r"""
This model describes a Lorentzian shaped peak on a flat background.

Definition
----------

The scattering intensity $I(q)$ is calculated as

.. math::

    I(q) = \frac{scale}{\bigl(1+\bigl(\frac{q-q_0}{B}\bigr)^2\bigr)} + background

with the peak having height of $I_0$ centered at $q_0$ and having
a HWHM (half-width half-maximum) of B.

For 2D data the scattering intensity is calculated in the same way as 1D,
where the $q$ vector is defined as

.. math::

    q = \sqrt{q_x^2 + q_y^2}


.. figure:: img/peak_lorentz_1d.jpg

    1D plot using the default values (w/200 data point).

References
----------

None.

"""

from numpy import inf, sqrt

name = "peak_lorentz"
title = "A Lorentzian peak on a flat background"
description = """\
      Class that evaluates a lorentzian  shaped peak.

        F(q) = scale/(1+[(q-q0)/B]^2 ) + background

        The model has three parameters:
            scale     =  scale
            peak_pos        =  peak position
            peak_hwhm        =  half-width-half-maximum of peak
            background=  incoherent background"""

category = "shape-independent"

#             ["name", "units", default, [lower, upper], "type", "description"],
parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak postion in q"],
              ["peak_hwhm", "1/Ang", 0.005, [-inf, inf], "", "HWHM of peak"],
             ]

def Iq(q, peak_pos, peak_hwhm):
    """
        Return I(q)
    """
    inten = (1/(1+((q-peak_pos)/peak_hwhm)**2))
    return inten
Iq.vectorized = True  # Iq accepts an array of q values

def Iqxy(qx, qy, *args):
    """
        Return I(qx, qy)
    """
    return Iq(sqrt(qx ** 2 + qy ** 2), *args)
Iqxy.vectorized = True # Iqxy accepts an array of qx, qy values


demo = dict(scale=100, background=1.0,
            peak_pos=0.05, peak_hwhm=0.005)

oldname = "PeakLorentzModel"
oldpars = dict(peak_pos='q0', peak_hwhm='B')

tests = [[{'scale':100.0, 'background':1.0}, 0.001, 2.0305]]