require Exporter;
package Math::VecStat;
@Math::VecStat::ISA=qw(Exporter);
@EXPORT_OK=qw(max min maxabs minabs sum average
vecprod ordered convolute
sumbyelement diffbyelement
allequal median);
$Math::VecStat::VERSION = '0.08';
use strict;
sub max {
my $v=ref($_[0]) ? $_[0] : \@_;
my $i=$#{$v};
my $j=$i;
my $m=$v->[$i];
while (--$i >= 0) { if ($v->[$i] > $m) { $m=$v->[$i]; $j=$i; }}
return wantarray ? ($m,$j): $m;
}
sub min {
my $v=ref($_[0]) ? $_[0] : \@_;
my $i=$#{$v};
my $j=$i;
my $m=$v->[$i];
while (--$i >= 0) { if ($v->[$i] < $m) { $m=$v->[$i]; $j=$i; }}
return wantarray ? ($m,$j): $m;
}
sub maxabs {
my $v=ref($_[0]) ? $_[0] : \@_;
my $i=$#{$v};
my $j=$i;
my $m=abs($v->[$i]);
while (--$i >= 0) { if (abs($v->[$i]) > $m) { $m=abs($v->[$i]); $j=$i}}
return (wantarray ? ($m,$j) : $m);
}
sub minabs {
my $v=ref($_[0]) ? $_[0] : \@_;
my $i=$#{$v};
my $j=$i;
my $m=abs($v->[$i]);
while (--$i >= 0) { if (abs($v->[$i]) < $m) { $m=abs($v->[$i]); $j=$i}}
return (wantarray ? ($m,$j) : $m);
}
sub sum {
my $v=ref($_[0]) ? $_[0] : \@_;
my $s=0;
foreach(@{$v}) { $s+=$_; }
return $s;
}
# spinellia@acm.org, handle the empty array case
sub average {
my $v=ref($_[0]) ? $_[0] : \@_;
return undef unless $#{$v} >= 0;
return $#{$v}==-1 ? 0 : sum($v)/(1+$#{$v});
}
sub vecprod {
my $c = shift;
my $v=ref($_[0]) ? $_[0] : \@_;
return undef unless $#{$v} >= 0;
my @result = map( $_ * $c, @{$v} );
return \@result;
}
sub ordered
{
my $v=ref($_[0]) ? $_[0] : \@_;
if( scalar( @{$v} ) < 2 ){ return 1; }
for(my $i=0; $i<$#{$v}; $i++ ){
return 0 if $v->[$i] > $v->[$i+1];
}
return 1;
}
sub allequal
{
my($v,$u) = @_;
return undef unless (defined($v) and defined($u)); # this is controversial
return undef unless ($#{$v} == $#{$u});
my $i= @{$v};
while (--$i >= 0) { return 0 unless( $v->[$i] == $u->[$i]); }
return 1;
}
sub sumbyelement
{
my($v,$u) = @_;
return undef unless ($#{$v} == $#{$u});
my @summed;
my $i= @{$v};
while (--$i >= 0) { $summed[$i] = $v->[$i] + $u->[$i]; }
return \@summed;
}
sub diffbyelement
{
my($v,$u) = @_;
return undef unless ($#{$v} == $#{$u});
my @summed;
my $i= @{$v};
while (--$i >= 0) { $summed[$i] = $v->[$i] - $u->[$i]; }
return \@summed;
}
sub convolute
{
my($v,$u) = @_;
return undef unless ($#{$v} == $#{$u});
my @conv;
my $i= @{$v};
while (--$i >= 0) { $conv[$i] = $v->[$i]*$u->[$i]; }
return \@conv;
}
sub _justToAvoidWarnings
{
my $a = $Math::VecStat::VERSION;
}
sub median
{
my $v=ref($_[0]) ? $_[0] : \@_;
my $n = scalar @{$v};
# generate a list of [value,index] pairs
my @tras = map( [$v->[$_],$_], 0..$#{$v} );
# sort by ascending value, then by original position
# suggested by david@jamesgang.com
my @sorted = sort { ($a->[0] <=> $b->[0])
or ($a->[1] <=> $b->[1]) } @tras;
# find the middle ordinal
my $med = int( $n / 2 );
# when there are several identical median values
# we arbitrarily (but consistently) choose the first one
# in the original array
while( ($med >= 1) && ($sorted[$med]->[0] == $sorted[$med-1]->[0]) ){
$med--;
}
return $sorted[$med];
}
1;
__END__
# $Id: VecStat.pm,v 1.5 1997/02/26 17:20:37 willijar Exp $
=head1 NAME
Math::VecStat - Some basic numeric stats on vectors
=head1 SYNOPSIS
use Math::VecStat qw(max min maxabs minabs sum average);
$max=max(@vector);
$max=max(\@vector);
($max,$imax)=max(@vector);
($max,$imax)=max(\@vector);
$min=min(@vector);
$min=min(\@vector);
($max,$imin)=min(@vector);
($max,$imin)=min(\@vector);
$max=maxabs(@vector);
$max=maxabs(\@vector);
($max,$imax)=maxabs(@vector);
($max,$imax)=maxabs(\@vector);
$min=minabs(@vector);
$min=minabs(\@vector);
($max,$imin)=minabs(@vector);
($max,$imin)=minabs(\@vector);
$sum=sum($v1,$v2,...);
$sum=sum(@vector);
$sum=sum(\@vector);
$average=average($v1,$v2,...);
$av=average(@vector);
$av=average(\@vector);
$ref=vecprod($scalar,\@vector);
$ok=ordered(@vector);
$ok=ordered(\@vector);
$ref=sumbyelement(\@vector1,\@vector2);
$ref=diffbyelement(\@vector1,\@vector2);
$ok=allequal(\@vector1,\@vector2);
$ref=convolute(\@vector1,\@vector2);
=head1 DESCRIPTION
This package provides some basic statistics on numerical
vectors. All the subroutines can take
a reference to the vector to be operated
on. In some cases a copy of the vector is acceptable,
but is not recommended for efficiency.
=over 5
=item max(@vector), max(\@vector)
return the maximum value of given values or vector. In an array
context returns the value and the index in the array where it
occurs.
=item min(@vector), min(\@vector)
return the minimum value of given values or vector, In an array
context returns the value and the index in the array where it
occurs.
=item maxabs(@vector), maxabs(\@vector)
return the maximum value of absolute of the given values or vector. In
an array context returns the value and the index in the array where it
occurs.
=item minabs(@vector), minabs(\@vector)
return the minimum value of the absolute of the given values or
vector. In an array context returns the value and the index in the
array where it occurs.
=item sum($v1,$v2,...), sum(@vector), sum(\@vector)
return the sum of the given values or vector
=item average($v1,$v2,..), average(@vector), average(\@vector)
return the average of the given values or vector
=item vecprod($a,$v1,$v2,..), vecprod($a,@vector), vecprod( $a, \@vector )
return a vector built by multiplying the scalar $a by each element of the
@vector.
=item ordered($v1,$v2,..), ordered(@vector), ordered(\@vector)
return nonzero iff the vector is nondecreasing with respect to its index.
To be used like
if( ordered( $lowBound, $value, $highBound ) ){
instead of the (slightly) more clumsy
if( ($lowBound <= $value) && ($value <= $highBound) ) {
=item sumbyelement( \@array1, \@array2 ), diffbyelement(\@array1,\@array2)
return the element-by-element sum or difference of two
identically-sized vectors. Given
$s = sumbyelement( [10,20,30], [1,2,3] );
$d = diffbyelement( [10,20,30], [1,2,3] );
C<$s> will be C<[11,22,33]>, C<$d> will be C<[9,18,27]>.
=item allequal( \@array1, \@array2 )
returns true if and only if the two arrays are numerically identical.
=item convolute( \@array1, \@array2 )
return a reference to an array containing the element-by-element
product of the two input arrays. I.e.,
$r = convolute( [1,2,3], [-1,2,1] );
returns a reference to
[-1,4,3]
=item median
evaluates the median, i.e. an element which separates the population
in two halves. It returns a reference to a list whose first element
is the median value and the second element is the index of the
median element in the original vector.
$a = Math::VecStat::median( [9,8,7,6,5,4,3,2,1] );
returns the list reference
[ 5, 4 ]
i.e. the median value is 5 and it is found at position 4 of the
original array.
If there are several elements of the array
having the median value, e.g. [1,3,3,3,5]. In this case
we choose always the first element in the original vector
which is a median. In the example, we return [3,1].
=head1 HISTORY
$Log: VecStat.pm,v $
Revision 1.9 2003/04/20 00:49:00 spinellia@acm.org
Perl 5.8 broke test 36, exposing inconsistency in C<median>. Fixed, thanks to david@jamesgang.com.
Revision 1.8 2001/01/26 11:10:00 spinellia@acm.org
Added function median.
Fixed test, thanks to Andreas Marcel Riechert <riechert@pobox.com>
Revision 1.7 2000/10/24 15:28:00 spinellia@acm.org
Added functions allequal diffbyelement
Created a reasonable test suite.
Revision 1.6 2000/06/29 16:06:37 spinellia@acm.org
Added functions vecprod, convolute, sumbyelement
Revision 1.5 1997/02/26 17:20:37 willijar
Added line before pod header so pod2man installs man page correctly
Revision 1.4 1996/02/20 07:53:10 willijar
Added ability to return index in array contex to max and min
functions. Added minabs and maxabs functions.
Thanks to Mark Borges <mdb@cdc.noaa.gov> for these suggestions.
Revision 1.3 1996/01/06 11:03:30 willijar
Fixed stupid bug that crept into looping in min and max functions
Revision 1.2 1995/12/26 09:56:38 willijar
Oops - removed xy data functions.
Revision 1.1 1995/12/26 09:39:07 willijar
Initial revision
=head1 BUGS
Let me know. I welcome any appropriate additions for this package.
=head1 AUTHORS
John A.R. Williams <J.A.R.Williams@aston.ac.uk>
Andrea Spinelli <spinellia@acm.org>
=cut
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