Re: [fluka-discuss]: Sampling from fluence using Source routine

From: Anna Ferrari <>
Date: Mon, 03 Feb 2014 02:25:21 +0100

Dear Sion,

I suggest first to read the Chapter 13.2.19 of the manual, "source.f
user-written source". You can find the way to implement in the source routine
a biased distribution. I copy here the part interesting for you:

* Sampling from a biased distribution

    The technique for sampling from a generic distribution described
    above can be extended to modify the probability of sampling in
    different parts of the interval (importance sampling). We
    replace f(x) by a weighted function g(x) = f(x) * h(x), where h(x)
    is any appropriate function of x we like to choose. We normalise g(x)
    in the same way as f(x) before:
                   /x /xmax /x
           G(x) = | g(x)dx / | g(x)dx = | f(x)*h(x)dx / B
                   /xmin /xmin /xmin
    and we need also the integral of f(x) over the whole interval:
               A = | f(x)dx

    All the sampling is done using the biased cumulative normalised
    function G instead of the original unbiased F: we sample a uniform
    pseudo-random number t as before, and we get the sampled value XX by
    inverting G(x):
               XX = G (t)
    The particle is assigned a weight B/(A * h(XX))

    A special case of importance sampling is when the biasing function
    chosen is the inverse of the unbiased distribution function:
               h(x) = 1/f(x)
               g(x) = f(x) * h(x) = 1
               G(x) = (x - xmin) / (xmax - xmin)
    In this case we sample a uniform pseudo-random number t using
    FLRNDM as shown above. The sampled value XX is simply given by:
                         XX = xmin + (xmax - xmin)*t
    and the particle is assigned a weight:
                 B/(A h(X)) = f(XX)*(xmax - xmin) / | f(x)dx
    But since FLUKA normalizes all results per unit primary weight, any
    constant factor is eliminated in the normalization. Therefore it is
    sufficient to assign each particle a weight f(x).

The answer to your first question should be now quite clear... the weight is
calculated as illustrated above, no reason to be an integer (why?).

2. No, the biasing of the primaries and the biasing of the secondaries and (I
would add) the importance sampling (which is particle and region-based) refer
to separate actions in the transport: the source generation in the first case
and the tracking of generated particles in the other two cases (respectively
secondaries and primary+secondaries). Obviously you have to take care that the
biasing you chose is meaningful and you don't underestimate important
3. I would not change the location of the lines you wrote(...why?)

Hope it helps,
kind regards,

Am Thu, 30 Jan 2014 16:07:31 -0500 schrieb Sion Koren <>:
> Dear friends,
> I would like to sample from fluence by sampling the energy uniformly and
>adjusting the weight accordingly.
> I have a few questions please:
> 1. Must a weight be an integer? Can the fluence spectra (photons per
>MeV per incident electron in my case) be multiplied for biasing?
> 2. Would it effect the usage of secondary particles biasing with the
>bias card?
> 3. In the Source.f subroutine the particle weight is dealt with at
>those lines:
> * Wt is the weight of the particle
> Can the location of these lines in the subroutine be modified?
> Can one please give an example of a correct way to modify the weight.
> Thanks in advance,
> Sion Koren, PhD, DABR
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Anna Ferrari
Institute of Radiation Physics
Helmholtz-Zentrum Dresden-Rossendorf e.V.
Tel. +49 351 260 2872

Vorstand: Prof. Dr. Dr. h. c. Roland Sauerbrey, Prof. Dr. Dr. h. c. Peter
Vereinsregister: VR 1693 beim Amtsgericht Dresden
Received on Mon Feb 03 2014 - 03:46:43 CET

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