Matrix reduction algorithms for GRESS (Gradient Enhanced Software System) and ADGEN (ADjoint matrix GENerator)
Technical Report
·
OSTI ID:5280422
The GRESS Version 0.0 code system was developed to automate the implementation of derivative-taking capabilities in existing FORTRAN 77 computer models. The GRESS CHAIN option is used to calculate and report first derivatives of model results with respect to user selected input data by application of the calculus chain rule. The GRESS ADjoint Matrix GENenerator (ADGEN) option is used to calculate first derivatives of selected model results with respect to all input data. The first part of this paper presents the mathematical foundations and algorithms as presently implemented in GRESS Version 0.0. Examples are used to describe the implementation of both the CHAIN and ADGEN options. Due to excessive execution time and memory requirements with the CHAIN option users are often limited to propagating derivatives for just a few parameters. The ADGEN option allows an almost unlimited number of parameters (i.e., input data); however, the data storage requirement for an ADGEN application was more than 322 megabytes for a code that executes in 1 minute on a VAX 8600 computer. The purpose for this paper is to present three new algorithms that could easily be implemented in GRESS Version 0.0 to dramatically reduce he data storage requirements and execution time for application of the ADGEN option. The new algorithms are described with examples. Test versions of these algorithms were implemented and tested. The application of these algorithms to the GRESS enhancement of the PRESTO-II computer model resulted in a significant reduction in execution time and a reduction in data storage requirements from 322 megabytes to 97 megabytes without any loss in the generality of the approach. 23 refs., 14 figs., 8 tabs.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- Sponsoring Organization:
- DOE/DP
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 5280422
- Report Number(s):
- ORNL/TM-11261; ON: DE90004374
- Country of Publication:
- United States
- Language:
- English
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