Re: Number of interval Intersections for a large number of intervals

*To*: mathgroup at smc.vnet.net*Subject*: [mg81718] Re: [mg81679] Number of interval Intersections for a large number of intervals*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Tue, 2 Oct 2007 05:36:10 -0400 (EDT)*References*: <4236415.1191246194428.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

[WRI: there's a Plot/Piecewise insect (bug?) noted below.] I'm having to guess a bit, but maybe this is what you mean: intervals = Sort /@ RandomReal[{-1, 1}, {10^5, 2}]; trans = Transpose@intervals; {{min, maxLow}, {minHigh, max}} = Through[{Min, Max}@#] & /@ trans; {low, high} = Interpolation[Transpose@{Sort@#, -1 + Range@Length@#}, InterpolationOrder -> 0] & /@ trans; Clear[count] count[x_] /; x < min = 0; count[x_] /; x > max = 0; count[x_] /; x < minHigh := low[x] count[x_] /; x > maxLow := low[maxLow] - high[x] count[x_] := low[x] - high[x]; First@Timing@Plot[count@x, {x, -1, 1}] 0.031 or Clear[count2] count2[x_] = Piecewise[{{0, x < min}, {low[x], x < minHigh}, {low[x] - high[x], x <= maxLow}, {low[maxLow] - high[x], x <= max}}]; First@Timing@Plot[count2@x, {x, -1, 1}] 0.047 INSECT report: If I use a small number of Intervals -- 10, say -- the two plots are different. The Piecewise version doesn't have "returns" at some of the discontinuities, even though the following plots the zero function as expected: Plot[count2@x - count@x, {x, -1, 1}] Is this an example of Exclusions->Automatic at work? If so, why aren't all the returns omitted? Bobby On Mon, 01 Oct 2007 03:50:26 -0500, P_ter <peter_van_summeren at yahoo.co.uk> wrote: > Hello, > I have as example on the interval [0.0,12000.0] thousands of smaller > intervals which overlap. I construct for each interval a UnitStep up and > one down(a block). I order and sum them and I give it to Reduce with the > question Reduce[SumOfAllBlocks[x]==<number>,x]. The result gives me the > overlapping intervals which overlap <number>. From the result I take > out the length of the overlaps and Tally them. It is safe, but slow. > Does anyone know something about this type of problems? With better > algorithms? > > -- DrMajorBob at bigfoot.com

**Follow-Ups**:**Re: Re: Number of interval Intersections for a large number of intervals***From:*Brett Champion <brettc@wolfram.com>