GammaSun V1.3

description: deconvolution program and solver for equation systems

suggested destination: \32bit\educate

GammaSun V1.3 is public domain

abstract:

GammaSun is mainly a deconvolution program for spectra
of photons, but may be used for solving i-dimensional
equation systems of the form too:

    y = R * x
    y = measured data
    x = true data
    R = response of the experiment

for the x. Expected you have measured experimental
data y, then you can calculate in some cases the
true experimental data x by solving the equation system:

    x = R^{-1} * y

R^{-1} is the inverse of the response matrix R 
of the experimental system.

With GammaSun R^{-1} can be calculated by:
    i)   Gauss-Jordan
    ii)  LU-decomposition
    iii) SVD-decomposition

The calculation of R^{-1} for higher dimensions
is not stable when using the machine precision
of 64 bit for mantissa and exponent. In those
cases minimization methods for chi in
    chi = y - R * x
may be more successful:

    iv)  SAND-II
    v)   SVD-Fit

Most of these methods are extreme time consumptive.
An alternative is a quick and dirty method:

    vi)  stripping method


Additional features of GammaSun are:

    - calculation of doses H^*, H_p, H'
    - smoothing data by Fourier, Savitzky-Golay
    - C-like parser-script language for a quick
      generation of response matrices
    - Peak analysis of deconvoluted spectra
    - plotting emission probability of several photons
    - simulation of response spectra for well determined 
      response matrices
    - numeric tests of the inverted matrix
    - checking the residuum


If you found bugs, or you want remark a suggestion send
it by using e-mail:

    Reinhard Alt    R.Alt@tu-bs.de




further reading
  - W. H. Press, P. A. Teukolsky, W. T. Vetterling, B. P. Flannery;
    em Numerical Recipes in C --- The Art of Scientific Computing
    Second Edition (1992), 
  - W. R. Leo; Techniques for Nuclear and Particle Physics Experiments --- A How-to Approach
    Springer-Verlag; 2. Auflage (1994); ISBN 3-540-57280-5
  - S. Berg, W. N. McElroy; A computer automated iterative method for neutron flux spectra
    determination by foil activation -- SAND-II;  Air Force Weapons Laboratory,
    Research and Technology Division; (1967)
  - U. Sch”tzig und H. Schrader;
    Halbwertszeiten und Photonen-Emissionswahrscheinlichkeiten von h„ufig
    verwendeten Radionukliden;
    4. erweiterte Auflage, PTB-Bericht PTB-Ra-16/4, ISBN 3-89429-349-7, (1993)
  - M. Matzke; Unfolding of Pulse Height Spectra -- The HEPRO Program System;
    Physikalisch-Technische Bundesanstalt (Deutschland) (1994)
  - GammaSun online manual

