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

• To: mathgroup at smc.vnet.net
• Subject: [mg64964] 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 05:14:56 -0500 (EST)
• Organization: Goteborg University
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Robert,
The fastest I can obtain is also using the Do command, but it seems to scale
quite good for large lists. First create two reasonable long lists:

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

To avoid building and rewriting of large lists in the memory, I write the

Timing[ resultfile= OpenWrite["C:\\Documents and Settings\\Your Name\\My
Documents\\Math\\PW.txt"];
WriteString[ resultfile,"overlaplist = {"];
list4= 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}]}]];
on1=False; on2=False; start=0;
Do[ Switch[ list4[ [ i,2]],
1, on1=True; If[ on2, start= list4[[ i,1]]],
2, on1=False; If[ on2, WriteString[resultfile, {start, list4[[
i,1]]},",\n"]],
3, on2=True; If[ on1, start= list4[[ i,1]]],
4, on2=False; If[ on1, WriteString[resultfile, {start, list4[[
i,1]]},",\n"]]], { i, Length[list4]}];
WriteString[resultfile,"Sequence[]};"];
Close[resultfile]]

This take around 32 seconds on my computer, and seems to scale linearly. You
can then simply read in the result by

<< "C:\\Documents and Settings\\Your Name\\My Documents\\Math\\PW.txt"

Best regards

Ingolf Dahl
Sweden

-----Original Message-----
From: Prince-Wright, Robert G SEPCO [mailto:robert.prince-wright at shell.com]
To: mathgroup at smc.vnet.net
Subject: [mg64964] [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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