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Manuscript Title: A program package for the Landau distribution.
Authors: K.S. Kolbig, B. Schorr
Program title: LANDAU
Catalogue identifier: ABAD_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 31(1984)97
Programming language: Fortran.
Computer: CDC 7600.
Operating system: CDC SCOPE.
RAM: 3K words
Word size: 60
Keywords: Nuclear physics, Landau density, Landau distribution, Landau random numbers, Ionization losses, Energy loss simulation, Energy loss data fitting.
Classification: 17.2.

Nature of problem:
The density phi(lambda) of the Landau distribution, as well as the corresponding distribution function Phi(lambda) and its inverse Psi(x), are used to describe the energy loss of charged particles traversing a thin layer of material. The first two moments Phi1(x), Phi2(x) of the densityfunction truncated on the right-hand tail, as well as the derivative phi'(lambda) = dphi(lambda)/dlambda, are also needed in this field. For Monte Carlo simulations it is of particular interest to have a random number generator for the full and the truncated Landau distribution. The function psi(x) for 0 < x < 1 can be used for this purpose. The other functions are important for fitting a truncated Landau distribution to measured or simulated energy-loss data.

Solution method:
 The functions        phi(lambda) : DESLAN(X)
                      phi(lambda) : DISLAN(X)
                     phi'(lambda) : DIFLAN(X)
                          phi1(x) : XM1LAN(X)
                          phi2(x) : XM2LAN(X)
are calculated from rational approximations and asymptotic expressions for any real argument lambda or x. In view of the high speed required, the program for the Landau random numbers
                           psi(x) : RANLAN(X
consists essentially of a table from which psi(x) is computed by linear or quadratic interpolation. In this case, x is restricted to 0 < x < 1.

Running time:
The following table gives an indication of the running time on the CDC 7600 computer for the different subprograms. The figures were obtained by computing 40000 function values for arguments distributed at random in the given intervals.
        Function               Interval             Time
    DELAN  phi(lambda)    -5 < lambda < 200          15.2
    DISLAN phi(lambda)    -5 < lambda < 200          14.3
    DIFLAN phi'(lambda)   -5 < lambda < 200          16.7
    XM1LAN phi1(x)        -5 <   x    < 200          17.3
    XM2LAN phi2(x)        -5 <   x    < 200          13.4
    RANLAN psi(x)          0 <   x    < 1             8.1