.. _power-law:

power_law
=======================================================

Simple power law with a flat background

========== =============================== ======= =============
Parameter  Description                     Units   Default value
========== =============================== ======= =============
scale      Scale factor or Volume fraction None                1
background Source background               |cm^-1|         0.001
power      Power law exponent              None                4
========== =============================== ======= =============

The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale.


This model calculates a simple power law with a flat background.

**Definition**

.. math::

    I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background}

Note the minus sign in front of the exponent. The exponent *power*
should therefore be entered as a **positive** number for fitting.

Also note that unlike many other models, *scale* in this model
is NOT explicitly related to a volume fraction. Be careful if
combining this model with other models.



.. figure:: img/power_law_autogenfig.png

    1D plot corresponding to the default parameters of the model.


**Source**

:download:`power_law.py <src/power_law.py>`

**References**

None.

**Authorship and Verification**

* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**