**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 **Suzane Cavalcanti** 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**.