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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}
References
----------
None.
Authorship and Verification
----------------------------
* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**
"""
import numpy as np
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-peak_pos)/sigma]^2 )+ background
"""
category = "shape-independent"
# ["name", "units", default, [lower, upper], "type","description"],
parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak position"],
["sigma", "1/Ang", 0.005, [0, inf], "",
"Peak width (standard deviation)"],
]
source = ["gaussian_peak.c"]
def random():
"""Return a random parameter set for the model."""
peak_pos = 10**np.random.uniform(-3, -1)
sigma = 10**np.random.uniform(-1.3, -0.3)*peak_pos
scale = 10**np.random.uniform(0, 4)
pars = dict(
#background=1e-8,
scale=scale,
peak_pos=peak_pos,
sigma=sigma,
)
return pars
|
