Summary

PSD Bounding Tools is a collection of MATLAB-based codes for calculating bounds on various descriptions of a particle size distribution (PSD) given only finitely many of its moments.  In particular, the collection includes functions for calculating bounds on:

• the number of particles in an arbitrary size interval,
• the particle size histogram,
• the cumulative distribution function (CDF), and
• the D10, D50, and D90 of the distribution.

The graphical example below shows bounds calculated for the CDF of a distribution.

Documentation

The mathematics behind each function is detailed in the paper Using Semidefinite Programming to Calculate Bounds on Particle Size Distributions. The codes used to generate the various examples found in the paper are part of the PSD Bounding Tools distribution.  These examples demonstrate the appropriate use of the bounding functions.

Using PSD Bounding Tools

PSD Bounding Tools is not in the public domain. However, we are glad to make it available, without charge, for both education and non-profit research purposes. To obtain a copy, please contact Shaylin Cetegen using your academic email for correspondence.

Running any of the codes included with PSD Bounding Tools requires that you have first installed CVX, which is available as a free download here.