def window_conv_depr():
nwf_vec = np.array([5, 10, 20, 40, 80, 160, 320])
diff_vec = np.zeros_like(nwf_vec, dtype=np.float)
for idx, nwf in enumerate(nwf_vec):
d = analytic_solution(beta=2.0, U=5.0, nw=1, nwf=nwf)
diff = np.max(np.abs(d.gamma_m.data - d.gamma_m_num.data))
diff_vec[idx] = diff
print('nwf, diff =', idx, nwf, diff)
print(diff_vec)
from triqs.plot.mpl_interface import oplot, oplotr, oploti, plt
x = 1. / nwf_vec
plt.figure(figsize=(3.25, 3))
plt.plot(x, diff_vec, 'o-', alpha=0.75)
plt.xlabel(r'$1/n_{w}$')
plt.ylabel(r'$\max|\Gamma_{ana} - \Gamma_{num}|$')
plt.ylim([0, diff_vec.max()])
plt.xlim([0, x.max()])
plt.tight_layout()
plt.savefig('figure_bse_hubbard_atom_convergence.pdf')
plt.show()
def plot_chi_k(p, color=None):
chi_k = p.chi_kw[:, Idx(0)]
k_vecs, k_plot, K_plot, K_labels = get_path()
kx, ky, kz = k_vecs.T
interp = np.vectorize(
lambda kx, ky, kz: np.squeeze(chi_k([kx, ky, kz]).real))
interp = interp(kx, ky, kz)
p.chi_G = np.squeeze(chi_k[Idx(0, 0, 0)].real)
line = plt.plot(k_plot,
interp,
'-',
label=r'$N_{\nu} = $' + '${:d}$'.format(p.nwf))
plt.gca().set_xticks(K_plot)
plt.gca().set_xticklabels(K_labels)
plt.grid(True)
plt.ylabel(r'$\chi(\mathbf{Q})$')
plt.legend(loc='best', fontsize=8)
return line[0].get_color()
def plot_field(out):
plt.figure(figsize=(3.25 * 2, 8))
for p in out.data:
subp = [2, 1, 1]
ax = plt.subplot(*subp)
subp[-1] += 1
oplotr(p.G_tau['up'], 'b', alpha=0.25)
oplotr(p.G_tau['dn'], 'g', alpha=0.25)
ax.legend().set_visible(False)
subp = [2, 1, 2]
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$\chi \approx %2.2f$' % out.chi)
plt.plot(out.h_vec, out.m_vec, '-og', alpha=0.5)
plt.plot(out.h_vec, out.m_ref_vec, 'xb', alpha=0.5)
plt.plot(out.h_vec, -out.chi * out.h_vec, '-r', alpha=0.5)
plt.tight_layout()
plt.savefig('figure_static_field.pdf')
for idx, nwf in enumerate(nwf_vec):
d = analytic_hubbard_atom(beta=2.0,
U=5.0,
nw=1,
nwf=nwf,
nwf_gf=2 * nwf)
diff_vec[idx] = np.max(np.abs(d.gamma_m.data - d.gamma_m_num.data))
print('nwf, diff =', idx, nwf, diff_vec[idx])
# ------------------------------------------------------------------
# -- Plot
from triqs.plot.mpl_interface import oplot, oplotr, oploti, plt
x = 1. / nwf_vec
plt.figure(figsize=(3.25, 3))
plt.plot(x, diff_vec, 'o-', alpha=0.75)
plt.xlabel(r'$1/n_{w}$')
plt.ylabel(r'$\max|\Gamma_{ana} - \Gamma_{num}|$')
plt.ylim([0, diff_vec.max()])
plt.xlim([0, x.max()])
plt.tight_layout()
plt.savefig('figure_bse_hubbard_atom_convergence.pdf')
plt.show()
return line[0].get_color()
plt.figure(figsize=(3.25 * 2, 3))
ps, color = [], None
for filename in np.sort(glob.glob('data_bse_nwf*.h5')):
with HDFArchive(filename, 'r') as a:
p = a['p']
subp = [1, 2, 1]
plt.subplot(*subp)
subp[-1] += 1
color = plot_chi_k(p)
plt.subplot(*subp)
subp[-1] += 1
plt.plot(1. / p.nwf, p.chi_G, 'o', color=color)
ps.append(p)
# -- Extrapolation to nwf -> oo
ps = ParameterCollections(objects=ps)
x, y = 1. / ps.nwf, ps.chi_G
sidx = np.argsort(x)
x, y = x[sidx], y[sidx]
p = np.polyfit(x, y, 1)
y0 = np.polyval(p, 0)
X = np.linspace(0, x.max())
Y = np.polyval(p, X)
subp = [1, 2, 1]
plt.subplot(*subp)
subp[-1] += 1
r'half-filled Hubbard atom $U=%2.2f$' % U)
# ------------------------------------------------------------------
# -- Analytic result
T = np.logspace(-3, 2, num=400)
beta = 1. / T
# -- Analytic magnetization expecation value
# -- and static susceptibility
Z = 2. + 2 * np.exp(-beta * 0.5 * U)
m2 = 0.25 * (2 / Z)
chi_m = 2. * beta * m2
plt.plot(1. / beta, chi_m, '-k', lw=0.5)
# ------------------------------------------------------------------
# -- external field pyed
filenames = glob.glob('pyed_beta*/data_pyed_extrap*.h5')
style = 'sk'
for filename in filenames:
print('--> Loading:', filename)
with HDFArchive(filename, 'r') as s:
field = s['field']
plt.plot(1. / field.beta, field.chi, style, alpha=0.25)
plt.plot(1. / field.beta, field.chi_exp, '.r', alpha=0.25)
ps = []
filenames = np.sort(glob.glob('data_B_*.h5'))
for filename in filenames:
with HDFArchive(filename, 'r') as a:
p = a['ps'].objects[-1]
ps.append(p)
ps = ParameterCollections(ps)
B, M = ps.B, ps.M
B = np.concatenate((-B[1:][::-1], B))
M = np.concatenate((-M[1:][::-1], M))
p = np.polyfit(M, B, 5)
m = np.linspace(-0.5, 0.5, num=1000)
b = np.polyval(p, m)
chi = 1. / np.polyval(np.polyder(p, 1), 0.).real
plt.figure(figsize=(3.25 * 1.5, 2.5 * 1.5))
plt.title(r'$\chi = \frac{dM}{dB}|_{B=0} \approx $' + '$ {:3.4f}$'.format(chi))
plt.plot(B, M, 'o', alpha=0.75, label='DMFT field')
plt.plot(b, m, '-', alpha=0.75, label='Poly fit')
plt.legend(loc='upper left')
plt.grid(True)
plt.xlabel(r'$B$')
plt.ylabel(r'$M$')
plt.xlim([B.min(), B.max()])
plt.ylim([-0.5, 0.5])
plt.tight_layout()
plt.savefig('figure_field.svg')
plt.show()
qidx = bzmesh.index_to_linear(q)
print('-' * 72)
print('q =', q)
print('qidx =', qidx)
print('q_list[qidx] =', q_list[qidx])
print('q_list[qidx]/np.pi =', np.array(q_list[qidx]) / np.pi)
data = np.squeeze(chi0w0.data[:, qidx])
print(data.shape)
plt.subplot(*subp)
subp[-1] += 1
plt.title(r'$q = \pi \times$ %s' % str(np.array(q_list[qidx]) / np.pi))
plt.plot(data.real)
plt.ylabel(r'Re[$\chi_0(i\omega)$]')
plt.ylim([-vmax, 0.1 * vmax])
plt.subplot(*subp)
subp[-1] += 1
plt.plot(data.imag)
plt.ylabel(r'Im[$\chi_0(i\omega)$]')
plt.subplot(*subp)
subp[-1] += 1
plt.pcolormesh(chi0q.data[:, :, qidx, 0, 0, 0, 0].real, **opt)
plt.colorbar()
plt.axis('equal')
plt.title(r'Re[$\chi_0(i\omega, i\nu)$]')
plt.xlabel(r'$\nu$')
#
################################################################################
from common import *
from triqs.plot.mpl_interface import oplot, oplotr, oploti, plt
with HDFArchive('data_sc.h5', 'r') as a:
ps = a['ps']
p = ps.objects[-1]
plt.figure(figsize=(3.25 * 2, 5))
subp = [2, 2, 1]
plt.subplot(*subp)
subp[-1] += 1
plt.plot(ps.iter, ps.dG_l, 's-')
plt.ylabel('$\max | \Delta G_l |$')
plt.xlabel('Iteration')
plt.semilogy([], [])
plt.subplot(*subp)
subp[-1] += 1
for b, g in p.G_l:
p.G_l[b].data[:] = np.abs(g.data)
oplotr(p.G_l['up'], 'o-', label=None)
plt.ylabel('$| G_l |$')
plt.semilogy([], [])
plt.subplot(*subp)
subp[-1] += 1
oplotr(p.G_tau_raw['up'], alpha=0.75, label='Binned')