Model components#

In HyperSpy a model consists of a sum of individual components. For convenience, HyperSpy provides a number of pre-defined model components as well as mechanisms to create your own components.

Pre-defined model components#

Various components are available in one (components1D) and two-dimensions (components2D) to construct a model.

The following general components are currently available for one-dimensional models:

The following components are currently available for two-dimensional models:

However, this doesn’t mean that you have to limit yourself to this meagre list of functions. As discussed below, it is very easy to turn a mathematical, fixed-pattern or Python function into a component.

Define components from a mathematical expression#

The easiest way to turn a mathematical expression into a component is using the Expression component. For example, the following is all you need to create a Gaussian component with more sensible parameters for spectroscopy than the one that ships with HyperSpy:

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

If the expression is inconvenient to write out in full (e.g. it’s long and/or complicated), multiple substitutions can be given, separated by semicolons. Both symbolic and numerical substitutions are allowed:

>>> expression = "h / sqrt(p2) ; p2 = 2 * m0 * e1 * x * brackets;"
>>> expression += "brackets = 1 + (e1 * x) / (2 * m0 * c * c) ;"
>>> expression += "m0 = 9.1e-31 ; c = 3e8; e1 = 1.6e-19 ; h = 6.6e-34"
>>> wavelength = hs.model.components1D.Expression(
... expression=expression,
... name="Electron wavelength with voltage")

Expression uses Sympy internally to turn the string into a function. By default it “translates” the expression using numpy, but often it is possible to boost performance by using numexpr instead.

It can also create 2D components with optional rotation. In the following example we create a 2D Gaussian that rotates around its center:

>>> g = hs.model.components2D.Expression(
... "k * exp(-((x-x0)**2 / (2 * sx ** 2) + (y-y0)**2 / (2 * sy ** 2)))",
... "Gaussian2d", add_rotation=True, position=("x0", "y0"),
... module="numpy", )

Define new components from a Python function#

Of course Expression is only useful for analytical functions. You can define more general components modifying the following template to suit your needs:

from hyperspy.component import Component

class MyComponent(Component):


    def __init__(self, parameter_1=1, parameter_2=2):
        # Define the parameters
        Component.__init__(self, ('parameter_1', 'parameter_2'))

        # Optionally we can set the initial values
        self.parameter_1.value = parameter_1
        self.parameter_2.value = parameter_2

        # The units (optional)
        self.parameter_1.units = 'Tesla'
        self.parameter_2.units = 'Kociak'

        # Once defined we can give default values to the attribute
        # For example we fix the attribure_1 (optional) = False

        # And we set the boundaries (optional)
        self.parameter_1.bmin = 0.
        self.parameter_1.bmax = None

        # Optionally, to boost the optimization speed we can also define
        # the gradients of the function we the syntax:
        # self.parameter.grad = function
        self.parameter_1.grad = self.grad_parameter_1
        self.parameter_2.grad = self.grad_parameter_2

    # Define the function as a function of the already defined parameters,
    # x being the independent variable value
    def function(self, x):
        p1 = self.parameter_1.value
        p2 = self.parameter_2.value
        return p1 + x * p2

    # Optionally define the gradients of each parameter
    def grad_parameter_1(self, x):
        Returns d(function)/d(parameter_1)
        return 0

    def grad_parameter_2(self, x):
        Returns d(function)/d(parameter_2)
        return x

Define components from a fixed-pattern#

The ScalableFixedPattern component enables fitting a pattern (in the form of a Signal1D instance) to data by shifting (shift) and scaling it in the x and y directions using the xscale and yscale parameters respectively.