adding peak_voigt model

[marimperorclerc]

No description provided.

[marimperorclerc]

Purpose of this PR is to add pseudo Voigt peak shape model.
It is a pure python model based on the one writen for the marketplace :
https://marketplace.sasview.org/uploads/619

If someone could help with the RUFF issue, I would be grateful !

[krzywon]

@marimperorclerc - I've applied the ruff fixes. If you would like to not have this type of issue in the future, please follow the instructions at https://github.com/orgs/SasView/discussions/3171#discussioncomment-17148772 to get ruff and pre-commit set up.

[pkienzle]

You can use Voigt rather than pseudo-Voigt:

def voigt(x, sigma, gamma):
    """
    Return the voigt function, which is the convolution of a Lorentz
    function with a Gaussian.

    :Parameters:
     gamma : real
      The half-width half-maximum of the Lorentzian
     sigma : real
      The 1-sigma width of the Gaussian, which is one standard deviation.

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

    Note: adjusted to use stddev and HWHM rather than FWHM parameters
    """
    # wofz function = w(z) = Fad[d][e][y]eva function = exp(-z**2)erfc(-iz)
    from scipy.special import wofz

    # TODO: if sigma == 0: return Lorentzian
    z = (x + 1j * gamma) / (sigma * np.sqrt(2))
    V = wofz(z) / (np.sqrt(2 * pi) * sigma)
    return V.real

For a 1000 point function on my mac this takes 47.5 μs vs 12.5 μs for the pseudo-Voigt function.

[pkienzle]

Rather than the "\" line extender use parentheses around the entire expression so it can break across multiple lines without the backslash.

Move the "+" operator to the beginning of the second line.

[pkienzle]

Convenient for whom? The width of the Gaussian and Lorentzian are easier to interpret physically. I don't think the optimizer will care which pair it is fitting. The only advantage seems to be that it is easier to guess the initial value of HWHM from the graph.

[pkienzle]

Both the gaussian and the lorentzian are symmetric about peak_pos, and so is the linear combination. It make look asymmetric due to log q scale, or because the resolution function Δq is increasing with q.

Mention that the voigt function is a convolution $(L_γ \star G_σ)(q)$. pseudo-Voigt approximates this with a linear combination of a lorentzian and a gaussian.

Add a note that the instrument resolution function contributes to the convolution. That is, if the resolution is a gaussian of approximately constant width Δq then $f(q) = (L_γ \star G_σ \star G_{Δq})(q) = (L_γ \star G_σ')(q)$ with σ'=√(σ² + Δq²) where σ is the width returned from the fit. The fitted σ is intrinsic to the sample. You will need to subtract the modified resolution width Δq/√(2 \ln 2) from the HWHM when guessing the peak_hwhm parameter value.