After writing this response I realized that you might be trying to calculate the least squares fit for multiple data sets at the same time. If you are, then the advice I gave isn't very useful. It turns out that closures might not be such a bad idea after all. Here is my attempt to solve the problem using closures.

#! /usr/bin/perl -w 
use strict;

# Create an array of closures
my @LS_closures = ( 
        create_LS_closure(),
        create_LS_closure(),
    );

while( <> ) {
    my ( $x1, $y1, $x2, $y2 ) = split;
    
    # add the current data to the closure
    $LS_closures[0]{add}->( $x1, $y1 );
    $LS_closures[1]{add}->( $x2, $y2 );
    
}

# calculate the least squares coefficient
my ( $a, $b ) = $LS_closures[0]{calcCoefs}->();
print "for the first set of data a = $a; b = $b\n";

( $a, $b ) = $LS_closures[1]{calcCoefs}->();
print "for the second set of data a = $a; b = $b\n";

# -----------------------------------------------
# The closure generating subroutine
sub create_LS_closure {

    # these variable are unique to each closure 
    # created
    my $sum_x = 0;
    my $sum_y = 0;
    my $sum_x2 = 0;
    my $sum_xy = 0;
    my $n = 0;
    
    return { 

        # This is the anonymous function for adding
        # data a to the least squares fit
        add => sub {
            my ($x, $y) = @_;
        
            $sum_x += $x;
            $sum_y += $y;
            $sum_x2 += $x * $x;
            $sum_xy += $x * $y;
            $n++;
        },
        
        # This is the anonymous function for
        # computing the coefficients of the
        # least squares fit
        calcCoefs => sub {
            my $a = ( $sum_y * $sum_x2 - $sum_x * $sum_xy ) /
                          ( $n * $sum_x2 - $sum_x * $sum_x );  
            my $b =     ( $n * $sum_xy - $sum_x * $sum_y ) /
                          ( $n * $sum_x2 - $sum_x * $sum_x );  
            return ($a, $b);
        }
    }
}
[download]

When given the following input

-2 -3 -2  3
-1 -1 -1  1
 0  1  0 -1
 1  3  1 -3
 2  5  2 -5
 3  7  3 -7

this program outputs

for the first set of data a = 1; b = 2
for the second set of data a = -1; b = -2

which is exactly correct

The calling code appears to be quite flexible, and the closure could probably be moved to a module. So it appears that using closures to calculate least squares fits might not be such a bad idea!

Comments? Questions?

enjoy

meta4

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