A new generation of task-parallel algorithms for matrix inversion in many-threaded CPUs

We take advantage of the new tasking features in OpenMP to propose advanced task-parallel algorithms for the inversion of dense matrices via Gauss-Jordan elimination. Our algorithms perform a partitioning of the matrix operand into two levels of tasks: The matrix is first divided vertically, by column blocks (or panels), in order to accommodate the standard partial pivoting scheme that ensures the numerical stability of the method. In addition, depending on the particular kernel to be applied, each panel is partitioned either horizontally by row blocks (tiles) or vertically by µ-panels (of columns), in order to extract sufficient task parallelism to feed a many-threaded general purpose processor (CPU). The results of the experimental evaluation show the performance benefits of the advanced tasking algorithms on an Intel Xeon Gold processor with 20 cores. This research was sponsored by projects RTI2018-093684-B-I00 and TIN2017-82972-R of Ministerio de Ciencia, Innovación y Universidades; project S2018/TCS-4423 of Comunidad de Madrid; and project PR65/19-22445 of Universidad Complutense de Madrid.