Re: finding local minima/maxima for a discrete array

Do you need to find at what indexes the minima/maxima occur, or just the values? Assuming values for the moment:

  my @minima;
  my @maxima;
  my $prev_cmp = 0;

  for (0 .. $#array - 1) {
    my $cmp = $array[$_] <=> $array[$_+1];
    if ($cmp != $prev_cmp) {
      push @minima, $array[$_] if $cmp < 0;
      push @maxima, $array[$_] if $cmp > 0;
      # when this and next elements are ==, defer checking for
      # minima/maxima till next loop iteration
      $prev_cmp = $cmp if $cmp;
    }
  }
  if (@array) {
    push @minima, $array[-1] if $prev_cmp >= 0;
    push @maxima, $array[-1] if $prev_cmp <= 0;
  }
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~~(untested, probably at least one bug).~~ Then select your top k from @minima and @maxima (or replace the pushes with an insertion sort and do it on the fly.)

Update: wow, seems to actually work. Note that I assume no NaNs in the array (see perlop for the effect of NaNs on <=>) and that the endpoints are considered minima/maxima/both (slight changes would be needed to do otherwise).

Update2: fixed bug when array is empty :), moved $cmp check (with no effect on results) & added a comment

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Re^2: finding local minima/maxima for a discrete array by wind (Priest) on Jul 31, 2007 at 08:24 UTC
You're right ysth, it does seem to work. :) Advice to the OP: It is a good idea for this type of problem to devise your own test suite before you start coding a solution. To demonstrate, here is a test script that I created for ysth's solution. It's not exactly comprehensive, but I attempt to take care of the most obvious of boundary conditions. The way it's coded, it would be easy for you to come up with a list of your own conditions that you want to test for. Or maybe rules that you would like to change. Such as is a point of inflection truly a local min or max? Your test suite can spell out what you expect or desire. use Test::More; use strict; ################################# # Test Data # Each element contains [ [Test Data], [Expected Min], [Expected Max] +] # Note: The reverse of any data, should simply reverse the expected re +sults. my @testdata = ( [# Empty [], [], [], ], [ # One Entry [3], [3], [3], ], [ # Two (Up slope) [2, 4], [2], [4], ], [ # Two (No slope) [3, 3], [3], [3], ], [ # Three (No slope) [4, 4, 4], [4], [4], ], [ # Three (Up slope, beginning point of inflection) [4, 4, 6], [4], [6], ], [ # Three (Up slope, ending point of inflection) [4, 6, 6], [4], [6], ], [ # Three (negative inflection) [3,6,2], [3, 2], [6], ], [ # Three (positive infection) [10, 5, 10], [5], [10, 10], ], [ # Mixed Data # mi Mi m i M i m Mi [qw(1 1 2 3 4 4 3 2 3 4 5 6 6 6 7 8 7 7 7 3 5 6 9 9)], [qw(1 2 3)], [qw(4 8 9)], ], ); # One test each for min and max, and then times two for reverse. plan tests => 2 * (2 * @testdata); ################################# # Tests foreach (@testdata) { my ($data, $min, $max) = @$_; my ($rmin, $rmax) = local_min_max(@$data); is_deeply($rmin, $min, "min of [@$data]"); is_deeply($rmax, $max, "max of [@$data]"); my @reversed = reverse @$data; ($rmin, $rmax) = local_min_max(@reversed); is_deeply($rmin, [reverse @$min], "min of [@reversed]"); is_deeply($rmax, [reverse @$max], "max of [@reversed]"); } ################################# # Functions sub local_min_max { # Boundary Conditions return ([], []) if @_ == 0; return ([@_], [@_]) if @_ == 1; my @array = @_; my @minima; my @maxima; my $prev_cmp = 0; for (0 .. $#array - 1) { my $cmp = $array[$_] <=> $array[$_+1]; if ($cmp && $cmp != $prev_cmp) { push @minima, $array[$_] if $cmp < 0; push @maxima, $array[$_] if $cmp > 0; $prev_cmp = $cmp; } } push @minima, $array[-1] if $prev_cmp >= 0; push @maxima, $array[-1] if $prev_cmp <= 0; return (\@minima, \@maxima); } [download] Ok, now back to less amusing problems. - Miller	[reply] [d/l]

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Re^2: finding local minima/maxima for a discrete array
by wind (Priest) on Jul 31, 2007 at 08:24 UTC

use Test::More;

use strict;

#################################
# Test Data

# Each element contains [ [Test Data], [Expected Min], [Expected Max] 
+]
# Note: The reverse of any data, should simply reverse the expected re
+sults.
my @testdata = (
    [# Empty
        [], [], [],
        ],
    [ # One Entry
        [3], [3], [3],
        ],
    [ # Two (Up slope)
        [2, 4], [2], [4],
        ],
    [ # Two (No slope)
        [3, 3], [3], [3],
        ],
    [ # Three (No slope)
        [4, 4, 4], [4], [4],
        ],
    [ # Three (Up slope, beginning point of inflection)
        [4, 4, 6], [4], [6],
        ],
    [ # Three (Up slope, ending point of inflection)
        [4, 6, 6], [4], [6],
        ],
    [ # Three (negative inflection)
        [3,6,2], [3, 2], [6],
        ],
    [ # Three (positive infection)
        [10, 5, 10], [5], [10, 10],
        ],
    [ # Mixed Data
        #    mi      Mi   m         i     M   i   m      Mi
        [qw(1 1 2 3 4 4 3 2 3 4 5 6 6 6 7 8 7 7 7 3 5 6 9 9)],
        [qw(1 2 3)],
        [qw(4 8 9)],
        ],
);

# One test each for min and max, and then times two for reverse.
plan tests => 2 * (2 * @testdata);


#################################
# Tests

foreach (@testdata) {
    my ($data, $min, $max) = @$_;

    my ($rmin, $rmax) = local_min_max(@$data);
    is_deeply($rmin, $min, "min of [@$data]");
    is_deeply($rmax, $max, "max of [@$data]");

    my @reversed = reverse @$data;
    ($rmin, $rmax) = local_min_max(@reversed);
    is_deeply($rmin, [reverse @$min], "min of [@reversed]");
    is_deeply($rmax, [reverse @$max], "max of [@reversed]");
}

    
#################################
# Functions

sub local_min_max {
    # Boundary Conditions
    return ([], []) if @_ == 0;
    return ([@_], [@_]) if @_ == 1;
    
    my @array = @_;
    
    my @minima;
    my @maxima;
    my $prev_cmp = 0;

    for (0 .. $#array - 1) {
        my $cmp = $array[$_] <=> $array[$_+1];
        if ($cmp && $cmp != $prev_cmp) {
            push @minima, $array[$_] if $cmp < 0;
            push @maxima, $array[$_] if $cmp > 0;
            $prev_cmp = $cmp;
        }
    }
    
    push @minima, $array[-1] if $prev_cmp >= 0;
    push @maxima, $array[-1] if $prev_cmp <= 0;
    
    return (\@minima, \@maxima);
}
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