1. NAME AND TITLE

LOUHI82: General Purpose Unfolding Program with Linear and Nonlinear Regularizations.

2. CONTRIBUTOR

Helsinki University of Technology, Espoo, Finland.

3. CODING LANGUAGE AND COMPUTER

Fortran IV; UNIVAC 1108.

4. NATURE OF PROBLEM SOLVED

The interpretation of several physical measurements requires the unfolding or deconvolution of the solution of Fredholm integral equations of the first kind. Examples include neutron spectroscopy with activation detectors, moderating spheres, or proton recoil measurements. LOUHI82 is designed to be applicable to a large number of physical problems and to be extended to incorporate other unfolding methods.

5. METHOD OF SOLUTION

The unfolding problem is cast as a least squares problem whose objective function includes, in addition to matching the measured data, prior information of the smoothness, shape, and magnitude of the solution. These conditions are formulated either as a linear regularization problem that can be solved through fast matrix inversion techniques or a nonlinear regularization problem allowing also for logarithmic or relative weighting of the conditions and guaranteeing a non-negative solution by using gradient minimization methods.

6. RESTRICTIONS OR LIMITATIONS

Designed for so-called few channel problems, the dimensions of the present version allow for up to 100 arguments and solution points.

7. TYPICAL RUNNING TIME

Problems with 10 response functions and 40 solution points typically require about 4s of UNIVAC 1108 cpu time with the faster linear method and about 15s with the iterative nonlinear method.

8. COMPUTER HARDWARE REQUIREMENTS

UNIVAC 1108.

9. COMPUTER SOFTWARE REQUIREMENTS

Fortran IV, EXEC8 Operating System.

10. REFERENCES

a. Included in documentation:

J. V. Sandberg, "Differences of the LOUHI82 Input from the LOUHI78 Input," TKK-F-C69 (February 1983).

J. T. Routti and J. V. Sandberg, "General Purpose Unfolding Program LOUHI78 with Linear and Nonlinear Regularizations," Computer Physics Communications 21 (1980) 119-144.

b. Background information:

J. T. Routti and J. V. Sandberg, "Multialgorithm Unfolding Studies of Neutron Spectra from Activation Detectors," TKK-F-A392 (August 1979).

J. V. Sandberg, "Application of the Program LOUHI82 to Reactor Neutron Spectrum Unfolding," TKK-F-A524 (July 1983).

J. V. Sandberg and J. T. Routti, "Unfolding TRIGA Reactor Neutron Spectra from Multicomponent Activation Detector Data with LOUHI82," Nuclear Technology 63 (October 1983) 170-175.

11. CONTENTS OF CODE PACKAGE

Included are the referenced documents (10.a) and one (1.2MB) DOS diskette containing a complete runstream of source code, compilation and loading commands, and test input data.

12. DATE OF ABSTRACT

June 1987.