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

• To: mathgroup at smc.vnet.net
• Subject: [mg64981] Re: [mg64935] Fastest method for comparing overlapping times in random time series
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Fri, 10 Mar 2006 05:15:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Robert again,
Here is another, more "functional" variant of my solution. Here no file is
written. It has approximately the same speed as the one I have sent earlier.

Prepare 2 lists of 500000 pairs:

list1 = Partition[Sort[Table[Random[Real,
{0, 10000}], {1000000}]], 2];
list2 = Partition[Sort[Table[Random[Real,
{0, 10000}], {1000000}]], 2];

Define a routine for the task:

bothon[list1_, list2_] := Module[{on1, on2, start},
on1 = False; on2 = False;
(Switch[#1[[2]], 1, on1 = True;
If[on2, start = #1[[1]]]; Sequence @@ {}, 2,
on1 = False; If[on2, {start, #1[[1]]},
Sequence @@ {}], 3, on2 = True;
If[on1, start = #1[[1]]]; Sequence @@ {}, 4,
on2 = False; If[on1, {start, #1[[1]]},
Sequence @@ {}]] & ) /@
Sort[Join[list1 /. {{0, 0} -> Sequence[],
{a1_Real, a2_Real} :> Sequence[{a1, 1},
{a2, 2}]}, list2 /. {{0, 0} -> Sequence[],
{a1_Real, a2_Real} :> Sequence[{a1, 3},
{a2, 4}]}]]]

If we call this function, and measure the time,

Timing[outlist = bothon[list1, list2]; ]

then I get 37 seconds on my computer.

You might check

Length[outlist]

should give approx 500000, and

Sum[outlist[[i,2]] - outlist[[i,1]],
{i, Length[outlist]}]

should be approx 2500.

Best regards

Ingolf Dahl
Sweden

> -----Original Message-----
> From: Prince-Wright, Robert G SEPCO
To: mathgroup at smc.vnet.net
> [mailto:robert.prince-wright at shell.com]
> Sent: den 8 mars 2006 07:00
> To: mathgroup at smc.vnet.net
> Subject: [mg64981] [mg64935] Fastest method for comparing overlapping
> times in random time series
>
> 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
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>
>  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
>
>

```

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