NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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STAY-SL | PSR-0113/01 | Tested | 01-MAR-1979 |

Machines used:

Package ID | Orig. computer | Test computer |
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PSR-0113/01 | IBM 360 series | IBM 360 series |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

The dosimetry unfolding problem consists in finding a spectrum which will reproduce a set of measured activities given the dosimetry cross sections. Most cur- rently available dosimetry unfolding codes provide a solution by in- troducing a trial spectrum which is modified iteratively by means of an algorithm. No or very little information is provided by these codes concerning the "uncertainties" in their solutions due to input data "uncertainties". The relationship of their solution to other possible solutions is not established.

STAY-SL does not solve the usual dosimetry unfolding problem in the sense that it provides a statement of the most likely joint probabi- lity density function of the group fluxes, i.e. the spectrum, given the joint probability density function of some measured activation, dosimetry cross sections and some a priori input group fluxes. The density functions are assumed to be normal and independent for the three classes of input data. The joint probability density functions of each class of input data except for being normal may be comple- tely arbitrary. With the above restrictions on the density functions of the input data, STAY-SL may be thought of as performing the com- plete "error analysis" in the solution to the dosimetry unfolding problem.

The dosimetry unfolding problem consists in finding a spectrum which will reproduce a set of measured activities given the dosimetry cross sections. Most cur- rently available dosimetry unfolding codes provide a solution by in- troducing a trial spectrum which is modified iteratively by means of an algorithm. No or very little information is provided by these codes concerning the "uncertainties" in their solutions due to input data "uncertainties". The relationship of their solution to other possible solutions is not established.

STAY-SL does not solve the usual dosimetry unfolding problem in the sense that it provides a statement of the most likely joint probabi- lity density function of the group fluxes, i.e. the spectrum, given the joint probability density function of some measured activation, dosimetry cross sections and some a priori input group fluxes. The density functions are assumed to be normal and independent for the three classes of input data. The joint probability density functions of each class of input data except for being normal may be comple- tely arbitrary. With the above restrictions on the density functions of the input data, STAY-SL may be thought of as performing the com- plete "error analysis" in the solution to the dosimetry unfolding problem.

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4. METHOD OF SOLUTION

STAY-SL uses the least-squares method to obtain its solution. Because the three different types of input data are assumed to have independent probability density functions, in particular the activation data, the method of solution is extremely fast and requires only the inversion of a small matrix of dimensions equal to the number of activation measurements. This matrix will very seldom be singular; therefore, a solution may almost always be obtained.

Although the method is also formally equivalent to a "dosimetry cross section adjustment", the "adjusted cross sections" are not solved for. The joint probability density function of the output group fluxes, which is the solution, reflects the uncertainties in the input dosimetry cross sections as given by their input joint probability density function.

Because the activation data are assumed to have a probability den- sity function, independent of the other input data, the method is equivalent to an application of Bayes' theorem where the activation data are used tp improve upon some a priori knowledge of the distri- bution of the spectrum being solved for, given a priori distribution of the dosimetry cross sections.

The solution being based upon the least-squares method is the best possible one in the sense that the elements of the output covariance matrix are minimum.

STAY-SL uses the least-squares method to obtain its solution. Because the three different types of input data are assumed to have independent probability density functions, in particular the activation data, the method of solution is extremely fast and requires only the inversion of a small matrix of dimensions equal to the number of activation measurements. This matrix will very seldom be singular; therefore, a solution may almost always be obtained.

Although the method is also formally equivalent to a "dosimetry cross section adjustment", the "adjusted cross sections" are not solved for. The joint probability density function of the output group fluxes, which is the solution, reflects the uncertainties in the input dosimetry cross sections as given by their input joint probability density function.

Because the activation data are assumed to have a probability den- sity function, independent of the other input data, the method is equivalent to an application of Bayes' theorem where the activation data are used tp improve upon some a priori knowledge of the distri- bution of the spectrum being solved for, given a priori distribution of the dosimetry cross sections.

The solution being based upon the least-squares method is the best possible one in the sense that the elements of the output covariance matrix are minimum.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

As currently dimensioned, the code can solve for up to 20 activations and 200 group fluxes. These dimensions could easily be changed if desired.

Except as stated above concerning the normal distribution law used and independence of the distributions of the three different classes of input data, there are no restrictions to the code.

A solution will always be produced, no matter how unlikely the input data, although a warning will be given in the output, provided the matrix being inverted does not approach singularity, in which case the run will be aborted and a diagnostic given. The test for app- roach to singularity of the matrix is believed to be conservative and could possible be relaxed if ever needed.

As currently dimensioned, the code can solve for up to 20 activations and 200 group fluxes. These dimensions could easily be changed if desired.

Except as stated above concerning the normal distribution law used and independence of the distributions of the three different classes of input data, there are no restrictions to the code.

A solution will always be produced, no matter how unlikely the input data, although a warning will be given in the output, provided the matrix being inverted does not approach singularity, in which case the run will be aborted and a diagnostic given. The test for app- roach to singularity of the matrix is believed to be conservative and could possible be relaxed if ever needed.

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8. RELATED AND AUXILIARY PROGRAMS

are:

GROUP: A utility program to prepare the dosimetry cross sections for input to STAY-SL. A 1/E + fission spectrum option is provided to prepare an input group flux file for STAY-SL.

FCOV : A utility program which may be used to generate a crude relative covariance matrix of the input group fluxes in the format required by STAY-SL.

XCOV : A utility program which may be used to generate a crude relative covariance matrix of the dosimetry cross sections in the format required by STAY-SL.

are:

GROUP: A utility program to prepare the dosimetry cross sections for input to STAY-SL. A 1/E + fission spectrum option is provided to prepare an input group flux file for STAY-SL.

FCOV : A utility program which may be used to generate a crude relative covariance matrix of the input group fluxes in the format required by STAY-SL.

XCOV : A utility program which may be used to generate a crude relative covariance matrix of the dosimetry cross sections in the format required by STAY-SL.

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10. REFERENCES

- F.G. Perey:

"Least Squares Dosimetry Unfolding: The Program STAY-SL"

ORNL/TM-6062, ENDF-254 (1977).

- F.G. Perey:

"Uncertainty Analysis of Dosimetry Spectrum Unfolding"

paper to be presented at the second ASTM-EURATOM Symposium on

Reactor Dosimetry, Palo Alto, California, October 3-7, 1977.

- F.G. Perey:

"Spectrum Unfolding by the Least-Squares Method"

paper to be presented at the IAEA Technical Committee Meeting on

Current Status of Neutron Spectrum Unfolding, Oak Ridge,

Tennessee, October 10-12, 1977.

- F.G. Perey:

"Least Squares Dosimetry Unfolding: The Program STAY-SL"

ORNL/TM-6062, ENDF-254 (1977).

- F.G. Perey:

"Uncertainty Analysis of Dosimetry Spectrum Unfolding"

paper to be presented at the second ASTM-EURATOM Symposium on

Reactor Dosimetry, Palo Alto, California, October 3-7, 1977.

- F.G. Perey:

"Spectrum Unfolding by the Least-Squares Method"

paper to be presented at the IAEA Technical Committee Meeting on

Current Status of Neutron Spectrum Unfolding, Oak Ridge,

Tennessee, October 10-12, 1977.

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11. MACHINE REQUIREMENTS

A standard PDP-10 is required. The core requirements are 17 K words plus a sharable FORTRAN high segment.

Disc space should not usually be a problem for storing the input data file. As currently dimensioned, STAY-SL could require a very large file to contain the covariance matrix of the dosimetry cross sections having up to 8.4 millions numbers. Such a large covariance matrix could not be generated using XCOV, the maximum possible dimensions being 0.8 million numbers. Such large covariance matrices need never be used since they are required by the code to calculate up to 210 numbers and the concept of effective covariance matrices described in the documentation of XCOV utilized to obtain these 210 numbers.

A standard PDP-10 is required. The core requirements are 17 K words plus a sharable FORTRAN high segment.

Disc space should not usually be a problem for storing the input data file. As currently dimensioned, STAY-SL could require a very large file to contain the covariance matrix of the dosimetry cross sections having up to 8.4 millions numbers. Such a large covariance matrix could not be generated using XCOV, the maximum possible dimensions being 0.8 million numbers. Such large covariance matrices need never be used since they are required by the code to calculate up to 210 numbers and the concept of effective covariance matrices described in the documentation of XCOV utilized to obtain these 210 numbers.

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PSR-0113/01

File name | File description | Records |
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PSR0113_01.001 | GROUP --- SOURCE PROGRAM (F4,EBCDIC) | 122 |

PSR0113_01.002 | GROUP --- DD CARD + SAMPLE INPUT DATA | 340 |

PSR0113_01.003 | FCOV --- SOURCE PROGRAM (F4,EBCDIC) | 80 |

PSR0113_01.004 | FCOV --- DD CARD + SAMPLE INPUT DATA | 9 |

PSR0113_01.005 | XCOV --- SOURCE PROGRAM (F4,EBCDIC) | 93 |

PSR0113_01.006 | XCOV --- DD CARD + SAMPLE INPUT DATA | 52 |

PSR0113_01.007 | STAY --- SOURCE PROGRAM (F4,EBCDIC) | 472 |

PSR0113_01.008 | STAY --- DD CARD + SAMPLE INPUT DATA | 40 |

PSR0113_01.009 | STAY --- SOURCE PRINTED OUTPUT | 538 |

Keywords: dosimeters, flux distribution, group constants, spectra unfolding.