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].

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>