Polynomial regression: Difference between revisions

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=={{header|Perl}}==

This script depends on the Math::MatrixReal CPAN module to compute matrix determinants.

This script depends on the <tt>Math::MatrixReal</tt> CPAN module to compute matrix determinants.

<lang Perl>use strict;

#!bin/usr/perl

use strict;

use warnings;

use 5.020;

#This is a script to calculate an equation for a given set of coordinates.

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=pod

Step 1: Get each x coordinate all at once (delimited by " ") and each for y at once

on the next prompt in the same format (delimited by " ").

=cut

sub getPairs() {

my $buffer = <STDIN>;

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#This whole thing depends on the number of x's being the same as the number of y's

my $pairs = scalar(@x);

=pod

Step 2: Devise the base equation of our polynomial using the following idea

There is some polynomial of degree n (n == number of pairs - 1) such that

f(x)=ax^n + bx^(n-1) + ... yx + z

=cut

#Create an array of coefficients and their degrees with the format ("coefficent degree")

my @alphabet;

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=pod

Step 3: Using the array of coeffs and their degrees, set up individual equations solving for

each coordinate pair. Why put it in this format? It interfaces witht he Math::MatrixReal package better this way.

=cut

my @coeffs;

for(my $count = 0; $count < $pairs; $count++) {

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$row .= ("$_\n");

}

=pod

Step 4: We now have rows of x's raised to powers. With this in mind, we create a coefficient matrix.

=cut

my $matrix = Math::MatrixReal->new_from_string($row);

my $buffMatrix = $matrix->new_from_string($row);

=pod

Step 5: Now that we've gotten the matrix to do what we want it to do, we need to calculate the various determinants of the matrices

=cut

my $coeffDet = $matrix->det();

=pod

Step 6: Now that we have the determinant of the coefficient matrix, we need to find the determinants of the coefficient matrix with each column (1 at a time) replaced with the y values.

=cut

#NOTE: Unlike in Perl, matrix indices start at 1, not 0.

for(my $rows = my $column = 1; $column <= $pairs; $column++) {

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=pod

Step 7: Now that we've found the values of a, b, ... y, z of the original polynomial, it's time to form our polynomial!

=cut

my $polynomial;

for(my $i = 0; $i < $pairs-1; $i++) {

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</lang>

⚫

<pre>Please enter the values for the x coordinates, each delimited by a space. (Ex: 0 1 2 3)

<pre>

⚫

Please enter the values for the x coordinates, each delimited by a space. (Ex: 0 1 2 3)

0 1 2 3 4 5 6 7 8 9 10

Please enter the values for the y coordinates, each delimited by a space. (Ex: 0 1 2 3)

1 6 17 34 57 86 121 162 209 262 321

An approximating polynomial for your dataset is 3x^2 + 2x + 1.

An approximating polynomial for your dataset is 3x^2 + 2x + 1.</pre>

</pre>

=={{header|Perl 6}}==