Toward Software Tools for Memory-Efficient Matrix Algebra

一个科学程序是一个数学程序，所以有两个因素影响它的性能。 一个是执行算术所需的时间。 另一个是在计算机的存储器层次结构中移动数据所需的时间。 在今天的大型应用中，后期成本往往占主导地位。 该基金资助的工作集中在解决矩阵代数问题的有效计算方法上，这些问题出现在各种科学和工程应用中。这些问题的代码通常被构造为对称为基本线性代数子程序（BLAS）的例程的调用序列。以这种方式编程提高了程序的可读性和可维护性，但在内存效率方面代价很高，特别是对于高阶矩阵。将学习如何将多个BLAS例程联合收割机组合成一个例程，执行多个BLAS的功能的学生。 他将研究如何通过新颖的算法和性能编程技术来创建组合BLAS，并在此过程中为它们的创建开发一种通用方法。 他的工作将最终形成一个工具的基础上，重新组合BLAS自动。 组合例程可以显著减少从主存读取的数据量。 初步结果包括高达90%的加速。

A scientific program is a mathematical one so there are two factorscontributing to its performance. One is the time required to performarithmetic. The other is the time needed to move data through thememory hierarchy of the computer. In today's large applications, thelatter cost often dominates. The work funded by this grant focuses onefficient computational methods for solving the problems in matrix algebrathat arise in a wide variety of science and engineering applications.Codes for such problems are typically constructed as sequences of calls tothe routines known as the Basic Linear Algebra Subprograms (BLAS). Writingprograms in this way promotes readability and maintainability but canbe costly in terms of memory efficiency especially for matrices oflarge order.The grant will be used primarily to support a Ph.D. student who willstudy ways to combine multiple BLAS routines into a single routine thatperforms the functions of more than one BLAS. He will examine ways tocreate composed BLAS via novel algorithms and performance programmingtechniques, developing a general methodology for their creation in theprocess. His work will ultimately form the basis for a tool that createscomposed BLAS automatically. Composed routines can significantly reducethe amount of data read from main memory. Preliminary results includespeedups as large as 90\%.