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[MUG] Finding the maximum value of a function over a range

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[MUG] Finding the maximum value of a function over a range
Author: Roush, Craig Ryan UMKC-Student    Posted: Wed, 17 Apr 2002 23:04:51 -0500
>> From: "Roush, Craig Ryan (UMKC-Student)" "crrea2" I have a function that is dependent on a variable phi, where phi ranges from 0 to 2*Pi, Is there a way I can calculate the maximum value of the function over that range so I can normalize that function to a unity value of 1? Thanks! Craig

[MUG] Re: Finding the maximum value of a function over a range
Author: Maple User Group    Posted: Mon, 22 Apr 2002 15:05:28 -0400
>> From: Maple User Group "maple_gr" |> From: "Roush, Craig Ryan (UMKC-Student)" "crrea2" | I have a function that is dependent on a variable phi, where phi | ranges from 0 to 2*Pi, Is there a way I can calculate the maximum | value of the function over that range so I can normalize that function | to a unity value of 1? Thanks! Craig -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Sun, 21 Apr 2002 05:02:10 +0200 From: Helmut Kahovec "helmut.kahovec" To: "maple-list" Subject: Finding the maximum value of a function over a range If you have Maple7 then look at the online help page of 'minimize'. Kind regards Helmut -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Willard, Daniel Dr DUSA-OR" "daniel.willard" To: "''" Subject: Finding the maximum value of a function over a range Date: Thu, 18 Apr 2002 12:38:01 -0400 Calling the function F, solve dF/d(phi)=0. If no answer, try the function <extrema>. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Thu, 18 Apr 2002 10:25:16 -0700 (PDT) From: Robert Israel "israel" To: "maple-list" Subject: Finding the maximum value of a function over a range It depends. You could try > maximize(f(phi), phi = 0 .. 2*Pi); This uses the usual symbolic methods, which will generally require solving the equation f'(phi) = 0. This may or may not be possible in closed form, so you may not get an answer. In addition (depending on which release of Maple you're using) maximize has a number of bugs. To get a numerical approximation of an answer, you might try gmax from my Maple Advisor Database, http://www.math.ubc.ca/~israel/advisor. Robert Israel "israel" Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Subject: Finding the maximum value of a function over a range Date: Thu, 18 Apr 2002 12:37:09 -0500 From: "Roush, Craig Ryan (UMKC-Student)" "crrea2" To: "Robert Israel" "israel" yes, it is not possible to solve the equations that I am using in closed form, they are for the electric field of an antenna array. I just need to normalize the function so that I have plots that I can compare reasonably well, I have tried, gmax, findmax that I found online, and not one of those would find the max of my equation. Any other suggestions? Craig Roush -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Thu, 18 Apr 2002 11:25:04 -0700 (PDT) From: Robert Israel "israel" To: "Roush, Craig Ryan (UMKC-Student)" "crrea2" Subject: Finding the maximum value of a function over a range If you can plot the function on the interval, then you can extract the maximum of the y-values of the plotted points. For example: > P:= plot(f(phi), phi=0..2*Pi): A:= remove(has, op([1,1],P), undefined): MAX:= max(op(map(t -> t[2], A))); Robert Israel "israel" Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2

[MUG] Re: Finding the maximum value of a function over a range
Author: Theodore Kolokolnikov    Posted: Thu, 25 Apr 2002 15:56:25 -0700
>> From: Theodore Kolokolnikov "tkolokol" > from: "Roush, Craig Ryan (UMKC-Student)" "crrea2" > I have tried, gmax, findmax that I found online, and not one of > those would find the max of my equation. Any other suggestions? > Craig Roush I've used "slink" program, available from: http://www.maths.qmw.ac.uk/~fjw/public_maple/ It can minimize functions of many variables. It works in situations where Maple's "minimize" doesn't. Theodore.

[MUG] Re: Finding the maximum value of a function over a rang e
Author: Willard, Daniel Dr DUSA-OR    Posted: Tue, 30 Apr 2002 16:19:18 -0400
>> From: "Willard, Daniel Dr DUSA-OR" "daniel.willard" Have you tried "extrema"? > From: "Roush, Craig Ryan (UMKC-Student)" "crrea2" > I have tried, gmax, findmax that I found online, and not one of > those would find the max of my equation. Any other suggestions?

[MUG] Re: Finding the maximum value of a function over a range
Author: Jeff Wright    Posted: Thu, 9 May 2002 12:25:40 -0700
>> From: "Jeff Wright" "jhwright" Based on suggestions from the group, I have successfully used something like the following to get numerical extrema. #Assume that f is defined externally, and return the value of z that maximizes f. maxf := proc(f, zmin, zmax) local p1, points, maxval,maxpt; p1 := plot(f(z), z=zmin .. zmax): #create plot structure from which to grab results points := op([1,1],p1): # extract list of points maxval:= max(op(map(t -> t[2], points))): #find max value maxpt := select(t-> t[2]=maxval, points)[]: # get ordered pair for max value if(maxpt[2]<0) then maxpt[2]:=0; fi ; return(maxpt): end proc ; ------------------------------ Jeffrey H. Wright, Ph.D. Department of Math and Computer Science University of San Diego 5998 Alcala Park San Diego, CA 92110-2492 "jhwright" 619-260-7491

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