r"""

Definition
----------

This model describes a Gaussian shaped peak on a flat background

.. math::

    I(q) = (\text{scale}) \exp\left[ -\tfrac12 (q-q_0)^2 / \sigma^2 \right]
        + \text{background}

with the peak having height of *scale* centered at $q_0$ and having a standard
deviation of $\sigma$. The FWHM (full-width half-maximum) is $2.354 \sigma$.

For 2D data, 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}


.. image:: img/gaussian_peak_1d.jpg

    1D plot using the default values (w/500 data points).

Reference
---------

None.
"""

from numpy import inf

name = "gaussian_peak"
title = "Gaussian shaped peak"
description = """
    Model describes a Gaussian shaped peak including a flat background
    Provide F(q) = scale*exp( -1/2 *[(q-q0)/sigma]^2 )+ background
"""
category = "shape-independent"

#             ["name", "units", default, [lower, upper], "type","description"],
parameters = [["q0", "1/Ang", 0.05, [-inf, inf], "", "Peak position"],
              ["sigma", "1/Ang", 0.005, [0, inf], "",
               "Peak width (standard deviation)"],
             ]

# No volume normalization despite having a volume parameter
# This should perhaps be volume normalized?
form_volume = """
    return 1.0;
    """

Iq = """
    double scaled_dq = (q - q0)/sigma;
    return exp(-0.5*scaled_dq*scaled_dq); //sqrt(2*M_PI*sigma*sigma);
    """


Iqxy = """
    // never called since no orientation or magnetic parameters.
    //return -1.0;
    return Iq(sqrt(qx*qx + qy*qy), q0, sigma);
    """


# VR defaults to 1.0

demo = dict(scale=1, background=0, q0=0.05, sigma=0.005)
oldname = "PeakGaussModel"
oldpars = dict(sigma='B')