NAME

Math::LinearApprox - fast linear approximation of 2D sequential points

SYNOPSIS

    use Math::LinearApprox qw( linear_approx linear_approx_str );

    # OO style
    my @points = ( 0, 4 );
    my $la = Math::LinearApprox->new();
    my $la = Math::LinearApprox->new(\@points);
    $la->add_point( 2, 1 );
    $la->add_point( 7, 0 );
    print $la->equation_str();
    my ($A, $B) = $la->equation();

    # Procedural style
    my @points = ( 0, 4, 2, 1, 7, 0 );
    print linear_approx_str(\@points);

DESCRIPTION

Typically there are several methods of linear approximation in use to approximate 2D points series, including least squares method. All of them requires a lot of multiplication operations.

I have invented new numerical method which requires less complex instructions and much more suitable for approximation of really huge arrays of data. This method description and comparative analysis will be published in a separate scientific paper soon.

Currently there is a requirement for all the points to be sorted by X axis. Also currently this method uses all the points and does not include any filtering abilities. Hopefully, they will be added soon.

Each point should be specified by $x, $y pair of coordinates. You can either push the points from anywhere into the model -- they are not being saved AS-IS -- or populate the model with @points = ($x, $y, ...) reference.

SUBROUTINES

add_point

To fill the model with data one can call $obj->add_point( $x, $y ). This function returns nothing meaningful. Perl will cast anything illegal passed as $x, $y into numbers. So it is your responsibility to validate your points in advance.

$x is X coordinate of the point.

$y is Y coordinate of the point.

equation

Since any line that is not perpendicular to X axis could be represented in a form of y = A * x + B, then $obj->equation() returns ($A, $B) coefficients. The method returns undef unless the model could not be represented in such a form.

equation_str

The $obj->equation_str returns stringified equation of the model either in form "y = A * x + B", or "x = X" in case all points are vertically distributed. The method dies unless the model could not be approximated. In most cases it is due to absense of points in the model.

linear_approx

The linear_approx( \@points ) is a procedural style alias for new( \@points )->equation().

linear_approx_str

The linear_approx_str( \@points ) is a procedural style alias for new( \@points )->equation_str().

new

$obj = Math::LinearApprox->new() is an object constructor that will instantiate the approximation model. The only parameter is optional -- reference to array of points: [$x1, $y1, $x2, $y2, ...].

AUTHOR

Sergei Zhmylev, <zhmylove@cpan.org>

BUGS

Please report any bugs or feature requests to official GitHub page at https://github.com/zhmylove/math-linearapprox. You also can use official CPAN bugtracker by reporting to bug-math-linearapprox at rt.cpan.org, or through the web interface at https://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math-LinearApprox. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

INSTALLATION

To install this module, run the following commands:

    $ perl Makefile.PL
    $ make
    $ make test
    $ make install

LICENSE AND COPYRIGHT

This software is Copyright (c) 2021 by Sergei Zhmylev.

This is free software, licensed under:

  The Artistic License 2.0 (GPL Compatible)

cpanm Math::LinearApprox

perl -MCPAN -e shell
install Math::LinearApprox