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Re: checking for overlap

• To: mathgroup at smc.vnet.net
• Subject: [mg20087] Re: checking for overlap
• From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
• Date: Thu, 30 Sep 1999 02:43:05 -0400
• Organization: Defence Evaluation and Research Agency
• References: <7ssfbm$bgd@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

> DennisW555 <dennisw555 at aol.com> wrote in message
news:7ssfbm$bgd at smc.vnet.net...
> I am looking for an elegant way of checking for overlap.
>
> Suppose I have a set of time intervals given by
> ints = {{t1,t2},{t3,t4},{t5,t6}. ...} and another set of times
> tvals = {u1,u2,u3, ...}.
>  What is a fast, elegant way of checking which of the tvals is within any
of
> the ints time intervals

Preamble: I have $Version = "4.0 for Microsoft Windows (April 21, 1999)"

Here is an example of how you can solve this one:

1. Generate a list of 10 random intervals in [0,1].

ints = Table[{Random[], Random[]}, {10}]

2. Generate a list of 3 random numbers in [0,1].

tvals = Table[Random[], {3}]

3. Form the Outer product of these two lists, feeding the arguments
appropriately to the interval membership function IntervalMemberQ.

mems = Outer[IntervalMemberQ[Interval[#1], #2] &, ints, tvals, 1]

The result of this is a list of lists with all of the results you required.

Here are the results of an example run:

ints = {{0.79438, 0.947129}, {0.355177, 0.291621}, {0.599038, 0.879794},
{0.649917,
    0.266863}, {0.262309, 0.714362}, {0.179651, 0.0462716}, {0.387754,
    0.0416916}, {0.381449, 0.46665}, {0.534931, 0.2277}, {0.364545,
0.148582}}

tvals = {0.708023, 0.229474, 0.951056}

mems = {{False, False, False}, {False, False, False}, {True, False, False},
{False,
    False, False}, {True, False, False}, {False, False, False}, {False,
True,
    False}, {False, False, False}, {False, True, False}, {False, True,
False}}


--
Stephen P Luttrell
Room EX21, Defence Evaluation and Research Agency
Malvern, Worcs, WR14 3PS, U.K.
luttrell at signal.dera.gov.uk
01684-894046 (phone), 01684-894384 (fax)
http://www.dera.gov.uk/cis5pip/Welcome.html