**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.

**KEYWORDS: ** UNFOLDING; ACTIVATION DETECTORS