Polynomial regression: Difference between revisions
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<lang parigp>lsf(X,Y,n)=my(M=matrix(#X,n,i,j,X[i]^(j-1))); Polrev(matsolve(M~*M,M~*Y~) |
<lang parigp>lsf(X,Y,n)=my(M=matrix(#X,n,i,j,X[i]^(j-1))); Polrev(matsolve(M~*M,M~*Y~) |
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lsf([0..10], [1,6,17,34,57,86,121,162,209,262,321], 3)</lang> |
lsf([0..10], [1,6,17,34,57,86,121,162,209,262,321], 3)</lang> |
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=={{header|Perl}}== |
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This script depends on the Math::MatrixReal CPAN module to compute matrix determinants. |
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<lang Perl> |
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#!bin/usr/perl |
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use strict; |
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use warnings; |
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use 5.020; |
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#This is a script to calculate an equation for a given set of coordinates. |
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#Input will be taken in sets of x and y. It can handle a grand total of 26 pairs. |
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#For matrix functions, we depend on the Math::MatrixReal package. |
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use Math::MatrixReal; |
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=pod |
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Step 1: Get each x coordinate all at once (delimited by " ") and each for y at once |
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on the next prompt in the same format (delimited by " "). |
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=cut |
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sub getPairs() { |
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my $buffer = <STDIN>; |
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chomp($buffer); |
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return split(" ", $buffer); |
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} |
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say("Please enter the values for the x coordinates, each delimited by a space. \(Ex: 0 1 2 3\)"); |
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my @x = getPairs(); |
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say("Please enter the values for the y coordinates, each delimited by a space. \(Ex: 0 1 2 3\)"); |
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my @y = getPairs(); |
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#This whole thing depends on the number of x's being the same as the number of y's |
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my $pairs = scalar(@x); |
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=pod |
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Step 2: Devise the base equation of our polynomial using the following idea |
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There is some polynomial of degree n (n == number of pairs - 1) such that |
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f(x)=ax^n + bx^(n-1) + ... yx + z |
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=cut |
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#Create an array of coefficients and their degrees with the format ("coefficent degree") |
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my @alphabet; |
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my @degrees; |
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for(my $alpha = "a", my $degree = $pairs - 1; $degree >= 0; $degree--, $alpha++) { |
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push(@alphabet, "$alpha"); |
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push(@degrees, "$degree"); |
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} |
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=pod |
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Step 3: Using the array of coeffs and their degrees, set up individual equations solving for |
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each coordinate pair. Why put it in this format? It interfaces witht he Math::MatrixReal package better this way. |
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=cut |
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my @coeffs; |
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for(my $count = 0; $count < $pairs; $count++) { |
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my $buffer = "[ "; |
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foreach (@degrees) { |
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$buffer .= (($x[$count] ** $_) . " "); |
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} |
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push(@coeffs, ($buffer . "]")); |
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} |
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my $row; |
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foreach (@coeffs) { |
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$row .= ("$_\n"); |
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} |
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=pod |
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Step 4: We now have rows of x's raised to powers. With this in mind, we create a coefficient matrix. |
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=cut |
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my $matrix = Math::MatrixReal->new_from_string($row); |
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my $buffMatrix = $matrix->new_from_string($row); |
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=pod |
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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 |
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=cut |
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my $coeffDet = $matrix->det(); |
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=pod |
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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. |
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=cut |
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#NOTE: Unlike in Perl, matrix indices start at 1, not 0. |
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for(my $rows = my $column = 1; $column <= $pairs; $column++) { |
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#Reassign the values in the current column to the y values |
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foreach (@y) { |
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$buffMatrix->assign($rows, $column, $_); |
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$rows++; |
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} |
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#Find the values for the variables a, b, ... y, z in the original polynomial |
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#To round the difference of the determinants, I had to get creative |
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my $buffDet = $buffMatrix->det() / $coeffDet; |
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my $tempDet = int(abs($buffDet) + .5); |
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$alphabet[$column - 1] = $buffDet >= 0 ? $tempDet : 0 - $tempDet; |
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#Reset the buffer matrix and the row counter |
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$buffMatrix = $matrix->new_from_string($row); |
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$rows = 1; |
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} |
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=pod |
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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! |
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=cut |
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my $polynomial; |
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for(my $i = 0; $i < $pairs-1; $i++) { |
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if($alphabet[$i] == 0) { |
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next; |
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} |
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if($alphabet[$i] == 1) { |
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$polynomial .= ($degrees[$i] . " + "); |
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} |
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if($degrees[$i] == 1) { |
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$polynomial .= ($alphabet[$i] . "x" . " + "); |
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} |
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else { |
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$polynomial .= ($alphabet[$i] . "x^" . $degrees[$i] . " + "); |
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} |
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} |
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#Now for the last piece of the poly: the x-intercept. |
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$polynomial .= $alphabet[scalar(@alphabet)-1]; |
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print("An approximating polynomial for your dataset is $polynomial.\n"); |
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</lang> |
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{{output}} |
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<pre> |
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Please enter the values for the x coordinates, each delimited by a space. (Ex: 0 1 2 3) |
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0 1 2 3 4 5 6 7 8 9 10 |
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Please enter the values for the y coordinates, each delimited by a space. (Ex: 0 1 2 3) |
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1 6 17 34 57 86 121 162 209 262 321 |
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An approximating polynomial for your dataset is 3x^2 + 2x + 1. |
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</pre> |
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=={{header|Python}}== |
=={{header|Python}}== |