def _update_propars_atom(self, index):
# Prepare some things
charges = self._cache.load('charges', alloc=self.natom, tags='o')[0]
begin = self.hebasis.get_atom_begin(index)
nbasis = self.hebasis.get_atom_nbasis(index)
# Compute charge and delta aim density
charge, delta_aim = self._get_charge_and_delta_aim(index)
charges[index] = charge
# Preliminary check
if charges[index] > nbasis:
raise RuntimeError('The charge on atom %i becomes too positive: %f > %i. (infeasible)' % (index, charges[index], nbasis))
# Define the least-squares system
A, B, C = self._get_he_system(index, delta_aim)
# preconditioning
scales = np.sqrt(np.diag(A))
A = A/scales/scales.reshape(-1,1)
B /= scales
# resymmetrize A due to potential round-off errors after rescaling
# (minor thing)
A = 0.5*(A + A.T)
# Find solution
# constraint for total population of pro-atom
qp_r = np.array([np.ones(nbasis)/scales])
qp_s = np.array([-charges[index]])
# inequality constraints to keep coefficients larger than -1 or 0.
lower_bounds = np.zeros(nbasis)
for j0 in xrange(nbasis):
lower_bounds[j0] = self.hebasis.get_lower_bound(index, j0)*scales[j0]
# call the quadratic solver with modified b due to non-zero lower bound
qp_a = A
qp_b = B - np.dot(A, lower_bounds)
qp_s -= np.dot(qp_r, lower_bounds)
qps = QPSolver(qp_a, qp_b, qp_r, qp_s)
qp_x = qps.find_brute()[1]
# convert back to atom_pars
atom_propars = qp_x + lower_bounds
rrms = np.dot(np.dot(A, atom_propars) - 2*B, atom_propars)/C + 1
if rrms > 0:
rrmsd = np.sqrt(rrms)
else:
rrmsd = -0.01
# correct for scales
atom_propars /= scales
if log.do_high:
log(' %10i (%.0f%%):&%s' % (index, rrmsd*100, ' '.join('% 6.3f' % c for c in atom_propars)))
self.cache.load('propars')[begin:begin+nbasis] = atom_propars
def solve(self, dms_output, focks_output):
# interpolation only makes sense if there are two points
assert self.nused >= 2
# Fill in the missing commutators
self._complete_edots_matrix()
assert not np.isnan(self.edots[:self.nused,:self.nused]).any()
# Setup the equations
b, e = self._setup_equations()
# Check if solving these equations makes sense.
if b.max() - b.min() == 0 and e.max() - e.min() == 0:
raise NoSCFConvergence('Convergence criteria too tight for EDIIS')
# solve the quadratic programming problem
qps = QPSolver(b, e, np.ones((1,self.nused)), np.array([1.0]), eps=1e-6)
if self.nused < 10:
energy, coeffs = qps.find_brute()
guess = None
else:
guess = np.zeros(self.nused)
guess[e.argmax()] = 1.0
energy, coeffs = qps.find_local(guess, 1.0)
# for debugging purposes (negligible computational overhead)
try:
qps.check_solution(coeffs)
except:
qps.log(guess)
raise
cn = qps.compute_cn(coeffs != 0.0)
# assign extrapolated fock
error = self._build_combinations(coeffs, dms_output, focks_output)
return energy, coeffs, cn, 'E', error
def solve(self, dm_output, fock_output):
'''Extrapolate a new density and/or fock matrix that should have the smallest commutator norm.
**Arguments:**
dm_output
The output for the density matrix. If set to None, this is
argument is ignored.
fock_output
The output for the Fock matrix. If set to None, this is
argument is ignored.
'''
# interpolation only makes sense if there are two points
assert self.nused >= 2
# Fill in the missing commutators
self._complete_edots_matrix()
assert not np.isnan(self.edots[:self.nused, :self.nused]).any()
# Setup the equations
b, e = self._setup_equations()
# Check if solving these equations makes sense.
if b.max() - b.min() == 0 and e.max() - e.min() == 0:
raise NoSCFConvergence('Convergence criteria too tight for EDIIS')
# solve the quadratic programming problem
qps = QPSolver(b,
e,
np.ones((1, self.nused)),
np.array([1.0]),
eps=1e-6)
if self.nused < 10:
energy, coeffs = qps.find_brute()
guess = None
else:
guess = np.zeros(self.nused)
guess[e.argmax()] = 1.0
energy, coeffs = qps.find_local(guess, 1.0)
# for debugging purposes
try:
qps.check_solution(coeffs)
except:
qps.log(guess)
raise
cn = qps.compute_cn(coeffs != 0.0)
# assign extrapolated fock
self._build_combinations(coeffs, dm_output, fock_output)
return energy, coeffs, cn, 'E'
def solve(self, dm_output, fock_output):
'''Extrapolate a new density and/or fock matrix that should have the smallest commutator norm.
**Arguments:**
dm_output
The output for the density matrix. If set to None, this is
argument is ignored.
fock_output
The output for the Fock matrix. If set to None, this is
argument is ignored.
'''
# interpolation only makes sense if there are two points
assert self.nused >= 2
# Fill in the missing commutators
self._complete_edots_matrix()
assert not np.isnan(self.edots[:self.nused,:self.nused]).any()
# Setup the equations
b, e = self._setup_equations()
# Check if solving these equations makes sense.
if b.max() - b.min() == 0 and e.max() - e.min() == 0:
raise NoSCFConvergence('Convergence criteria too tight for EDIIS')
# solve the quadratic programming problem
qps = QPSolver(b, e, np.ones((1,self.nused)), np.array([1.0]), eps=1e-6)
if self.nused < 10:
energy, coeffs = qps.find_brute()
guess = None
else:
guess = np.zeros(self.nused)
guess[e.argmax()] = 1.0
energy, coeffs = qps.find_local(guess, 1.0)
# for debugging purposes
try:
qps.check_solution(coeffs)
except:
qps.log(guess)
raise
cn = qps.compute_cn(coeffs != 0.0)
# assign extrapolated fock
self._build_combinations(coeffs, dm_output, fock_output)
return energy, coeffs, cn, 'E'
def _update_propars_atom(self, index):
# Prepare some things
charges = self._cache.load('charges', alloc=self.natom, tags='o')[0]
begin = self.hebasis.get_atom_begin(index)
nbasis = self.hebasis.get_atom_nbasis(index)
# Compute charge and delta aim density
charge, delta_aim = self._get_charge_and_delta_aim(index)
charges[index] = charge
# Preliminary check
if charges[index] > nbasis:
raise RuntimeError(
'The charge on atom %i becomes too positive: %f > %i. (infeasible)'
% (index, charges[index], nbasis))
# Define the least-squares system
A, B, C = self._get_he_system(index, delta_aim)
# preconditioning
scales = np.sqrt(np.diag(A))
A = A / scales / scales.reshape(-1, 1)
B /= scales
# resymmetrize A due to potential round-off errors after rescaling
# (minor thing)
A = 0.5 * (A + A.T)
# Find solution
# constraint for total population of pro-atom
qp_r = np.array([np.ones(nbasis) / scales])
qp_s = np.array([-charges[index]])
# inequality constraints to keep coefficients larger than -1 or 0.
lower_bounds = np.zeros(nbasis)
for j0 in xrange(nbasis):
lower_bounds[j0] = self.hebasis.get_lower_bound(index,
j0) * scales[j0]
# call the quadratic solver with modified b due to non-zero lower bound
qp_a = A
qp_b = B - np.dot(A, lower_bounds)
qp_s -= np.dot(qp_r, lower_bounds)
qps = QPSolver(qp_a, qp_b, qp_r, qp_s)
qp_x = qps.find_brute()[1]
# convert back to atom_pars
atom_propars = qp_x + lower_bounds
rrms = np.dot(np.dot(A, atom_propars) - 2 * B, atom_propars) / C + 1
if rrms > 0:
rrmsd = np.sqrt(rrms)
else:
rrmsd = -0.01
# correct for scales
atom_propars /= scales
if log.do_high:
log(' %10i (%.0f%%):&%s' %
(index, rrmsd * 100, ' '.join('% 6.3f' % c
for c in atom_propars)))
self.cache.load('propars')[begin:begin + nbasis] = atom_propars