Algorithm 1005: Fortran Subroutines for Reverse Mode Algorithmic Differentiation of BLAS Matrix Operations
Authors: 
Kristjan Jonasson, Sven Sigurdsson, Hordur Freyr Yngvason, Petur Orri Ragnarsson, Pall MelstedAuthors Info & Claims
Kristjan Jonasson, Sven Sigurdsson, Hordur Freyr Yngvason, Petur Orri Ragnarsson, Pall MelstedAuthors Info & ClaimsArticle No.: 9, Pages 1 - 20
Abstract
A set of Fortran subroutines for reverse mode algorithmic (or automatic) differentiation of the basic linear algebra subprograms (BLAS) is presented. This is preceded by a description of the mathematical tools used to obtain the formulae of these derivatives, with emphasis on special matrices supported by the BLAS: triangular, symmetric, and band. All single and double precision BLAS derivatives have been implemented, together with the Cholesky factorization from Linear Algebra Package (LAPACK). The subroutines are written in Fortran 2003 with a Fortran 77 interface to allow use from C and C++, as well as dynamic languages such as R, Python, Matlab, and Octave. The subroutines are all implemented by calling BLAS, thereby attaining fast runtime. Timing results show derivative runtimes that are about twice those of the corresponding BLAS, in line with theory. The emphasis is on reverse mode because it is more important for the main application that we have in mind, numerical optimization. Two examples are presented, one dealing with the least squares modeling of groundwater, and the other dealing with the maximum likelihood estimation of the parameters of a vector autoregressive time series. The article contains comprehensive tables of formulae for the BLAS derivatives as well as for several non-BLAS matrix operations commonly used in optimization.
Supplementary Material
Software for Fortran Subroutines for Reverse Mode Algorithmic Differentiation of BLAS Matrix Operations
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Index Terms
- Algorithm 1005: Fortran Subroutines for Reverse Mode Algorithmic Differentiation of BLAS Matrix Operations
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Published In
March 2020
214 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/3387915
- Editors:
- Zhaojun Bai,
- Wolfgang Bangerth
Copyright © 2020 Owner/Author.
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 20 March 2020
Accepted: 01 August 2019
Revised: 01 August 2019
Received: 01 December 2017
Published in TOMS Volume 46, Issue 1
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