def test_sum_of_exponentials():
"""
correlation: Test the sum of exponentials.
"""
tlist = [0.0, 0.5, 1.0, 1.5, 2.0]
# Complex coefficients and frequencies.
ck1 = [0.5 + 2j, -0.1]
vk1 = [-0.5 + 3j, 1 - 1j]
corr1 = sum_of_exponentials(ck1, vk1, tlist)
y1 = np.array([
0.4 + 2.0j,
-1.67084356 + 0.57764922j,
-0.61828702 - 0.92938927j,
0.84201641 + 0.0170242j,
0.68968912 + 1.32694318j,
])
assert_array_almost_equal(corr1, y1)
# Real coefficients and frequencies.
ck2 = [0.5, -0.3]
vk2 = [-0.9, -0.3]
corr2 = sum_of_exponentials(ck2, vk2, tlist)
y2 = np.array([0.2, 0.060602, -0.018961, -0.061668, -0.081994])
assert_array_almost_equal(corr2, y2)
def test_biexp_fit():
"""
correlation: Tests biexponential fitting.
"""
tlist = np.linspace(0.0, 10, 100)
ck = [-0.21, -0.13]
vk = [-0.4, -1.5]
corr = sum_of_exponentials(ck, vk, tlist)
ck_fit, vk_fit = biexp_fit(tlist, corr)
corr_fit = sum_of_exponentials(ck_fit, vk_fit, tlist)
max_error = np.max(np.abs(corr - corr_fit))
max_amplitude = np.max(np.abs(corr))
assert max_error < max_amplitude / 1e3
"--",
color="red",
label="Unconstrained fitting")
ax1.plot(w,
total_spectrum_constrained,
"--",
color="b",
label="Constrained fitting")
ax1.set_xlabel(r"$\omega$")
ax1.set_ylabel(r"$S(\omega)$")
ax1.legend()
ax1.set_title("Total spectrum of the correlation")
plt.savefig("plots/positivity_spectrum.png", bbox_inches="tight")
plt.show()
reconstructed_mats = sum_of_exponentials(ck2, vk2, tlist)
reconstructed_mats_constrained = sum_of_exponentials(ck2c, vk2c, tlist)
#compare original and new fit in terms of correlations
fig, [ax1, ax2] = plt.subplots(1, 2, figsize=(13, 4))
ax1.plot(tlist, mats_data_zero, label="Original data")
ax1.plot(tlist, reconstructed_mats, linestyle='--', label="Unconstrained")
ax1.plot(tlist,
reconstructed_mats_constrained,
linestyle='-.',
label="Constrained")
ax1.set_ylabel("Correlation (Matsubara))")
ax1.set_xlabel("t")
ax1.legend()
ax2.plot(tlist,
Calculate Matsubara and Non-matsubara correlations for the underdamped
brownian motion spectral density.
"""
import numpy as np
from matsubara.correlation import (nonmatsubara_exponents,
matsubara_zero_analytical, biexp_fit,
sum_of_exponentials)
import matplotlib.pyplot as plt
coup_strength, bath_broad, bath_freq = 0.2, 0.05, 1.
tlist = np.linspace(0, 100, 1000)
# Zero temperature case beta = 1/kT
beta = np.inf
ck1, vk1 = nonmatsubara_exponents(coup_strength, bath_broad, bath_freq, beta)
corr_nonmats = sum_of_exponentials(1j * ck1, vk1, tlist)
# Analytical zero temperature calculation of the Matsubara correlation
mats_data_zero = matsubara_zero_analytical(coup_strength, bath_broad,
bath_freq, tlist)
# Fitting a biexponential function
ck20, vk20 = biexp_fit(tlist, mats_data_zero)
print("Non matsubara coefficients: ", ck1)
print("Non matsubara frequencies:", vk1)
print("Fitted matsubara coefficients: ", ck20)
print("Fitted matsubara frequencies:", vk20)
# Plotting the fit and non Matsubara parts
corr_fit = sum_of_exponentials(ck20, vk20, tlist)
def test_exponents():
"""
correlation: Tests the Matsubara and non Matsubara exponents.
"""
lam, gamma, w0 = 0.2, 0.05, 1.0
tlist = np.linspace(0, 100, 1000)
# Finite temperature cases
beta = 0.1
N_exp = 200
ck_nonmats = [0.190164 - 0.004997j, 0.21017 + 0.004997j]
vk_nonmats = [-0.025 + 0.999687j, -0.025 - 0.999687j]
ck1, vk1 = nonmatsubara_exponents(lam, gamma, w0, beta)
assert_array_almost_equal(ck1, ck_nonmats)
assert_array_almost_equal(vk1, vk_nonmats)
ck2, vk2 = matsubara_exponents(lam, gamma, w0, beta, N_exp)
corr_fit = sum_of_exponentials(np.concatenate([ck1, ck2]),
np.concatenate([vk1, vk2]), tlist)
corr = sum_of_exponentials(ck_nonmats, vk_nonmats, tlist)
max_residue = np.max(np.abs(corr_fit - corr))
max_amplitude = np.max(np.abs(corr))
assert_(max_residue < max_amplitude / 1e5)
# Lower temperature
beta = 1.0
N_exp = 100
ck_nonmats = [0.011636 - 0.00046j, 0.031643 + 0.00046j]
vk_nonmats = [-0.025 + 0.999687j, -0.025 - 0.999687j]
ck1, vk1 = nonmatsubara_exponents(lam, gamma, w0, beta)
assert_array_almost_equal(ck1, ck_nonmats)
assert_array_almost_equal(vk1, vk_nonmats)
ck2, vk2 = matsubara_exponents(lam, gamma, w0, beta, N_exp)
corr_fit = sum_of_exponentials(np.concatenate([ck1, ck2]),
np.concatenate([vk1, vk2]), tlist)
corr = sum_of_exponentials(ck_nonmats, vk_nonmats, tlist)
max_residue = np.max(np.abs(corr_fit - corr))
max_amplitude = np.max(np.abs(corr))
assert_(max_residue < max_amplitude / 1e3)
# Zero temperature case
beta = np.inf
N_exp = 100
ck_nonmats = [0.0, 0.020006]
vk_nonmats = [-0.025 + 0.999687j, -0.025 - 0.999687j]
ck1, vk1 = nonmatsubara_exponents(lam, gamma, w0, beta)
assert_array_almost_equal(ck1, ck_nonmats)
assert_array_almost_equal(vk1, vk_nonmats)
ck2, vk2 = matsubara_exponents(lam, gamma, w0, beta, N_exp)
mats_data_zero = matsubara_zero_analytical(lam, gamma, w0, tlist)
ck_mats_zero = [-0.000208, -0.000107]
vk_mats_zero = [-1.613416, -0.329604]
ck20, vk20 = biexp_fit(tlist, mats_data_zero)
assert_array_almost_equal(ck20, ck_mats_zero)
assert_array_almost_equal(vk20, vk_mats_zero)