Re: A NDSolve within a FindMinimum/NMinimize

*To*: mathgroup at smc.vnet.net*Subject*: [mg90608] Re: A NDSolve within a FindMinimum/NMinimize*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 16 Jul 2008 06:27:38 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g5htfb$j7t$1@smc.vnet.net>

philip.ingrey at googlemail.com wrote: > I'm trying to find the value of a coefficient that minimizes a > function. Below is a simplified version of the problem: > Using a Table to print out some results is fine: > > Table[{a, s = NDSolve[{El'[x] + a Sin[x] El[x] == 0, El[0] == a}, El, > {x, -1, 1}]; ((El[1] /. s) a)[[1]]}, {a, -1, 1, 0.1}] > > But a NMinimize or FindMinimum gives errors: > > NMinimize[s = NDSolve[{El'[x] + a Sin[x] El[x] == 0, El[0] == a}, El, > {x, -1, 1}]; (El[1] /. s) a, a] > > As it seams to try and evaluate the NDSolve then apply a value for a, > is there a way to solve this? Contrary to Table[], NMinimize[] has none of the attributes of the Hold* family, so it does not prevent the evaluation of its arguments before is own evaluation. In[1]:= Attributes@{NMinimize, Table} Out[1]= {{Protected, ReadProtected}, {HoldAll, Protected}} One way of fixing this is to write a function that is called only for numeric argument and contains your original compound expression, possibly with the use of construct such as Module[] to localize variables. In[2]:= f[a_?NumericQ] := Module[{s}, s = NDSolve[{El'[x] + a Sin[x] El[x] == 0, El[0] == a}, El, {x, -1, 1}]; First[(El[1] /. s) a] ] NMinimize[f[a], a] % // Chop Out[3]= {5.54633*10^-17, {a -> -7.44737*10^-9}} Out[4]= {0, {a -> -7.44737*10^-9}} Regards, -- Jean-Marc