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Re: Finding bounds of the domain of a Piecewise function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72881] Re: [mg72866] Finding bounds of the domain of a Piecewise function
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Wed, 24 Jan 2007 05:22:02 -0500 (EST)
*Reply-to*: hanlonr at cox.net
f[x_]:=Piecewise[{
{f1[x], a <= x <= b},
{f2[x], c <= x <= d},
{f3[x], e <= x <= g}
}]
Max@@f[x][[1,All,2,-1]]
Max[b,d,g]
Bob Hanlon
---- "." <ggroup at sarj.ca> wrote:
> Hi All,
>
> I have a routine that builds up a complicated Piecewise function, f[x].
> All the pieces in the piecewise are restricted to some finite range
> (the ranges for each piece may be very different). I want to find the
> absolute extreme x values which will give me a non-zero f[x].
>
> So have something along the lines of:
>
> f[x_]:=Piecewise[{
> {f1[x], a <= x <= b},
> {f2[x], c <= x <= d},
> {f3[x], e <= x <= g}
> }]
>
> We can assume that a < b, c < d and e < g (all bounds are real and have
> a numeric value). We can also assume that the ranges are
> non-overlapping (it seems PiecewiseExpand takes care of that).
> However, we can *not* assume that the segments are sorted by the x
> range. Note also that the real problem will have many more segments
> than just 3.
>
> For the purposes of discussion, assume that Max[b,d,g] == b. I want to
> find a robust and reasonably fast way of extracting b.
>
> One idea is:
> Max[
> Reap[
> f[x][[1,All,2]]/.{r_?NumericQ :> Sow[r]}
> ][[2]]
> ]
>
> However, this seems like a bit of a hack (it is very much limited to
> the details of this particular problem). Is there a better way which
> doesn't require quite so many assumptions?
>
> Thanks!
>
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