in reply to Re: Average start time handling midnight
in thread Average start time handling midnight

Not that complicated, really, although it does seem a bit silly to do trigonometry where simple arithmetic would suffice. 

#! /usr/bin/perl -wl

my @times = qw( 17:00 19:00 11:00 13:00 23:00 01:00
                10:30 13:00 19:40 01:20 16:00 02:00 );

# keep angles in range -pi .. pi
sub _PI () { 2 * atan2(1, 0) }
sub _TC () { 24 * 60 / (2 * _PI) }

sub time2angle {
    map {
        my ($h, $m) = split /:/;
        _PI - (60 * $h + $m) / _TC
    } @_
}
sub angle2time {
    map {
        my $m = int _TC * (_PI - $_);
        sprintf "%02d:%02d", $m / 60, $m % 60
    } @_
}

use List::Util qw( sum );
sub circ_avg { atan2 sum(map sin, @_), sum(map cos, @_) }

for (; @times > 1; shift @times) {
    my @t = @times[0, 1];
    print "@t => @{[angle2time circ_avg time2angle @t]}";
}

[download]

Thank you for the wikipedia link.

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Re^3: Average start time handling midnight
by pryrt (Abbot) on Jul 21, 2016 at 22:40 UTC

    When averaging two times, yes, it's silly. But when averaging more than two, it comes out with a very different result.

    ... # your code thru the definition of sub circ_avg;

print "@times";
print "            => circle vs line";
print "            => @{[angle2time circ_avg time2angle @times]} vs @{
+[angle2time( sum( time2angle @times ) / @times ) ]}";

for (; @times > 1; shift @times) {
    my @t = @times[0, 1];
    print "@t => @{[angle2time circ_avg time2angle @t]} vs @{[angle2ti
+me( sum( time2angle @t ) / @t ) ]}";
}

__END__
__OUTPUT__
17:00 19:00 11:00 13:00 23:00 01:00 10:30 13:00 19:40 01:20 16:00 02:0
+0
            => circle vs line
            => 17:46 vs 12:12
17:00 19:00 => 18:00 vs 18:00
19:00 11:00 => 15:00 vs 15:00
11:00 13:00 => 12:00 vs 12:00
13:00 23:00 => 18:00 vs 18:00
23:00 01:00 => 00:00 vs 12:00
01:00 10:30 => 05:45 vs 05:45
10:30 13:00 => 11:45 vs 11:45
13:00 19:40 => 16:20 vs 16:20
19:40 01:20 => 22:30 vs 10:30
01:20 16:00 => 20:40 vs 08:40
16:00 02:00 => 21:00 vs 09:00

    [download]

    The pairs of times come out to a simple average that mostly matches the circles (except on the ones with midnight between time1 and time2); but you get very different results between the two averages for the entire list. Previously, I had compared my own implementation of the angular average (yours is better) to the results of salva's solution of finding the center-with-minimum-variance and found that the results for salva's example list (or a list of random times) gave very similar means to the angular average, which would be very different from the arithmetic mean for the same set of data

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[d/l]

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