RE: A weight Problem in uniform sampling

From: Chris Theis (
Date: Wed Jun 27 2007 - 18:25:50 CEST

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    Hello Laurent,

    > I try to sample a synchrotron source for Fluka calculations and i use
    > for that source.f . I perform an uniform sampling over my energy range
    > [1:500] keV and this sampling is very efficient (I manage to sample
    > the energies).

    Actually your sampling is efficient only at the first glance because you
    have the same chance to sample parts of your spectrum which are not very
    important (=low weight), as you have sampling the important ones (=high
    weight). Depending on your spectrum and the respective weights this
    approach might work, but I'd recommend a different way to elude the
    problems you're running into.
    > 2) If an uniform sampling is not desirable for this type of spectra
    > (because of the huge weight interval), do you recommends a better
    > function that 1/N(E) to biase the spectra ?

    Instead of sampling the energy interval uniformly and tampering with the
    weights of the particles you could do it the other way round. Namely,
    you sample the important parts of your spectrum (those with the high
    weights) with a higher probability than those that have a lower
    contribution to the result. This way you do not need to change the
    weight and introduce large weight fluctuations.

    There are a number of ways that you could to this:

    *) Inversion method: You calculate the the integral of your spectrum
    iteratively over all bins. In the end you'll end up with a table of N
    bins, like your original spectrum, and each bin X contains the integral
    from the start-bin up to bin index X. After normalization this will give
    you the tabulated cumulative distribution function of your spectrum. Now
    you can sample this function uniformly and mapping the result back to
    the original spectrum you can determine the energy of the particle that
    should be started.

    *) Rejection sampling for your spectrum either with a uniform function
    as a delimiter or a biased function. However, these things are a little
    trickier to implement and the efficiency strongly depends on the
    delimiting function.

    *) Transformation method, if your spectrum can be described by an
    analytical function that is bijective and integrable.



    Chris Theis
    CERN/SC-RP - European Organization for Nuclear Research
    1211 Geneva 23, Switzerland
    Phone: +41 22 767 8069                    Office: 892-2A-015
    e-mail:           www:

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