Symbolic use of numerical function FindRoot via ?NumericQ
- To: mathgroup at smc.vnet.net
- Subject: [mg48506] Symbolic use of numerical function FindRoot via ?NumericQ
- From: "Michael Beqq" <mbekkali at iastate.edu>
- Date: Fri, 4 Jun 2004 04:49:20 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I've use symbolical evalution of numerical functions all the time but still have not mastered it. Now I got stuck on the following problem: I have a function g[x1,x2,y1,y2]. I need to solve for x1,x2 and y1,y2 that maximize g[x1,x2,y1,y2] in 2 steps,- in step 1 I need to find x1*=x1[y1,y2] and x2*=x2[y1,y2]. Then I substitute solutions, *'s, into g[.] to get g[y1,y2] and then solve for solve for y1* and y2*. This is a classical 2-stage problem in Economics. Is there a way to do that in Mathematica 5 using FindRoot command. I tried using SetDelayed and ?NumericQ options however get error messages that the function g[.]'s is not a list of numbers with dimension {2} at {2 values}. Here is more precise code: g[x1_x2_,y1_,y2_]=g[x1,x2,y1,y2]"g is some function of 4 variables"; {x1[y1_,y2_?Numeric],x2[y1_,y2_?Numeric]}:=Evaluate[{x1,x2}/.FindRoot[Evalua te[{D[g[x1,x2,y1,y2],x1]]==0,D[g[x1,x2,y1,y2],x2]]==0},{x1,x10},{x2,x20}]] (* another website showed different code, i.e. x[(y1_,y2_)?Number] but I assume it is just semantics*) FindRoot[Evaluate[{D[g[y1,y2],y1]]==0,D[g[y1,y2],y2]]==0},{y1,y10},{y2,y20}] ] where {x10,x20,y10,y20}=some numbers. Thank you in advance.