def test_fourier():
lattice = Lattice([2, 2])
boundary_conditions = (periodic, antiperiodic)
x = [0.3, 0.76, 0.1j, 0.83]
y = fourier_transform(x, lattice, boundary_conditions)
# test inverse fourier transform
z = inverse_fourier_transform(y, lattice, boundary_conditions)
err = sum(abs(a - b) for a, b in zip(x, z))
assert err < 1e-10
def triangular_lattice_dwave():
lattice = HexagonalLattice([12, 12])
boundary_conditions = (periodic, antiperiodic)
#alpha = pi/100
#t1 = np.cos(alpha)
#delta1 = np.sin(alpha)
t1 = 1.0
delta1 = 5.0
mu = -0.3
Nsites = len(lattice)
t_R = np.zeros(Nsites, dtype=complex)
delta_R = np.zeros(Nsites, dtype=complex)
n = 0
for nn in lattice.nearest_neighbors(lattice[0], double_count=True):
site_R, phase = lattice.enforce_boundary(nn, boundary_conditions)
ind_R = lattice.index(site_R)
t_R[ind_R] = t1 * phase
# delta_R[ind_R] = delta1 * np.exp(2*pi*1j*n/3.0) * phase # d+id
delta_R[ind_R] = delta1 * np.exp(2*pi*1j*n/3.0).real * phase # d
n = n+1
epsilon_k = fourier_transform(list(-t_R), lattice, boundary_conditions)
xi_k = [ep-mu for ep in epsilon_k]
delta_k = fourier_transform(list(delta_R), lattice, boundary_conditions)
E_k = [np.sqrt(xi*xi + np.abs(delta)*np.abs(delta)) for xi, delta in zip(xi_k, delta_k)]
posEvals = np.sort(np.array(E_k, dtype=complex).real)
g_k = [delta / ( xi + E ) for xi, delta, E in zip(xi_k, delta_k, E_k)]
phi_r = inverse_fourier_transform(g_k, lattice, boundary_conditions)
phi_r = np.array(phi_r, dtype=complex)
print 'phi_r:'
print phi_r
print
phiMat = np.zeros((Nsites, Nsites), dtype=complex)
for ind_r in range(0, Nsites):
for ind_rp in range(0, Nsites):
site_r = lattice[ind_r]
site_rp = lattice[ind_rp]
site_r_minus_rp, phase = lattice.enforce_boundary(site_r.negative_displaced(site_rp.bs), boundary_conditions)
ind_r_minus_rp = lattice.index(site_r_minus_rp)
phiMat[ind_r, ind_rp] = phase * phi_r[ind_r_minus_rp]
# Check that phiMat is symmetric:
#assert( np.max(np.abs(phiMat - phiMat.transpose())) < 1e-12 )
print '"Symmetricness" of phiMat = ', np.max(np.abs(phiMat - phiMat.transpose()))
#np.savetxt('phiMat_TI.dat', phiMat.view(float))
##### Plot some stuff #####
fig = plt.figure(figsize=(17,15))
plt.plot([ xi.real for xi in xi_k], 'o-', label=r'$\xi_k$')
plt.plot([ delta.real for delta in delta_k ], 's-', label=r'$\Delta_k$')
plt.plot([ E.real for E in E_k ], '^-', label=r'$E_k=\sqrt{\xi_k^2 + |\Delta_k|^2}$')
plt.plot([ (xi + E).real for xi, E in zip(xi_k, E_k) ], 'd-', label=r'$\xi_k + E_k$')
plt.axhline(y=0, linewidth=1, color='k', linestyle='--')
plt.xlim(0, len(xi_k))
plt.setp(plt.gca().get_xmajorticklabels(), fontsize=25)
plt.setp(plt.gca().get_ymajorticklabels(), fontsize=25)
plt.xlabel('$k$', fontsize=25)
plt.ylabel('Energies', fontsize=25)
plt.legend(loc='best', fontsize=20)
fig = plt.figure(figsize=(17,15))
plt.plot([ g.real for g in g_k ], 'o-', label=r'$g_k$')
plt.plot([ phi.real for phi in phi_r ], 's-', label=r'$\phi(r)$')
plt.axhline(y=0, linewidth=1, color='k', linestyle='--')
plt.xlim(0, len(phi_r))
plt.setp(plt.gca().get_xmajorticklabels(), fontsize=25)
plt.setp(plt.gca().get_ymajorticklabels(), fontsize=25)
plt.xlabel('$k,\,r$', fontsize=25)
plt.ylabel('Amplitudes', fontsize=25)
plt.legend(loc='best', fontsize=20)
plot_pairing_matrix(phiMat, callshow=False)
plt.show()
