NAME

           Math::VecStat - Some basic numeric stats on vectors

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);

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.

       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.

       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.

       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.

       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.

       sum($v1,$v2,...), sum(@vector), sum(\@vector)
            return the sum of the given values or vector

       average($v1,$v2,..), average(@vector), average(\@vector)
            return the average of the given values or vector

       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.

       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) ) {

       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] );

            $s will be "[11,22,33]", $d will be "[9,18,27]".

       allequal( \@array1, \@array2 )
            returns true if and only if the two arrays are numerically identical.

       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]

       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].  =back =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

BUGS

       Let me know. I welcome any appropriate additions for this package.

AUTHORS

       John A.R. Williams <J.A.R.Williams@aston.ac.uk> Andrea Spinelli <spinellia@acm.org>