Re: Area of inside contour of continuous function?
- To: mathgroup at smc.vnet.net
- Subject: [mg84238] Re: Area of inside contour of continuous function?
- From: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
- Date: Fri, 14 Dec 2007 23:17:24 -0500 (EST)
- References: <email@example.com>
This does the sort of thing that you want:
In:= f[x_,y_,a_,b_]:=1-a x^2-b y^2;
Out= -(((-1+k^2) \[Pi])/(2 Sqrt[a b]))
West Malvern, UK
"Gareth Russell" <russell at njit.edu> wrote in message
news:fjun8o$24v$1 at smc.vnet.net...
> Hi Group,
> I have a two-parameter smooth continuous function f[x_,y_] that is
> unimodal (it's a log-likeihood function), and I know maxf, the height
> of the peak. I would like to calculate the area inside a contour that
> is a given number of units u below the peak. What is the easiest way to
> do this?
> My own idea is to construct a separate function with discontinuities
> along the lines of
> And do numerical integration over a region big enough to contain the
> contour (which of course, I can see from a ContourPlot).
> But am I missing something much easier? Searching the mathgroup
> archives I came across how to find the area of a discrete polygon, so I
> realize that another method would be to extract the contour data from
> the ContourPlot object and apply that, but it seems like a bit of hack!
> Gareth Russell
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