def get_abs_corr_zeta(
weight_percent, mass_thickness,
take_off_angle): # take_off_angle, temporary value for testing
"""
Calculate absorption correction terms.
Parameters
----------
weight_percent: list of signal
Composition in weight percent.
mass_thickness: signal
Density-thickness map in kg/m^2
take_off_angle: float
X-ray take-off angle in degrees.
"""
from hyperspy.misc import material
toa_rad = np.radians(take_off_angle)
csc_toa = 1.0 / np.sin(toa_rad)
# convert from cm^2/g to m^2/kg
mac = stack(
material.mass_absorption_mixture(weight_percent=weight_percent),
show_progressbar=False) * 0.1
acf = mac.data * mass_thickness.data * csc_toa
acf = acf / (1.0 - np.exp(-(acf)))
return acf
def atomic_to_weight(atomic_percent, elements='auto'):
"""Convert atomic percent to weight percent.
Parameters
----------
atomic_percent: list of float or list of signals
The atomic fractions (composition) of the sample.
elements: list of str
A list of element abbreviations, e.g. ['Al','Zn']. If elements is
'auto', take the elements in en each signal metadata of the
atomic_percent list.
Returns
-------
weight_percent : as atomic_percent
composition in weight percent.
Examples
--------
Calculate the weight percent of modern bronze given its atomic percent:
>>> hs.material.atomic_to_weight([93.2, 6.8], ("Cu", "Sn"))
array([ 88.00501989, 11.99498011])
"""
from hyperspy.signals import BaseSignal
elements = _elements_auto(atomic_percent, elements)
if isinstance(atomic_percent[0], BaseSignal):
weight_percent = stack(atomic_percent)
weight_percent.data = _atomic_to_weight(
weight_percent.data, elements)
weight_percent = weight_percent.split()
return weight_percent
else:
return _atomic_to_weight(atomic_percent, elements)
def atomic_to_weight(atomic_percent, elements="auto"):
"""Convert atomic percent to weight percent.
Parameters
----------
atomic_percent: list of float or list of signals
The atomic fractions (composition) of the sample.
elements: list of str
A list of element abbreviations, e.g. ['Al','Zn']. If elements is
'auto', take the elements in en each signal metadata of the
atomic_percent list.
Returns
-------
weight_percent : as atomic_percent
composition in weight percent.
Examples
--------
Calculate the weight percent of modern bronze given its atomic percent:
>>> hs.material.atomic_to_weight([93.2, 6.8], ("Cu", "Sn"))
array([ 88.00501989, 11.99498011])
"""
from hyperspy.signals import Signal
elements = _elements_auto(atomic_percent, elements)
if isinstance(atomic_percent[0], Signal):
weight_percent = stack(atomic_percent)
weight_percent.data = _atomic_to_weight(weight_percent.data, elements)
weight_percent = weight_percent.split()
return weight_percent
else:
return _atomic_to_weight(atomic_percent, elements)
def weight_to_atomic(weight_percent, elements='auto'):
"""Convert weight percent (wt%) to atomic percent (at.%).
Parameters
----------
weight_percent: list of float or list of signals
The weight fractions (composition) of the sample.
elements: list of str
A list of element abbreviations, e.g. ['Al','Zn']. If elements is
'auto', take the elements in en each signal metadata of th
weight_percent list.
Returns
-------
atomic_percent : as weight_percent
Composition in atomic percent.
Examples
--------
Calculate the atomic percent of modern bronze given its weight percent:
>>> utils.material.weight_to_atomic((88, 12), ("Cu", "Sn"))
array([ 93.19698614, 6.80301386])
"""
from hyperspy.signals import Signal
elements = _elements_auto(weight_percent, elements)
if isinstance(weight_percent[0], Signal):
atomic_percent = stack(weight_percent)
atomic_percent.data = _weight_to_atomic(atomic_percent.data, elements)
atomic_percent.data = np.nan_to_num(atomic_percent.data)
atomic_percent = atomic_percent.split()
return atomic_percent
else:
return _weight_to_atomic(weight_percent, elements)
def get_abs_corr_cross_section(
composition, number_of_atoms, take_off_angle,
probe_area): # take_off_angle, temporary value for testing
"""
Calculate absorption correction terms.
Parameters
----------
number_of_atoms: list of signal
Stack of maps with number of atoms per pixel.
take_off_angle: float
X-ray take-off angle in degrees.
"""
from hyperspy.misc import material
toa_rad = np.radians(take_off_angle)
Av = constants.Avogadro
elements = [
intensity.metadata.Sample.elements[0] for intensity in number_of_atoms
]
atomic_weights = np.array([
elements_db[element]['General_properties']['atomic_weight']
for element in elements
])
number_of_atoms = stack(number_of_atoms).data
#calculate the total_mass per pixel, or mass thicknessself.
total_mass = np.zeros_like(number_of_atoms[0], dtype='float')
for i, (weight) in enumerate(atomic_weights):
total_mass += (number_of_atoms[i] * weight / Av / probe_area / 1E-15)
# determine mass absorption coefficients and convert from cm^2/g to m^2/atom.
mac = stack(
material.mass_absorption_mixture(
weight_percent=material.atomic_to_weight(composition))) * 0.1
acf = np.zeros_like(number_of_atoms)
constant = 1 / (Av * math.sin(toa_rad) * probe_area * 1E-16)
#determine an absorption coeficcient per element per pixel.
for i, (weight) in enumerate(atomic_weights):
expo = (mac.data[i] * total_mass * constant)
acf[i] = expo / (1 - math.e**(-expo))
return acf
def test_quantification(self):
s = self.s
m = s.create_model()
m.fit()
intensities = m.get_lines_intensity()
quant = s.quantification(intensities, method='CL',
factors=[1.0, 1.0, 1.0],
composition_units='weight')
np.testing.assert_allclose(utils.stack(quant, axis=0), [50, 20, 30])
def test_quantification(self):
s = self.s
# to have enough intensities, so that the default values for
# `navigation_mask` of 1.0 in `quantification` doesn't mask the data
s = s * 1000
m = s.create_model()
m.fit()
intensities = m.get_lines_intensity()
quant = s.quantification(intensities, method='CL',
factors=[1.0, 1.0, 1.0],
composition_units='weight')
np.testing.assert_allclose(utils.stack(quant, axis=0), [50, 20, 30])
def density_of_mixture_of_pure_elements(weight_percent,
elements='auto',
mean='harmonic'):
"""Calculate the density of a mixture of elements.
The density of the elements is retrieved from an internal database. The
calculation is only valid if there is no interaction between the
components.
Parameters
----------
weight_percent: list of float or list of signals
A list of weight percent for the different elements. If the total
is not equal to 100, each weight percent is divided by the sum
of the list (normalization).
elements: list of str
A list of element symbols, e.g. ['Al', 'Zn']. If elements is 'auto',
take the elements in en each signal metadata of the weight_percent
list.
mean: 'harmonic' or 'weighted'
The type of mean use to estimate the density
Returns
-------
density: The density in g/cm3.
Examples
--------
Calculate the density of modern bronze given its weight percent:
>>> utils.material.density_of_mixture_of_pure_elements(
(88, 12),("Cu", "Sn"))
8.6903187973131466
"""
from hyperspy.signals import Signal
elements = _elements_auto(weight_percent, elements)
if isinstance(weight_percent[0], Signal):
density = weight_percent[0]._deepcopy_with_new_data(
_density_of_mixture_of_pure_elements(stack(weight_percent).data,
elements,
mean=mean))
return density
else:
return _density_of_mixture_of_pure_elements(weight_percent,
elements,
mean=mean)
def density_of_mixture_of_pure_elements(weight_percent,
elements='auto',
mean='harmonic'):
"""Calculate the density of a mixture of elements.
The density of the elements is retrieved from an internal database. The
calculation is only valid if there is no interaction between the
components.
Parameters
----------
weight_percent: list of float or list of signals
A list of weight percent for the different elements. If the total
is not equal to 100, each weight percent is divided by the sum
of the list (normalization).
elements: list of str
A list of element symbols, e.g. ['Al', 'Zn']. If elements is 'auto',
take the elements in en each signal metadata of the weight_percent
list.
mean: 'harmonic' or 'weighted'
The type of mean use to estimate the density
Returns
-------
density: The density in g/cm3.
Examples
--------
Calculate the density of modern bronze given its weight percent:
>>> utils.material.density_of_mixture_of_pure_elements(
(88, 12),("Cu", "Sn"))
8.6903187973131466
"""
from hyperspy.signals import Signal
elements = _elements_auto(weight_percent, elements)
if isinstance(weight_percent[0], Signal):
density = weight_percent[0]._deepcopy_with_new_data(
_density_of_mixture_of_pure_elements(
stack(weight_percent).data, elements, mean=mean))
return density
else:
return _density_of_mixture_of_pure_elements(weight_percent,
elements, mean=mean)
def get_derivative(signal, diff_axes, diff_order):
if signal.axes_manager.signal_dimension == 1:
signal = signal.diff(order=diff_order, axis=-1)
else:
# n-d signal case.
# Compute the differences for each signal axis, unfold the
# signal axes and stack the differences over the signal
# axis.
if diff_axes is None:
diff_axes = signal.axes_manager.signal_axes
iaxes = [axis.index_in_axes_manager for axis in diff_axes]
else:
iaxes = diff_axes
diffs = [signal.derivative(order=diff_order, axis=i) for i in iaxes]
for signal in diffs:
signal.unfold()
signal = stack(diffs, axis=-1)
del diffs
return signal
def get_derivative(signal, diff_axes, diff_order):
if signal.axes_manager.signal_dimension == 1:
signal = signal.diff(order=diff_order, axis=-1)
else:
# n-d signal case.
# Compute the differences for each signal axis, unfold the
# signal axes and stack the differences over the signal
# axis.
if diff_axes is None:
diff_axes = signal.axes_manager.signal_axes
iaxes = [axis.index_in_axes_manager
for axis in diff_axes]
else:
iaxes = diff_axes
diffs = [signal.derivative(order=diff_order, axis=i)
for i in iaxes]
for signal in diffs:
signal.unfold()
signal = stack(diffs, axis=-1)
del diffs
return signal
def weight_to_atomic(weight_percent, elements='auto'):
"""Convert weight percent (wt%) to atomic percent (at.%).
Parameters
----------
weight_percent: list of float or list of signals
The weight fractions (composition) of the sample.
elements: list of str
A list of element abbreviations, e.g. ['Al','Zn']. If elements is
'auto', take the elements in en each signal metadata of th
weight_percent list.
Returns
-------
atomic_percent : as weight_percent
Composition in atomic percent.
Examples
--------
Calculate the atomic percent of modern bronze given its weight percent:
>>> hs.material.weight_to_atomic((88, 12), ("Cu", "Sn"))
array([ 93.19698614, 6.80301386])
"""
from hyperspy.signals import BaseSignal
elements = _elements_auto(weight_percent, elements)
if isinstance(weight_percent[0], BaseSignal):
atomic_percent = stack(weight_percent)
atomic_percent.data = _weight_to_atomic(
atomic_percent.data, elements)
atomic_percent.data = np.nan_to_num(atomic_percent.data)
atomic_percent = atomic_percent.split()
for i, el in enumerate(elements):
atomic_percent[i].metadata.General.title = 'atomic percent of ' + el
return atomic_percent
else:
return _weight_to_atomic(weight_percent, elements)
def blind_source_separation(self,
number_of_components=None,
algorithm='sklearn_fastica',
diff_order=1,
diff_axes=None,
factors=None,
comp_list=None,
mask=None,
on_loadings=False,
pretreatment=None,
**kwargs):
"""Blind source separation (BSS) on the result on the
decomposition.
Available algorithms: FastICA, JADE, CuBICA, and TDSEP
Parameters
----------
number_of_components : int
number of principal components to pass to the BSS algorithm
algorithm : {FastICA, JADE, CuBICA, TDSEP}
diff_order : int
Sometimes it is convenient to perform the BSS on the derivative of
the signal. If diff_order is 0, the signal is not differentiated.
diff_axes : None or list of ints or strings
If None, when `diff_order` is greater than 1 and `signal_dimension`
(`navigation_dimension`) when `on_loadings` is False (True) is
greater than 1, the differences are calculated across all
signal (navigation) axes. Otherwise the axes can be specified in
a list.
factors : Signal or numpy array.
Factors to decompose. If None, the BSS is performed on the
factors of a previous decomposition. If a Signal instance the
navigation dimension must be 1 and the size greater than 1. If a
numpy array (deprecated) the factors are stored in a 2d array
stacked over the last axis.
comp_list : boolen numpy array
choose the components to use by the boolean list. It permits
to choose non contiguous components.
mask : bool numpy array or Signal instance.
If not None, the signal locations marked as True are masked. The
mask shape must be equal to the signal shape
(navigation shape) when `on_loadings` is False (True).
on_loadings : bool
If True, perform the BSS on the loadings of a previous
decomposition. If False, performs it on the factors.
pretreatment: dict
**kwargs : extra key word arguments
Any keyword arguments are passed to the BSS algorithm.
"""
from hyperspy.signal import Signal
from hyperspy._signals.spectrum import Spectrum
lr = self.learning_results
if factors is None:
if not hasattr(lr, 'factors') or lr.factors is None:
raise AttributeError(
'A decomposition must be performed before blind '
'source seperation or factors must be provided.')
else:
if on_loadings:
factors = self.get_decomposition_loadings()
else:
factors = self.get_decomposition_factors()
# Check factors
if not isinstance(factors, Signal):
if isinstance(factors, np.ndarray):
warnings.warn(
"factors as numpy arrays will raise an error in "
"HyperSpy 0.9 and newer. From them on only passing "
"factors as HyperSpy Signal instances will be "
"supported.",
DeprecationWarning)
# We proceed supposing that the factors are spectra stacked
# over the last dimension to reproduce the deprecated
# behaviour.
# TODO: Don't forget to change `factors` docstring when
# removing this.
factors = Spectrum(factors.T)
else:
# Change next error message when removing the
# DeprecationWarning
raise ValueError(
"`factors` must be either a Signal instance or a "
"numpy array but an object of type %s was provided." %
type(factors))
# Check factor dimensions
if factors.axes_manager.navigation_dimension != 1:
raise ValueError("`factors` must have navigation dimension"
"equal one, but the navigation dimension "
"of the given factors is %i." %
factors.axes_manager.navigation_dimension
)
elif factors.axes_manager.navigation_size < 2:
raise ValueError("`factors` must have navigation size"
"greater than one, but the navigation "
"size of the given factors is %i." %
factors.axes_manager.navigation_size)
# Check mask dimensions
if mask is not None:
ref_shape, space = (factors.axes_manager.signal_shape,
"navigation" if on_loadings else "signal")
if isinstance(mask, np.ndarray):
warnings.warn(
"Bare numpy array masks are deprecated and will be removed"
" in next HyperSpy 0.9.",
DeprecationWarning)
ref_shape = ref_shape[::-1]
if mask.shape != ref_shape:
raise ValueError(
"The `mask` shape is not equal to the %s shape."
"Mask shape: %s\tSignal shape in array: %s" %
(space, str(mask.shape), str(ref_shape)))
else:
if on_loadings:
mask = self._get_navigation_signal(data=mask)
else:
mask = self._get_signal_signal(data=mask)
elif isinstance(mask, Signal):
if mask.axes_manager.signal_shape != ref_shape:
raise ValueError(
"The `mask` signal shape is not equal to the %s shape."
" Mask shape: %s\t%s shape:%s" %
(space,
str(mask.axes_manager.signal_shape),
space,
str(ref_shape)))
# Note that we don't check the factor's signal dimension. This is on
# purpose as an user may like to apply pretreaments that change their
# dimensionality.
# The diff_axes are given for the main signal. We need to compute
# the correct diff_axes for the factors.
# Get diff_axes index in axes manager
if diff_axes is not None:
diff_axes = [1 + axis.index_in_axes_manager for axis in
[self.axes_manager[axis] for axis in diff_axes]]
if not on_loadings:
diff_axes = [index - self.axes_manager.navigation_dimension
for index in diff_axes]
# Select components to separate
if number_of_components is not None:
comp_list = range(number_of_components)
elif comp_list is not None:
number_of_components = len(comp_list)
else:
if lr.output_dimension is not None:
number_of_components = lr.output_dimension
comp_list = range(number_of_components)
else:
raise ValueError(
"No `number_of_components` or `comp_list` provided.")
factors = stack([factors.inav[i] for i in comp_list])
# Apply differences pre-processing if requested.
if diff_order > 0:
factors = get_derivative(factors,
diff_axes=diff_axes,
diff_order=diff_order)
if mask is not None:
# The following is a little trick to dilate the mask as
# required when operation on the differences. It exploits the
# fact that np.diff autimatically "dilates" nans. The trick has
# a memory penalty which should be low compare to the total
# memory required for the core application in most cases.
mask_diff_axes = (
[iaxis - 1 for iaxis in diff_axes]
if diff_axes is not None
else None)
mask.change_dtype("float")
mask.data[mask.data == 1] = np.nan
mask = get_derivative(mask,
diff_axes=mask_diff_axes,
diff_order=diff_order)
mask.data[np.isnan(mask.data)] = 1
mask.change_dtype("bool")
# Unfold in case the signal_dimension > 1
factors.unfold()
if mask is not None:
mask.unfold()
factors = factors.data.T[~mask.data]
else:
factors = factors.data.T
# Center and scale the data
factors, invsqcovmat = centering_and_whitening(factors)
# Perform actual BSS
if algorithm == 'orthomax':
_, unmixing_matrix = orthomax(factors, **kwargs)
unmixing_matrix = unmixing_matrix.T
elif algorithm == 'sklearn_fastica':
if not import_sklearn.sklearn_installed:
raise ImportError(
"The optional package scikit learn is not installed "
"and it is required for this feature.")
if 'tol' not in kwargs:
kwargs['tol'] = 1e-10
lr.bss_node = import_sklearn.FastICA(
**kwargs)
lr.bss_node.whiten = False
lr.bss_node.fit(factors)
try:
unmixing_matrix = lr.bss_node.unmixing_matrix_
except AttributeError:
# unmixing_matrix was renamed to components
unmixing_matrix = lr.bss_node.components_
else:
if mdp_installed is False:
raise ImportError(
'MDP is not installed. Nothing done')
temp_function = getattr(mdp.nodes, algorithm + "Node")
lr.bss_node = temp_function(**kwargs)
lr.bss_node.train(factors)
unmixing_matrix = lr.bss_node.get_recmatrix()
w = np.dot(unmixing_matrix, invsqcovmat)
if lr.explained_variance is not None:
# The output of ICA is not sorted in any way what makes it
# difficult to compare results from different unmixings. The
# following code is an experimental attempt to sort them in a
# more predictable way
sorting_indices = np.argsort(np.dot(
lr.explained_variance[:number_of_components],
np.abs(w.T)))[::-1]
w[:] = w[sorting_indices, :]
lr.unmixing_matrix = w
lr.on_loadings = on_loadings
self._unmix_components()
self._auto_reverse_bss_component(lr)
lr.bss_algorithm = algorithm
def blind_source_separation(self,
number_of_components=None,
algorithm='sklearn_fastica',
diff_order=1,
diff_axes=None,
factors=None,
comp_list=None,
mask=None,
on_loadings=False,
pretreatment=None,
**kwargs):
"""Blind source separation (BSS) on the result on the
decomposition.
Available algorithms: FastICA, JADE, CuBICA, and TDSEP
Parameters
----------
number_of_components : int
number of principal components to pass to the BSS algorithm
algorithm : {FastICA, JADE, CuBICA, TDSEP}
diff_order : int
Sometimes it is convenient to perform the BSS on the derivative of
the signal. If diff_order is 0, the signal is not differentiated.
diff_axes : None or list of ints or strings
If None, when `diff_order` is greater than 1 and `signal_dimension`
(`navigation_dimension`) when `on_loadings` is False (True) is
greater than 1, the differences are calculated across all
signal (navigation) axes. Otherwise the axes can be specified in
a list.
factors : Signal or numpy array.
Factors to decompose. If None, the BSS is performed on the
factors of a previous decomposition. If a Signal instance the
navigation dimension must be 1 and the size greater than 1. If a
numpy array (deprecated) the factors are stored in a 2d array
stacked over the last axis.
comp_list : boolen numpy array
choose the components to use by the boolean list. It permits
to choose non contiguous components.
mask : bool numpy array or Signal instance.
If not None, the signal locations marked as True are masked. The
mask shape must be equal to the signal shape
(navigation shape) when `on_loadings` is False (True).
on_loadings : bool
If True, perform the BSS on the loadings of a previous
decomposition. If False, performs it on the factors.
pretreatment: dict
**kwargs : extra key word arguments
Any keyword arguments are passed to the BSS algorithm.
"""
from hyperspy.signal import Signal
from hyperspy._signals.spectrum import Spectrum
lr = self.learning_results
if factors is None:
if not hasattr(lr, 'factors') or lr.factors is None:
raise AttributeError(
'A decomposition must be performed before blind '
'source seperation or factors must be provided.')
else:
if on_loadings:
factors = self.get_decomposition_loadings()
else:
factors = self.get_decomposition_factors()
# Check factors
if not isinstance(factors, Signal):
if isinstance(factors, np.ndarray):
warnings.warn(
"factors as numpy arrays will raise an error in "
"HyperSpy 0.9 and newer. From them on only passing "
"factors as HyperSpy Signal instances will be "
"supported.", DeprecationWarning)
# We proceed supposing that the factors are spectra stacked
# over the last dimension to reproduce the deprecated
# behaviour.
# TODO: Don't forget to change `factors` docstring when
# removing this.
factors = Spectrum(factors.T)
else:
# Change next error message when removing the
# DeprecationWarning
raise ValueError(
"`factors` must be either a Signal instance or a "
"numpy array but an object of type %s was provided." %
type(factors))
# Check factor dimensions
if factors.axes_manager.navigation_dimension != 1:
raise ValueError("`factors` must have navigation dimension"
"equal one, but the navigation dimension "
"of the given factors is %i." %
factors.axes_manager.navigation_dimension)
elif factors.axes_manager.navigation_size < 2:
raise ValueError("`factors` must have navigation size"
"greater than one, but the navigation "
"size of the given factors is %i." %
factors.axes_manager.navigation_size)
# Check mask dimensions
if mask is not None:
ref_shape, space = (factors.axes_manager.signal_shape,
"navigation" if on_loadings else "signal")
if isinstance(mask, np.ndarray):
warnings.warn(
"Bare numpy array masks are deprecated and will be removed"
" in next HyperSpy 0.9.", DeprecationWarning)
ref_shape = ref_shape[::-1]
if mask.shape != ref_shape:
raise ValueError(
"The `mask` shape is not equal to the %s shape."
"Mask shape: %s\tSignal shape in array: %s" %
(space, str(mask.shape), str(ref_shape)))
else:
if on_loadings:
mask = self._get_navigation_signal(data=mask)
else:
mask = self._get_signal_signal(data=mask)
elif isinstance(mask, Signal):
if mask.axes_manager.signal_shape != ref_shape:
raise ValueError(
"The `mask` signal shape is not equal to the %s shape."
" Mask shape: %s\t%s shape:%s" %
(space, str(mask.axes_manager.signal_shape), space,
str(ref_shape)))
# Note that we don't check the factor's signal dimension. This is on
# purpose as an user may like to apply pretreaments that change their
# dimensionality.
# The diff_axes are given for the main signal. We need to compute
# the correct diff_axes for the factors.
# Get diff_axes index in axes manager
if diff_axes is not None:
diff_axes = [
1 + axis.index_in_axes_manager
for axis in [self.axes_manager[axis] for axis in diff_axes]
]
if not on_loadings:
diff_axes = [
index - self.axes_manager.navigation_dimension
for index in diff_axes
]
# Select components to separate
if number_of_components is not None:
comp_list = range(number_of_components)
elif comp_list is not None:
number_of_components = len(comp_list)
else:
if lr.output_dimension is not None:
number_of_components = lr.output_dimension
comp_list = range(number_of_components)
else:
raise ValueError(
"No `number_of_components` or `comp_list` provided.")
factors = stack([factors.inav[i] for i in comp_list])
# Apply differences pre-processing if requested.
if diff_order > 0:
factors = get_derivative(factors,
diff_axes=diff_axes,
diff_order=diff_order)
if mask is not None:
# The following is a little trick to dilate the mask as
# required when operation on the differences. It exploits the
# fact that np.diff autimatically "dilates" nans. The trick has
# a memory penalty which should be low compare to the total
# memory required for the core application in most cases.
mask_diff_axes = ([iaxis - 1 for iaxis in diff_axes]
if diff_axes is not None else None)
mask.change_dtype("float")
mask.data[mask.data == 1] = np.nan
mask = get_derivative(mask,
diff_axes=mask_diff_axes,
diff_order=diff_order)
mask.data[np.isnan(mask.data)] = 1
mask.change_dtype("bool")
# Unfold in case the signal_dimension > 1
factors.unfold()
if mask is not None:
mask.unfold()
factors = factors.data.T[~mask.data]
else:
factors = factors.data.T
# Center and scale the data
factors, invsqcovmat = centering_and_whitening(factors)
# Perform actual BSS
if algorithm == 'orthomax':
_, unmixing_matrix = orthomax(factors, **kwargs)
unmixing_matrix = unmixing_matrix.T
elif algorithm == 'sklearn_fastica':
if not import_sklearn.sklearn_installed:
raise ImportError(
"The optional package scikit learn is not installed "
"and it is required for this feature.")
if 'tol' not in kwargs:
kwargs['tol'] = 1e-10
lr.bss_node = import_sklearn.FastICA(**kwargs)
lr.bss_node.whiten = False
lr.bss_node.fit(factors)
try:
unmixing_matrix = lr.bss_node.unmixing_matrix_
except AttributeError:
# unmixing_matrix was renamed to components
unmixing_matrix = lr.bss_node.components_
else:
if mdp_installed is False:
raise ImportError('MDP is not installed. Nothing done')
temp_function = getattr(mdp.nodes, algorithm + "Node")
lr.bss_node = temp_function(**kwargs)
lr.bss_node.train(factors)
unmixing_matrix = lr.bss_node.get_recmatrix()
w = np.dot(unmixing_matrix, invsqcovmat)
if lr.explained_variance is not None:
# The output of ICA is not sorted in any way what makes it
# difficult to compare results from different unmixings. The
# following code is an experimental attempt to sort them in a
# more predictable way
sorting_indices = np.argsort(
np.dot(lr.explained_variance[:number_of_components],
np.abs(w.T)))[::-1]
w[:] = w[sorting_indices, :]
lr.unmixing_matrix = w
lr.on_loadings = on_loadings
self._unmix_components()
self._auto_reverse_bss_component(lr)
lr.bss_algorithm = algorithm
def mass_absorption_mixture(weight_percent,
elements='auto',
energies='auto'):
"""Calculate the mass absorption coefficient for X-ray absorbed in a
mixture of elements.
The mass absorption coefficient is calculated as a weighted mean of the
weight percent and is retrieved from the database of Chantler2005.
Parameters
----------
weight_percent: list of float or list of signals
The composition of the absorber(s) in weight percent. The first
dimension of the matrix corresponds to the elements.
elements: list of str or 'auto'
The list of element symbol of the absorber, e.g. ['Al','Zn']. If
elements is 'auto', take the elements in each signal metadata of the
weight_percent list.
energies: list of float or list of str or 'auto'
The energy or energies of the X-ray in keV, or the name of the X-rays,
e.g. 'Al_Ka'. If 'auto', take the lines in each signal metadata of the
weight_percent list.
Examples
--------
>>> hs.material.mass_absorption_mixture(
>>> elements=['Al','Zn'], weight_percent=[50,50], energies='Al_Ka')
2587.41616439
Return
------
float or array of float
mass absorption coefficient(s) in cm^2/g
See also
--------
hs.material.mass_absorption_coefficient
Note
----
See http://physics.nist.gov/ffast
Chantler, C.T., Olsen, K., Dragoset, R.A., Kishore, A.R., Kotochigova,
S.A., and Zucker, D.S. (2005), X-Ray Form Factor, Attenuation and
Scattering Tables (version 2.1).
"""
from hyperspy.signals import BaseSignal
elements = _elements_auto(weight_percent, elements)
energies = _lines_auto(weight_percent, energies)
if isinstance(weight_percent[0], BaseSignal):
weight_per = np.array([wt.data for wt in weight_percent])
mac_res = stack([weight_percent[0].deepcopy()] * len(energies))
mac_res.data = \
_mass_absorption_mixture(weight_per, elements, energies)
mac_res = mac_res.split()
for i, energy in enumerate(energies):
mac_res[i].metadata.set_item("Sample.xray_lines", ([energy]))
mac_res[i].metadata.General.set_item(
"title", "Absoprtion coeff of"
" %s in %s" % (energy, mac_res[i].metadata.General.title))
if mac_res[i].metadata.has_item("Sample.elements"):
del mac_res[i].metadata.Sample.elements
return mac_res
else:
return _mass_absorption_mixture(weight_percent, elements, energies)
def test_has_warning(self, axis, caplog):
with caplog.at_level(logging.WARNING):
_ = stack([self.s1, self.s2], axis=axis)
assert "Axis calibration mismatch detected along axis 1" in caplog.text