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 pytriqs.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_histos(title,histos):
a = plt.gca()
a.set_xlim((0,beta))
a.set_xlabel('$\\Delta\\tau$')
a.set_ylabel(title)
for name, histo in histos.items():
w = histo.data
dtau = [histo.mesh_point(n) for n in range(len(histo))]
plt.plot(dtau,w,label=name,linewidth=0.7)
a.legend(loc='upper center',prop={'size':10})
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})$')
plt.legend(loc='best', fontsize=8)
return line[0].get_color()
def plot_ps(ps):
subp = [2, 1, 1]
plt.subplot(*subp)
subp[-1] += 1
plt.plot(ps.iter, ps.dG_l, 's-', label=r'$\Delta G_l$')
plt.plot(ps.iter, ps.dM, 'o-', label=r'$\Delta M$')
plt.semilogy([], [])
plt.ylabel('$\Delta G_l$, $\Delta M$')
plt.legend(loc='best')
plt.xlabel('Iteration')
plt.subplot(*subp)
subp[-1] += 1
plt.plot(ps.iter, ps.B, 's-', label=r'$B$')
plt.plot(ps.iter, ps.M, 'o-', label=r'$M$')
plt.ylabel(r'$M$, $B$')
plt.legend(loc='best')
plt.xlabel('Iteration')
plt.tight_layout()
plt.savefig('figure_field_sc.svg')
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)
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')
plt.figure(figsize=(3.25, 2 * 3))
plt.title('Magnetic Susceptibility\n Hubbard atom + 2 bath sites.')
# ------------------------------------------------------------------
# -- 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([], [], style, alpha=0.25, label='ed field')
# ------------------------------------------------------------------
# -- dynamic pomerol
filenames = glob.glob('pomerol_*/*.h5')
styles = {2: '.m', 4: '.c', 8: '.y'}
for filename in filenames:
print '--> Loading:', filename
with HDFArchive(filename, 'r') as s:
p = s['p']
with HDFArchive(filename, 'w') as a:
a['order_max'] = order_max
a['n_min'], a['n_max'] = n_min, n_max
a['Delta_iw'] = Delta_iw
a['Delta_iw_ref'] = Delta_iw_ref
a['Delta_iw_fit'] = Delta_iw_fit
# -- Plot
from pytriqs.plot.mpl_interface import oplot, oplotr, oploti, plt
plt.figure(figsize=(10, 10))
ylim = [-4, 4]
plt.plot([w_min.imag]*2, ylim, 'sr-', lw=0.5)
plt.plot([w_max.imag]*2, ylim, 'sr-', lw=0.5)
for i1, i2 in itertools.product(range(2), repeat=2):
oplotr(Delta_iw[i1, i2], alpha=0.1)
oploti(Delta_iw[i1, i2], alpha=0.1)
oplotr(Delta_iw_ref[i1, i2], lw=4, alpha=0.25)
oploti(Delta_iw_ref[i1, i2], lw=4, alpha=0.25)
oplotr(Delta_iw_fit[i1, i2])
oploti(Delta_iw_fit[i1, i2])
ax = plt.gca()
ax.legend_ = None
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()
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
plt.plot(0, y0, 'rx')
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)
plt.figure(figsize=(3.25 * 2, 8))
subp = [3, 1, 1]
plt.subplot(*subp)
subp[-1] += 1
#oplotr(O_tau_regr, '-', label=r'cthyb regr $-\langle n_\uparrow(\tau) n_\downarrow \rangle$ (should be bad)', alpha=1.0, lw=1.0, zorder=100)
oplotr(cthyb.O_tau,
'-',
label=r'cthyb $\langle n_\uparrow(\tau) n_\downarrow \rangle$',
alpha=0.5,
lw=0.5)
oplotr(pyed.O_tau,
label=r'pyed $\langle n_\uparrow(\tau) n_\downarrow \rangle$')
plt.plot(0, cthyb.exp_val, 'or', alpha=0.25, clip_on=False)
plt.plot(0, pyed.exp_val, 'xg', alpha=0.25, clip_on=False)
plt.subplot(*subp)
subp[-1] += 1
tau = np.array([float(t) for t in cthyb.O_tau.mesh])
tau_ref = np.array([float(t) for t in pyed.O_tau.mesh])
O_ref = pyed.O_tau.data.copy()
O_interp = np.interp(tau, tau_ref, O_ref)
O_tau_diff = cthyb.O_tau.copy()
O_tau_diff.data[:] -= O_interp
O_tau_diff.name = r'$\Delta$' + 'O_tau'
oplotr(O_tau_diff, '-', label=r'cthyb - pyed', alpha=0.75)
from pytriqs.gf import *
from pytriqs.plot.mpl_interface import plt
arch = HDFArchive('legendre.h5', 'r')
ed_arch = HDFArchive('legendre.ed.h5', 'r')
plt.figure()
subp = [2, 1, 1]
plt.subplot(*subp)
subp[-1] += 1
for spin in ("up", "dn"):
plt.plot(arch['G_l'][spin].data.flatten(),
label="cthyb," + {
'up': "$\uparrow\uparrow$",
'dn': "$\downarrow\downarrow$"
}[spin])
plt.plot(ed_arch[spin].data.flatten(),
label="ED," + {
'up': "$\uparrow\uparrow$",
'dn': "$\downarrow\downarrow$"
}[spin])
axes = plt.gca()
axes.set_xlabel('$l$')
axes.set_ylabel('$G_l$')
axes.set_ylim((-2.0, 1.0))
axes.legend(loc='lower center', prop={'size': 10})
plt.subplot(*subp)
for q in [ [0,0,0], [n_k/2, n_k/2, 0], [n_k/2, 0, 0] ]:
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'$\nu$')
plt.ylabel(r'$\omega$')
#!/bin/env pytriqs
from pytriqs.archive import *
from pytriqs.gf.local import *
from pytriqs.plot.mpl_interface import plt
arch = HDFArchive('legendre.h5','r')
ed_arch = HDFArchive('legendre.ed.h5','r')
for spin in ("up","dn"):
plt.plot(arch['G_l'][spin].data.flatten(),label="cthyb," + {'up':"$\uparrow\uparrow$",'dn':"$\downarrow\downarrow$"}[spin])
plt.plot(ed_arch[spin].data.flatten(),label="ED," + {'up':"$\uparrow\uparrow$",'dn':"$\downarrow\downarrow$"}[spin])
axes = plt.gca()
axes.set_xlabel('$l$')
axes.set_ylabel('$G_l$')
axes.set_ylim((-2.0,1.0))
axes.legend(loc='lower center',prop={'size':10})
plt.savefig('G_l.pdf')
#
################################################################################
from common import *
from pytriqs.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')
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()
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 pytriqs.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()