ANGELO-LAMBDA: Covariance Matrix Interpolation and Mathematical Verification.
NEA Databank, Le Seine St Germain, 12, boulevard des Iles, 92130 Issy-les-Moulineaux, France.
Fortran-90; DOS or Linux PC (RSICC ID: P00544MNYCP01).
The codes ANGELO-2.3 and LAMBDA-2.3 are used for the interpolation of the cross-section covariance data from the original to a user-defined energy group structure, and for the mathematical tests of the matrices, respectively. The LAMBDA-2.3 code calculates the eigenvalues of the matrices (both for the original or the converted) and lists them accordingly into positive and negative matrices. This verification is strongly recommended before using any covariance matrices. They were specifically developed for the OECD LWR UAM benchmark, particularly for processing the ZZ-SCALE5.1/COVA-44G cross section covariance matrix library retrieved from the SCALE-5.1 package. Either the original SCALE-5.1 libraries or the libraries separated into several files by nuclides can be (in principle) processed by the ANGELO/LAMBDA codes; but the use of the one-nuclide data is strongly recommended. Due to large deviations of the correlation matrix terms from unity observed in some SCALE5.1 covariance matrices, the previous, more severe acceptance condition in the ANGELO2.3 code was released. Where correlation coefficients exceed 1.0, only a warning message is issued and coefficients are replaced by 1.0. This release contains minor updates over the previous version, P00544MNYCP00.
ANGELO-2.3 interpolates the covariance matrices to a union grid using flat weighting. The LAMBDA-2.3 code includes the mathematical routines to calculate the eigenvalues of the covariance matrices.
The algorithm used in ANGELO is relatively simple; therefore the interpolations involving energy group structure, which are very different from the original (e.g. large difference in the number of energy groups), may not be accurate. In particular, in the case of the MT=1018 data (fission spectra covariances) the algorithm may not be convenient, and the matrices produced may require corrections as described in the ENDF-6 Format Manual before being used.
Typically a few minutes on a PC are required to convert the matrices for the 20 materials included in the test case.
ANGELO-LAMBDA works with personal computers running either Windows or Linux operating systems.
The PC version was compiled with Lahey/Fujitsu Fortran 95 release 5.50h. This release was tested at RSICC on a Pentium PC running the Microsoft Windows XP operating system with Lahey/Fujitsu Fortran 95 release 5.50d.
10.a included in documentation:
Short manual for ANGELO2.3 and LAMBDA2.3 codes.
K. Ivanov, M. Avramova, I. Kodeli, and E. Sartori, Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation and Safety Analysis of LWRs, Volume I: Specification and Support Data for the Neutronics Cases (Phase I), NEA/NSC/DOC(2007)23, OECD Nuclear Energy Agency, (December 2007).
10.b background information
I. Kodeli, E. Sartori, “Neutron Cross-Section Covariance Data in Multigroup Form and Procedure for Interpolation to Users' Group Structures for Uncertainty Analysis Applications,” in Proc. of PHYSOR'90, Int. Conf. on the Physics of Reactors: Operation, Design and Computation, Marseille, PI-11 - PI-20, 23-27 April 1990, Marseille; NEA computer package NEA-1264/03 - /05 (ZZ-VITAMIN-J/COVA: Covariance Matrix Library based on JEF-1, ENDF/B-IV and -V data);
I. Kodeli, “VITAMIN-J/COVA/EFF-3 Cross-Section Covariance Matrix Library and its Use to Analyse Benchmark Experiments in SINBAD Database,” Fus. Eng. Design 75-79 (2005) 1021-1025; NEA Package NEA-1264/05 (ZZ-VITA.-J/COVA/EFF3 Cross-section covariance data from EFF-3)
R. E. MacFarlane and D. W. Muir, The NJOY Nuclear Data Processing System, Version 97, Manual, LA-12740-M (1994).
B. L. Broadhead, SCALE 5.1 Cross-Section Covariance Libraries, ORNL/TM-2005/39, Version 5.1, Vol. I, Book 3, Sect. M19, November 2006.
Covariance matrix libraries like ZZ-SCALE5.1/COVA-44G (USCD-1236/01), ZZ-COV-15GROUP-2006 (NEA-1730), or older (ZZ-VITAMIN J/COVA (NEA-1264), ZZ-DOSCOV (DLC-0090), ZZ-COVERV (DLC-0077)).
NJOY-99 code (module COVR).
ANGELO-LAMBDA is distributed on CD Rom containing referenced documents, Fortran 90 source code, test cases, and executables for Windows and Linux.
January 2010, October 2010.
KEYWORDS: COVARIANCE MATRICES, UNCERTAINTY ANALYSIS