September 2017 Update
This commit is contained in:
Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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@ -0,0 +1,24 @@
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# The polynomial approximation
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f(x) = a*x**2 + b*x + c
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# Initial values for parameters
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a = 0.1
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b = 0.1
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c = 0.1
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# Fit f to the following data by modifying the variables a, b, c
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fit f(x) '-' via a, b, c
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0 1
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1 6
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2 17
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3 34
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4 57
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5 86
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6 121
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7 162
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8 209
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9 262
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10 321
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e
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print sprintf("\n --- \n Polynomial fit: %.4f x^2 + %.4f x + %.4f\n", a, b, c)
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@ -14,9 +14,9 @@ var (
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)
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func main() {
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a := Vandermonde(x, 2)
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b := mat64.NewDense(11, 1, y)
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c := mat64.NewDense(3, 1, nil)
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a := Vandermonde(x, degree)
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b := mat64.NewDense(len(y), 1, y)
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c := mat64.NewDense(degree+1, 1, nil)
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qr := new(mat64.QR)
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qr.Factorize(a)
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@ -1,15 +0,0 @@
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REAL :: n=10, x(n), y(n), m=3, p(m)
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x = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
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y = (1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
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p = 2 ! initial guess for the polynom's coefficients
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SOLVE(NUL=Theory()-y(nr), Unknown=p, DataIdx=nr, Iters=iterations)
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WRITE(ClipBoard, Name) p, iterations
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FUNCTION Theory()
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! called by the solver of the SOLVE function. All variables are global
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Theory = p(1)*x(nr)^2 + p(2)*x(nr) + p(3)
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END
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@ -1,2 +0,0 @@
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SOLVE performs a (nonlinear) least-square fit (Levenberg-Marquardt):
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p(1)=2.997135145; p(2)=2.011348347; p(3)=0.9906627242; iterations=19;
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@ -1,4 +0,0 @@
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function polyfit(x, y, n)
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A = [ float(x[i])^p for i = 1:length(x), p = 0:n ]
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A \ y
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end
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@ -1,7 +0,0 @@
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julia> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
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julia> y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
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julia> polyfit(x, y, 2)
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3-element Array{Float64,1}:
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1.0
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2.0
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3.0
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@ -1,2 +1 @@
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V=[1,6,17,34,57,86,121,162,209,262,321]~;
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M=matrix(#V,3,i,j,(i-1)^(j-1));Polrev(matsolve(M~*M,M~*V))
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polinterpolate([0..10],[1,6,17,34,57,86,121,162,209,262,321])
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@ -1,2 +1,2 @@
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lsf(X,Y,n)=my(M=matrix(#X,n+1,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], 2)
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V=[1,6,17,34,57,86,121,162,209,262,321]~;
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M=matrix(#V,3,i,j,(i-1)^(j-1));Polrev(matsolve(M~*M,M~*V))
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@ -0,0 +1,2 @@
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lsf(X,Y,n)=my(M=matrix(#X,n+1,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], 2)
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46
Task/Polynomial-regression/Phix/polynomial-regression-1.phix
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46
Task/Polynomial-regression/Phix/polynomial-regression-1.phix
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@ -0,0 +1,46 @@
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constant x = {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 n = length(x)
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function regression()
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atom {xm, ym, x2m, x3m, x4m, xym, x2ym} @= 0
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for i=1 to n do
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atom xi = x[i],
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yi = y[i]
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xm += xi
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ym += yi
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x2m += power(xi,2)
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x3m += power(xi,3)
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x4m += power(xi,4)
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xym += xi*yi
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x2ym += power(xi,2)*yi
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end for
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xm /= n
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ym /= n
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x2m /= n
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x3m /= n
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x4m /= n
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xym /= n
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x2ym /= n
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atom Sxx = x2m-power(xm,2),
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Sxy = xym-xm*ym,
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Sxx2 = x3m-xm*x2m,
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Sx2x2 = x4m-power(x2m,2),
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Sx2y = x2ym-x2m*ym,
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B = (Sxy*Sx2x2-Sx2y*Sxx2)/(Sxx*Sx2x2-power(Sxx2,2)),
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C = (Sx2y*Sxx-Sxy*Sxx2)/(Sxx*Sx2x2-power(Sxx2,2)),
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A = ym-B*xm-C*x2m
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return {C,B,A}
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end function
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atom {a,b,c} = regression()
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function f(atom x)
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return a*x*x+b*x+c
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end function
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printf(1,"y=%gx^2+%gx+%g\n",{a,b,c})
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printf(1,"\n x y f(x)\n")
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for i=1 to n do
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printf(1," %2d %3d %3g\n",{x[i],y[i],f(x[i])})
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end for
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22
Task/Polynomial-regression/Phix/polynomial-regression-2.phix
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22
Task/Polynomial-regression/Phix/polynomial-regression-2.phix
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@ -0,0 +1,22 @@
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include pGUI.e
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constant x = {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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IupOpen()
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Ihandle plot = IupPlot("GRID=YES, MARGINLEFT=50, MARGINBOTTOM=40")
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-- (just add ", AXS_YSCALE=LOG10" for a nice log scale)
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IupPlotBegin(plot, 0)
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for i=1 to length(x) do
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IupPlotAdd(plot, x[i], y[i])
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end for
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{} = IupPlotEnd(plot)
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Ihandle dlg = IupDialog(plot)
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IupSetAttributes(dlg, "RASTERSIZE=%dx%d", {640, 480})
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IupSetAttribute(dlg, "TITLE", "simple plot")
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IupShow(dlg)
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IupMainLoop()
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IupClose()
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@ -1,2 +1 @@
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(Intercept) x I(x^2)
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1 2 3
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coef(lm(y ~ poly(x, 2, raw=T)))
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@ -1,3 +0,0 @@
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x <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
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y <- c(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
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coef(lm(y ~ x + I(x^2)))
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51
Task/Polynomial-regression/REXX/polynomial-regression.rexx
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51
Task/Polynomial-regression/REXX/polynomial-regression.rexx
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/* REXX ---------------------------------------------------------------
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* Implementation of http://keisan.casio.com/exec/system/14059932254941
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*--------------------------------------------------------------------*/
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xl='0 1 2 3 4 5 6 7 8 9 10'
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yl='1 6 17 34 57 86 121 162 209 262 321'
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n=11
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Do i=1 To n
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Parse Var xl x.i xl
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Parse Var yl y.i yl
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End
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xm=0
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ym=0
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x2m=0
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x3m=0
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x4m=0
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xym=0
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x2ym=0
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Do i=1 To n
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xm=xm+x.i
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ym=ym+y.i
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x2m=x2m+x.i**2
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x3m=x3m+x.i**3
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x4m=x4m+x.i**4
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xym=xym+x.i*y.i
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x2ym=x2ym+(x.i**2)*y.i
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End
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xm =xm /n
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ym =ym /n
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x2m=x2m/n
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x3m=x3m/n
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x4m=x4m/n
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xym=xym/n
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x2ym=x2ym/n
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Sxx=x2m-xm**2
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Sxy=xym-xm*ym
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Sxx2=x3m-xm*x2m
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Sx2x2=x4m-x2m**2
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Sx2y=x2ym-x2m*ym
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B=(Sxy*Sx2x2-Sx2y*Sxx2)/(Sxx*Sx2x2-Sxx2**2)
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C=(Sx2y*Sxx-Sxy*Sxx2)/(Sxx*Sx2x2-Sxx2**2)
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A=ym-B*xm-C*x2m
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Say 'y='a'+'||b'*x+'c'*x**2'
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Say ' Input "Approximation"'
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Say ' x y y1'
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Do i=1 To 11
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Say right(x.i,2) right(y.i,3) format(fun(x.i),5,3)
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End
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Exit
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fun:
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Parse Arg x
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Return a+b*x+c*x**2
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@ -1,18 +1,18 @@
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var Matrix = require('Math::Matrix');
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var Matrix = require('Math::Matrix')
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func regress(x, y, degree) {
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var x_data = x.map { |xi| (0..degree).map { |pow| (xi**pow).to_f } };
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var x_data = x.map {|xi| (0..degree).map {|pow| xi**pow } }
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var mx = Matrix.new(x_data...);
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var my = Matrix.new(y.map{[_]}...);
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var mx = Matrix.new(x_data...)
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var my = Matrix.new(y.map{[_]}...)
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mx.transpose.multiply(mx).invert.multiply(mx.transpose).multiply(my).transpose;
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mx.transpose.multiply(mx).invert.multiply(mx.transpose).multiply(my).transpose
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}
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var betas = regress(
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[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
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[1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321],
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2
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);
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)
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betas.print;
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betas.print
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33
Task/Polynomial-regression/Stata/polynomial-regression.stata
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33
Task/Polynomial-regression/Stata/polynomial-regression.stata
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@ -0,0 +1,33 @@
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. clear
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. input x y
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0 1
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1 6
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2 17
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3 34
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4 57
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5 86
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6 121
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7 162
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8 209
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9 262
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10 321
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end
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. regress y c.x##c.x
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Source | SS df MS Number of obs = 11
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-------------+---------------------------------- F(2, 8) = .
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Model | 120362 2 60181 Prob > F = .
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Residual | 0 8 0 R-squared = 1.0000
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-------------+---------------------------------- Adj R-squared = 1.0000
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Total | 120362 10 12036.2 Root MSE = 0
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------------------------------------------------------------------------------
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y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
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-------------+----------------------------------------------------------------
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x | 2 . . . . .
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c.x#c.x | 3 . . . . .
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_cons | 1 . . . . .
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------------------------------------------------------------------------------
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@ -0,0 +1,7 @@
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var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
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xs:=GSL.VectorFromData(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10);
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ys:=GSL.VectorFromData(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321);
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v :=GSL.polyFit(xs,ys,2);
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v.format().println();
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GSL.Helpers.polyString(v).println();
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GSL.Helpers.polyEval(v,xs).format().println();
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polyfit(T(T(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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T(T(1.0,6.0,17.0,34.0,57.0,86.0,121.0,162.0,209.0,262.0,321.0)), 2)
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.flatten().println();
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