**RSICC CODE PACKAGE PSR-264**

**1. NAME AND TITLE**

ACORNS: Analysis of Correlation Matrices Used in Neutron Spectrometry, Versions 2003-1 and 2003-2.

**2. CONTRIBUTOR**

Institute of Nuclear Techniques, Budapest University of Technology and Economics, Budapest, Hungary.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 90: Personal computers (P00264IBMPC01).

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**4. NATURE OF PROBLEM SOLVED**

The program ACORNS performs the complete analysis of the input covariance and/or relative covariance and/or correlation matrices, first of all used in the activation neutron spectrometry. These matrices have to be positive definite. To check the fulfillment of this requirement, the program calculates the eigenvalues and eigenvectors of those. If all the eigenvalues are positive, the program optionally performs the factor analysis. The user's input can be either made manually, or the cross section libraries generated by the code X333.

**5. METHOD OF SOLUTION**

The algorithm of the program ACORNS is the Kaiser's "varimax" rotation. Depending on the available data, diagonalization of the covariance/relative covariance/correlation matrices of neutron spectra/reaction rates/cross sections is performed. The input is qualified on the basis of the eigenvalues. Optionally, the program performs factor analysis to help determine common reasons of correlations of the quantities investigated.

**6. RESTRICTIONS OR LIMITATIONS**

The size of the matrices to be analyzed is limited by the computer accuracy. The Version 2003-1 of the program allows input of single precision covariance/relative covariance/correlation matrices up to size 100x100. The Version 2003-2 allows input of single/double precision covariance/relative covariance/correlation matrices up to size 200x200.

**7. TYPICAL RUNNING TIME**

Running time varies from a few seconds to some minutes depending on the user's input data set (number and size of the covariance/relative covariance/correlation matrices to be analyzed) and the CPU speed.

**8. COMPUTER HARDWARE REQUIREMENTS**

This release was developed and tested on personal computers. It is expected to run on any computer which has a Fortran 90 compiler. The size of the required free memory is approx. 2 MB; free hard disk space is approx. 14 MB.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The included PC executables were created with Lahey/Fujitsu Fortran 95 Release 5.60h under the Windows operating system. A standard Fortran 90 compiler is required to run on other operating systems. The codes were tested at RSICC under Windows XP. Compiling the version 2003-2 requires a compiler which can process SELECTED_REAL-KIND(30).

**10. REFERENCES**

E. J. Szondi, "User's Guide to the Covariance Information Analyzing Program ACORNS (Versions 2003-1 and 2003-2)," Budapest University of Technology and Economic, [file acorns.pdf] (April 2003).

E. J. Szondi, "The Covariance Matrix of Neutron Spectra," BME-TR-RES-10/86 [file convspec.pdf] (January 1986).

"Application of Factor Analysis to Neutron Spectrum Unfolding", BME-TR-RES-2182, Nuclear Reactor of the Technical University of Budapest [file fat_cove.pdf] (March 1982).

**11. CONTENTS OF CODE PACKAGE**

ACORNS is distributed on a CD in a WinZIP file which includes referenced electronic documents, source code, PC executables and sample problem.

**12. DATE OF ABSTRACT**

May 1988; revised January 2004.

** KEYWORDS:** ACTIVATION DETECTORS; COVARIANCE DATA PROCESSING;
UNCERTAINTY ANALYSIS; UNFOLDING