Re: Crossing of 3D functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg57160] Re: Crossing of 3D functions*From*: Maxim <ab_def at prontomail.com>*Date*: Thu, 19 May 2005 03:08:43 -0400 (EDT)*References*: <d5sks6$o2t$1@smc.vnet.net> <d69uuf$94p$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Mon, 16 May 2005 11:07:59 +0000 (UTC), Paawel <fonfastik at interia.pl> wrote: > Hello again > > The point of this question is to obtain the function of crossing of > these supersurfaces. Once I have this fcrossing function I want to > find a local minimum (1<r<2, 90<f<180). So I want to find a local > minimum, and plot this function. > > Regards > I assume that you want to minimize another function (func below) along the curve F1 == F2. Then you can either solve for f explicitly and use FindMinimum or search for a constrained minimum with NMinimize: In[1]:= {{r1, r2}, {f1, f2}} = {{1, 2}, {90, 180}}; F1[r_, f_] = 3.92 + 3.758/E^(6.152*(-1.184 + r)) - (6.288336759430112*(1 - 0.00008280000000000001*(180 - f)^2))/E^(3.076*(-1.184 + r)); F2[r_, f_] = 0.479 + 0.479/E^(9.986*(-1.375 + r)) - (0.958*(1 - 0.00107*(133 - f)^2))/E^(4.993*(-1.375 + r)); func[r_, f_] = 50000*(r - 1.2)^2 + (f - 135)^2; Lsol = Solve[F1[r, f] == F2[r, f], f]; FindMinimum[func[r, f] /. Lsol[[2]], {r, (r1 + r2)/2, r1, r2}] Out[6]= {176.96819, {r -> 1.1620375}} In[7]:= NMinimize[{func[r, f], F1[r, f] == F2[r, f]}, {{r, r1, r2}, {f, f1, f2}}] Out[7]= {176.96819, {f -> 145.24258, r -> 1.1620374}} Also you can use FindRoot, which can handle equations that don't have closed-form solutions and is faster than NMinimize: In[8]:= R[f_?NumericQ] := r /. FindRoot[F1[r, f] == F2[r, f], {r, (r1 + r2)/2, r1, r2}] Plot[func[R[f], f], {f, f1, f2}] FindMinimum[func[R[f], f], {f, (f1 + f2)/2, f1, f2}] Out[10]= {176.96819, {f -> 145.24259}} This works because there is only one root for each value of f. Maxim Rytin m.r at inbox.ru