NEA-1026 LOUHI82.

1. NAME OR DESIGNATION OF PROGRAM:  LOUHI82.

3. DESCRIPTION OF PROGRAM OR FUNCTION

Unfolding or deconvolution of the solution of Fredholm integral equations of the first kind is required in the interpretation of several physical measurements. Examples of such include neutron spectroscopy with activation detectors, moderating spheres or proton recoil measurements, and numerous others of analogous nature. The mathematical problem typically does not have a unique solution and in consequence prior knowledge of the solutions must be used by regularization or other methods to obtain physically meaningful solutions.

LOUHI82 contains response functions identified as follows:

Au197G, Au97Gc, Au97N2, Sc45Ng, Sc45Gc, U238Ng, U238Gc, U238Nf, U235Nf, U235Fc, Np237F, Co59Ng, Co59Gc, Fe58Ng, Fe58Gc, Fe54Np, Ti46Np, Ti48Np, Ni60Np, Ni58Np, DAMAGE.

4. METHOD OF SOLUTION

The unfolding problem is formulated as a generalized 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, as available. These conditions are formulated either as a linear regularization problem  which 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 nonnegative  solution by using gradient minimization methods.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Designed primarily for the so-called few-channel problems the dimensions of the present version allow for up to 40 arguments and solution points.

6. TYPICAL RUNNING TIME

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

NEA-DB ran the test case included in this package on an IBM 3090 computer in 37 seconds of CPU time.

7. UNUSUAL FEATURES OF THE PROGRAM

LOUHI82 is designed to be applicable to a large number of physical problems and to be extended to incorporate also other unfolding methods, such as parametric representation and linear programming techniques to make it a truly  general purpose program offering a multitude of algorithms to choose and compare.

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES:

- J.V. Sandberg:
  Application of the Program LOUHI82 to Reactor
  Neutron Spectrum Unfolding.
  TKK-F-A524(1983)  (July 15, 1983)
- J.V. Sandberg:
  Differences of the LOUHI82 Input from the LOUHI78 Input
  TKK-F-C69  (February 24, 1983)
- J.T. Routti and J.V. Sandberg:
  General Purpose Unfolding Program LOUHI78 with Linear and
  Nonlinear Regularizations.
  Reprint from "Computer Physics Communications", 21 (1980), 119-144
- J.V. Sandberg and J.T. Routti:
  Unfolding Triga Reactor Neutron Spectra from Multicomponent
  Activation Detector Data with LOUHI82.
  Reprint from "Nuclear Technology", 63 (1983), 170-175

11. MACHINE REQUIREMENTS:

To run the test case on IBM 3090, 404K bytes of main storage were required.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

MVS/XA (IBM 3090).

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHORS

           J.T. Routi and J.V. Sandberg
           Helsinki University of Technology
           Department of Technical Physics
           SF-02150 Espoo, Finland

File name	File description	Records
NEA1026_01.001	INFORMATION FILE	65
NEA1026_01.002	LOUHI82 FORTRAN SOURCE PROGRAM	3320
NEA1026_01.003	JCL TO RUN THE SAMPLE CASE ON IBM	104
NEA1026_01.004	SAMPLE CASE INPUT	435
NEA1026_01.005	SAMPLE CASE OUTPUT	2425