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Re: Area of inside contour of continuous function?

  • To: mathgroup at
  • Subject: [mg84238] Re: Area of inside contour of continuous function?
  • From: "Steve Luttrell" <steve at>
  • Date: Fri, 14 Dec 2007 23:17:24 -0500 (EST)
  • References: <fjun8o$24v$>

This does the sort of thing that you want:

In[1]:= f[x_,y_,a_,b_]:=1-a x^2-b y^2;

In[2]:= Integrate[f[x,y,a,b]Boole[f[x,y,a,b]>k 

Out[2]= -(((-1+k^2) \[Pi])/(2 Sqrt[a b]))

Steve Luttrell
West Malvern, UK

"Gareth Russell" <russell at> wrote in message 
news:fjun8o$24v$1 at
> 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
> g[x_,y_]:=If[f[x,y]>(maxf-u),1,0]
> 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!
> Thanks,
> Gareth
> -- 
> Gareth Russell

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