Re: Data averages by time of day

Interpolation isn't probably relevant in this case. Bestfit curve (or approximation) which Abigail mentions is. This is why: we want averages (read: good, useful values) in arbitrary Xs, while interpolation produces a function which will exactly evaluate to those Ys from those Xs we used as data for interpolation. Nothing said about Xs between original datapoints, they can be anything. Think of a sine wave which perfectly interpolates points (0, 0), (pi, 0), ..., (n*pi, 0).

Approximation minimizes distance between the curve and each of the datapoints (the datacloud) to produce exactly what you want: a function to calculate useful value in any point of the X axis.

Give Math::Approx a try. Like this:

my %data = (
    mins_from_midnight('07:01') => 82,
    mins_from_midnight('23:48') => 188,
# ...
);

my $approx = Math::Approx->new(undef, 3, %data);
print $approx->approx(mins_from_midnight('15:40'));
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Update: and yes, the day you took a specific datapoint does not matter. Anyway, you want average and that means all the days are the same for your task. That's ok.

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Re: Re: Data averages by time of day
by blue_cowdawg (Monsignor) on Feb 26, 2004 at 19:34 UTC

I love it! :-)

Peter L. Berghold -- Unix Professional Peter at Berghold dot Net
	Dog trainer, dog agility exhibitor, brewer of fine Belgian style ales. Happiness is a warm, tired, contented dog curled up at your side and a good Belgian ale in your chalice.

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Re: Re: Data averages by time of day
by tsee (Curate) on Feb 28, 2004 at 18:48 UTC

use Math::Approx::Symbolic;

my %data = (
    (7*60+1) => 82,
    (23*60+48) => 188,
);

my $approx = Math::Approx::Symbolic->new(undef, 3, %data);

my $sym = $approx->symbolic();
print "$sym\n";

my $prettier = $sym->to_latex();
print "$prettier\n";

# Computing y-values:
print $sym->value(x => time_of_day()), "\n";

# Doing that faster:
use Math::Symbolic::Compiler;
my ($closure) = $sym->to_sub();
print $closure->(time_of_day()), "\n";

# Way faster:
use Math::Symbolic::Custom::CCompiler;
my $inlined_c = $sym->to_compiled_c();
print $inlined_c->(time_of_day()), "\n";
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