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MathGroup Archive 2008

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Re: Extrema of 2D Interpolating function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91440] Re: [mg91435] Extrema of 2D Interpolating function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 22 Aug 2008 03:10:25 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

Use FindRoot

approx[x_, base_] := RootApproximant[x/base, 2]*base

data = Flatten[Table[{{x, y}, Sin[x] Sin[y]},
    {x, 0, 2 Pi, Pi/3}, {y, 0, 2 Pi, Pi/3}], 1];

f[x_, y_] = Interpolation[data][x, y];

Plot3D[f[x, y], {x, 0, 2 Pi}, {y, 0, 2 Pi}]

soln = FindRoot[{D[f[x, y], x] == 0, D[f[x, y], y] == 0},
     {{x, #[[1]]}, {y, #[[2]]}}] & /@
   {{1, 1}, {1, 5}, {3, 3}, {5, 
     1}, {5, 5}};

soln /. n_?NumberQ :> approx[n, Pi]

{{x -> Pi/2, y -> Pi/2}, {x -> Pi/2, y -> (3*Pi)/2}, {x -> Pi, 
  y -> Pi}, 
   {x -> (3*Pi)/2, y -> Pi/2}, {x -> (3*Pi)/2, y -> (3*Pi)/2}}


Bob Hanlon

---- Modeler <eabad at ulb.ac.be> wrote: 

=============
Hi, I'd like to compute the minima  and the saddle points of a 2D interpolating function f[x,y] obtained from a list of points with mathematica 6.0 (if possible in a specified x-y range0. The Nsolve standard routines do not seem to work in this case. Can anyone help? Thanks in advance.




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