tye:

Yeah, I knew you weren't trying to find the curve for the sequences. The formula I gave was for minimizing the sum of the square of the difference between series 1 and A * series 2. That's so you could find A, the scaling factor you were looking for.

Having said that, however, when I tried to code it up, I found that I couldn't figure out how to express it as a curve fit problem. So instead I hacked up an iterative approach:

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

my @E1 = (2, 3.23, 7, 9, 11.3479);
my @E2 = (3.3333, 1.433, 8.0577, 9.7344, 13.3377);

my ($Alow, $Ahi, $Astep) =
#       (.5, 5, .1);
#       (0.8, 1.0, 0.025);
#       (0.85, 0.9, 0.005);
        (0.87, 0.88, 0.001);

for (my $A=$Alow; $A <= $Ahi; $A+=$Astep) {
        printf "%7.4f %5.3f\n", $A, current_error($A);
}

sub current_error {
        my $A = shift;
        my $err=0;
        for (my $i=0; $i<@E1; ++$i) {
                my $t = $E1[$i] - $A*$E2[$i];
                $err += $t*$t;
        }
        return $err;
}

[download]

And the last run gave me:

Roboticus@Roboticus-PC ~
$ ./curvefit.pl
 0.8700 5.091
 0.8710 5.088
 0.8720 5.086
 0.8730 5.085
 0.8740 5.084
 0.8750 5.085
 0.8760 5.085
 0.8770 5.087
 0.8780 5.089
 0.8790 5.092
 0.8800 5.096

[download]

So it looks like your multiplier is going to be roughly 0.874. If you need to consider a constant offset, you'll (obviously) have to nest in another loop to vary the constant as well. Since you didn't indicate the need for one, I didn't bother.

...roboticus

In reply to Re^3: Stumped with a math question in my Perl program (log scale) by roboticus
in thread Stumped with a math question in my Perl program by Anonymous Monk

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