Re: [xsl] help with random number generation

["Martin Honnen martin.honnen@xxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>]

On 11/16/2022 8:31 PM, C. M. Sperberg-McQueen cmsmcq@xxxxxxxxxxxxxxxxx
wrote:
> Some readers of this list may know enough about pseudo-random number
> generators and their use to advise me.  I hope so!
>
> I am writing an XSLT program to simulate a process, with the aim of
> using it to make Monte Carlo estimates of the probability that the
> process will produce different kinds of results.  The state of the
> simulation is represented by an XML document whose size and shape vary
> over time; at each timeslice, we apply templates to the tree produced by
> the preceding timeslice, and generate a new tree.  The simulation is
> intended to implement a simple birth-and-death model of a population:
> for each 'live' node in the tree, we choose randomly whether it gets a
> new child in this time slice or not, and also choose randomly whether
> the node dies in this time slice or not. We start with a single live
> individual and end up with a family tree.  (My interest in the
> simulation, if it matters, is in observing the effects of changes to the
> assumed birth and death rates on the resulting population of trees, and
> the probability that family trees of a given shape will develop.)
>
> In a Monte Carlo simulation, the quality of the random numbers used is
> likely to matter a good deal.  In particular, if there is too tight a
> correlation among the random numbers, the results are going to be biased
> in ways that are going to be very hard to understand and explain (and in
> some cases, hard to detect).
>
> XPath 3.0 has a random-number-generator() function which I would like to
> use if I can, but the setup I have chosen seems to impose some barriers.
>
>   - I can't just call fn:random-number-generator() each time I need a
>     random number, because the function is specified as deterministic,
>     and while the implementation-dependent seed may vary from run to run
>     of my stylesheet, it should not vary within the run.
>
>     If you want more than one random number, the idea is to use something
>     like
>
>       <xsl;variable name="rmap" as="map(*)"
>                     select="random-number-generator()"/>
>
>     for the first call, get your number using $map('number'), and make
>     the second call with something like
>
>       <xsl;variable name="rmap2" as="map(*)"
>                     select="$map('next')()"/>
>
>     and so on.  The seed to be used by the next call is embedded in the
>     function returns as the 'next' member of the map.
>
>   - I can do this as I descend the tree, so that the parent element
>     generates the random numbers it needs and then passes the appropriate
>     function to its child.
>
>     In that case, I'll get (what I hope is) a nice sequence of random
>     numbers as I descend the tree.  But each child is going to get the
>     same random-number generation function, which will mean that each
>     child is going to get the same random numbers and the simulation will
>     show siblings always behaving the same way.  Not a good idea.  I need
>     to thread a single sequence of random numbers (and generators)
>     through the tree, so that each node uses a different seed and will
>     get different random numbers.
>
>   - So maybe I could use an accumulator?
>
>     That will allow each node to get and use a different hidden seed, but
>     as far as I can tell, each time slice is going to start its traversal
>     of the tree with the same initial function, which means the root of
>     the tree is always going to get the same random numbers, and its
>     behavior will be the same in every timeslice.


In what setting do you work?

With Saxon PE/EE (and I think SaxonJS) there is saxon:timestamp() so e.g.


B  <xsl:accumulator name="rnd" as="map(*)"
initial-value="random-number-generator(saxon:timestamp())">
B B B  <xsl:accumulator-rule match="*" select="$value?next()"/>
B  </xsl:accumulator>


might work better than


B  <xsl:accumulator name="rnd" as="map(*)"
initial-value="random-number-generator(current-dateTime())">
B B B  <xsl:accumulator-rule match="*" select="$value?next()"/>
B  </xsl:accumulator>


The rest of your requirements were too complicated for me to follow through.