show residuals of circle fit
- To: mathgroup at smc.vnet.net
- Subject: [mg79900] show residuals of circle fit
- From: will <willpowers69 at hotmail.com>
- Date: Wed, 8 Aug 2007 04:53:39 -0400 (EDT)
Dear Mathforum, I am having a problem with displaying residuals after fitting a circle to a set of points. I am using some code that I found on the mathgroup site (see:http://forums.wolfram.com/mathgroup/archive/2003/Jan/msg00019.html) to generate the points and fit the circle: points generation and display: points = Table[theta = Random[]; {2*Cos[theta] + 1 + .05*Random[], 2*Sin[theta] - 3 + .05*Random[]}, {30}] plot = ListPlot[points, AspectRatio -> Automatic] circle fitting and display with points: fit circle: hypersphereFit[data_List] := Module[{mat, rhs, qq, rr, params, cen}, mat = Map[Append[#, 1] &, data]; rhs = Map[#.# &, data]; {qq, rr} = QRDecomposition[mat]; params = LinearSolve[rr, qq.rhs]; cen = Drop[params, -1]/2; {Sqrt[Last[params] + cen.cen], cen}] display circle (using Graphics[Circle[]] inputing the results from the above function) and points: Show[Graphics[ Circle[Part[hypersphereFit[points], 2], Part[hypersphereFit[points], 1], {0, 1}]], plot] now i really want to be able to display the residuals for the points, but can't figure out how to. If it is any help i use the following code when displaying residuals from a quadratic curve fit: quadratic fit: func = Fit[points, {1, x, x^2}, x] define range of plot: Insert[Part[Sort[points], {1, -1}, 1], x, 1] out: {x, 2.1305, 3.04856} copy and paste this output into the range for the Plot function: Show[Graphics[ Plot[func, {x, 2.1305, 3.04856}]], ListPlot[points, PlotStyle -> {Red, PointSize[Small]}], Axes -> True, AspectRatio -> Automatic] this shows the quadratic fitted line with the points then calculate and display the residuals for the quadratic fit: res = Transpose[{First /@ points, Last /@ points - (func /. x -> First /@ points)}]; ListPlot[res] I would really, really like to be able to do this residuals calculation and display for the circle fit. Any help would be much appreciated, William Parr
- Follow-Ups:
- Re: show residuals of circle fit
- From: Daniel Lichtblau <danl@wolfram.com>
- Re: show residuals of circle fit