Data science uses math extensively to analyze problems. There are numerous Java math libraries available, many of which support concurrent operations. In this chapter, we introduced a number of libraries and techniques to provide some insight into how they can be used to support and improve the performance of applications.

We started with a discussion of how simple matrix multiplication is performed. A basic Java implementation was presented. In later sections, we duplicated the implementation using other APIs and technologies.

Many higher level APIs, such as DL4J, support a number of useful data analysis techniques. Beneath these APIs often lies concurrent support for multiple CPUs and GPUs. Sometimes this support is configurable, as is the case for DL4J. We briefly discussed how we can configure ND4J to support multiple processors.

The map-reduce algorithm has found extensive use in the data science community. We took advantage of the parallel processing power of this framework to calculate the average of a given set of values, the page counts for a set of books. This technique used Apache's Hadoop to perform the map and reduce functions.

Mathematical techniques are supported by a large number of libraries. Many of these libraries do not directly support parallel operations. However, understanding what is available and how they can be used is important. To that end, we demonstrated how three different Java APIs can be used: jblas, Apache Commons Math, and ND4J.

OpenCL is an API that supports parallel operations on a variety of hardware platforms, processor types, and languages. This support is fairly low level. There are a number of Java bindings for OpenCL, which we reviewed.

Aparapi is a higher level of support for Java that can use CPUs, CUDA, or OpenCL to effect parallel operations. We demonstrated this support using the matrix multiplication example.

We wrapped up our discussion with an introduction to Java 8 streams and lambda expressions. These language elements can support parallel operations to improve an application's performance. In addition, this can often provide a more elegant and more maintainable implementation once the programmer becomes familiar with the techniques. We also demonstrated techniques for performing map-reduce using Java 8.

In the next chapter, we will conclude the book by illustrating how many of the techniques introduced can be used to build a complete application.