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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*: <fjun8o$24v$1@smc.vnet.net>
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
f[0,0,a,b]],{x,-\[Infinity],\[Infinity]},{y,-\[Infinity],\[Infinity]},Assumptions->a>0&&b>0&&0<k<1]
Out[2]= -(((-1+k^2) \[Pi])/(2 Sqrt[a b]))
Steve Luttrell
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
>
> 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
> NJIT
>
>
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