Re: Quadratic Form Contours
- To: mathgroup at smc.vnet.net
- Subject: [mg57732] Re: Quadratic Form Contours
- From: dh <dh at metrohm.ch>
- Date: Tue, 7 Jun 2005 02:03:33 -0400 (EDT)
- References: <d7pa71$sqt$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Joerg, To use "Ellipsoid" we need the semi-length and directions of the axes. The direction we obtain from: Eigenvectors[A] the half-length from: Sqrt[ b/Eigenvalues[A]] Therefore, an ellipsoid would be specified by: Ellipsoid[{x,y}, Sqrt[ b/Eigenvalues[A]], Eigenvectors[A] ] The erason for this is: If you turn the coordinate system in direction of the Eigenvectors, the quadratic form looks like: x1^2/ew1 + x2^2/ew2 == b where ew means eigenvalue. sincerely, Daniel Joerg Schaber wrote: > Hi, > > does anybody know a simple way to calculate 2-D ellipsoids in x={x1,x2} > of a quadatric form solving xAx=b for a graphical output, i.e. contour > lines of the quadrtic form expressed as the Graphics primitive Ellipsoid? > I suppose that the option ParameterConfidenceRegion of NonlinearRegress > does something like that, but how? > > best, > > joerg >