Voigt Expression

voigt.py

import numpy as np
from hyperspy._components.expression import Expression
from distutils.version import LooseVersion
import sympy


class Voigt(Expression):

    r"""
    Voigt component
    ---------------
    Symmetric peak shape based on the convolution of a Lorentzian and Normal 
    distribution. In this case using an approximate formula by David (see Notes)
    
    .. math:: 

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

    ============== =============
    Variable        Parameter 
    ============== =============
    :math:`x_0`     centre 
    :math:`A`       area
    :math:`\gamma`  gamma
    :math:`\sigma`  fwhm
    ============== =============


    Parameters
    -----------
    centre : float
     Location of the maximum of the peak.
    area : float
     Intensity below the peak.
    lwidth : float
     HWHM of the Lorentzian distribution
    gwidth: float
     FWHM of the Gaussian distribution

    Notes
    -----
    W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64
    """

    def __init__(self, centre=0., area=1., lwidth=0.2, gwidth=0.05, 
                 module="scipy", **kwargs):
        if LooseVersion(sympy.__version__) < LooseVersion("1.3"):
            raise ImportError("The `Voigt` component requires "
                              "SymPy >= 1.3")
        super(Voigt, self).__init__(
            expression="area * real(V); \
                V = wofz(z) / (sqrt(2.0 * 3.14159265359) * sigma); \
                z = (x - centre + 1j * lwidth) / (sigma * sqrt(2.0)); \
                sigma = gwidth / 2.3548200450309493",
            name="Voigt",
            centre=centre,
            area=area,
            lwidth=lwidth,
            gwidth=gwidth,
            module=module,
            autodoc=False,
            **kwargs,
        )

        # Boundaries
        self.area.bmin = 0.
        self.lwidth.bmin = 0.
        self.gwidth.bmin = 0.

        self.isbackground = False
        self.convolved = True