def bond_dimension(data, foreach=[], deg=1, num_points=None):
en_vs_bond = pyalps_dset.collectXY(pyalps_dset.flatten(data), 'max_bond_dimension', 'Energy', foreach=foreach)
extrap = []
fits = []
for d in en_vs_bond:
bond_dims = deepcopy(d.x)
d.x = 1./d.x
d.x = d.x[::-1]
d.y = d.y[::-1]
sel = np.ones(len(d.x), dtype=bool)
if num_points is not None and num_points < len(d.x): sel[num_points:] = False
coeff = np.polyfit(d.x[sel], d.y[sel], deg=deg)
r2 = rsquared(d.x[sel], d.y[sel], coeff)
fit_cut = d.x[num_points-1] if num_points is not None and num_points < len(d.x) else d.x[-1]
d.props['fitted_r2'] = r2
d.props['fit_deg'] = deg
d.props['fit_numpoints'] = num_points
d.props['fit_cut'] = fit_cut
d.props['fitted_coeff'] = coeff
d.props['fitted_energy'] = coeff[-1]
dd = pyalps_dset.DataSet()
dd.props = deepcopy(d.props)
dd.props['fitted_r2'] = r2
dd.props['fit_deg'] = deg
dd.props['fitted_coeff'] = coeff
dd.x = np.linspace(0, max(d.x))
dd.y = np.polyval(coeff, dd.x)
fits.append(dd)
dd = pyalps_dset.DataSet()
dd.props = deepcopy(d.props)
dd.props['max_bond_dimension'] = 'inf'
dd.x = np.array([])
dd.y = np.array([ coeff[-1] ])
extrap.append(dd)
d.props['line'] = 'scatter'
d.props['bond_dims'] = bond_dims
return extrap, en_vs_bond, fits
def compute(filling, bond_dim, odd_sizes=False, amplitude_points=None):
## Load all system sizes
if odd_sizes:
densities = map(lambda parms: to_dataset(*utils.load_or_evaluate('density_fit', density.evaluate_fit, **parms)),
utils.iter_odd_system_size(bond_dim=bond_dim, filling=filling))
else:
densities = map(lambda parms: to_dataset(*utils.load_or_evaluate('density_fit', density.evaluate_fit, **parms)),
utils.iter_system_size(bond_dim=bond_dim, filling=filling))
densities = filter(lambda d: d.props is not None, densities)
if len(densities) < 3:
print 'WARNING:', 'Only got {} valid densities, you need at least 3.'.format(len(densities))
d = pyalps_dset.DataSet()
d.props = None
return d
# check that particle density in the middle is symmetric, otherwise exclude dataset
# for L=192 it is better to use only M > 2000
# def symm_middle_filter(d):
# x = int(d.props['L'] / 2)
# delta = abs(d.y[x] - d.y[x-1]) if d.props['L']%2==0 else abs(d.y[x+1] - d.y[x-1])
# if delta > 5e-5:
# print '# Discard L={L:.0f}, n={filling}, tperp={t\'}, M={max_bond_dimension:.0f} : {delta}'.format(delta=delta, **d.props)
# return False
# return True
# densities = filter(symm_middle_filter, densities)
## Only even number of pairs
densities = filter(lambda d: d.props['L']%2 != 0 or d.props['Nup_total'] % 2 == 0, densities)
amplitudes = map(compute_amplitude, densities)
for d in amplitudes:
if d.props['density_fit_error'] > abs(d.y[0]):
print 'WARNING:', 'Error in density fit is higher than amplitude magnitude.'
print 'Error per site is', d.props['density_fit_error'], 'Amplidue is', d.y[0]
print 'Dataset was:', 'L=%s filling=%s t_perp=%s M=%s' % (d.props['L'], d.props['filling'], d.props['t\''], d.props['max_bond_dimension'])
common_props = pyalps_dset.dict_intersect([d.props for d in amplitudes])
amp_vs_L = pyalps_dset.collectXY(amplitudes, 'L', 'Amplitude')
d = amp_vs_L[0]
## fit finite size analysis
sel = np.ones(len(d.x), dtype=bool)
if amplitude_points is not None and amplitude_points < len(d.x): sel[:-amplitude_points] = False
cov = np.ones((2,2))*np.nan
if sum(sel) > 2:
coeff, cov = np.polyfit(np.log(d.x[sel]), np.log(d.y[sel]), deg=1, cov=True)
else:
coeff = np.polyfit(np.log(d.x[sel]), np.log(d.y[sel]), deg=1)
r2 = rsquared(np.log(d.x), np.log(d.y), coeff)
fit_range = [d.x[0], d.x[-1]]
if amplitude_points is not None and amplitude_points < len(d.x): fit_range[0] = d.x[-amplitude_points]
## compute new Krho
slope = coeff[0]
errslope = np.sqrt(cov[0,0])
Krho = -2. * slope
errKrho = 2. * errslope
print 'M={} t_perp={} filling={:4.4f} -> Krho={:.3f} +/- {:.3f} : R^2 {:.4f}'.format(common_props['max_bond_dimension'], common_props['t\''], common_props['filling'], Krho, errKrho, r2)
d.props['fit_range'] = fit_range
d.props['fit_numpoints'] = amplitude_points
d.props['fitted_coeff'] = coeff
d.props['fitted_Krho'] = Krho
d.props['fitted_Krho_error'] = errKrho
d.props['fitted_r2'] = r2
return d
