Polynomial regression: Difference between revisions
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This task is intended as a subtask for [[Measure relative performance of sorting algorithms implementations]]. |
This task is intended as a subtask for [[Measure relative performance of sorting algorithms implementations]]. |
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=={{header|Ada}}== |
=={{header|Ada}}== |
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2.000000 |
2.000000 |
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3.000000</pre> |
3.000000</pre> |
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=={{header|C sharp|C#}}== |
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{{libheader|Math.Net}} |
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<lang csharp> public static double[] Polyfit(double[] x, double[] y, int degree) |
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{ |
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// Vandermonde matrix |
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var v = new DenseMatrix(x.Length, degree + 1); |
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for (int i = 0; i < v.RowCount; i++) |
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for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j); |
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var yv = new DenseVector(y).ToColumnMatrix(); |
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QR qr = v.QR(); |
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// Math.Net doesn't have an "economy" QR, so: |
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// cut R short to square upper triangle, then recompute Q |
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var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1); |
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var q = v.Multiply(r.Inverse()); |
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var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv)); |
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return p.Column(0).ToArray(); |
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}</lang> |
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Example: |
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<lang C sharp> static void Main(string[] args) |
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{ |
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const int degree = 2; |
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var x = new[] {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}; |
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var y = new[] {1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0}; |
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var p = Polyfit(x, y, degree); |
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foreach (var d in p) Console.Write("{0} ",d); |
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Console.WriteLine(); |
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for (int i = 0; i < x.Length; i++ ) |
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Console.WriteLine("{0} => {1} diff {2}", x[i], Polyval(p,x[i]), y[i] - Polyval(p,x[i])); |
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Console.ReadKey(true); |
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}</lang> |
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=={{header|C++}}== |
=={{header|C++}}== |
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9 262 262.0 |
9 262 262.0 |
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10 321 321.0</pre> |
10 321 321.0</pre> |
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=={{header|C#|C sharp}}== |
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{{libheader|Math.Net}} |
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<lang csharp> public static double[] Polyfit(double[] x, double[] y, int degree) |
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{ |
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// Vandermonde matrix |
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var v = new DenseMatrix(x.Length, degree + 1); |
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for (int i = 0; i < v.RowCount; i++) |
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for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j); |
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var yv = new DenseVector(y).ToColumnMatrix(); |
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QR qr = v.QR(); |
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// Math.Net doesn't have an "economy" QR, so: |
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// cut R short to square upper triangle, then recompute Q |
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var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1); |
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var q = v.Multiply(r.Inverse()); |
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var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv)); |
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return p.Column(0).ToArray(); |
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}</lang> |
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Example: |
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<lang C sharp> static void Main(string[] args) |
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{ |
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const int degree = 2; |
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var x = new[] {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}; |
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var y = new[] {1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0}; |
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var p = Polyfit(x, y, degree); |
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foreach (var d in p) Console.Write("{0} ",d); |
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Console.WriteLine(); |
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for (int i = 0; i < x.Length; i++ ) |
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Console.WriteLine("{0} => {1} diff {2}", x[i], Polyval(p,x[i]), y[i] - Polyval(p,x[i])); |
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Console.ReadKey(true); |
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}</lang> |
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=={{header|Common Lisp}}== |
=={{header|Common Lisp}}== |
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1 6 17 34 57 86 121 162 209 262 321 |
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.</pre> |
An approximating polynomial for your dataset is 3x^2 + 2x + 1.</pre> |
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=={{header|Perl 6}}== |
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We'll use a Clifford algebra library. |
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<lang perl6>use Clifford; |
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constant @x1 = <0 1 2 3 4 5 6 7 8 9 10>; |
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constant @y = <1 6 17 34 57 86 121 162 209 262 321>; |
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constant $x0 = [+] @e[^@x1]; |
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constant $x1 = [+] @x1 Z* @e; |
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constant $x2 = [+] @x1 »**» 2 Z* @e; |
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constant $y = [+] @y Z* @e; |
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my $J = $x1 ∧ $x2; |
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my $I = $x0 ∧ $J; |
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my $I2 = ($I·$I.reversion).Real; |
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.say for |
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(($y ∧ $J)·$I.reversion)/$I2, |
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(($y ∧ ($x2 ∧ $x0))·$I.reversion)/$I2, |
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(($y ∧ ($x0 ∧ $x1))·$I.reversion)/$I2;</lang> |
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{{out}} |
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<pre>1 |
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2 |
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3 |
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</pre> |
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=={{header|Phix}}== |
=={{header|Phix}}== |
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IupMainLoop() |
IupMainLoop() |
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IupClose()</lang> |
IupClose()</lang> |
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=={{header|PowerShell}}== |
=={{header|PowerShell}}== |
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<lang PowerShell> |
<lang PowerShell> |
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| Line 1,644: | Line 1,615: | ||
3 1.99999999999998 1.00000000000005 |
3 1.99999999999998 1.00000000000005 |
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</pre> |
</pre> |
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=={{header|Python}}== |
=={{header|Python}}== |
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{{out}} |
{{out}} |
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[[File:polyreg-racket.png]] |
[[File:polyreg-racket.png]] |
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=={{header|Raku}}== |
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(formerly Perl 6) |
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We'll use a Clifford algebra library. |
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<lang perl6>use Clifford; |
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constant @x1 = <0 1 2 3 4 5 6 7 8 9 10>; |
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constant @y = <1 6 17 34 57 86 121 162 209 262 321>; |
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constant $x0 = [+] @e[^@x1]; |
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constant $x1 = [+] @x1 Z* @e; |
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constant $x2 = [+] @x1 »**» 2 Z* @e; |
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constant $y = [+] @y Z* @e; |
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my $J = $x1 ∧ $x2; |
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my $I = $x0 ∧ $J; |
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my $I2 = ($I·$I.reversion).Real; |
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.say for |
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(($y ∧ $J)·$I.reversion)/$I2, |
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(($y ∧ ($x2 ∧ $x0))·$I.reversion)/$I2, |
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(($y ∧ ($x0 ∧ $x1))·$I.reversion)/$I2;</lang> |
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{{out}} |
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<pre>1 |
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2 |
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3 |
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</pre> |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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}</lang> |
}</lang> |
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=={{header|Sidef}}== |
=={{header|Sidef}}== |
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{{trans|Ruby}} |
{{trans|Ruby}} |
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Degrees of freedom: 8 |
Degrees of freedom: 8 |
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Standard error of y estimate: 2,79482284961344E-14 </pre> |
Standard error of y estimate: 2,79482284961344E-14 </pre> |
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=={{header|zkl}}== |
=={{header|zkl}}== |
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Using the GNU Scientific Library |
Using the GNU Scientific Library |
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