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Manuscript Title: General purpose unfolding program LOUHI78 with linear and nonlinear regularizations.
Authors: J.T. Routti, J.V. Sandberg
Program title: LOUHI78
Catalogue identifier: AAVD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 21(1980)119
Programming language: Fortran.
Computer: UNIVAC1108.
Operating system: EXEC8.
RAM: 53K words
Word size: 36
Keywords: Fredholm integral Equations, Unfolding, Activation measurement Analysis, Least squares method, Regularization methods, General purpose, Fit, Nuclear physics, General experiment.
Classification: 4.9, 17.4.

Nature of problem:
Unfolding or deconvolution or 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.

Solution method:
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 logarithmatic or relative weighting of the conditions and guaranteeing a nonnegative solution by using gradient minimization methods. LOUHI78 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.

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

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