def plot_convergence(filename):
with h5py.File('afqmc.h5', 'r') as fh5:
hcore = fh5['Hamiltonian/hcore'][:].view(numpy.complex128)[:, :, 0]
energies = []
errs = []
tau_bps = []
sym_md = get_metadata(filename)
bp_md = get_metadata(filename, 'Observables/BackPropagated/')
taus = bp_md['BackPropSteps']
for i, t in enumerate(taus):
# skip the first block for equilibration
skip = 1
nelec = sym_md['NAEA'] + sym_md['NAEB']
# We can extract the averaged 1RDM.
rdm_av, rdm_errs = average_one_rdm(filename, eqlb=skip, ix=i)
nelec_rdm = (rdm_av[0].trace()).real
assert (nelec_rdm - nelec < 1e-12)
# Often it is simpler to compute error bars if we first contract the 1RDM.
# For example, we can compute the one-body energy from the averaged RDM as.
e1b = numpy.einsum('ij,sij->', hcore, rdm_av).real
# Or we can instead compute the average of the one-body energies.
e1b_series, err = compute_one_body(filename, hcore, skip, i)
energies.append(e1b_series)
errs.append(err)
# get back propagation time
tau_bps.append(t * sym_md['Timestep'])
assert (e1b - e1b_series < 1e-12)
# Finally plot the one-body energy and check the estimator is converged with
# respect to back propagation time.
if have_mpl:
plt.errorbar(tau_bps, energies, yerr=errs, fmt='o')
plt.xlabel(r'$\tau_{BP}$')
plt.ylabel(r'$E_{1B}$ (Ha)')
plt.savefig('h1e_conv.pdf', bbox_inches='tight')
def average_on_top_pdm(filename, estimator='back_propagated', eqlb=1, skip=1, ix=None):
"""Average on-top pair density matrix.
Returns n2(r,r) for a given real space grid.
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
opdm : :class:`numpy.ndarray`
Averaged diagonal on-top pair density matrix.
opdm_err : :class:`numpy.ndarray`
Error bars for diagonal on-top pair density matrix elements.
"""
md = get_metadata(filename)
mean, err = average_observable(filename, 'on_top_pdm', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
# TODO: Update appropriately.
return mean, err
def average_one_rdm(filename,
estimator='back_propagated',
eqlb=1,
skip=1,
ix=None):
"""Average AFQMC 1RDM.
Returns P_{sij} = <c_{is}^+ c_{js}^> as a (nspin, M, M) dimensional array.
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
one_rdm : :class:`numpy.ndarray`
Averaged 1RDM.
one_rdm_err : :class:`numpy.ndarray`
Error bars for 1RDM elements.
"""
md = get_metadata(filename)
mean, err = average_observable(filename,
'one_rdm',
eqlb=eqlb,
skip=skip,
estimator=estimator,
ix=ix)
nbasis = md['NMO']
wt = md['WalkerType']
try:
walker = WALKER_TYPE[wt]
except IndexError:
print('Unknown walker type {}'.format(wt))
if walker == 'closed':
return 2 * mean.reshape(1, nbasis, nbasis), err.reshape(
1, nbasis, nbasis)
elif walker == 'collinear':
return mean.reshape((2, nbasis, nbasis)), err.reshape(
(2, nbasis, nbasis))
elif walker == 'non_collinear':
return mean.reshape((1, 2 * nbasis, 2 * nbasis)), err.reshape(
(1, 2 * nbasis, 2 * nbasis))
else:
print('Unknown walker type.')
return None
def average_atom_correlations(filename, estimator='back_propagated', eqlb=1, skip=1, ix=None):
"""Average atom centered correlations.
Returns <C(I)>, <S(I)>, <C(I)C(J)> and <S(I)S(J)> for a given set of atomic sites.
C = (nup + ndown), S = (nup - ndown)
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
c_mean : :class:`numpy.ndarray`
Averaged charge.
c_err : :class:`numpy.ndarray`
Error bars for charge.
s_mean : :class:`numpy.ndarray`
Averaged spin.
s_err : :class:`numpy.ndarray`
Error bars for spin.
cc_mean : :class:`numpy.ndarray`
Averaged charge-charge correlation function.
cc_err : :class:`numpy.ndarray`
Error bars for charge-charge correlation function.
ss_mean : :class:`numpy.ndarray`
Averaged spin-spin correlation function.
ss_err : :class:`numpy.ndarray`
Error bars for spin-spin correlation function.
"""
md = get_metadata(filename)
c_mean, c_err = average_observable(filename, 'c_atom_correlation', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
s_mean, s_err = average_observable(filename, 's_atom_correlation', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
m_mean, m_err = average_observable(filename, 'm_atom_correlation', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
cc_mean, cc_err = average_observable(filename, 'cc_atom_correlation', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
ss_mean, ss_err = average_observable(filename, 'ss_atom_correlation', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
# TODO: get npts from metadata local to cc_correlation
npts = int(sqrt(cc_mean.shape[0]))
return c_mean, c_err, s_mean, s_err, m_mean, m_err, cc_mean.reshape((npts,-1)), cc_err.reshape((npts,-1)), \
ss_mean.reshape((npts,-1)), ss_err.reshape((npts,-1))
def average_two_rdm(filename, estimator='back_propagated', eqlb=1, skip=1, ix=None):
"""Average AFQMC 2RDM.
Returns a list of 2RDMS, where
2RDM[s1s2,i,k,j,l] = <c_{i}^+ c_{j}^+ c_{l} c_{k}>.
For closed shell systems, returns [(a,a,a,a),(a,a,b,b)]
For collinear systems, returns [(a,a,a,a),(a,a,b,b),(b,b,b,b)]
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
two_rdm : :class:`numpy.ndarray`
List of averaged 2RDM.
two_rdm_err : :class:`numpy.ndarray`
List of error bars for 2RDM elements.
"""
md = get_metadata(filename)
mean, err = average_observable(filename, 'two_rdm', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
nbasis = md['NMO']
wt = md['WalkerType']
try:
walker = WALKER_TYPE[wt]
except IndexError:
print('Unknown walker type {}'.format(wt))
if walker == 'closed':
return mean.reshape(2,nbasis,nbasis,nbasis,nbasis), err.reshape(2,nbasis,nbasis,nbasis,nbasis)
elif walker == 'collinear':
return mean.reshape(3,nbasis,nbasis,nbasis,nbasis), err.reshape(3,nbasis,nbasis,nbasis,nbasis)
elif walker == 'non_collinear':
return mean.reshape(2*nbasis,2*nbasis,2*nbasis,2*nbasis), err.reshape(2*nbasis,2*nbasis,2*nbasis, 2*nbasis)
else:
print('Unknown walker type.')
return None
def average_gen_fock(filename, fock_type='plus', estimator='back_propagated',
eqlb=1, skip=1, ix=None):
"""Average AFQMC genralised Fock matrix.
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
fock_type : string
Which generalised Fock matrix to extract. Optional (plus/minus).
Default: plus.
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
gfock : :class:`numpy.ndarray`
Averaged 1RDM.
gfock_err : :class:`numpy.ndarray`
Error bars for 1RDM elements.
"""
md = get_metadata(filename)
name = 'gen_fock_' + fock_type
mean, err = average_observable(filename, name, eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
nbasis = md['NMO']
wt = md['WalkerType']
try:
walker = WALKER_TYPE[wt]
except IndexError:
print('Unknown walker type {}'.format(wt))
if walker == 'closed':
return mean.reshape(1,nbasis,nbasis), err.reshape(1,nbasis, nbasis)
elif walker == 'collinear':
return mean.reshape((2,nbasis,nbasis)), err.reshape((2, nbasis, nbasis))
elif walker == 'non_collinear':
return mean.reshape((1,2*nbasis,2*nbasis)), err.reshape((1,2*nbasis, 2*nbasis))
else:
print('Unknown walker type.')
return None
def average_observable(filename,
name,
eqlb=1,
estimator='back_propagated',
ix=None,
skip=1):
"""Compute mean and error bar for AFQMC HDF5 observable.
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
name : string
Name of observable (see estimates.py for list).
eqlb : int
Number of blocks for equilibration. Default 1.
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
mean : :class:`numpy.ndarray`
Averaged quantity.
err : :class:`numpy.ndarray`
Error bars for quantity.
"""
md = get_metadata(filename)
free_proj = md['FreeProjection']
if free_proj:
mean = None
err = None
print("# Error analysis for free projection not implemented.")
else:
data = extract_observable(filename,
name=name,
estimator=estimator,
ix=ix)
mean = numpy.mean(data[eqlb:len(data):skip], axis=0)
err = scipy.stats.sem(data[eqlb:len(data):skip].real, axis=0)
return mean, err
def average_diag_two_rdm(filename, estimator='back_propagated', eqlb=1, skip=1, ix=None):
"""Average diagonal part of 2RDM.
Returns <c_{is}^+ c_{jt}^+ c_{jt} c_{is}> as a (2M,2M) dimensional array.
Parameters
----------
filename : string
QMCPACK output containing density matrix (*.h5 file).
estimator : string
Estimator type to analyse. Options: back_propagated or mixed.
Default: back_propagated.
eqlb : int
Number of blocks for equilibration. Default 1.
skip : int
Number of blocks to skip in between measurements equilibration.
Default 1 (use all data).
ix : int
Back propagation path length to average. Optional.
Default: None (chooses longest path).
Returns
-------
two_rdm : :class:`numpy.ndarray`
Averaged diagonal 2RDM.
two_rdm_err : :class:`numpy.ndarray`
Error bars for diagonal 2RDM elements.
"""
md = get_metadata(filename)
mean, err = average_observable(filename, 'diag_two_rdm', eqlb=eqlb, skip=skip,
estimator=estimator, ix=ix)
nbasis = md['NMO']
wt = md['WalkerType']
try:
walker = WALKER_TYPE[wt]
except IndexError:
print('Unknown walker type {}'.format(wt))
if walker == 'closed':
dm_size = nbasis*(2*nbasis-1) - nbasis*(nbasis-1) // 2
assert mean.shape == dm_size
two_rdm = numpy.zeros((2*nbasis, 2*nbasis), dtype=mean.dtype)
two_rdm_err = numpy.zeros((2*nbasis, 2*nbasis), dtype=mean.dtype)
ij = 0
for i in range(nbasis):
for j in range(i+1, 2*nbasis):
two_rdm[i,j] = mean[ij]
two_rdm_err[i,j] = err[ij]
two_rdm[j,i] = mean[ij].conj()
two_rdm_err[j,i] = err[ij].conj()
ij += 1
two_rdm[nbasis:,nbasis:] = two_rdm[:nbasis,:nbasis].copy()
elif walker == 'collinear':
dm_size = nbasis*(2*nbasis-1)
assert mean.shape == dm_size
two_rdm = numpy.zeros((2*nbasis, 2*nbasis), dtype=mean.dtype)
two_rdm_err = numpy.zeros((2*nbasis, 2*nbasis), dtype=mean.dtype)
ij = 0
for i in range(2*nbasis):
for j in range(i+1, 2*nbasis):
two_rdm[i,j] = mean[ij]
two_rdm_err[i,j] = err[ij]
two_rdm[j,i] = mean[ij].conj()
two_rdm_err[j,i] = err[ij].conj()
ij += 1
elif walker == 'non_collinear':
print("Non-collinear wavefunction not supported.")
return None
else:
print('Unknown walker type.')
return None
# Diagonal is zero
return two_rdm, two_rdm_err
