def create_ll_signal(signal_shape=1000):
offset = 0
zlp_param = {'A': 10000.0, 'centre': 0.0 + offset, 'sigma': 15.0}
zlp = Gaussian(**zlp_param)
plasmon_param = {'A': 2000.0, 'centre': 200.0 + offset, 'sigma': 75.0}
plasmon = Gaussian(**plasmon_param)
axis = np.arange(signal_shape)
data = zlp.function(axis) + plasmon.function(axis)
ll = EELSSpectrum(data)
ll.axes_manager[-1].offset = -offset
ll.axes_manager[-1].scale = 0.1
return ll
def create_ll_signal(signal_shape=1000):
offset = 0
zlp_param = {'A': 10000.0, 'centre': 0.0 + offset, 'sigma': 15.0}
zlp = Gaussian(**zlp_param)
plasmon_param = {'A': 2000.0, 'centre': 200.0 + offset, 'sigma': 75.0}
plasmon = Gaussian(**plasmon_param)
axis = np.arange(signal_shape)
data = zlp.function(axis) + plasmon.function(axis)
ll = EELSSpectrum(data)
ll.axes_manager[-1].offset = -offset
ll.axes_manager[-1].scale = 0.1
return ll
def get_holz_heterostructure_test_signal(lazy=False):
"""Get HyperSpy 2D signal with 2D navigation dimensions for HOLZ testing.
The centre, radius and intensity of the ring varies as a function of probe
position. The disk centre position varies as a function of probe position.
Parameters
----------
lazy : bool, default False
Returns
-------
holz_signal : HyperSpy 2D signal
Example
-------
>>> s = pxm.dummy_data.get_holz_heterostructure_test_signal()
>>> s.plot()
Load as lazy
>>> s = pxm.dummy_data.get_holz_heterostructure_test_signal(lazy=True)
"""
probe_size_x, probe_size_y = 40, 40
px, py = np.mgrid[0:probe_size_x:1, 0:probe_size_y:1]
x, y = np.mgrid[36:38:40j, 41:43:40j]
disk_r = 10
disk_I = np.ones_like(x) * 100 + np.random.random() * 20
g_r = Gaussian(A=20, centre=25, sigma=5)
ring_r = np.ones_like(x) * 30 + g_r.function(py)
g_I = Gaussian(A=30, centre=25, sigma=3)
ring_I = np.ones_like(x) * 20 + g_I.function(py)
s = mdtd.generate_4d_data(
probe_size_x=probe_size_x,
probe_size_y=probe_size_y,
image_size_x=80,
image_size_y=80,
disk_x=x,
disk_y=y,
disk_r=disk_r,
disk_I=disk_I,
ring_x=x,
ring_y=y,
ring_r=ring_r,
ring_I=ring_I,
add_noise=True,
lazy=lazy,
)
return s
def setup_method(self, method):
s = EDSTEMSpectrum(np.ones([2, 2, 1024]))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 1e-2
energy_axis.units = 'keV'
energy_axis.name = "Energy"
s.set_microscope_parameters(beam_energy=200,
live_time=2.5,
tilt_stage=0.0,
azimuth_angle=0,
elevation_angle=35,
energy_resolution_MnKa=130,
beam_current=0.05)
elements = ['Al', 'Zn']
xray_lines = ['Al_Ka', 'Zn_Ka']
intensities = [300, 500]
for i, xray_line in enumerate(xray_lines):
gauss = Gaussian()
line_energy, FWHM = s._get_line_energy(xray_line, FWHM_MnKa='auto')
gauss.centre.value = line_energy
gauss.A.value = intensities[i]
gauss.sigma.value = FWHM
s.data[:] += gauss.function(energy_axis.axis)
s.set_elements(elements)
s.add_lines(xray_lines)
s.axes_manager[0].scale = 0.5
s.axes_manager[1].scale = 0.5
s.axes_manager[0].units = 'nm'
s.axes_manager[1].units = 'nm'
self.signal = s
def setup_method(self, method):
s = EDSTEMSpectrum(np.ones([2, 2, 1024]))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 1e-2
energy_axis.units = 'keV'
energy_axis.name = "Energy"
s.set_microscope_parameters(beam_energy=200,
live_time=2.5, tilt_stage=0.0,
azimuth_angle=0, elevation_angle=35,
energy_resolution_MnKa=130,
beam_current=0.05)
elements = ['Al', 'Zn']
xray_lines = ['Al_Ka', 'Zn_Ka']
intensities = [300, 500]
for i, xray_line in enumerate(xray_lines):
gauss = Gaussian()
line_energy, FWHM = s._get_line_energy(xray_line, FWHM_MnKa='auto')
gauss.centre.value = line_energy
gauss.A.value = intensities[i]
gauss.sigma.value = FWHM
s.data[:] += gauss.function(energy_axis.axis)
s.set_elements(elements)
s.add_lines(xray_lines)
s.axes_manager[0].scale = 0.5
s.axes_manager[1].scale = 0.5
self.signal = s
def setup_method(self, method):
gaussian = Gaussian()
gaussian.A.value = 20
gaussian.sigma.value = 10
gaussian.centre.value = 50
self.signal = Signal1D(gaussian.function(np.arange(0, 100, 0.01)))
self.signal.axes_manager[0].scale = 0.01
def test_function():
g = Gaussian()
g.centre.value = 1
g.sigma.value = 2 / sigma2fwhm
g.A.value = 3 * sqrt2pi * g.sigma.value
assert_allclose(g.function(2), 1.5)
assert_allclose(g.function(1), 3)
def test_estimate_parameters_binned(only_current, binned, lazy, uniform):
s = Signal1D(np.empty((100, )))
s.axes_manager.signal_axes[0].is_binned = binned
axis = s.axes_manager.signal_axes[0]
axis.scale = 1
axis.offset = -20
g1 = Gaussian(50015.156, 10 / sigma2fwhm, 10)
s.data = g1.function(axis.axis)
if not uniform:
axis.convert_to_non_uniform_axis()
if lazy:
s = s.as_lazy()
g2 = Gaussian()
if binned and uniform:
factor = axis.scale
elif binned:
factor = np.gradient(axis.axis)
else:
factor = 1
assert g2.estimate_parameters(s,
axis.low_value,
axis.high_value,
only_current=only_current)
assert g2._axes_manager[-1].is_binned == binned
np.testing.assert_allclose(g1.A.value, g2.A.value * factor)
assert abs(g2.centre.value - g1.centre.value) <= 1e-3
assert abs(g2.sigma.value - g1.sigma.value) <= 0.1
def setUp(self):
s = EDSTEMSpectrum(np.ones([2, 2, 1024]))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 1e-2
energy_axis.units = "keV"
energy_axis.name = "Energy"
s.set_microscope_parameters(
beam_energy=200,
live_time=3.1,
tilt_stage=0.0,
azimuth_angle=None,
elevation_angle=35,
energy_resolution_MnKa=130,
)
s.metadata.Acquisition_instrument.TEM.Detector.EDS.real_time = 2.5
s.metadata.Acquisition_instrument.TEM.beam_current = 0.05
elements = ["Al", "Zn"]
xray_lines = ["Al_Ka", "Zn_Ka"]
intensities = [300, 500]
for i, xray_line in enumerate(xray_lines):
gauss = Gaussian()
line_energy, FWHM = s._get_line_energy(xray_line, FWHM_MnKa="auto")
gauss.centre.value = line_energy
gauss.A.value = intensities[i]
gauss.sigma.value = FWHM
s.data[:] += gauss.function(energy_axis.axis)
s.set_elements(elements)
s.add_lines(xray_lines)
s.axes_manager[0].scale = 0.5
s.axes_manager[1].scale = 0.5
self.signal = s
def setup_method(self, method):
gaussian = Gaussian()
gaussian.A.value = 20
gaussian.sigma.value = 10
gaussian.centre.value = 50
self.signal = Signal1D(gaussian.function(np.arange(0, 100, 0.01)))
self.signal.axes_manager[0].scale = 0.01
def test_fit_component(self):
m = self.model
axis = self.axis
g1 = Gaussian()
m.append(g1)
m.fit_component(g1, signal_range=(4000, 6000))
np.testing.assert_allclose(self.g.function(axis),
g1.function(axis),
rtol=self.rtol,
atol=10e-3)
def setup_method(self, method):
g = Gaussian()
g.A.value = 10000.0
g.centre.value = 5000.0
g.sigma.value = 500.0
axis = np.arange(10000)
s = Signal1D(g.function(axis))
m = s.create_model()
self.model = m
self.g = g
self.axis = axis
def setup_method(self, method):
g1 = Gaussian(centre=10)
g2 = Gaussian(centre=20)
g3 = Gaussian(centre=30)
g3.A.twin = g2.A
g3.A.twin_function_expr = "-0.5*x"
g2.A.twin = g1.A
g2.A.twin_function_expr = "-0.5*x"
g1.A.value = 20
x = np.linspace(0, 50, 1000)
y = g1.function(x) + g2.function(x) + g3.function(x)
s = Signal1D(y)
s.axes_manager[-1].scale = x[1] - x[0]
gs = [g1, g2, g3]
m = s.create_model()
m.extend(gs)
self.s, self.m, self.gs = s, m, gs
def setup_method(self, method):
g = Gaussian()
g.A.value = 10000.0
g.centre.value = 5000.0
g.sigma.value = 500.0
axis = np.arange(10000)
s = Signal1D(g.function(axis))
m = s.create_model()
self.model = m
self.g = g
self.axis = axis
self.rtol = 0.00
def setup_method(self, method):
gs1 = Gaussian()
gs1.A.value = 10000.0
gs1.centre.value = 5000.0
gs1.sigma.value = 500.0
gs2 = Gaussian()
gs2.A.value = 60000.0
gs2.centre.value = 2000.0
gs2.sigma.value = 300.0
gs3 = Gaussian()
gs3.A.value = 20000.0
gs3.centre.value = 6000.0
gs3.sigma.value = 100.0
axis = np.arange(10000)
total_signal = (gs1.function(axis) +
gs2.function(axis) +
gs3.function(axis))
s = Signal1D(total_signal)
m = s.create_model()
g1 = Gaussian()
g2 = Gaussian()
g3 = Gaussian()
m.append(g1)
m.append(g2)
m.append(g3)
self.model = m
self.gs1 = gs1
self.gs2 = gs2
self.gs3 = gs3
self.g1 = g1
self.g2 = g2
self.g3 = g3
self.axis = axis
self.rtol = 0.01
def test_function_nd(binned):
s = Signal1D(np.empty((100,)))
axis = s.axes_manager.signal_axes[0]
axis.scale = 1
axis.offset = -20
g1 = Gaussian(50015.156, 10/sigma2fwhm, 10)
s.data = g1.function(axis.axis)
s.metadata.Signal.binned = binned
s2 = stack([s] * 2)
g2 = Gaussian()
factor = axis.scale if binned else 1
g2.estimate_parameters(s2, axis.low_value, axis.high_value, False)
assert g2.binned == binned
assert_allclose(g2.function_nd(axis.axis) * factor, s2.data)
def setup_method(self, method):
# Create an empty spectrum
s = EDSSEMSpectrum(np.zeros((2, 2, 3, 100)))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 0.04
energy_axis.units = 'keV'
energy_axis.name = "Energy"
g = Gaussian()
g.sigma.value = 0.05
g.centre.value = 1.487
s.data[:] = g.function(energy_axis.axis)
s.metadata.Acquisition_instrument.SEM.Detector.EDS.live_time = 3.1
s.metadata.Acquisition_instrument.SEM.beam_energy = 15.0
self.signal = s
def setUp(self):
# Create an empty spectrum
s = EDSSEMSpectrum(np.zeros((2, 2, 3, 100)))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 0.04
energy_axis.units = "keV"
energy_axis.name = "Energy"
g = Gaussian()
g.sigma.value = 0.05
g.centre.value = 1.487
s.data[:] = g.function(energy_axis.axis)
s.metadata.Acquisition_instrument.SEM.Detector.EDS.live_time = 3.1
s.metadata.Acquisition_instrument.SEM.beam_energy = 15.0
self.signal = s
def create_sum_of_gaussians(convolved=False):
param1 = {'A': A_value_gaussian[0],
'centre': centre_value_gaussian[0] / scale,
'sigma': sigma_value_gaussian[0] / scale}
gs1 = Gaussian(**param1)
param2 = {'A': A_value_gaussian[1],
'centre': centre_value_gaussian[1] / scale,
'sigma': sigma_value_gaussian[1] / scale}
gs2 = Gaussian(**param2)
param3 = {'A': A_value_gaussian[2],
'centre': centre_value_gaussian[2] / scale,
'sigma': sigma_value_gaussian[2] / scale}
gs3 = Gaussian(**param3)
axis = np.arange(1000)
data = gs1.function(axis) + gs2.function(axis) + gs3.function(axis)
if convolved:
to_convolved = create_ll_signal(data.shape[0]).data
data = np.convolve(data, to_convolved) / sum(to_convolved)
s = Signal1D(data[:1000])
s.axes_manager[-1].scale = scale
return s
def test_fit_component(self, signal_range):
m = self.model
axis = self.axis
g = self.g
g1 = Gaussian()
m.append(g1)
cf = ComponentFit(m, g1, signal_range=signal_range)
if signal_range == 'interactive':
cf.ss_left_value, cf.ss_right_value = (4000, 6000)
cf._fit_fired()
np.testing.assert_allclose(g.function(axis),
g1.function(axis),
rtol=0.0,
atol=10e-3)
def create_sum_of_gaussians(convolved=False):
param1 = {'A': A_value_gaussian[0],
'centre': centre_value_gaussian[0] / scale,
'sigma': sigma_value_gaussian[0] / scale}
gs1 = Gaussian(**param1)
param2 = {'A': A_value_gaussian[1],
'centre': centre_value_gaussian[1] / scale,
'sigma': sigma_value_gaussian[1] / scale}
gs2 = Gaussian(**param2)
param3 = {'A': A_value_gaussian[2],
'centre': centre_value_gaussian[2] / scale,
'sigma': sigma_value_gaussian[2] / scale}
gs3 = Gaussian(**param3)
axis = np.arange(1000)
data = gs1.function(axis) + gs2.function(axis) + gs3.function(axis)
if convolved:
to_convolved = create_ll_signal(data.shape[0]).data
data = np.convolve(data, to_convolved) / sum(to_convolved)
s = Signal1D(data[:1000])
s.axes_manager[-1].scale = scale
return s
def test_estimate_parameters_negative_scale():
s = Signal1D(np.empty((100,)))
axis = s.axes_manager.signal_axes[0]
axis.scale = -1
axis.offset = 100
g1 = Gaussian(50015.156, 15/sigma2fwhm, 50)
s.data = g1.function(axis.axis)
g2 = Gaussian()
with pytest.raises(ValueError):
g2.estimate_parameters(s, 40, 60)
assert g2.estimate_parameters(s, 90, 10)
np.testing.assert_allclose(g1.A.value, g2.A.value)
assert abs(g2.centre.value - g1.centre.value) <= 1e-3
assert abs(g2.sigma.value - g1.sigma.value) <= 0.1
def test_estimate_parameters_binned(only_current, binned):
s = Signal1D(np.empty((100,)))
s.metadata.Signal.binned = binned
axis = s.axes_manager.signal_axes[0]
axis.scale = 1
axis.offset = -20
g1 = Gaussian(50015.156, 10/sigma2fwhm, 10)
s.data = g1.function(axis.axis)
g2 = Gaussian()
factor = axis.scale if binned else 1
assert g2.estimate_parameters(s, axis.low_value, axis.high_value,
only_current=only_current)
assert g2.binned == binned
assert_allclose(g1.A.value, g2.A.value * factor)
assert abs(g2.centre.value - g1.centre.value) <= 1e-3
assert abs(g2.sigma.value - g1.sigma.value) <= 0.1
def setup_method(self, method):
np.random.seed(1)
axes = np.array([[100 * np.random.random() + np.arange(0., 600, 1)
for i in range(3)] for j in range(4)])
g = Gaussian()
g.A.value = 30000.
g.centre.value = 300.
g.sigma.value = 150.
data = g.function(axes)
s = Signal1D(data)
s.axes_manager[-1].offset = -150.
s.axes_manager[-1].scale = 0.5
s.add_gaussian_noise(2.0)
m = s.create_model()
g = Gaussian()
g.A.ext_force_positive = True
g.A.ext_bounded = True
m.append(g)
g.active_is_multidimensional = True
for index in m.axes_manager:
m.fit()
self.model = m