def test_power_spectrum_from_profile(self):
#
# this test was added, because there were issues calling
# power spectrum 1D with a window given
#
t = UniformLineScan([2, 4, 6, 8], 4)
t.power_spectrum_from_profile(window='hann')
def test_uniform():
for periodic in [True, False]:
for L in [1.3, 10.6]:
for k in [2, 4]:
for n in [16, 128]:
x = np.arange(n) * L / n
h = np.sin(2 * np.pi * k * x / L)
t = UniformLineScan(h, physical_sizes=L, periodic=periodic)
q, C = t.power_spectrum_from_profile()
# The ms height of the sine is 1/2. The sum over the PSD
# (from -q to +q) is the ms height. Our PSD only contains
# *half* of the full PSD (on the +q branch, the -q branch
# is identical), therefore the sum over it is 1/4.
assert_almost_equal(C.sum() / L, 1 / 4)
if periodic:
# The value at the individual wavevector must also
# equal 1/4. This is only exactly true for the
# periodic case. In the nonperiodic, this is convolved
# with the Fourier transform of the window function.
C /= L
r = np.zeros_like(C)
r[k] = 1 / 4
assert_array_almost_equal(C, r)
def test_default_window_1D():
x = np.linspace(0, 1, 200)
heights = np.cos(2 * np.pi * x * 8.3)
topography = UniformLineScan(heights, physical_sizes=1, periodic=True)
if True:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot(*topography.power_spectrum_from_profile(),
label="periodic=True")
ax.set_xscale("log")
ax.set_yscale("log")
topography = UniformLineScan(heights, physical_sizes=1, periodic=False)
if True:
import matplotlib.pyplot as plt
ax.plot(*topography.power_spectrum_from_profile(),
label="periodic=False")
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_ylim(bottom=1e-6)
ax.legend()
plt.show(block=True)