  Topological data analysis provides a multiscale description of the geometry
and topology of quantitative data. The persistence landscape is a topological
summary that can be easily combined with tools from statistics and machine
learning. We give efficient algorithms for calculating persistence landscapes,
their averages, and distances between such averages. We discuss an
implementation of these algorithms and some related procedures. These are
intended to facilitate the combination of statistics and machine learning with
topological data analysis. We present an experiment showing that the
low-dimensional persistence landscapes of points sampled from spheres (and
boxes) of varying dimensions differ.
