tasks a-s

Task/Polynomial-regression/0DESCRIPTION

@@ -0,0 +1,11 @@
+Find an approximating polynom of known degree for a given data.
+
+Example:
+For input data:
+ x = {0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10};
+ y = {1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321};
+The approximating polynom is:
+ 3 x<sup>2</sup> + 2 x + 1
+Here, the polynom's coefficients are (3, 2, 1).
+
+This task is intended as a subtask for [[Measure relative performance of sorting algorithms implementations]].

Task/Polynomial-regression/1META.yaml

@@ -0,0 +1,2 @@
+---
+note: Mathematical operations|Matrices

Task/Polynomial-regression/ALGOL-68/polynomial-regression.alg

@@ -0,0 +1,114 @@
+MODE FIELD = REAL;
+
+MODE
+  VEC = [0]FIELD,
+  MAT = [0,0]FIELD;
+
+PROC VOID raise index error := VOID: (
+  print(("stop", new line));
+  stop
+);
+
+COMMENT from http://rosettacode.org/wiki/Matrix_Transpose#ALGOL_68 END COMMENT
+OP ZIP = ([,]FIELD in)[,]FIELD:(
+  [2 LWB in:2 UPB in,1 LWB in:1UPB in]FIELD out;
+  FOR i FROM LWB in TO UPB in DO
+     out[,i]:=in[i,]
+  OD;
+  out
+);
+
+COMMENT from http://rosettacode.org/wiki/Matrix_multiplication#ALGOL_68 END COMMENT
+OP * = (VEC a,b)FIELD: ( # basically the dot product #
+    FIELD result:=0;
+    IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
+    FOR i FROM LWB a TO UPB a DO result+:= a[i]*b[i] OD;
+    result
+  );
+
+OP * = (VEC a, MAT b)VEC: ( # overload vector times matrix #
+    [2 LWB b:2 UPB b]FIELD result;
+    IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
+    FOR j FROM 2 LWB b TO 2 UPB b DO result[j]:=a*b[,j] OD;
+    result
+  );
+
+OP * = (MAT a, b)MAT: ( # overload matrix times matrix #
+     [LWB a:UPB a, 2 LWB b:2 UPB b]FIELD result;
+     IF 2 LWB a/=LWB b OR 2 UPB a/=UPB b THEN raise index error FI;
+     FOR k FROM LWB result TO UPB result DO result[k,]:=a[k,]*b OD;
+     result
+   );
+
+COMMENT from http://rosettacode.org/wiki/Pyramid_of_numbers#ALGOL_68 END COMMENT
+OP / = (VEC a, MAT b)VEC: ( # vector division #
+  [LWB a:UPB a,1]FIELD transpose a;
+  transpose a[,1]:=a;
+  (transpose a/b)[,1]
+);
+
+OP / = (MAT a, MAT b)MAT:( # matrix division #
+  [LWB b:UPB b]INT p ;
+  INT sign;
+  [,]FIELD lu = lu decomp(b, p, sign);
+  [LWB a:UPB a, 2 LWB a:2 UPB a]FIELD out;
+  FOR col FROM 2 LWB a TO 2 UPB a DO
+    out[,col] := lu solve(b, lu, p, a[,col]) [@LWB out[,col]]
+  OD;
+  out
+);
+
+FORMAT int repr = $g(0)$,
+       real repr = $g(-7,4)$;
+
+PROC fit =  (VEC x, y, INT order)VEC:
+BEGIN
+   [0:order, LWB x:UPB x]FIELD a;  # the plane #
+   FOR i FROM 2 LWB a TO 2 UPB a  DO
+      FOR j FROM LWB a TO UPB a DO
+         a [j, i] := x [i]**j
+      OD
+   OD;
+   ( y * ZIP a ) / ( a * ZIP a )
+END # fit #;
+
+PROC print polynomial = (VEC x)VOID: (
+   BOOL empty := TRUE;
+   FOR i FROM UPB x BY -1 TO LWB x DO
+     IF x[i] NE 0 THEN
+       IF x[i] > 0 AND NOT empty THEN print ("+") FI;
+       empty := FALSE;
+       IF x[i] NE 1 OR i=0 THEN
+         IF ENTIER x[i] = x[i] THEN
+           printf((int repr, x[i]))
+         ELSE
+           printf((real repr, x[i]))
+         FI
+       FI;
+       CASE i+1 IN
+         SKIP,print(("x"))
+       OUT
+         printf(($"x**"g(0)$,i))
+       ESAC
+     FI
+   OD;
+   IF empty THEN print("0") FI;
+   print(new line)
+);
+
+fitting: BEGIN
+   VEC c =
+          fit
+          (  (0.0, 1.0,  2.0,  3.0,  4.0,  5.0,   6.0,   7.0,   8.0,   9.0,  10.0),
+             (1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0),
+             2
+          );
+   print polynomial(c);
+   VEC d =
+          fit
+          ( (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
+            (2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0),
+            2
+          );
+   print polynomial(d)
+END # fitting #

Task/Polynomial-regression/Ada/polynomial-regression-1.ada

@@ -0,0 +1,12 @@
+with Ada.Numerics.Real_Arrays;  use Ada.Numerics.Real_Arrays;
+
+function Fit (X, Y : Real_Vector; N : Positive) return Real_Vector is
+   A : Real_Matrix (0..N, X'Range);  -- The plane
+begin
+   for I in A'Range (2) loop
+      for J in A'Range (1) loop
+         A (J, I) := X (I)**J;
+      end loop;
+   end loop;
+   return Solve (A * Transpose (A), A * Y);
+end Fit;

Task/Polynomial-regression/Ada/polynomial-regression-2.ada

@@ -0,0 +1,15 @@
+with Fit;
+with Ada.Float_Text_IO;  use Ada.Float_Text_IO;
+
+procedure Fitting is
+   C : constant Real_Vector :=
+          Fit
+          (  (0.0, 1.0,  2.0,  3.0,  4.0,  5.0,   6.0,   7.0,   8.0,   9.0,  10.0),
+             (1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0),
+             2
+          );
+begin
+   Put (C (0), Aft => 3, Exp => 0);
+   Put (C (1), Aft => 3, Exp => 0);
+   Put (C (2), Aft => 3, Exp => 0);
+end Fitting;

Task/Polynomial-regression/BBC-BASIC/polynomial-regression.bbc

@@ -0,0 +1,49 @@
+      INSTALL @lib$+"ARRAYLIB"
+
+      Max% = 10000
+      DIM vector(5), matrix(5,5)
+      DIM x(Max%), x2(Max%), x3(Max%), x4(Max%), x5(Max%)
+      DIM x6(Max%), x7(Max%), x8(Max%), x9(Max%), x10(Max%)
+      DIM y(Max%), xy(Max%), x2y(Max%), x3y(Max%), x4y(Max%), x5y(Max%)
+
+      npts% = 11
+      x() = 0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10
+      y() = 1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321
+
+      sum_x = SUM(x())
+      x2()  = x() * x()   : sum_x2  = SUM(x2())
+      x3()  = x() * x2()  : sum_x3  = SUM(x3())
+      x4()  = x2() * x2() : sum_x4  = SUM(x4())
+      x5()  = x2() * x3() : sum_x5  = SUM(x5())
+      x6()  = x3() * x3() : sum_x6  = SUM(x6())
+      x7()  = x3() * x4() : sum_x7  = SUM(x7())
+      x8()  = x4() * x4() : sum_x8  = SUM(x8())
+      x9()  = x4() * x5() : sum_x9  = SUM(x9())
+      x10() = x5() * x5() : sum_x10 = SUM(x10())
+
+      sum_y = SUM(y())
+      xy()  = x() * y()   : sum_xy  = SUM(xy())
+      x2y() = x2() * y()  : sum_x2y = SUM(x2y())
+      x3y() = x3() * y()  : sum_x3y = SUM(x3y())
+      x4y() = x4() * y()  : sum_x4y = SUM(x4y())
+      x5y() = x5() * y()  : sum_x5y = SUM(x5y())
+
+      matrix() = \
+      \ npts%,  sum_x,   sum_x2,  sum_x3,  sum_x4,  sum_x5, \
+      \ sum_x,  sum_x2,  sum_x3,  sum_x4,  sum_x5,  sum_x6, \
+      \ sum_x2, sum_x3,  sum_x4,  sum_x5,  sum_x6,  sum_x7, \
+      \ sum_x3, sum_x4,  sum_x5,  sum_x6,  sum_x7,  sum_x8, \
+      \ sum_x4, sum_x5,  sum_x6,  sum_x7,  sum_x8,  sum_x9, \
+      \ sum_x5, sum_x6,  sum_x7,  sum_x8,  sum_x9,  sum_x10
+
+      vector() = \
+      \ sum_y,  sum_xy,  sum_x2y, sum_x3y, sum_x4y, sum_x5y
+
+      PROC_invert(matrix())
+      vector() = matrix().vector()
+
+      @% = &2040A
+      PRINT "Polynomial coefficients = "
+      FOR term% = 5 TO 0 STEP -1
+        PRINT ;vector(term%) " * x^" STR$(term%)
+      NEXT

Task/Polynomial-regression/C-sharp/polynomial-regression-1.cs

@@ -0,0 +1,15 @@
+        public static double[] Polyfit(double[] x, double[] y, int degree)
+        {
+            // Vandermonde matrix
+            var v = new DenseMatrix(x.Length, degree + 1);
+            for (int i = 0; i < v.RowCount; i++)
+                for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j);
+            var yv = new DenseVector(y).ToColumnMatrix();
+            QR qr = v.QR();
+            // Math.Net doesn't have an "economy" QR, so:
+            // cut R short to square upper triangle, then recompute Q
+            var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1);
+            var q = v.Multiply(r.Inverse());
+            var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv));
+            return p.Column(0).ToArray();
+        }

Task/Polynomial-regression/C-sharp/polynomial-regression-2.cs

@@ -0,0 +1,12 @@
+        static void Main(string[] args)
+        {
+            const int degree = 2;
+            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};
+            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};
+            var p = Polyfit(x, y, degree);
+            foreach (var d in p) Console.Write("{0} ",d);
+            Console.WriteLine();
+            for (int i = 0; i < x.Length; i++ )
+                Console.WriteLine("{0} => {1} diff {2}", x[i], Polyval(p,x[i]), y[i] - Polyval(p,x[i]));
+            Console.ReadKey(true);
+        }

Task/Polynomial-regression/C/polynomial-regression-1.c

@@ -0,0 +1,8 @@
+#ifndef _POLIFITGSL_H
+#define _POLIFITGSL_H
+#include <gsl/gsl_multifit.h>
+#include <stdbool.h>
+#include <math.h>
+bool polynomialfit(int obs, int degree,
+		   double *dx, double *dy, double *store); /* n, p */
+#endif

Task/Polynomial-regression/C/polynomial-regression-2.c

@@ -0,0 +1,42 @@
+#include "polifitgsl.h"
+
+bool polynomialfit(int obs, int degree,
+		   double *dx, double *dy, double *store) /* n, p */
+{
+  gsl_multifit_linear_workspace *ws;
+  gsl_matrix *cov, *X;
+  gsl_vector *y, *c;
+  double chisq;
+
+  int i, j;
+
+  X = gsl_matrix_alloc(obs, degree);
+  y = gsl_vector_alloc(obs);
+  c = gsl_vector_alloc(degree);
+  cov = gsl_matrix_alloc(degree, degree);
+
+  for(i=0; i < obs; i++) {
+    gsl_matrix_set(X, i, 0, 1.0);
+    for(j=0; j < degree; j++) {
+      gsl_matrix_set(X, i, j, pow(dx[i], j));
+    }
+    gsl_vector_set(y, i, dy[i]);
+  }
+
+  ws = gsl_multifit_linear_alloc(obs, degree);
+  gsl_multifit_linear(X, y, c, cov, &chisq, ws);
+
+  /* store result ... */
+  for(i=0; i < degree; i++)
+  {
+    store[i] = gsl_vector_get(c, i);
+  }
+
+  gsl_multifit_linear_free(ws);
+  gsl_matrix_free(X);
+  gsl_matrix_free(cov);
+  gsl_vector_free(y);
+  gsl_vector_free(c);
+  return true; /* we do not "analyse" the result (cov matrix mainly)
+		  to know if the fit is "good" */
+}

Task/Polynomial-regression/C/polynomial-regression-3.c

@@ -0,0 +1,21 @@
+#include <stdio.h>
+
+#include "polifitgsl.h"
+
+#define NP 11
+double x[] = {0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10};
+double y[] = {1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321};
+
+#define DEGREE 3
+double coeff[DEGREE];
+
+int main()
+{
+  int i;
+
+  polynomialfit(NP, DEGREE, x, y, coeff);
+  for(i=0; i < DEGREE; i++) {
+    printf("%lf\n", coeff[i]);
+  }
+  return 0;
+}

Task/Polynomial-regression/Common-Lisp/polynomial-regression-1.lisp

@@ -0,0 +1,9 @@
+;; Least square fit of a polynomial of order n the x-y-curve.
+(defun polyfit (x y n)
+  (let* ((m (cadr (array-dimensions x)))
+         (A (make-array `(,m ,(+ n 1)) :initial-element 0)))
+    (loop for i from 0 to (- m 1) do
+          (loop for j from 0 to n do
+                (setf (aref A i j)
+                      (expt (aref x 0 i) j))))
+    (lsqr A (mtp y))))

Task/Polynomial-regression/Common-Lisp/polynomial-regression-2.lisp

@@ -0,0 +1,5 @@
+(let ((x (make-array '(1 11) :initial-contents '((0 1 2 3 4 5 6 7 8 9 10))))
+      (y (make-array '(1 11) :initial-contents '((1 6 17 34 57 86 121 162 209 262 321)))))
+  (polyfit x y 2))
+
+#2A((0.9999999999999759d0) (2.000000000000005d0) (3.0d0))

Task/Polynomial-regression/Fortran/polynomial-regression-1.f

@@ -0,0 +1,64 @@
+module fitting
+contains
+
+  function polyfit(vx, vy, d)
+    implicit none
+    integer, intent(in)                   :: d
+    integer, parameter                    :: dp = selected_real_kind(15, 307)
+    real(dp), dimension(d+1)              :: polyfit
+    real(dp), dimension(:), intent(in)    :: vx, vy
+
+    real(dp), dimension(:,:), allocatable :: X
+    real(dp), dimension(:,:), allocatable :: XT
+    real(dp), dimension(:,:), allocatable :: XTX
+
+    integer :: i, j
+
+    integer     :: n, lda, lwork
+    integer :: info
+    integer, dimension(:), allocatable :: ipiv
+    real(dp), dimension(:), allocatable :: work
+
+    n = d+1
+    lda = n
+    lwork = n
+
+    allocate(ipiv(n))
+    allocate(work(lwork))
+    allocate(XT(n, size(vx)))
+    allocate(X(size(vx), n))
+    allocate(XTX(n, n))
+
+    ! prepare the matrix
+    do i = 0, d
+       do j = 1, size(vx)
+          X(j, i+1) = vx(j)**i
+       end do
+    end do
+
+    XT  = transpose(X)
+    XTX = matmul(XT, X)
+
+    ! calls to LAPACK subs DGETRF and DGETRI
+    call DGETRF(n, n, XTX, lda, ipiv, info)
+    if ( info /= 0 ) then
+       print *, "problem"
+       return
+    end if
+    call DGETRI(n, XTX, lda, ipiv, work, lwork, info)
+    if ( info /= 0 ) then
+       print *, "problem"
+       return
+    end if
+
+    polyfit = matmul( matmul(XTX, XT), vy)
+
+    deallocate(ipiv)
+    deallocate(work)
+    deallocate(X)
+    deallocate(XT)
+    deallocate(XTX)
+
+  end function
+
+end module

Task/Polynomial-regression/Fortran/polynomial-regression-2.f

@@ -0,0 +1,19 @@
+program PolynomalFitting
+  use fitting
+  implicit none
+
+  ! let us test it
+  integer, parameter      :: degree = 2
+  integer, parameter      :: dp = selected_real_kind(15, 307)
+  integer                 :: i
+  real(dp), dimension(11) :: x = (/ (i,i=0,10) /)
+  real(dp), dimension(11) :: y = (/ 1,   6,  17,  34, &
+                                   57,  86, 121, 162, &
+                                   209, 262, 321 /)
+  real(dp), dimension(degree+1) :: a
+
+  a = polyfit(x, y, degree)
+
+  write (*, '(F9.4)') a
+
+end program

Task/Polynomial-regression/GAP/polynomial-regression.gap

@@ -0,0 +1,12 @@
+PolynomialRegression := function(x, y, n)
+	local a;
+	a := List([0 .. n], i -> List(x, s -> s^i));
+	return TransposedMat((a * TransposedMat(a))^-1 * a * TransposedMat([y]))[1];
+end;
+
+x := [0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10];
+y := [1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321];
+
+# Return coefficients in ascending degree order
+PolynomialRegression(x, y, 2);
+# [ 1, 2, 3 ]

Task/Polynomial-regression/Go/polynomial-regression.go

@@ -0,0 +1,40 @@
+package main
+
+import (
+    "code.google.com/p/gomatrix/matrix"
+    "fmt"
+)
+
+var xGiven = []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
+var yGiven = []float64{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
+var degree = 2
+
+func main() {
+    m := len(yGiven)
+    n := degree + 1
+    y := matrix.MakeDenseMatrix(yGiven, m, 1)
+    x := matrix.Zeros(m, n)
+    for i := 0; i < m; i++ {
+        ip := float64(1)
+        for j := 0; j < n; j++ {
+            x.Set(i, j, ip)
+            ip *= xGiven[i]
+        }
+    }
+
+    q, r := x.QR()
+    qty, err := q.Transpose().Times(y)
+    if err != nil {
+        fmt.Println(err)
+        return
+    }
+    c := make([]float64, n)
+    for i := n - 1; i >= 0; i-- {
+        c[i] = qty.Get(i, 0)
+        for j := i + 1; j < n; j++ {
+            c[i] -= c[j] * r.Get(i, j)
+        }
+        c[i] /= r.Get(i, i)
+    }
+    fmt.Println(c)
+}

Task/Polynomial-regression/Haskell/polynomial-regression-1.hs

@@ -0,0 +1,11 @@
+import Data.List
+import Data.Array
+import Control.Monad
+import Control.Arrow
+import Matrix.LU
+
+ppoly p x = map (x**) p
+
+polyfit d ry = elems $ solve mat vec  where
+   mat = listArray ((1,1), (d,d)) $ liftM2 concatMap ppoly id [0..fromIntegral $ pred d]
+   vec = listArray (1,d) $ take d ry

Task/Polynomial-regression/Haskell/polynomial-regression-2.hs

@@ -0,0 +1,2 @@
+*Main> polyfit 3 [1,6,17,34,57,86,121,162,209,262,321]
+[1.0,2.0,3.0]

Task/Polynomial-regression/HicEst/polynomial-regression-1.hicest

@@ -0,0 +1,15 @@
+REAL :: n=10, x(n), y(n), m=3, p(m)
+
+   x = (0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10)
+   y = (1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321)
+
+   p = 2 ! initial guess for the polynom's coefficients
+
+   SOLVE(NUL=Theory()-y(nr), Unknown=p, DataIdx=nr, Iters=iterations)
+
+   WRITE(ClipBoard, Name) p, iterations
+
+FUNCTION Theory()
+   ! called by the solver of the SOLVE function. All variables are global
+   Theory = p(1)*x(nr)^2 + p(2)*x(nr) + p(3)
+ END

Task/Polynomial-regression/HicEst/polynomial-regression-2.hicest

@@ -0,0 +1,2 @@
+SOLVE performs a (nonlinear) least-square fit (Levenberg-Marquardt):
+p(1)=2.997135145; p(2)=2.011348347; p(3)=0.9906627242; iterations=19;

Task/Polynomial-regression/J/polynomial-regression-1.j

@@ -0,0 +1,3 @@
+   X=:i.# Y=:1 6 17 34 57 86 121 162 209 262 321
+   Y (%. (^/ x:@i.@#)) X
+1 2 3 0 0 0 0 0 0 0 0

Task/Polynomial-regression/J/polynomial-regression-2.j

@@ -0,0 +1,2 @@
+   Y (%. (i.3) ^/~ ]) X
+1 2 3

Task/Polynomial-regression/MATLAB/polynomial-regression.m

@@ -0,0 +1,7 @@
+>> x = [0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10];
+>> y = [1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321];
+>> polyfit(x,y,2)
+
+ans =
+
+   2.999999999999998   2.000000000000019   0.999999999999956

Task/Polynomial-regression/Mathematica/polynomial-regression.math

@@ -0,0 +1,2 @@
+data = Transpose@{Range[0, 10], {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}};
+Fit[data, {1, x, x^2}, x]

Task/Polynomial-regression/Octave/polynomial-regression.octave

@@ -0,0 +1,3 @@
+x = [0:10];
+y = [1,   6,  17,  34,  57,  86, 121, 162, 209, 262, 321];
+coeffs = polyfit(x, y, 2)

Task/Polynomial-regression/PARI-GP/polynomial-regression-1.pari

@@ -0,0 +1 @@
+polinterpolate([0,1,2,3,4,5,6,7,8,9,10],[1,6,17,34,57,86,121,162,209,262,321])

Task/Polynomial-regression/PARI-GP/polynomial-regression-2.pari

@@ -0,0 +1,2 @@
+V=[1,6,17,34,57,86,121,162,209,262,321]~;
+M=matrix(#V,3,i,j,(i-1)^(j-1));Polrev(matsolve(M~*M,M~*V))

Task/Polynomial-regression/Python/polynomial-regression-1.py

@@ -0,0 +1,5 @@
+>>> x = [0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]
+>>> y = [1,   6,  17,  34,  57,  86, 121, 162, 209, 262, 321]
+>>> coeffs = numpy.polyfit(x,y,deg=2)
+>>> coeffs
+array([ 3.,  2.,  1.])

Task/Polynomial-regression/Python/polynomial-regression-2.py

@@ -0,0 +1,3 @@
+>>> yf = numpy.polyval(numpy.poly1d(coeffs), x)
+>>> yf
+array([   1.,    6.,   17.,   34.,   57.,   86.,  121.,  162.,  209., 262.,  321.])

Task/Polynomial-regression/Python/polynomial-regression-3.py

@@ -0,0 +1,2 @@
+>>> '%.1g' % max(y-yf)
+'1e-013'

Task/Polynomial-regression/Python/polynomial-regression-4.py

@@ -0,0 +1,2 @@
+>>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+>>> y = [2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0]

Task/Polynomial-regression/Python/polynomial-regression-5.py

@@ -0,0 +1,4 @@
+>>> p = numpy.poly1d(numpy.polyfit(x, y, deg=2), variable='N')
+>>> print p
+       2
+1.085 N + 10.36 N - 0.6164

Task/Polynomial-regression/R/polynomial-regression-1.r

@@ -0,0 +1,3 @@
+x <- c(0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10)
+y <- c(1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321)
+coef(lm(y ~ x + I(x^2)))

Task/Polynomial-regression/R/polynomial-regression-2.r

@@ -0,0 +1,2 @@
+(Intercept)           x      I(x^2)
+          1           2           3

Task/Polynomial-regression/Ruby/polynomial-regression-1.rb

@@ -0,0 +1,10 @@
+require 'matrix'
+
+def regress x, y, degree
+  x_data = x.map { |xi| (0..degree).map { |pow| (xi**pow).to_f } }
+
+  mx = Matrix[*x_data]
+  my = Matrix.column_vector(y)
+
+  ((mx.t * mx).inv * mx.t * my).transpose.to_a[0]
+end

Task/Polynomial-regression/Ruby/polynomial-regression-2.rb

@@ -0,0 +1,5 @@
+betas = regress [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
+                [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321],
+                2
+
+p betas

Task/Polynomial-regression/TI-89-BASIC/polynomial-regression.ti-89

@@ -0,0 +1,5 @@
+DelVar x
+seq(x,x,0,10) → xs
+{1,6,17,34,57,86,121,162,209,262,321} → ys
+QuadReg xs,ys
+Disp regeq(x)

Task/Polynomial-regression/Tcl/polynomial-regression.tcl

@@ -0,0 +1,49 @@
+package require math::linearalgebra
+
+proc build.matrix {xvec degree} {
+    set sums [llength $xvec]
+    for {set i 1} {$i <= 2*$degree} {incr i} {
+        set sum 0
+        foreach x $xvec {
+            set sum [expr {$sum + pow($x,$i)}]
+        }
+        lappend sums $sum
+    }
+
+    set order [expr {$degree + 1}]
+    set A [math::linearalgebra::mkMatrix $order $order 0]
+    for {set i 0} {$i <= $degree} {incr i} {
+        set A [math::linearalgebra::setrow A $i [lrange $sums $i $i+$degree]]
+    }
+    return $A
+}
+
+proc build.vector {xvec yvec degree} {
+    set sums [list]
+    for {set i 0} {$i <= $degree} {incr i} {
+        set sum 0
+        foreach x $xvec y $yvec {
+            set sum [expr {$sum + $y * pow($x,$i)}]
+        }
+        lappend sums $sum
+    }
+
+    set x [math::linearalgebra::mkVector [expr {$degree + 1}] 0]
+    for {set i 0} {$i <= $degree} {incr i} {
+        set x [math::linearalgebra::setelem x $i [lindex $sums $i]]
+    }
+    return $x
+}
+
+# Now, to solve the example from the top of this page
+set x {0   1   2   3   4   5   6   7   8   9  10}
+set y {1   6  17  34  57  86 121 162 209 262 321}
+
+# build the system A.x=b
+set degree 2
+set A [build.matrix $x $degree]
+set b [build.vector $x $y $degree]
+# solve it
+set coeffs [math::linearalgebra::solveGauss $A $b]
+# show results
+puts $coeffs

Task/Polynomial-regression/Ursala/polynomial-regression-1.ursala

@@ -0,0 +1,5 @@
+#import std
+#import nat
+#import flo
+
+(fit "n") ("x","y") = ..dgelsd\"y" (gang \/*pow float*x iota successor "n")* "x"

Task/Polynomial-regression/Ursala/polynomial-regression-2.ursala

@@ -0,0 +1,6 @@
+x = <0.,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.>
+y = <1.,6.,17.,34.,57.,86.,121.,162.,209.,262.,321.>
+
+#cast %eL
+
+example = fit2(x,y)