## Abstract

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige–Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.

Original language | English (US) |
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Pages (from-to) | 5-12 |

Number of pages | 8 |

Journal | Molecular Physics |

Volume | 115 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 17 2017 |

## Keywords

- Relativistic
- diagonalisation
- quaternion

## ASJC Scopus subject areas

- Biophysics
- Molecular Biology
- Condensed Matter Physics
- Physical and Theoretical Chemistry