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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
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