`components1D`#

Components that can be used to define a 1D model for e.g. curve fitting.

Writing a new template is easy: see the user guide documentation on creating components.

For more details see each component docstring.#

Arctan: Arctan function component.
Bleasdale: Bleasdale function component.
Doniach: Doniach Sunjic lineshape component.
Erf: Error function component.
Exponential: Exponential function component.
Expression: Create a component from a string expression.
Gaussian: Normalized Gaussian function component.
GaussianHF: Normalized gaussian function component, with a fwhm parameter
HeavisideStep: The Heaviside step function.
Logistic: Logistic function (sigmoid or s-shaped curve) component.
Lorentzian: Cauchy-Lorentz distribution (a.k.a. Lorentzian function) component.
Offset: Component to add a constant value in the y-axis.
Polynomial: n-order polynomial component.
PowerLaw: Power law component.

RC

ScalableFixedPattern: Fixed pattern component with interpolation support.
SkewNormal: Skew normal distribution component.
SplitVoigt: Split pseudo-Voigt component.
Voigt: Voigt component.

class hyperspy.api.model.components1D.Arctan(A=1.0, k=1.0, x0=1.0, module=['numpy', 'scipy'], **kwargs)#

Bases: Expression

Arctan function component.

\[f(x) = A \cdot \arctan \left[ k \left( x-x_0 \right) \right]\]

Variable	Parameter
\(A\)	A
\(k\)	k
\(x_0\)	x0

Parameters:

Afloat: Amplitude parameter. \(\lim_{x\to -\infty}f(x)=-A\) and \(\lim_{x\to\infty}f(x)=A\)
kfloat: Slope (steepness of the step). The larger \(k\), the sharper the step.
x0float: Center parameter (position of zero crossing \(f(x_0)=0\)).

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

class hyperspy.api.model.components1D.Bleasdale(a=1.0, b=1.0, c=1.0, module=None, **kwargs)#

Bases: Expression

Bleasdale function component.

Also called the Bleasdale-Nelder function. Originates from the description of the yield-density relationship in crop growth.

\[f(x) = \left(a+b\cdot x\right)^{-1/c}\]

Parameters:

afloat, default=1.0: The value of Parameter a.
bfloat, default=1.0: The value of Parameter b.
cfloat, default=1.0: The value of Parameter c.
**kwargs: Extra keyword arguments are passed to Expression.

Notes

For \((a+b\cdot x)\leq0\), the component will be set to 0.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

grad_a(x)#: Returns d(function)/d(parameter_1)

grad_b(x)#: Returns d(function)/d(parameter_1)

grad_c(x)#: Returns d(function)/d(parameter_1)

class hyperspy.api.model.components1D.Doniach(centre=0.0, A=1.0, sigma=1.0, alpha=0.5, module=['numpy', 'scipy'], **kwargs)#

Bases: Expression

Doniach Sunjic lineshape component.

\[ f(x) = \frac{A \cos[ \frac{{\pi\alpha}}{2}+ (1-\alpha)\tan^{-1}(\frac{x-centre+dx}{\sigma})]} {(\sigma^2 + (x-centre+dx)^2)^{\frac{(1-\alpha)}{2}}} \] \[ dx = \frac{2.354820\sigma}{2 tan[\frac{\pi}{2-\alpha}]} \]

Variable	Parameter
\(A\)	A
\(\sigma\)	sigma
\(\alpha\)	alpha
\(centre\)	centre

Parameters:

Afloat: Height
sigmafloat: Variance parameter of the distribution
alphafloat: Tail or asymmetry parameter
centrefloat: Location of the maximum (peak position).
**kwargs: Extra keyword arguments are passed to the Expression component.

Notes

This is an asymmetric lineshape, originially design for xps but generally useful for fitting peaks with low side tails See Doniach S. and Sunjic M., J. Phys. 4C31, 285 (1970) or http://www.casaxps.com/help_manual/line_shapes.htm for a more detailed description

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the Donach by calculating the median (centre) and the variance parameter (sigma).

Note that an insufficient range will affect the accuracy of this method and that this method doesn’t estimate the asymmetry parameter (alpha).

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool: Returns True when the parameters estimation is successful

Examples

>>> g = hs.model.components1D.Lorentzian()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

class hyperspy.api.model.components1D.Erf(A=1.0, sigma=1.0, origin=0.0, module=['numpy', 'scipy'], **kwargs)#

Bases: Expression

Error function component.

\[f(x) = \frac{A}{2}~\mathrm{erf}\left[\frac{(x - x_0)}{\sqrt{2} \sigma}\right]\]

Variable	Parameter
\(A\)	A
\(\sigma\)	sigma
\(x_0\)	origin

Parameters:

Afloat: The min/max values of the distribution are -A/2 and A/2.
sigmafloat: Width of the distribution.
originfloat: Position of the zero crossing.
**kwargs: Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

class hyperspy.api.model.components1D.Exponential(A=1.0, tau=1.0, module=None, **kwargs)#

Bases: Expression

Exponential function component.

\[f(x) = A\cdot\exp\left(-\frac{x}{\tau}\right)\]

Variable	Parameter
\(A\)	A
\(\tau\)	tau

Parameters:

A: float: Maximum intensity
tau: float: Scale parameter (time constant)
**kwargs: Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the parameters for the exponential component by splitting the signal window into two regions and using their geometric means

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

class hyperspy.api.model.components1D.Expression(expression, name, position=None, module='numpy', autodoc=True, add_rotation=False, rotation_center=None, rename_pars={}, compute_gradients=True, linear_parameter_list=None, check_parameter_linearity=True, **kwargs)#

Bases: Component

Create a component from a string expression.

It automatically generates the partial derivatives and the class docstring.

Parameters:

expressionstr: Component function in SymPy text expression format with substitutions separated by ;. See examples and the SymPy documentation for details. In order to vary the components along the signal dimensions, the variables x and y must be included for 1D or 2D components. Also, if module is “numexpr” the functions are limited to those that numexpr support. See its documentation for details.
namestr: Name of the component.
positionstr, optional: The parameter name that defines the position of the component if applicable. It enables interative adjustment of the position of the component in the model. For 2D components, a tuple must be passed with the name of the two parameters e.g. (“x0”, “y0”).
moduleNone or str {"numpy" | "numexpr" | "scipy"}, default “numpy”: Module used to evaluate the function. numexpr is often faster but it supports fewer functions and requires installing numexpr. If None, the “numexpr” will be used if installed.
add_rotationbool, default False: This is only relevant for 2D components. If True it automatically adds rotation_angle parameter.
rotation_centerNone or tuple: If None, the rotation center is the center i.e. (0, 0) if position is not defined, otherwise the center is the coordinates specified by position. Alternatively a tuple with the (x, y) coordinates of the center can be provided.
rename_parsdict: The desired name of a parameter may sometimes coincide with e.g. the name of a scientific function, what prevents using it in the expression. rename_parameters is a dictionary to map the name of the parameter in the expression` to the desired name of the parameter in the Component. For example: {“_gamma”: “gamma”}.
compute_gradientsbool, optional: If True, compute the gradient automatically using sympy. If sympy does not support the calculation of the partial derivatives, for example in case of expression containing a “where” condition, it can be disabled by using compute_gradients=False.
linear_parameter_listlist: A list of the components parameters that are known to be linear parameters.
check_parameter_linearitybool: If True, automatically check if each parameter is linear and set its corresponding attribute accordingly. If False, the default is to set all parameters, except for those who are specified in linear_parameter_list.
**kwargsdict: Keyword arguments can be used to initialise the value of the parameters.

Notes

As of version 1.4, Sympy’s lambdify function, that the Expression components uses internally, does not support the differentiation of some expressions, for example those containing a “where” condition. In such cases, the gradients can be set manually if required.

Examples

The following creates a Gaussian component and set the initial value of the parameters:

>>> hs.model.components1D.Expression(
... expression="height * exp(-(x - x0) ** 2 * 4 * log(2)/ fwhm ** 2)",
... name="Gaussian",
... height=1,
... fwhm=1,
... x0=0,
... position="x0",)
<Gaussian (Expression component)>

Substitutions for long or complicated expressions are separated by semicolumns:

>>> expr = 'A*B/(A+B) ; A = sin(x)+one; B = cos(y) - two; y = tan(x)'
>>> comp = hs.model.components1D.Expression(
...    expression=expr,
...    name='my function'
... )
>>> comp.parameters
(<Parameter one of my function component>,
 <Parameter two of my function component>)

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

compile_function(module, position=False)#: Compile the function and calculate the gradient automatically when possible. Useful to recompile the function and gradient with a different module.

function_nd(*args)#: Returns a numpy array containing the value of the component for all indices. If enough memory is available, this is useful to quickly to obtain the fitted component without iterating over the navigation axes.

class hyperspy.api.model.components1D.Gaussian(A=1.0, sigma=1.0, centre=0.0, module=None, **kwargs)#

Bases: Expression

Normalized Gaussian function component.

\[f(x) = \frac{A}{\sigma \sqrt{2\pi}}\exp\left[ -\frac{\left(x-x_0\right)^{2}}{2\sigma^{2}}\right]\]

Variable	Parameter
\(A\)	A
\(\sigma\)	sigma
\(x_0\)	centre

Parameters:

Afloat: Area, equals height scaled by \(\sigma\sqrt{(2\pi)}\). GaussianHF implements the Gaussian function with a height parameter corresponding to the peak height.
sigmafloat: Scale parameter of the Gaussian distribution.
centrefloat: Location of the Gaussian maximum (peak position).
**kwargs: Extra keyword arguments are passed to the Expression component.

Variable	Parameter
\(h\)	height
\(W\)	fwhm
\(c\)	centre

See also

Gaussian

Attributes:

Afloat: Convenience attribute to get, set the area and defined for compatibility with Gaussian component.
sigmafloat: Convenience attribute to get, set the width and defined for compatibility with Gaussian component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the gaussian by calculating the momenta.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

Notes

Adapted from https://scipy-cookbook.readthedocs.io/items/FittingData.html

Examples

>>> g = hs.model.components1D.GaussianHF()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

integral_as_signal()#: Utility function to get gaussian integral as Signal1D

class hyperspy.api.model.components1D.HeavisideStep(A=1.0, n=0.0, module='numpy', compute_gradients=True, **kwargs)#

Bases: Expression

The Heaviside step function.

Based on the corresponding numpy function using the half maximum definition for the central point:

\[\begin{split}f(x) = \begin{cases} 0 & x<n\\ A/2 & x=n\\ A & x>n \end{cases}\end{split}\]

Variable	Parameter
\(n\)	centre
\(A\)	height

Parameters:

nfloat: Location parameter defining the x position of the step.
Afloat: Height parameter for x>n.
**kwargs: Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

class hyperspy.api.model.components1D.Logistic(a=1.0, b=1.0, c=1.0, origin=0.0, module=None, **kwargs)#

Bases: Expression

Logistic function (sigmoid or s-shaped curve) component.

\[f(x) = \frac{a}{1 + b\cdot \mathrm{exp}\left[-c \left((x - x_0\right)\right]}\]

Variable	Parameter
\(A\)	a
\(b\)	b
\(c\)	c
\(x_0\)	origin

Parameters:

afloat: The curve’s maximum y-value, \(\mathrm{lim}_{x\to\infty}\left(y\right) = a\)
bfloat: Additional parameter: b>1 shifts origin to larger values; 0<b<1 shifts origin to smaller values; b<0 introduces an asymptote
cfloat: Logistic growth rate or steepness of the curve
originfloat: Position of the sigmoid’s midpoint
**kwargsdict: Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

class hyperspy.api.model.components1D.Lorentzian(A=1.0, gamma=1.0, centre=0.0, module=None, **kwargs)#

Bases: Expression

Cauchy-Lorentz distribution (a.k.a. Lorentzian function) component.

\[f(x)=\frac{A}{\pi}\left[\frac{\gamma}{\left(x-x_{0}\right)^{2} +\gamma^{2}}\right]\]

Variable	Parameter
\(A\)	A
\(\gamma\)	gamma
\(x_0\)	centre

Parameters:

Afloat: Area parameter, where \(A/(\gamma\pi)\) is the maximum (height) of peak.
gammafloat: Scale parameter corresponding to the half-width-at-half-maximum of the peak, which corresponds to the interquartile spread.
centrefloat: Location of the peak maximum.
**kwargs: Extra keyword arguments are passed to the Expression component.
For convenience the `fwhm` and `height` attributes can be used to get and set
the full-with-half-maximum and height of the distribution, respectively.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the Lorentzian by calculating the median (centre) and half the interquartile range (gamma).

Note that an insufficient range will affect the accuracy of this method.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

Notes

Adapted from gaussian.py and https://en.wikipedia.org/wiki/Cauchy_distribution

Examples

>>> g = hs.model.components1D.Lorentzian()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

class hyperspy.api.model.components1D.Offset(offset=0.0)#

Bases: Component

Component to add a constant value in the y-axis.

\[f(x) = k\]

Variable	Parameter
\(k\)	offset

Parameters:

offsetfloat: The offset to be fitted

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the parameters by the two area method

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

function_nd(axis)#: Returns a numpy array containing the value of the component for all indices. If enough memory is available, this is useful to quickly to obtain the fitted component without iterating over the navigation axes.

class hyperspy.api.model.components1D.Polynomial(order=2, module=None, **kwargs)#

Bases: Expression

n-order polynomial component.

Polynomial component consisting of order + 1 parameters. The parameters are named “a” followed by the corresponding order, i.e.

\[f(x) = a_{2} x^{2} + a_{1} x^{1} + a_{0}\]

Zero padding is used for polynomial of order > 10.

Parameters:

orderint: Order of the polynomial, must be different from 0.
**kwargs: Keyword arguments can be used to initialise the value of the parameters, i.e. a2=2, a1=3, a0=1. Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the parameters by the two area method

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

class hyperspy.api.model.components1D.PowerLaw(A=1000000.0, r=3.0, origin=0.0, left_cutoff=0.0, module=None, compute_gradients=False, **kwargs)#

Bases: Expression

Power law component.

\[f(x) = A\cdot(x-x_0)^{-r}\]

Variable	Parameter
\(A\)	A
\(r\)	r
\(x_0\)	origin

Parameters:

Afloat: Height parameter.
rfloat: Power law coefficient.
originfloat: Location parameter.
**kwargs: Extra keyword arguments are passed to the Expression component.

Attributes:

left_cutofffloat: For x <= left_cutoff, the function returns 0. Default value is 0.0.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False, out=False)#

Estimate the parameters for the power law component by the two area method.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False, estimates the parameters for the full dataset.
outbool: If True, returns the result arrays directly without storing in the parameter maps/values. The returned order is (A, r).

Returns:

bool: Exit status required for the remove_background() function.

class hyperspy.api.model.components1D.RC(Vmax=1.0, V0=0.0, tau=1.0, module=None, **kwargs)#

Bases: Expression

RC function component (based on the time-domain capacitor voltage response of an RC-circuit)

\[f(x) = V_\mathrm{0} + V_\mathrm{max} \left[1 - \mathrm{exp}\left( -\frac{x}{\tau}\right)\right]\]

Variable	Parameter
\(V_\mathrm{max}\)	Vmax
\(V_\mathrm{0}\)	V0
\(\tau\)	tau

Parameters:

Vmaxfloat: maximum voltage, asymptote of the function for \(\mathrm{lim}_{x\to\infty}\)
V0float: vertical offset
taufloat: tau=RC is the RC circuit time constant (voltage rise time)
**kwargs: Extra keyword arguments are passed to the Expression component.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

class hyperspy.api.model.components1D.ScalableFixedPattern(signal1D, yscale=1.0, xscale=1.0, shift=0.0, interpolate=True)#

Bases: Component

Fixed pattern component with interpolation support.

\[f(x) = a \cdot s \left(b \cdot x - x_0\right) + c\]

Variable	Parameter
\(a\)	yscale
\(b\)	xscale
\(x_0\)	shift

Parameters:

yscalefloat: The scaling factor in y (intensity axis).
xscalefloat: The scaling factor in x.
shiftfloat: The shift of the component
interpolatebool: If False no interpolation is performed and only a y-scaled spectrum is returned.

Examples

The fixed pattern is defined by a Signal1D of navigation 0 which must be provided to the ScalableFixedPattern constructor, e.g.:

>>> s = hs.load('data.hspy') 
>>> my_fixed_pattern = hs.model.components1D.ScalableFixedPattern(s) 

Attributes:

yscaleParameter: The scaling factor in y (intensity axis).
xscaleParameter: The scaling factor in x.
shiftParameter: The shift of the component
interpolatebool: If False no interpolation is performed and only a y-scaled spectrum is returned.

Methods

prepare_interpolator(**kwargs)

Fine-tune the interpolation.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

function_nd(axis)#: Returns a numpy array containing the value of the component for all indices. If enough memory is available, this is useful to quickly to obtain the fitted component without iterating over the navigation axes.

gui(display=True, toolkit=None, **kwargs)#

Display or return interactive GUI element if available.

Parameters:

displaybool: If True, display the user interface widgets. If False, return the widgets container in a dictionary, usually for customisation or testing.
toolkitstr, iterable of str or None: If None (default), all available widgets are displayed or returned. If string, only the widgets of the selected toolkit are displayed if available. If an interable of toolkit strings, the widgets of all listed toolkits are displayed or returned.

prepare_interpolator(**kwargs)#

Fine-tune the interpolation.

Parameters:

xarray: The spectral axis of the fixed pattern
**kwargsdict: Keywords argument are passed to scipy.interpolate.make_interp_spline()

class hyperspy.api.model.components1D.SkewNormal(x0=0.0, A=1.0, scale=1.0, shape=0.0, module=['numpy', 'scipy'], **kwargs)#

Bases: Expression

Skew normal distribution component.

Asymmetric peak shape based on a normal distribution.
For definition see
https://en.wikipedia.org/wiki/Skew_normal_distribution
See also http://azzalini.stat.unipd.it/SN/

\[\begin{split}f(x) &= 2 A \phi(x) \Phi(x) \\ \phi(x) &= \frac{1}{\sqrt{2\pi}}\mathrm{exp}{\left[ -\frac{t(x)^2}{2}\right]} \\ \Phi(x) &= \frac{1}{2}\left[1 + \mathrm{erf}\left(\frac{ \alpha~t(x)}{\sqrt{2}}\right)\right] \\ t(x) &= \frac{x-x_0}{\omega}\end{split}\]

Variable	Parameter
\(x_0\)	x0
\(A\)	A
\(\omega\)	scale
\(\alpha\)	shape

Parameters:

x0float: Location of the peak position (not maximum, which is given by the mode property).
Afloat: Height parameter of the peak.
scalefloat: Width (sigma) parameter.
shape: float: Skewness (asymmetry) parameter. For shape=0, the normal distribution (Gaussian) is obtained. The distribution is right skewed (longer tail to the right) if shape>0 and is left skewed if shape<0.
**kwargs: Extra keyword arguments are passed to the Expression component.

Notes

The properties mean (position), variance, skewness and mode (position of maximum) are defined for convenience.

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the skew normal distribution by calculating the momenta.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

Notes

Adapted from Lin, Lee and Yen, Statistica Sinica 17, 909-927 (2007) https://www.jstor.org/stable/24307705

Examples

>>> g = hs.model.components1D.SkewNormal()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager._axes[-1].offset = -10
>>> s.axes_manager._axes[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

property mean#: Mean (position) of the component.

property mode#: Mode (position of maximum) of the component.

property skewness#: Skewness of the component.

property variance#: Variance of the component.

class hyperspy.api.model.components1D.SplitVoigt(A=1.0, sigma1=1.0, sigma2=1.0, fraction=0.0, centre=0.0)#

Bases: Component

Split pseudo-Voigt component.

\[ pV(x,centre,\sigma) = (1 - \eta) G(x,centre,\sigma) + \eta L(x,centre,\sigma) \] \[ f(x) = \begin{cases} pV(x,centre,\sigma_1), & x \leq centre\\ pV(x,centre,\sigma_2), & x > centre \end{cases} \]

Variable	Parameter
\(A\)	A
\(\eta\)	fraction
\(\sigma_1\)	sigma1
\(\sigma_2\)	sigma2
\(centre\)	centre

Notes

This is a voigt function in which the upstream and downstream variance or sigma is allowed to vary to create an asymmetric profile In this case the voigt is a pseudo voigt consisting of a mixed gaussian and lorentzian sum

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the split voigt function by calculating the: momenta the gaussian.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool

Notes

Adapted from https://scipy-cookbook.readthedocs.io/items/FittingData.html

Examples

>>> g = hs.model.components1D.SplitVoigt()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

function(x)#

Split pseudo voigt - a linear combination of gaussian and lorentzian

Parameters:

xarray: independent variable
Afloat: area of pvoigt peak
centerfloat: center position
sigma1float: standard deviation <= center position
sigma2float: standard deviation > center position
fractionfloat: weight for lorentzian peak in the linear combination, and (1-fraction) is the weight for gaussian peak.

function_nd(axis)#: Returns a numpy array containing the value of the component for all indices. If enough memory is available, this is useful to quickly to obtain the fitted component without iterating over the navigation axes.

class hyperspy.api.model.components1D.Voigt(centre=10.0, area=1.0, gamma=0.2, sigma=0.1, module=['numpy', 'scipy'], **kwargs)#

Bases: Expression

Voigt component.

Symmetric peak shape based on the convolution of a Lorentzian and Normal (Gaussian) distribution:

\[f(x) = G(x) \cdot L(x)\]

where \(G(x)\) is the Gaussian function and \(L(x)\) is the Lorentzian function. In this case using an approximate formula by David (see Notes). This approximation improves on the pseudo-Voigt function (linear combination instead of convolution of the distributions) and is, to a very good approximation, equivalent to a Voigt function:

\[\begin{split}z(x) &= \frac{x + i \gamma}{\sqrt{2} \sigma} \\ w(z) &= \frac{e^{-z^2} \text{erfc}(-i z)}{\sqrt{2 \pi} \sigma} \\ f(x) &= A \cdot \Re\left\{ w \left[ z(x - x_0) \right] \right\}\end{split}\]

Variable	Parameter
\(x_0\)	centre
\(A\)	area
\(\gamma\)	gamma
\(\sigma\)	sigma

Parameters:

centrefloat: Location of the maximum of the peak.
areafloat: Intensity below the peak.
gammafloat: \(\gamma\) = HWHM of the Lorentzian distribution.
sigma: float: \(2 \sigma \sqrt{(2 \log(2))}\) = FWHM of the Gaussian distribution.
**kwargs: Extra keyword arguments are passed to the Expression component.

Notes

For convenience the gwidth and lwidth attributes can also be used to set and get the FWHM of the Gaussian and Lorentzian parts of the distribution, respectively. For backwards compatability, FWHM is another alias for the Gaussian width.

W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64, doi:10.1107/S0021889886089999

Parameters:

parameter_name_listlist: The list of parameter names.
linear_parameter_listlist, optional: The list of linear parameter. The default is None.

estimate_parameters(signal, x1, x2, only_current=False)#

Estimate the Voigt function by calculating the momenta of the Gaussian.

Parameters:

signalSignal1D
x1float: Defines the left limit of the spectral range to use for the estimation.
x2float: Defines the right limit of the spectral range to use for the estimation.
only_currentbool: If False estimates the parameters for the full dataset.

Returns:

bool: Exit status required for the remove_background() function.

Notes

Adapted from https://scipy-cookbook.readthedocs.io/items/FittingData.html

Examples

>>> g = hs.model.components1D.Voigt()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)
True

components1D#

For more details see each component docstring.#

`components1D`#