def kernel_eig(hamiltonian, equations, amplitudes, tolerance=1e-9):
"""
Coupled-cluster solver (eigenvalue problem).
Args:
hamiltonian (dict): hamiltonian matrix elements or pyscf ERIS;
equations (callable): coupled-cluster equations;
amplitudes (iterable): starting amplitudes (a list of OrderedDicts);
tolerance (float): convergence criterion;
Returns:
Resulting coupled-cluster amplitudes and energy if specified.
"""
# Convert ERIS to hamiltonian dict if needed
if not isinstance(hamiltonian, dict):
hamiltonian = eris_hamiltonian(hamiltonian)
# Preconditioning
e_occ = numpy.diag(hamiltonian["oo"])
e_vir = numpy.diag(hamiltonian["vv"])
# Antisymmetry data
sample = amplitudes[0].values()
labels = list(i.metadata["labels"] for i in sample)
ixs = list(ltri_ix_amplitudes(i) for i in sample)
shapes = list(i.shape for i in sample)
def matvec(vec):
result = []
for i in vec:
a = v2a_sym(i, labels, shapes, ixs)
a = OrderedDict(zip(amplitudes[0].keys(), a))
r = oneshot(equations, hamiltonian, a)
result.append(a2v_sym(r, ixs))
return result
def precond(res, e0, x0):
a = v2a_sym(res, labels, shapes, ixs)
a = list(
MetaArray(i, **j.metadata)
for i, j in zip(a, amplitudes[0].values()))
a = res2amps(a, e_occ, e_vir, constant=e0)
return a2v_sym(a, ixs)
amplitudes_plain = tuple(a2v_sym(i.values(), ixs) for i in amplitudes)
conv, values, vectors = davidson(matvec,
amplitudes_plain,
precond,
tol=tolerance,
nroots=len(amplitudes))
if any(not i for i in conv):
warn("Following eigenvalues did not converge: {}".format(
list(i for i, x in enumerate(conv) if not x)))
return values, list(v2a_sym(i, labels, shapes, ixs) for i in vectors)
def kernel_eig(hamiltonian, equations, amplitudes, tolerance=1e-9):
"""
Coupled-cluster solver (eigenvalue problem).
Args:
hamiltonian (dict): hamiltonian matrix elements or pyscf ERIS;
equations (callable): coupled-cluster equations;
amplitudes (iterable): starting amplitudes (a list of OrderedDicts);
tolerance (float): convergence criterion;
Returns:
Resulting coupled-cluster amplitudes and energy if specified.
"""
# Convert ERIS to hamiltonian dict if needed
if not isinstance(hamiltonian, dict):
hamiltonian = eris_hamiltonian(hamiltonian)
# Preconditioning
e_occ = numpy.diag(hamiltonian["oo"])
e_vir = numpy.diag(hamiltonian["vv"])
# Antisymmetry data
sample = amplitudes[0].values()
labels = list(i.metadata["labels"] for i in sample)
ixs = list(ltri_ix_amplitudes(i) for i in sample)
shapes = list(i.shape for i in sample)
def matvec(vec):
result = []
for i in vec:
a = v2a_sym(i, labels, shapes, ixs)
a = OrderedDict(zip(amplitudes[0].keys(), a))
r = oneshot(equations, hamiltonian, a)
result.append(a2v_sym(r, ixs))
return result
def precond(res, e0, x0):
a = v2a_sym(res, labels, shapes, ixs)
a = list(MetaArray(i, **j.metadata) for i, j in zip(a, amplitudes[0].values()))
a = res2amps(a, e_occ, e_vir, constant=e0)
return a2v_sym(a, ixs)
amplitudes_plain = tuple(a2v_sym(i.values(), ixs) for i in amplitudes)
conv, values, vectors = davidson(matvec, amplitudes_plain, precond, tol=tolerance, nroots=len(amplitudes))
if any(not i for i in conv):
warn("Following eigenvalues did not converge: {}".format(list(
i for i, x in enumerate(conv) if not x
)))
return values, list(v2a_sym(i, labels, shapes, ixs) for i in vectors)
def solve(myMF, dm_guess=None, safe_guess=True):
assert hasattr(myMF, "mol")
assert hasattr(myMF, "mo_occ")
assert hasattr(myMF, "mo_coeff")
assert myMF.mol.nelectron % 2 == 0 # RHF possible
S_ao = myMF.get_ovlp(myMF.mol)
OEI_ao = myMF.get_hcore(myMF.mol)
numPairs = myMF.mol.nelectron // 2
numVirt = OEI_ao.shape[0] - numPairs
numVars = numPairs * numVirt
if dm_guess is None:
if (len(myMF.mo_occ) == 0) or (safe_guess == True):
dm_ao = myMF.get_init_guess(key=myMF.init_guess, mol=myMF.mol)
else:
dm_ao = np.dot(np.dot(myMF.mo_coeff, np.diag(myMF.mo_occ)), myMF.mo_coeff.T)
else:
dm_ao = np.array(dm_guess, copy=True)
myJK_ao = __JKengine(myMF)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
energies, orbitals = scipy.linalg.eigh(a=FOCK_ao, b=S_ao)
dm_ao = 2 * np.dot(orbitals[:, :numPairs], orbitals[:, :numPairs].T)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
FOCK_mo = np.dot(orbitals.T, np.dot(FOCK_ao, orbitals))
grdnorm = 4 * np.linalg.norm(FOCK_mo[:numPairs, numPairs:])
energy = myMF.mol.energy_nuc() + 0.5 * np.einsum("ij,ij->", OEI_ao + FOCK_ao, dm_ao)
logger.note(myMF, "RHF:NewtonRaphson :: Starting augmented Hessian Newton-Raphson RHF.")
iteration = 0
while grdnorm > 1e-7:
iteration += 1
tempJK_mo = __JKengine(myMF, orbitals)
ini_guess = np.ones([numVars + 1], dtype=float)
for occ in range(numPairs):
for virt in range(numVirt):
ini_guess[occ + numPairs * virt] = -FOCK_mo[occ, numPairs + virt] / max(
FOCK_mo[numPairs + virt, numPairs + virt] - FOCK_mo[occ, occ], 1e-6
)
def myprecon(resid, eigval, eigvec):
myprecon_cutoff = 1e-10
local_myprecon = np.zeros([numVars + 1], dtype=float)
for occ in range(numPairs):
for virt in range(numVirt):
denominator = FOCK_mo[numPairs + virt, numPairs + virt] - FOCK_mo[occ, occ] - eigval
if abs(denominator) < myprecon_cutoff:
local_myprecon[occ + numPairs * virt] = eigvec[occ + numPairs * virt] / myprecon_cutoff
else:
# local_myprecon = eigvec / ( diag(H) - eigval ) = K^{-1} u
local_myprecon[occ + numPairs * virt] = eigvec[occ + numPairs * virt] / denominator
if abs(eigval) < myprecon_cutoff:
local_myprecon[numVars] = eigvec[numVars] / myprecon_cutoff
else:
local_myprecon[numVars] = -eigvec[numVars] / eigval
# alpha_myprecon = - ( r, K^{-1} u ) / ( u, K^{-1} u )
alpha_myprecon = -np.einsum("i,i->", local_myprecon, resid) / np.einsum("i,i->", local_myprecon, eigvec)
# local_myprecon = r - ( r, K^{-1} u ) / ( u, K^{-1} u ) * u
local_myprecon = resid + alpha_myprecon * eigvec
for occ in range(numPairs):
for virt in range(numVirt):
denominator = FOCK_mo[numPairs + virt, numPairs + virt] - FOCK_mo[occ, occ] - eigval
if abs(denominator) < myprecon_cutoff:
local_myprecon[occ + numPairs * virt] = -local_myprecon[occ + numPairs * virt] / myprecon_cutoff
else:
local_myprecon[occ + numPairs * virt] = -local_myprecon[occ + numPairs * virt] / denominator
if abs(eigval) < myprecon_cutoff:
local_myprecon[numVars] = -local_myprecon[occ + numPairs * virt] / myprecon_cutoff
else:
local_myprecon[numVars] = local_myprecon[occ + numPairs * virt] / eigval
return local_myprecon
eigenval, eigenvec = linalg_helper.davidson(
aop=__wrapAugmentedHessian(FOCK_mo, numPairs, numVirt, tempJK_mo),
x0=ini_guess,
precond=myprecon,
# tol=1e-14, \
# max_cycle=50, \
max_space=20,
# lindep=1e-16, \
# max_memory=2000, \
nroots=1,
)
# logger.note(myMF, " RHF:NewtonRaphson :: # JK computs (iteration %d) = %d", iteration, tempJK_mo.iter)
eigenvec = eigenvec / eigenvec[numVars]
update = np.reshape(eigenvec[:-1], (numPairs, numVirt), order="F")
xmat = np.zeros([OEI_ao.shape[0], OEI_ao.shape[0]], dtype=float)
xmat[:numPairs, numPairs:] = -update
xmat[numPairs:, :numPairs] = update.T
unitary = scipy.linalg.expm(xmat)
orbitals = np.dot(orbitals, unitary)
dm_ao = 2 * np.dot(orbitals[:, :numPairs], orbitals[:, :numPairs].T)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
FOCK_mo = np.dot(orbitals.T, np.dot(FOCK_ao, orbitals))
grdnorm = 4 * np.linalg.norm(FOCK_mo[:numPairs, numPairs:])
energy = myMF.mol.energy_nuc() + 0.5 * np.einsum("ij,ij->", OEI_ao + FOCK_ao, dm_ao)
logger.note(myMF, " RHF:NewtonRaphson :: gradient norm (iteration %d) = %1.3g", iteration, grdnorm)
logger.note(myMF, " RHF:NewtonRaphson :: RHF energy (iteration %d) = %1.15g", iteration, energy)
logger.note(myMF, "RHF:NewtonRaphson :: Convergence reached.")
logger.note(myMF, "RHF:NewtonRaphson :: Converged RHF energy = %1.15g", energy)
energies, orbitals = scipy.linalg.eigh(a=FOCK_ao, b=S_ao)
myMF.mo_coeff = orbitals
myMF.mo_occ = np.zeros([OEI_ao.shape[0]], dtype=int)
myMF.mo_occ[:numPairs] = 2
myMF.mo_energy = energies
myMF.hf_energy = energy
myMF.converged = True
return myMF
def solve(myMF, dm_guess=None, safe_guess=True):
assert (hasattr(myMF, 'mol'))
assert (hasattr(myMF, 'mo_occ'))
assert (hasattr(myMF, 'mo_coeff'))
assert (myMF.mol.nelectron % 2 == 0) # RHF possible
S_ao = myMF.get_ovlp(myMF.mol)
OEI_ao = myMF.get_hcore(myMF.mol)
numPairs = myMF.mol.nelectron // 2
numVirt = OEI_ao.shape[0] - numPairs
numVars = numPairs * numVirt
if (dm_guess is None):
if ((len(myMF.mo_occ) == 0) or (safe_guess == True)):
dm_ao = myMF.get_init_guess(key=myMF.init_guess, mol=myMF.mol)
else:
dm_ao = np.dot(np.dot(myMF.mo_coeff, np.diag(myMF.mo_occ)),
myMF.mo_coeff.T)
else:
dm_ao = np.array(dm_guess, copy=True)
myJK_ao = __JKengine(myMF)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
energies, orbitals = scipy.linalg.eigh(a=FOCK_ao, b=S_ao)
dm_ao = 2 * np.dot(orbitals[:, :numPairs], orbitals[:, :numPairs].T)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
FOCK_mo = np.dot(orbitals.T, np.dot(FOCK_ao, orbitals))
grdnorm = 4 * np.linalg.norm(FOCK_mo[:numPairs, numPairs:])
energy = myMF.mol.energy_nuc() + 0.5 * np.einsum('ij,ij->',
OEI_ao + FOCK_ao, dm_ao)
logger.note(
myMF,
"RHF:NewtonRaphson :: Starting augmented Hessian Newton-Raphson RHF.")
iteration = 0
while (grdnorm > 1e-7):
iteration += 1
tempJK_mo = __JKengine(myMF, orbitals)
ini_guess = np.ones([numVars + 1], dtype=float)
for occ in range(numPairs):
for virt in range(numVirt):
ini_guess[occ + numPairs *
virt] = -FOCK_mo[occ, numPairs + virt] / max(
FOCK_mo[numPairs + virt, numPairs + virt] -
FOCK_mo[occ, occ], 1e-6)
def myprecon(resid, eigval, eigvec):
myprecon_cutoff = 1e-10
local_myprecon = np.zeros([numVars + 1], dtype=float)
for occ in range(numPairs):
for virt in range(numVirt):
denominator = FOCK_mo[numPairs + virt, numPairs +
virt] - FOCK_mo[occ, occ] - eigval
if (abs(denominator) < myprecon_cutoff):
local_myprecon[occ + numPairs * virt] = eigvec[
occ + numPairs * virt] / myprecon_cutoff
else:
# local_myprecon = eigvec / ( diag(H) - eigval ) = K^{-1} u
local_myprecon[occ + numPairs * virt] = eigvec[
occ + numPairs * virt] / denominator
if (abs(eigval) < myprecon_cutoff):
local_myprecon[numVars] = eigvec[numVars] / myprecon_cutoff
else:
local_myprecon[numVars] = -eigvec[numVars] / eigval
# alpha_myprecon = - ( r, K^{-1} u ) / ( u, K^{-1} u )
alpha_myprecon = -np.einsum('i,i->', local_myprecon,
resid) / np.einsum(
'i,i->', local_myprecon, eigvec)
# local_myprecon = r - ( r, K^{-1} u ) / ( u, K^{-1} u ) * u
local_myprecon = resid + alpha_myprecon * eigvec
for occ in range(numPairs):
for virt in range(numVirt):
denominator = FOCK_mo[numPairs + virt, numPairs +
virt] - FOCK_mo[occ, occ] - eigval
if (abs(denominator) < myprecon_cutoff):
local_myprecon[
occ + numPairs * virt] = -local_myprecon[
occ + numPairs * virt] / myprecon_cutoff
else:
local_myprecon[occ +
numPairs * virt] = -local_myprecon[
occ + numPairs * virt] / denominator
if (abs(eigval) < myprecon_cutoff):
local_myprecon[numVars] = -local_myprecon[
occ + numPairs * virt] / myprecon_cutoff
else:
local_myprecon[numVars] = local_myprecon[occ + numPairs *
virt] / eigval
return local_myprecon
eigenval, eigenvec = linalg_helper.davidson( aop=__wrapAugmentedHessian( FOCK_mo, numPairs, numVirt, tempJK_mo ), \
x0=ini_guess, \
precond=myprecon, \
#tol=1e-14, \
#max_cycle=50, \
max_space=20, \
#lindep=1e-16, \
#max_memory=2000, \
nroots=1 )
#logger.note(myMF, " RHF:NewtonRaphson :: # JK computs (iteration %d) = %d", iteration, tempJK_mo.iter)
eigenvec = eigenvec / eigenvec[numVars]
update = np.reshape(eigenvec[:-1], (numPairs, numVirt), order='F')
xmat = np.zeros([OEI_ao.shape[0], OEI_ao.shape[0]], dtype=float)
xmat[:numPairs, numPairs:] = -update
xmat[numPairs:, :numPairs] = update.T
unitary = scipy.linalg.expm(xmat)
orbitals = np.dot(orbitals, unitary)
dm_ao = 2 * np.dot(orbitals[:, :numPairs], orbitals[:, :numPairs].T)
FOCK_ao = OEI_ao + myJK_ao.getJK_ao(dm_ao)
FOCK_mo = np.dot(orbitals.T, np.dot(FOCK_ao, orbitals))
grdnorm = 4 * np.linalg.norm(FOCK_mo[:numPairs, numPairs:])
energy = myMF.mol.energy_nuc() + 0.5 * np.einsum(
'ij,ij->', OEI_ao + FOCK_ao, dm_ao)
logger.note(
myMF,
" RHF:NewtonRaphson :: gradient norm (iteration %d) = %1.3g",
iteration, grdnorm)
logger.note(
myMF,
" RHF:NewtonRaphson :: RHF energy (iteration %d) = %1.15g",
iteration, energy)
logger.note(myMF, "RHF:NewtonRaphson :: Convergence reached.")
logger.note(myMF, "RHF:NewtonRaphson :: Converged RHF energy = %1.15g",
energy)
energies, orbitals = scipy.linalg.eigh(a=FOCK_ao, b=S_ao)
myMF.mo_coeff = orbitals
myMF.mo_occ = np.zeros([OEI_ao.shape[0]], dtype=int)
myMF.mo_occ[:numPairs] = 2
myMF.mo_energy = energies
myMF.e_tot = energy
myMF.converged = True
return myMF
def optimize( self, threshold=1e-6 ):
r'''Augmented Hessian Newton-Raphson optimization of the localization cost function, using an exact gradient and hessian
Args:
threshold : The convergence threshold for the orbital rotation gradient
Returns:
The orbital coefficients of the orthonormal localized orbitals, expressed in terms of the AO
'''
# To break up symmetrical orbitals
flatx = ( 0.0123 / self.numVars ) * np.ones( [ self.numVars ], dtype=float )
self.__update_unitary( flatx )
#self.__debug_gradient()
#self.__debug_hessian_matvec()
#self.__debug_diag_hessian()
self.grd_norm = 1.0
iteration = 0
max_cf_encountered = 0.0
logger.debug(self, "Localizer :: At iteration %d the cost function = %1.13f", iteration, -self.__costfunction())
logger.debug(self, "Localizer :: Linear size of the augmented Hessian = %d", self.numVars+1)
while ( self.grd_norm > threshold ):
iteration += 1
self.__set_gradient() # Sets self.gradient and self.grd_norm
ini_guess = np.zeros( [ self.numVars + 1 ], dtype=float )
diag_h = np.zeros( [ self.numVars + 1 ], dtype=float )
ini_guess[ self.numVars ] = 1.0
diag_h[ :-1 ] = self.__diag_hessian()
for elem in range( self.numVars ):
if ( abs( diag_h[ elem ] ) < 1e-6 ):
ini_guess[ elem ] = -self.gradient[ elem ] / 1e-6
else:
ini_guess[ elem ] = -self.gradient[ elem ] / diag_h[ elem ] # Minus the gradient divided by the diagonal elements of the hessian
if ( self.use_hess == True ):
def myprecon( resid, eigval, eigvec ):
myprecon_cutoff = 1e-10
local_myprecon = np.zeros( [ self.numVars + 1 ], dtype=float )
for elem in range( self.numVars + 1 ):
if ( abs( diag_h[ elem ] - eigval ) < myprecon_cutoff ):
local_myprecon[ elem ] = eigvec[ elem ] / myprecon_cutoff
else:
# local_myprecon = eigvec / ( diag(H) - eigval ) = K^{-1} u
local_myprecon[ elem ] = eigvec[ elem ] / ( diag_h[ elem ] - eigval )
# alpha_myprecon = - ( r, K^{-1} u ) / ( u, K^{-1} u )
alpha_myprecon = - np.einsum( 'i,i->', local_myprecon, resid ) / np.einsum( 'i,i->', local_myprecon, eigvec )
# local_myprecon = r - ( r, K^{-1} u ) / ( u, K^{-1} u ) * u
local_myprecon = resid + alpha_myprecon * eigvec
for elem in range( self.numVars + 1 ):
if ( abs( diag_h[ elem ] - eigval ) < myprecon_cutoff ):
local_myprecon[ elem ] = - local_myprecon[ elem ] / myprecon_cutoff
else:
local_myprecon[ elem ] = - local_myprecon[ elem ] / ( diag_h[ elem ] - eigval )
return local_myprecon
#self.ahnr_cnt = 0
eigenval, eigenvec = linalg_helper.davidson( aop=self.__augmented_hessian_matvec, \
x0=ini_guess, \
precond=myprecon, \
#tol=1e-14, \
#max_cycle=50, \
max_space=20, \
#lindep=1e-16, \
#max_memory=2000, \
nroots=1 )
else:
eigenvec = np.array( ini_guess, copy=True )
flatx = eigenvec[ :-1 ] / eigenvec[ self.numVars ]
update_norm = np.linalg.norm( flatx )
cost_func_prev = -self.__costfunction()
self.__update_unitary( flatx )
cost_func_now = -self.__costfunction()
counter = 0
while ( counter < 8 ) and ( cost_func_now < cost_func_prev ):
logger.debug(self, "Localizer :: Taking half a step back")
flatx *= 0.5
self.__update_unitary( -flatx )
cost_func_now = -self.__costfunction()
counter += 1
if ( cost_func_now > max_cf_encountered ):
max_cf_encountered = cost_func_now
logger.debug(self, "Localizer :: Gradient norm = %g", self.grd_norm)
logger.debug(self, "Localizer :: Update norm = %g", update_norm)
logger.debug(self, "Localizer :: At iteration %d the cost function = %1.13f", iteration, cost_func_now)
logger.debug(self, " Diff. with prev. CF = %g", cost_func_now - cost_func_prev )
logger.debug(self, " Diff. with max. CF = %g", cost_func_now - max_cf_encountered )
if ( iteration % 10 == 0 ):
self.__reorthogonalize()
cost_func_now = -self.__costfunction()
logger.note(self, "Localization procedure converged in %d iterations.", iteration)
self.__reorder_orbitals()
converged_coeff = np.dot( self.coeff, self.u )
return converged_coeff
def optimize(self, threshold=1e-6):
r'''Augmented Hessian Newton-Raphson optimization of the localization cost function, using an exact gradient and hessian
Args:
threshold : The convergence threshold for the orbital rotation gradient
Returns:
The orbital coefficients of the orthonormal localized orbitals, expressed in terms of the AO
'''
# To break up symmetrical orbitals
flatx = (0.0000 / self.numVars) * np.ones([self.numVars], dtype=float)
self.__update_unitary(flatx)
#self.__debug_gradient()
#self.__debug_hessian_matvec()
#self.__debug_diag_hessian()
self.grd_norm = 1.0
iteration = 0
max_cf_encountered = 0.0
logger.debug(
self, "Localizer :: At iteration %d the cost function = %1.13f",
iteration, -self.__costfunction())
logger.debug(self,
"Localizer :: Linear size of the augmented Hessian = %d",
self.numVars + 1)
while (self.grd_norm > threshold):
iteration += 1
self.__set_gradient() # Sets self.gradient and self.grd_norm
ini_guess = np.zeros([self.numVars + 1], dtype=float)
diag_h = np.zeros([self.numVars + 1], dtype=float)
ini_guess[self.numVars] = 1.0
diag_h[:-1] = self.__diag_hessian()
for elem in range(self.numVars):
if (abs(diag_h[elem]) < 1e-6):
ini_guess[elem] = -self.gradient[elem] / 1e-6
else:
ini_guess[elem] = -self.gradient[elem] / diag_h[
elem] # Minus the gradient divided by the diagonal elements of the hessian
if (self.use_hess == True):
def myprecon(resid, eigval, eigvec):
myprecon_cutoff = 1e-10
local_myprecon = np.zeros([self.numVars + 1], dtype=float)
for elem in range(self.numVars + 1):
if (abs(diag_h[elem] - eigval) < myprecon_cutoff):
local_myprecon[
elem] = eigvec[elem] / myprecon_cutoff
else:
# local_myprecon = eigvec / ( diag(H) - eigval ) = K^{-1} u
local_myprecon[elem] = eigvec[elem] / (
diag_h[elem] - eigval)
# alpha_myprecon = - ( r, K^{-1} u ) / ( u, K^{-1} u )
alpha_myprecon = -np.einsum(
'i,i->', local_myprecon, resid) / np.einsum(
'i,i->', local_myprecon, eigvec)
# local_myprecon = r - ( r, K^{-1} u ) / ( u, K^{-1} u ) * u
local_myprecon = resid + alpha_myprecon * eigvec
for elem in range(self.numVars + 1):
if (abs(diag_h[elem] - eigval) < myprecon_cutoff):
local_myprecon[
elem] = -local_myprecon[elem] / myprecon_cutoff
else:
local_myprecon[elem] = -local_myprecon[elem] / (
diag_h[elem] - eigval)
return local_myprecon
#self.ahnr_cnt = 0
eigenval, eigenvec = linalg_helper.davidson( aop=self.__augmented_hessian_matvec, \
x0=ini_guess, \
precond=myprecon, \
#tol=1e-14, \
#max_cycle=50, \
max_space=20, \
#lindep=1e-16, \
#max_memory=2000, \
nroots=1 )
else:
eigenvec = np.array(ini_guess, copy=True)
flatx = eigenvec[:-1] / eigenvec[self.numVars]
update_norm = np.linalg.norm(flatx)
cost_func_prev = -self.__costfunction()
self.__update_unitary(flatx)
cost_func_now = -self.__costfunction()
counter = 0
while (counter < 8) and (cost_func_now < cost_func_prev):
logger.debug(self, "Localizer :: Taking half a step back")
flatx *= 0.5
self.__update_unitary(-flatx)
cost_func_now = -self.__costfunction()
counter += 1
if (cost_func_now > max_cf_encountered):
max_cf_encountered = cost_func_now
logger.debug(self, "Localizer :: Gradient norm = %g",
self.grd_norm)
logger.debug(self, "Localizer :: Update norm = %g", update_norm)
logger.debug(
self,
"Localizer :: At iteration %d the cost function = %1.13f",
iteration, cost_func_now)
logger.debug(self, " Diff. with prev. CF = %g",
cost_func_now - cost_func_prev)
logger.debug(self, " Diff. with max. CF = %g",
cost_func_now - max_cf_encountered)
if (iteration % 10 == 0):
self.__reorthogonalize()
cost_func_now = -self.__costfunction()
logger.note(self, "Localization procedure converged in %d iterations.",
iteration)
self.__reorder_orbitals()
converged_coeff = np.dot(self.coeff, self.u)
return converged_coeff
e_hoqmo, e_luqmo = gf.as_occupied().e[-1], gf.as_virtual().e[0]
v_hoqmo, v_luqmo = gf.as_occupied().v[:,-1], gf.as_virtual().v[:,0]
print('RAGF2(2,2):')
print('IP = %.6f weight = %.6f' % (-e_hoqmo, np.linalg.norm(v_hoqmo)))
print('EA = %.6f weight = %.6f' % (e_luqmo, np.linalg.norm(v_luqmo)))
print('Gap = %.6f' % (e_luqmo - e_hoqmo))
# Method 3: using a more efficient solver:
f_phys = rhf.get_fock(gf2_c.rdm1, basis='mo')
nroots = 5
def aop(x): return gf2_c.se.dot(f_phys, x)
def precond(dx, e, x0): return dx / (np.concatenate([np.diag(f_phys), gf2_c.se.e]) - e)
def pick(w, v, nroots, callback):
mask = np.argsort(abs(w-gf2_c.chempot))
return w[mask], v[:,mask], 0
e, v = davidson(aop, np.eye(nroots, gf2_c.nphys+gf2_c.naux), precond, nroots=nroots, max_cycle=10*nroots, pick=pick)
e_hoqmo, e_luqmo = np.max(e[e < gf2_c.chempot]), np.min(e[e >= gf2_c.chempot])
v_hoqmo, v_luqmo = v[np.argmax(e[e < gf2_c.chempot])], v[np.argmin(e[e >= gf2_c.chempot])]
print('RAGF2(3,3):')
print('IP = %.6f weight = %.6f' % (-e_hoqmo, np.linalg.norm(v_hoqmo[:rhf.nao])))
print('EA = %.6f weight = %.6f' % (e_luqmo, np.linalg.norm(v_luqmo[:rhf.nao])))
print('Gap = %.6f' % (e_luqmo - e_hoqmo))
# CCSD:
ccsd = cc.CCSD(rhf)
ccsd.run()
e_ip, v_ip = ccsd._pyscf.ipccsd()[:2]
e_ea, v_ea = ccsd._pyscf.eaccsd()[:2]
print('EOM-CCSD:')
print('IP = %.6f weight = %.6f' % (e_ip, np.linalg.norm(v_ip[:rhf.nao])))
print('EA = %.6f weight = %.6f' % (e_ea, np.linalg.norm(v_ea[:rhf.nao])))