def test_next_delta(g0_wk, gamma, expected_next_delta):
Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma)
next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r,
g0_wk, g0_wk)
np.testing.assert_allclose(next_delta.data,
expected_next_delta.data,
atol=10e-12)
def save_new_benchmarks(filename, p):
eliashberg_ingredients = create_eliashberg_ingredients(p)
g0_wk = eliashberg_ingredients.g0_wk
gamma = eliashberg_ingredients.gamma
Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma)
next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk)
Es, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM')
p.next_delta = next_delta
p.E = Es[0]
p.eigen_mode = eigen_modes[0]
write_TarGZ_HDFArchive(filename, p=p)
def test_eliashberg_product_for_same_initital_delta(g0_wk, gamma, gamma_big):
initial_delta = semi_random_initial_delta(g0_wk, seed=1337)
next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta)
gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma)
next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk,
initial_delta)
diff = compare_deltas([next_delta_summation, next_delta_fft])
print_diff(diff)
np.testing.assert_allclose(diff, 0, atol=p.atol)
print('The summation and FFT implementation of the eliashberg product'
' both yield the same result.')
def plot_output(g0_wk, gamma):
from triqs.plot.mpl_interface import oplot, plt
initial_delta = semi_random_initial_delta(g0_wk)
next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta)
gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma)
next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk,
initial_delta)
deltas = [initial_delta, next_delta_summation, next_delta_fft]
warnings.filterwarnings("ignore") #ignore some matplotlib warnings
subp = [4, 3, 1]
fig = plt.figure(figsize=(18, 15))
titles = ['Input', 'Summation', 'FFT']
for k_point in [Idx(0, 0, 0), Idx(1, 0, 0)]:
ax = plt.subplot(*subp)
subp[-1] += 1
oplot(g0_wk[:, k_point])
plt.title('GF')
ax = plt.subplot(*subp)
subp[-1] += 1
oplot(gamma[:, k_point])
plt.title('Gamma')
ax = plt.subplot(*subp)
subp[-1] += 1
oplot(gamma_dyn_tr[:, k_point])
plt.title('Gamma dyn tr')
for delta, title in zip(deltas, titles):
ax = plt.subplot(*subp)
subp[-1] += 1
oplot(delta[:, k_point])
plt.title(title)
ax.legend_ = None
plt.show()
def test_eliashberg_product_fft_constant(g0_wk, gamma):
gamma.data[:] = np.random.rand(*gamma.data.shape[1:])
gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma)
initial_delta = semi_random_initial_delta(g0_wk)
delta_1 = eliashberg_product_fft_constant(gamma_const_r, g0_wk,
initial_delta)
delta_2 = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk,
initial_delta)
np.testing.assert_allclose(delta_1.data, delta_2.data)
print(
'The functions eliashberg_product_fft and eliashberg_product_fft_constant'
' yield the same result for a Gamma that is only constant in momentum space.'
'\nThe function split_into_dynamic_wk_and_constant_k therefore also worked correcty.'
)
def test_eliashberg_product_for_different_initital_delta(
g0_wk, gamma, gamma_big):
initial_delta = semi_random_initial_delta(g0_wk, seed=1337)
next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta)
gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma)
initial_delta = semi_random_initial_delta(g0_wk, seed=1338)
next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk,
initial_delta)
diff = compare_deltas([next_delta_summation, next_delta_fft])
print_diff(diff)
try:
np.testing.assert_allclose(diff, 0, atol=p.atol)
raise ValueError
except AssertionError:
print(
'The summation and FFT implementation of the eliashberg product'
' both yield DIFFERENT results, as expected when using a different inital delta.'
)
U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0)
chi_s_big = solve_rpa_PH(chi0_wk_big, U_s)
chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation
gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s)
# -- Preprocess gamma for the FFT implementation
gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma_big)
gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k)
# -- Test the Eliashberg equation
next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk)
next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, g0_wk)
np.testing.assert_allclose(next_delta.data, next_delta_fft.data, atol=1e-7)
Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk)
Es_fft, eigen_modes_fft = solve_eliashberg_fft(gamma_big, g0_wk)
E = Es[0]
eigen_mode = eigen_modes[0]
E_fft = Es_fft[0]
eigen_mode_fft = eigen_modes_fft[0]
np.testing.assert_allclose(E, E_fft, atol=1e-7)
try:
np.testing.assert_allclose(eigen_mode.data, eigen_mode_fft.data, atol=1e-7)