IAEA1371 ZOTT99.
ZOTT99, Data Evaluation Using Partitioned Least-Squares
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES, AUXILIARIES, STATUS, REFERENCES, HARDWARE REQUIREMENTS, LANGUAGE, SOFTWARE REQUIREMENTS, OTHER RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES
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| Program name | Package id | Status | Status date |
|---|---|---|---|
| ZOTT99 | IAEA1371/01 | Tested | 18-OCT-1999 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| IAEA1371/01 | ALPHA/AXP,PC Windows | PC Pentium III 500 |
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3. DESCRIPTION OF PROGRAM OR FUNCTION
Given an existing combined set y(i) of differential and integral measurements with completely general covariances cyy(i,j) and a sensitivity matrix relating the expectation values of the various measurements, ZOTT obtains a new evaluation yp(i) with covariances cyyp(i,j). The results yp(i) are minimum-variance linear unbiased estimators of the true values, Expect[y(i)].
Given an existing combined set y(i) of differential and integral measurements with completely general covariances cyy(i,j) and a sensitivity matrix relating the expectation values of the various measurements, ZOTT obtains a new evaluation yp(i) with covariances cyyp(i,j). The results yp(i) are minimum-variance linear unbiased estimators of the true values, Expect[y(i)].
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4. METHODS
The method of solution is partitioned least squares, which is a form of minimum variance linear estimation (least squares) featuring reduced matrix-inversion requirements (relative to methods based on solving the conventional normal equations). Partitioned least squares permits general correlations among all data uncertainties (including cross-type correlations between differential and integral data). If the problem to be solved is precisely linear, and if correct input is supplied by the user, then the minimum-variance solution obtained with ZOTT99 is unique and exact. At user request, (by specifying inc=1), the code will perform a minimally invasive modification of the input covariance matrix to
enforce consistency (unit chi-squared). Only the diagonal elements
are changed, and an iteratitive procedure is followed in which only
one diagonal element is changed at a time, namely, the one which
produces the maximum benefit in lowering chi-squared. This process
is repeated until chi-squared reaches unity. Regardless of the
input value of inc, plots of the data uncertainties and the final
residuals are produced to permit the analyst to judge the desirabity
of invoking this option and the realism of the changes thereby
introduced. At the end of the run, these plots reside on ZOTTVU.PS for viewing with GhostView or similar PostScript viewer.
The method of solution is partitioned least squares, which is a form of minimum variance linear estimation (least squares) featuring reduced matrix-inversion requirements (relative to methods based on solving the conventional normal equations). Partitioned least squares permits general correlations among all data uncertainties (including cross-type correlations between differential and integral data). If the problem to be solved is precisely linear, and if correct input is supplied by the user, then the minimum-variance solution obtained with ZOTT99 is unique and exact. At user request, (by specifying inc=1), the code will perform a minimally invasive modification of the input covariance matrix to
enforce consistency (unit chi-squared). Only the diagonal elements
are changed, and an iteratitive procedure is followed in which only
one diagonal element is changed at a time, namely, the one which
produces the maximum benefit in lowering chi-squared. This process
is repeated until chi-squared reaches unity. Regardless of the
input value of inc, plots of the data uncertainties and the final
residuals are produced to permit the analyst to judge the desirabity
of invoking this option and the realism of the changes thereby
introduced. At the end of the run, these plots reside on ZOTTVU.PS for viewing with GhostView or similar PostScript viewer.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
Subroutine CLOCK is machine-dependent and must be either adapted to the user's machine or removed. The logarithmic option is a rigorous (that is, minimum- variance) procedure if, and only if, the relative uncertainties are small. With respect to storage limitations, this particular version is dimensioned for a total number of 220 (differential plus integral) measurements (variable NBIG), up to 66 of which may be integral, or redundant, measurements (variable NLIT), however, the code can easily be re-dimensioned for larger problems by changing the values of NLIT and NBIG in the program and making appropriate changes in all arrays having dimensions (66), (66,2), (66,66), (66,220), or (220,220). For very large problems one can optionally use the same memory locations for both of the large arrays cyy(i,j) and cyyp(i,j). If one choses to do this, one must also omit the eigenvalue-eigenvector analysis of the input covariance matrix (see SUBROUTINE EIGER). The EIGER analysis is very useful for detecting errors (especially negative eigenvalues) in the covariances, so the "large problem" option should not be activated unless it is essential. The changes necessary to activate the "large problem" option are bracketed by comment cards containing the string "clarge".
Subroutine CLOCK is machine-dependent and must be either adapted to the user's machine or removed. The logarithmic option is a rigorous (that is, minimum- variance) procedure if, and only if, the relative uncertainties are small. With respect to storage limitations, this particular version is dimensioned for a total number of 220 (differential plus integral) measurements (variable NBIG), up to 66 of which may be integral, or redundant, measurements (variable NLIT), however, the code can easily be re-dimensioned for larger problems by changing the values of NLIT and NBIG in the program and making appropriate changes in all arrays having dimensions (66), (66,2), (66,66), (66,220), or (220,220). For very large problems one can optionally use the same memory locations for both of the large arrays cyy(i,j) and cyyp(i,j). If one choses to do this, one must also omit the eigenvalue-eigenvector analysis of the input covariance matrix (see SUBROUTINE EIGER). The EIGER analysis is very useful for detecting errors (especially negative eigenvalues) in the covariances, so the "large problem" option should not be activated unless it is essential. The changes necessary to activate the "large problem" option are bracketed by comment cards containing the string "clarge".
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7. UNUSUAL FEATURES
Incorporates a universal, objective, and computationally efficient method for handling discrepant data sets, that is, data sets for which the chi-squared per degree of freedom exceeds unity. The algorithm employed, called the "method of least distortion", makes no changes to the covariance data for the subset of data that are already internally consistent at the start of the problem. The variances of all identified outliers are increased in a smooth way until chi-squared reaches the expected value of unity. For further details, see Item 4 above and Reference 1.
Incorporates a universal, objective, and computationally efficient method for handling discrepant data sets, that is, data sets for which the chi-squared per degree of freedom exceeds unity. The algorithm employed, called the "method of least distortion", makes no changes to the covariance data for the subset of data that are already internally consistent at the start of the problem. The variances of all identified outliers are increased in a smooth way until chi-squared reaches the expected value of unity. For further details, see Item 4 above and Reference 1.
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IAEA1371/01, included references:
- D.W. Muir :Treatment of Discrepant Data in the ZOTT99 Generalized Least Squares Program
Covariance Workshop Brookhaven, New York, USA 22-23 April 1999
- D.W. Muir:
Evaluation of Correlated Data Using Partitioned Least Squares:
A Minimum-Variance Derivation
LA-UR-2365 (Rev.) also published in Nuclear Science and
Engineering 101, 88-93 (January 1989).
- E.G. Axton:
Technical Notes - The Thermal-Neutron Capture Cross-Section of
55-Mn
Reprint: Ann.Nucl.Energy Vol. 12 No. 6 PP.315-317 (1985).
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13. SOFTWARE REQUIREMENTS
Specific information for version IAEA1371/01:
ZOTT99 has run on a DEC AlphaServer 2100, running OpenVMS Version 7.1, and on an Intel Pentium-II, running Windows NT 4.0. Compilation
was performed using the DEC Fortran (Fortran 77) compiler and the
Lahey Fortran 77 compiler, respectively.
Specific information for version IAEA1371/01:
ZOTT99 has run on a DEC AlphaServer 2100, running OpenVMS Version 7.1, and on an Intel Pentium-II, running Windows NT 4.0. Compilation
was performed using the DEC Fortran (Fortran 77) compiler and the
Lahey Fortran 77 compiler, respectively.
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IAEA1371/01
pczott99.exe PC executable using Lahey Frotran 77zott99.for Fortran source code
zott99.tst brief description of each of the 6 test problems
zott99_for_covar_ws.doc PC word-6 document describing ZOTT99
zottvu_archive.inp Manually edited Li-7(n,n't) data from EXFOR and ENDF/B-VI
zottvu_special.inp Portions of plot zottvu.tp1 & portions of zottvu_archive.inp
zott_tp1.com command file for test problem 1
zott_tp2.com command file for test problem 2
zott_tp3.com command file for test problem 3
zott_tp4.com command file for test problem 4
zott_tp5.com command file for test problem 5
zott_tp6.com command file for test problem 6
zottin.tp1 User input file for test problem 1
zottin.tp2 User input file for test problem 2
zottin.tp3 User input file for test problem 3
zottin.tp4 User input file for test problem 4
zottin.tp5 User input file for test problem 5
zottin.tp6 User input file for test problem 6
zottout_orig.tp1 Output listing for test problem 1
zottout_orig.tp2 Output listing for test problem 2
zottout_orig.tp3 Output listing for test problem 3
zottout_orig.tp4 Output listing for test problem 4
zottout_orig.tp5 Output listing for test problem 5
zottout_orig.tp6 Output listing for test problem 6
zottvu_tp3.ps postscript output from test problem 3
Keywords: consistency, correlations, covariance matrices, data evaluation, discrepancies, least square fit, method of least distortion, sensitivity.