def test_broadening_normalisation(self):
"""Check broadening implementations do not change overall intensity"""
np.random.seed(0)
# Use a strange bin width to catch bin-width-dependent behaviour
bins = np.linspace(0, 5000, 2000)
def sigma_func(frequencies):
return 2 + frequencies * 1e-2
n_peaks = 10
frequencies = np.random.random(n_peaks) * 4000
sigma = sigma_func(frequencies)
s_dft = np.random.random(n_peaks) * 10
pre_broadening_total = sum(s_dft)
# Full Gaussian should reproduce null total
for scheme in ('none', 'gaussian'):
freq_points, spectrum = broadening.broaden_spectrum(frequencies,
bins,
s_dft,
sigma,
scheme=scheme)
self.assertAlmostEqual(
sum(spectrum),
pre_broadening_total,
)
# Normal scheme reproduces area as well as total;
freq_points, full_spectrum = broadening.broaden_spectrum(
frequencies, bins, s_dft, sigma, scheme='normal')
self.assertAlmostEqual(
np.trapz(spectrum, x=freq_points),
pre_broadening_total * (bins[1] - bins[0]),
)
self.assertAlmostEqual(sum(spectrum), pre_broadening_total)
# truncated forms will be a little off but shouldn't be _too_ off
for scheme in ('gaussian_truncated', 'normal_truncated'):
freq_points, trunc_spectrum = broadening.broaden_spectrum(
frequencies, bins, s_dft, sigma, scheme)
self.assertLess(
abs(sum(full_spectrum) - sum(trunc_spectrum)) /
sum(full_spectrum), 0.03)
# Interpolated methods need histogram input and smooth sigma
hist_spec, _ = np.histogram(frequencies, bins, weights=s_dft)
hist_sigma = sigma_func(freq_points)
freq_points, interp_spectrum = broadening.broaden_spectrum(
freq_points, bins, hist_spec, hist_sigma, scheme='interpolate')
self.assertLess(
abs(sum(interp_spectrum) - pre_broadening_total) /
pre_broadening_total, 0.05)
def test_out_of_bounds(self):
"""Check schemes allowing arbitrary placement can handle data beyond bins"""
frequencies = np.array([2000.])
bins = np.linspace(0, 100, 100)
s_dft = np.array([1.])
sigma = np.array([3.])
schemes = ['none',
'gaussian', 'gaussian_truncated',
'normal', 'normal_truncated']
for scheme in schemes:
broadening.broaden_spectrum(frequencies, bins, s_dft, sigma, scheme=scheme)
def test_broaden_spectrum_values(self):
"""Check broadening implementations give similar values"""
# Use dense bins with a single peak for fair comparison
npts = 1000
bins = np.linspace(0, 100, npts + 1)
freq_points = (bins[1:] + bins[:-1]) / 2
sigma = freq_points * 0.1 + 1
s_dft = np.zeros(npts)
s_dft[npts // 2] = 2
schemes = ['gaussian', 'gaussian_truncated',
'normal', 'normal_truncated',
'interpolate']
results = {}
for scheme in schemes:
_, results[scheme] = broadening.broaden_spectrum(
freq_points, bins, s_dft, sigma, scheme)
for scheme in schemes:
# Interpolate scheme is approximate so just check a couple of sig.fig.
if scheme == 'interpolate':
places = 3
else:
places = 6
self.assertAlmostEqual(results[scheme][(npts // 2) + 20],
0.01257,
places=places)