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 all top 5 Cited by 24 Authors 2 Imada, Masatoshi 1 Bär, Christian 1 Bianchi, Lorenzo 1 Chételat, Didier 1 DeGrand, Thomas A. 1 Forini, Valentina 1 Ido, Kota 1 Kato, Takeo 1 Kawamura, Mitsuaki 1 Leder, Björn 1 Loring, Terry A. 1 Misawa, Takahiro 1 Morita, Satoshi 1 Motoyama, Yuichi 1 Narayanan, Rajendran 1 Ohgoe, Takahiro 1 Okubo, Tsuyoshi 1 Schaich, David 1 Todo, Synge 1 Töpfer, Philipp 1 Vescovi, Edoardo 1 Wells, Martin T. 1 Xu, RuQing G. 1 Yoshimi, Kazuyoshi all top 5 Cited in 6 Serials 3 Computer Physics Communications 1 ACM Transactions on Mathematical Software 1 Journal of Multivariate Analysis 1 Linear Algebra and its Applications 1 Numerical Linear Algebra with Applications 1 Journal of High Energy Physics all top 5 Cited in 6 Fields 5 Numerical analysis (65-XX) 3 Quantum theory (81-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year