counter = 0
while maxiter is None or counter < maxiter:
# Construct the Fock operator from scratch:
if history.nused == 0:
# Update the Fock matrix
fock.clear()
ham.compute_fock(fock, None)
# Put this state also in the history
energy = ham.compute() if history.need_energy else None
# Add the current fock+dm pair to the history
error = history.add(energy, wfn.dm_alpha, fock)
if log.do_high:
log(' DIIS add')
if error < 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, history.nused, energy_str
))
if log.do_high:
log.blank()
fock_interpolated = False
else:
energy = None
fock_interpolated = True
# Construct a new density matrix and fock matrix (based on the current
# density matrix or fock matrix). The fock matrix is modified in-place
# while the density matrix is stored in ham.system.wfn
mixing = cs_scf_step(energy, fock, fock_interpolated)
if mixing == 0.0:
converged = True
break
energy = ham.compute() if history.need_energy else None
# Write intermediate results to checkpoint
ham.system.update_chk('wfn')
# Add the current (dm, fock) pair to the history
if log.do_high:
log(' DIIS add')
error = history.add(energy, wfn.dm_alpha, fock)
# break when converged
if error < 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, history.nused, energy_str
))
if log.do_high:
log.blank()
# get extra/intra-polated Fock matrix
while True:
energy_approx, coeffs, cn, method = history.solve(dm, fock)
#if coeffs[coeffs<0].sum() < -1:
# if log.do_high:
# log(' DIIS (coeffs too negative) -> drop %i and retry' % history.stack[0].identity)
# history.shrink()
if history.nused <= 2:
break
if coeffs[-1] == 0.0:
if log.do_high:
log(' DIIS (last coeff zero) -> drop %i and retry' % history.stack[0].identity)
history.shrink()
else:
break
if False and len(coeffs) == 2:
tmp = dm.copy()
import matplotlib.pyplot as pt
xs = np.linspace(0.0, 1.0, 25)
a, b = 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))
history._build_combinations(x_coeffs, tmp, None)
wfn.clear()
wfn.update_dm('alpha', tmp)
ham.clear()
energies2.append(ham.compute())
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('ediis2_test_%05i.png' % counter)
wfn.clear()
wfn.update_dm('alpha', dm)
ham.clear()
if energy_approx is not None:
energy_change = energy_approx - min(state.energy for state in history.stack)
else:
energy_change = None
# log
if log.do_high:
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], history.nused, method,
change_str
))
if log.do_high:
log.blank()
if prune_old_states:
# get rid of old states with zero coeff
for i in xrange(history.nused):
if coeffs[i] == 0.0:
if log.do_high:
log(' DIIS insignificant -> drop %i' % history.stack[0].identity)
history.shrink()
else:
break
# counter
counter += 1
if log.do_medium:
if converged:
log('%4i %12.5e (converged)' % (counter, error))
log.blank()
if not skip_energy or history.need_energy:
if not history.need_energy:
ham.compute()
if log.do_medium:
ham.log_energy()
if not converged:
raise NoSCFConvergence
return counter
def __call__(self, ham, overlap, occ_model, *orbs):
"""Find a self-consistent set of orbitals.
Parameters
----------
ham : EffHam
An effective Hamiltonian.
overlap : np.ndarray, shape=(nbasis, nbasis)
The overlap operator.
occ_model : OccModel
Model for the orbital occupations.
orb1, orb2, ... : Orbitals
The initial orbitals. The number of dms must match ham.ndm.
"""
# Some type checking
if ham.ndm != len(orbs):
raise TypeError('The number of initial orbital expansions does not match the Hamiltonian.')
# Impose the requested occupation numbers
occ_model.assign(*orbs)
# Check the orthogonality of the orbitals
for orb in orbs:
orb.check_normalization(overlap)
if log.do_medium:
log('Starting plain SCF solver. ndm=%i' % ham.ndm)
log.hline()
log('Iter Error')
log.hline()
focks = [np.zeros(overlap.shape) for i in xrange(ham.ndm)]
dms = [None] * ham.ndm
converged = False
counter = 0
while self.maxiter is None or counter < self.maxiter:
# convert the orbital expansions to density matrices
for i in xrange(ham.ndm):
dms[i] = orbs[i].to_dm()
# feed the latest density matrices in the hamiltonian
ham.reset(*dms)
# Construct the Fock operator
ham.compute_fock(*focks)
# Check for convergence
error = 0.0
for i in xrange(ham.ndm):
error += orbs[i].error_eigen(focks[i], overlap)
if log.do_medium:
log('%4i %12.5e' % (counter, error))
if error < self.threshold:
converged = True
break
# If requested, add the level shift to the Fock operator
if self.level_shift > 0:
for i in xrange(ham.ndm):
# The normal behavior is to shift down the occupied levels.
focks[i] += -self.level_shift*get_level_shift(dms[i], overlap)
# Diagonalize the fock operators to obtain new orbitals and
for i in xrange(ham.ndm):
orbs[i].from_fock(focks[i], overlap)
# If requested, compensate for level-shift. This compensation
# is only correct when the SCF has converged.
if self.level_shift > 0:
orbs[i].energies[:] += self.level_shift*orbs[i].occupations
# Assign new occupation numbers.
occ_model.assign(*orbs)
# counter
counter += 1
if log.do_medium:
log.blank()
if not self.skip_energy:
ham.compute_energy()
if log.do_medium:
ham.log()
if not converged:
raise NoSCFConvergence
return counter
