.. _method-fsu_quasi_mc-quality_metrics:

"""""""""""""""
quality_metrics
"""""""""""""""


Calculate metrics to assess the quality of quasi-Monte Carlo samples



**Topics**


package_fsudace


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* No quality_metrics


**Description**


``quality_metrics`` calculates four quality metrics relating to the
volumetric spacing of the samples. The four quality metrics measure
different aspects relating to the uniformity of point samples in hypercubes.
Desirable properties of such point samples are:

- are the points equally spaced
- do the points cover the region
- and are they isotropically distributed
- with no directional bias in the spacing

The four quality
metrics we report are:

- h: the point distribution norm, which is a measure of uniformity of the point distribution
- chi: a regularity measure, and provides a measure of local uniformity of a set of points
- tau: the second moment trace measure
- d: the second moment determinant measure

All of these values are scaled so that smaller is
better (the smaller the metric, the better the uniformity of the point
distribution).



**Examples**


Complete explanation of these measures can be found in
:cite:p:`Gunzburger2004`.