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MathGroup Archive 2006

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Re: Fastest method for comparing overlapping times in random time series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64965] Re: [mg64935] Fastest method for comparing overlapping times in random time series
  • From: "Carl K. Woll" <carlw at wolfram.com>
  • Date: Fri, 10 Mar 2006 05:14:57 -0500 (EST)
  • References: <200603080559.AAA03078@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Prince-Wright, Robert G SEPCO wrote:
> I have two lists, list1{ {t1,t1+dt1}, {t2,t2+dt2},..{ti,ti+dti}}, and 
> list2, each representing 'time(i)' and corresponding 'time(i) + 
> deltatime(i)'. The time(i) values are determined by an exponential 
> inter-arrival time model, and the durations are a scaled uniform random 
> variable. Both lists are ordered on time(i). You can think of list 1 as 
> representing periods when System 1 is not working, and list 2 as the 
> periods when System 2 is not working. Example lists are given as Cell 
> Expressions below together with code to convert to a ticker-tape Plot 
> (you may need to stretch the graphic to see clearly). The challenge is 
> to develop a fast method for determining the periods when both Systems 
> are not working, i.e. to create a list corresponding to the start and 
> finish times of the overlaps.
> 
>  Thus far I have only managed to use a Do loop which is very slow for long lists!
> 
>  Bob
> 
[snip]
> 
>  Robert Prince-Wright
>  Risk Management Engineer, EP Americas
>  Shell Exploration & Production Company
>  Woodcreek, 200 North Dairy Ashford
>  Houston, TX 77079, USA
> 
>  Tel: +1 281 544 3016
>  Fax: +1 281 544 2238
>  Shell MeetMe Tel. +1 713 423 0600, Participant Code 62709127
>  Email: robert.prince-wright at shell.com
>  Internet: http://www.shell.com
> 

Use Interval objects:

In[23]:=
i1=Interval@@list1;
i2=Interval@@list2;
IntervalIntersection[i1,i2]

Out[25]=
Interval[{0,0},{7.97854,7.97952},{23.9643,24.0535},{31.0982,31.1416},{32.5135,
   32.547}]

will give you an Interval object with the overlaps.

Carl Woll
Wolfram Research


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