## Algorithm 923

swMATH ID: | 20231 |

Software Authors: | Wimmer, M. |

Description: | Algorithm 923: efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices. Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form. We develop efficient numerical methods for computing this tridiagonal form based on Gaussian elimination, using a skew-symmetric, blocked form of the Parlett-Reid algorithm, or based on unitary transformations, using block Householder transformations and Givens rotations, that are applicable to dense and banded matrices, respectively. We also give a complete and fully optimized implementation of these algorithms in Fortran (including a C interface), and also provide Python, Matlab and Mathematica implementations for convenience. Finally, we apply these methods to compute the topological charge of a class D nanowire, and show numerically the equivalence of definitions based on the Hamiltonian and the scattering matrix. |

Homepage: | http://dl.acm.org/citation.cfm?doid=2331130.2331138 |

Related Software: | GitHub; mVMC; Pfaffian; Mathematica; Matlab; LAPACK; ScaLAPACK; gnuplot; GotoBLAS; SageMath; AlgRemez; SUSY LATTICE; PRIMME |

Cited in: | 8 Documents |

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### Cited by 24 Authors

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### Cited in 6 Serials

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