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Manuscript Title: MAXENTWDF: a computer program for the maximum entropy estimation of a wave distribution function.
Authors: C. Delannoy, F. Lefeuvre
Program title: MAXENTWDF
Catalogue identifier: AAFV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 40(1986)389
Programming language: Fortran.
Computer: IBM 370.
Operating system: OS/VS.
RAM: 316K words
Word size: 32
Peripherals: disc.
Keywords: Geophysics, Wave distribution Function, Electromagnetic wave, Maximum theory.
Classification: 10, 13.

Nature of problem:
A random electromagnetic field can be described by a Wave Distribution Function (WDF) that specifies how the wave energy density is distributed with respect to the angular frequency omega and to the wave normal direction K. Such a WDF is related to the values of the N auto and cross-power spectra of the field components by the set of integral equations: Si=integral x1-x2 integral y1-y2 ai(x,y) G(x,y) dx dy; i = 1,...N where G(x,y) is the WDF, defined as positive everywhere, ai(x,y) are known kernels, and Si are N independent quantities derived from the power spectra. The point is to find an estimation of G(x,y) from given ai(x,y) functions and from measured values Si of the Si.

Solution method:
The solution which is chosen is the one which maximizes the entropy of the WDF and satisfies the data Si within the limits of the errors in those data. To avoid numerical instabilities in the solution, the measured as well as the theoretical data are transformed into an orthogonal system generated from the N functions ai. In that system, the model parameters are estimated by fitting, in the least square sense, the M more linearly independent data (M<=N). The validity of the solution is asserted computing prediction and stability parameters.

The Si are supposed to be unbiased and to have non correlated variance errors.

Running time:
10 s 82 for the test run.