Performance of Dense Eigensolvers on BlueGene/Q

Many scientific applications require the computation of about 10–30 % of the eigenvalues and eigenvectors of large dense symmetric or complex hermitian matrices. In this paper we will present performance evaluation results of the eigensolvers of the three libraries Elemental, ELPA, and ScaLAPACK on the BlueGene/Q architecture. All libraries include solvers for the computation of only a part of the spectrum. The most time-consuming part of the eigensolver is the reduction of the full eigenproblem to a tridiagonal one. Whereas Elemental and ScaLAPACK only offer routines to directly reduce the full matrix to a tridiagonal one, which only allows the use of BLAS 2 matrix-vector operations and needs a lot of communication, ELPA also offers a two-step reduction routine, first transforming the full matrix to banded form and thereafter to tridiagonal form. This two-step reduction shortens the reduction time significantly but at the cost of a higher complexity of the back transformation step. We will show up to which part of the eigenspectrum the use of the two-step reduction pays off.