Computer Programs
USCD1159 MATXTST.
last modified: 23-JUN-1989 | catalog | categories | new | search |

# USCD1159 MATXTST.

#### MATXTST, Basic Operations for Covariance Matrices

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1. NAME OR DESIGNATION OF PROGRAM:  MATXTST
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2. COMPUTERS
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Program name Package id Status Status date
MATXTST USCD1159/01 Tested 23-JUN-1989

Machines used:

Package ID Orig. computer Test computer
USCD1159/01 IBM PC IBM PC
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3. DESCRIPTION OF PROGRAM OR FUNCTION

MATXTST and MATXTST1 perform the following operations for a covariance matrix:
- test for singularity;
- test for positive definiteness;
- compute the inverse if the matrix is non-singular;
- compute the determinant;
- determine the number of positive, negative, and zero eigenvalues;
- examine all possible 3 X 3 cross correlations within a sub-matrix    corresponding to a leading principal minor which is non-positive
definite.

While the two programs utilize the same input, the calculational procedures employed are somewhat different and their functions are complementary. The available input options include: i) the full covariance matrix, ii) the basic variables plus the relative covariance matrix, or iii) uncertainties in the basic variables plus the correlation matrix.
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4. METHOD OF SOLUTION

MATXTST employs LINPACK subroutines SPOFA and SPODI to test for positive definiteness and to perform further optional calculations. Subroutine SPOFA factors a symmetric matrix M using the Cholesky algorithm to determine the elements of a matrix R which satisfies the relation M=R'R, where R' is the transposed matrix of R. Each leading principal minor of M is tested until the first one is found which is not positive definite.
MATXTST1 uses LINPACK subroutines SSICO, SSIFA, and SSIDI to estimate whether the matrix is near to singularity or not (SSICO), and to perform the matrix diagonalization process (SSIFA). The algorithm used in SSIFA is generalization of the Method of Lagrange  Reduction. SSIDI is used to compute the determinant and inertia of the matrix.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Matrices of sizes up to 50 X 50 elements can be treated by present versions of the programs.
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6. TYPICAL RUNNING TIME:
USCD1159/01
NEADB ran the sample cases for MATXTST and MATXST1 on a IBM PC/AT microcomputer in a few seconds.
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7. UNUSUAL FEATURES OF THE PROGRAM:
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8. RELATED AND AUXILIARY PROGRAMS

Algorithms from LINPACK and a collection of low-level subroutines called Basic Linear Algebra Subprograms (BLAS) have been employed in MATXTST and MATXTST1.
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9. STATUS
Package ID Status date Status
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10. REFERENCES:
USCD1159/01, included references:
- L.P. Geraldo and D.L. Smith:
Some Thoughts on Positive Definiteness in the Consideration of
Nuclear Data Covariance Matrices
ANL/NDM-104 (January 1988)
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11. MACHINE REQUIREMENTS:
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
USCD1159/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
USCD1159/01
MSDOS v. 3.21 with IBM PC Professional FORTRAN Version 1.00 compiler.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHORS

Luiz P. Geraldo and Donald Smith
Applied Physics Division
Argonne National Laboratory, U. S. A.
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16. MATERIAL AVAILABLE
USCD1159/01
File name File description Records
USCD1159_01.001 Information file 64
USCD1159_01.002 MATXTST source program (FORTRAN) 387
USCD1159_01.003 MATXTST1 source program (FORTRAN) 763
USCD1159_01.004 MATXTST (.EXE file) 0
USCD1159_01.005 MATXTST1 (.EXE file) 0
USCD1159_01.006 MATXTST test case input data 11
USCD1159_01.007 DOS file-names 6
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17. CATEGORIES
• P. General Mathematical and Computing System Routines

Keywords: covariance matrices, eigenvalues.