Just for completeness, here's the one I coded up yesterday morning:

$ cat choose_axes.pl

#!/usr/bin/env perl
use strict;
use warnings;

my @series = (
    [qw( 5 5 34 44 114 169 177 184 270 339 361 364 442
        511 530 554 555 587 709 709 735 778 791
        859 871 899 903 926 933 952 )],

    [  1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047,
      4095, 8191, 16383, 32767, 65535, 131071, 262143,
      524287, 1048575, 2097151, 4194303, 8388607,
      16777215, 33554431, 67108863, 134217727, 268435455,
      536870911, 1073741823 ],


    [ 1.713125e-005, 1.748086e-006, 2.101463e-006,
      1.977405e-006, 3.597675e-006, 3.725492e-006,
      3.924736e-006, 2.902199e-006, 3.988645e-006,
      8.210367e-006, 3.360837e-006, 5.202907e-006,
      7.082570e-006, 8.778026e-006, 7.079562e-005,
      9.100576e-005, 5.258545e-005, 9.292677e-005,
      1.789815e-004, 2.113948e-003, 7.229146e-004,
      1.428995e-003, 2.742045e-003, 5.552746e-003,
      1.822390e-002, 2.220999e-002, 4.316067e-002,
      8.876963e-002, 1.751072e-001, 3.494051e-001,
      7.155960e-001, 1.347822e+000 ],
);

for my $ar (@series) {
    my ($type, $min, $max) = choose_axis_params($ar);
    print "($min .. $max)  $type\n";
}

sub minmax {
    my $min = my $max = shift;
    while (@_) {
        my $t = shift;
        $min = $t<$min ? $t : $min;
        $max = $t>$max ? $t : $max;
    }
    return $min, $max;
}

sub check_axis {
    my $name = shift;
    my @points = @_;
    my ($min, $max) = minmax(@points);
    my $midpoint = ($min+$max)/2;

    my $cnt = 0;
    for my $t (@points) {
        ++$cnt if $t > $midpoint;
    }

    my $err = abs(@points/2 - $cnt);
    return $name, $min, $max, $midpoint, $cnt, $err;
}

sub choose_axis_params {
    my $r = shift;

    my ($min,$max) = minmax(@$r);
    $r = [ sort @$r ];

    my @axes;
    push @axes, [ check_axis('linear',@$r) ];
    push @axes, [ check_axis('log', map { log($_) } @$r) ];

    @axes = sort { $a->[-1] <=> $b->[-1] } @axes;

    #for my $r (@axes) {
    #    printf "%-8.8s (%s .. %s) %s, %s, %s\n", @$r;
    #}

    return @{$axes[0]};
}

$ perl choose_axes.pl
(5 .. 952)  linear
(0 .. 20.794415415867)  log
(-13.2569890828565 .. 0.298489956293335)  log

[download]

There's nothing special about it, as it chooses the distribution that more evenly splits the points over both halves of the interval. So it'll probably choose poorly on the vertical axis of a half-wave rectified sine wave or similar. (I'm guessing that it would choose a log axis instead of linear in that case...)

...roboticus

When your only tool is a hammer, all problems look like your thumb.

In reply to Re^4: Data range detection? by roboticus
in thread Data range detection? by BrowserUk

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