Re: Problem behavior with FindMaximum
- To: mathgroup at smc.vnet.net
- Subject: [mg59696] Re: [mg59671] Problem behavior with FindMaximum
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 18 Aug 2005 00:16:29 -0400 (EDT)
- References: <200508170800.EAA24807@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This is a common question. Just change the definition of myFunct2 to myFunc2[a_?NumericQ] := FindMaximum[myFunc1[a, b], {b, 0}][[1]] and you will get: FindMaximum[myFunc2[x], {x, 14}] {1., {x -> 16.}} I do not know a good answer to the question how to copy and paste error messages. I just copy them as Text and then manually remove the markup characters. Andrzej Kozlowski On 17 Aug 2005, at 10:00, James H. Steiger wrote: > Hello all: > > I wonder if you could give me some advice about behavior of > FindMaximum[] > that I cannot seem to decipher. > > There is a broad class of problems in statistics that involves > finding the > maximum > of a function of several parameters, all but one (call it "a") of > which are > *nuisance parameters*. > The function is evaluated at any value of "a" by maximizing it > w.r.t. all > the nuisance parameters. > > A simple example (constructed just for Mathgroup -- the actual > functions I work with are messier) should make this clear. > > > myFunc1[a_, b_] := 1/((a - 16)^2 + 1) - (a - b)^2 > myFunc2[a_] := FindMaximum[myFunc1[a, b], {b, 0}][[1]] > > FindMaximum returns a list, the first element of which is the > maximized > value of the function, > the second of which is a replacement rule specifying the value of b > at which > the maximum occurs. > > As you can quickly verify, myFunc2 is well behaved, and you can > plot myFunc2 > without incident. > > Plot[myFunc2[a],{a,14,18}] produces a nice plot with no error messages > > Here is where the problem arises. Suppose you want to use > FindMaximum[] to > obtain the maximum of myFunc2 which clearly occurs at > a=16. > > If you input the command > > FindMaximum[myFunc2[x],{x,14}] > > you obtain a pair of error messages (can anyone tell me how to copy > these in > Mathematica as text?) > > ----------------- > > FindMaximum::nnum: The function value 1/((1+<<1>>)^2) - (0.+a)^2 is > not a > number at {b}={0.} > > FindMaximum::nnum: The function value 0.2 - (14. -b)^2 is not a > number at > {a}={14.} > > ----------------- > > Is there some problem of "scope" of these variables that I am not > aware of? > Or is there some bug in FindMaximum[]? > Is there a fix? > > Thanks to all, > > Jim > > > James H. Steiger, Professor and Director > Quantitative Methods and Evaluation > Dept. of Psychology and Human Development > Vanderbilt University > Peabody College #512 > Nashville, TN, 37203 > > Phone: 615-322-7060 > email: james.h.steiger at vanderbilt.edu > >
- References:
- Problem behavior with FindMaximum
- From: "James H. Steiger" <jsteiger@bellsouth.net>
- Problem behavior with FindMaximum