Re: #1 FindRoot and protected variables? #2 Am I using the wrong method?

*To*: mathgroup at smc.vnet.net*Subject*: [mg21980] Re: [mg21968] #1 FindRoot and protected variables? #2 Am I using the wrong method?*From*: "Benjamin A. Jacobson" <bjacobson at illumitech.com>*Date*: Mon, 7 Feb 2000 13:02:32 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I didn't look through your code in detail--it's very long--but is it possible there should be a comma between the 2 elements: {a[2,5],0.95} {a[2,6],0.55} For me, a "Tag ... is protected" message usually means a simple syntax error like that. Ben Jacobson Illumitech Inc. At 03:02 AM 2/7/00 -0500, you wrote: > >Hello all. > >I'm working with some optimal control theory in economics and I'm having >some problems with the solutions of simultanious >equations. The program, which isn't very long and is intuitivelly for >non-economists, is reported after these questions. I hope some of you >can help me!!!! > >In a much smaller setup every thing works fine, but in the real setup >with some 8x8 matrices the FindRoot[] writes >that some of the elements in the matrices is Protected. I used the >?v[2,5] (v[2,5] is the element wich it claims to be protected) but with >no result. It does not recognize the parameter. >I have also tried to do a Unprotect[v[2,5]], but with no luck. I tried >with some different names for the matrices, but still with no luck. > >I have also tried the ordinary NSolve[] command, but the system is too >big and the computer takes a lot of time working on this problem. I'm >working on a Penthium I 200mmx so it should not be a computer problem >but instead because the resulting equations is highly non-linear. The >ConstrainedMax[] command is not working eather, since it will not accept >equalities as constraints. > >I have to solve the system like 300 times with different parameters >within 1.st of april. So I only want Mathematica to find the one of the >solution which I'm searching for. Or find a algorithm that works faster. > >My quistions is: > ># 1:What does it (Mathematica) mean by this : >FindRoot::"write": "Tag Times in (a[2, 5] a[2, 6] is Protected. > >Is it protected by default or have I done it in my program (not meaning >to) > ># 2 Am I using a wrong method or command - FindRoot[]. Is the Global >Optimum package better for this kind of problems. And isn't there a more >simple way to write the the FindRoot[] than I have done (it was the only >iterating process which worked for me - see buttom of page). > >#3 I have looked at the list of quistions to the Mathgroup on the >internet. Some economists dealing with optimal control problems has >asked the quistion if mathematica is usuable for these problems or some >other programs is better (like Gauss). But I have not seen any answers >on these quistions. >I hope some of you will react on my quistions. Regards Christian von >Pein - Den Danske Bank/Copenhagen University > >This reads a list of 54 caracters. Parameters from som regressions >(unequal - no. 1,3,5 etc) and standard diviations of parameters (egual - >2,4,6 etc.) > >m = ReadList["c:\var7999.prn",Number] > >k = 1; > >Sets up the model parameters : Matrices A and B > >A = >{{m[[k]],m[[k+2]],m[[k+4]],m[[k+6]],m[[k+8]],m[[k+10]],m[[k+14]],m[[k+16] >]},{1,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0},{m[[k+18]],m[[k+20]],m[[k+22]],m[[ >k+24]],m[[k+26]],m[[k+28]],m[[k+32]],m[[k+34]]},{0,0,0,1,0,0,0,0},{0,0,0, >0,1,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0}}; > >B = {{m[[k+12]]},{0},{0},{m[[k+30]]},{0},{0},{1},{0}}; > >Defines some variance-matrices > >{m[[k+1]]^2,m[[k+3]]^2,m[[k+5]]^2,m[[k+7]]^2,m[[k+9]]^2,m[[k+11]]^2,m[[k+ >15]]^2,m[[k+17]]^2}; > >SA11 = DiagonalMatrix[%]; > >{m[[k+19]]^2,m[[k+21]]^2,m[[k+23]]^2,m[[k+25]]^2,m[[k+27]]^2,m[[k+29]]^2, >m[[k+33]]^2,m[[k+35]]^2}; > >SA22 = DiagonalMatrix[%]; > >Discount factor: > >d = 0.987; > >Defining two matrices > >Q = DiagonalMatrix[{1,0,0,1,0,0,0,0}]; > >V = Array[a,{8,8}]; > >This is the equations I am interested in: e is the main attraction > >e = - Inverse[Transpose[B] . (V + Transpose[V]) . B + 2 v[1,1] >(m[[k+13]]^2) + 2 v[4,4] (m[[k+31]]^2)] . (Transpose[B] . (V + >Transpose[V]) . A ); > >and e can be found numerically by iterating on the Ricatti-equation were >H = V > >H = Q + d Transpose[A + B . e] . V . (A + B . e) + d v[1,1] (SA11 + >(Transpose[e] ( m[[k+13]]^2)) . e) + d v[4,4] (SA22 + (Transpose[e] >(m[[k+31]]^2)) . e); > >To get solutions I could make NSolve[] but this takes a couple of days >(at least three), so I try to find the relevant solution by giving some >start values: > >(Go to buttom to find how Mathematica is reacting) > >FindRoot[{V[[1,1]] == H[[1,1]], V[[1,2]] == H[[1,2]],V[[1,3]] >== H[[1,3]], > >V[[1,4]] == H[[1,4]],V[[1,5]] == H[[1,5]] > >,V[[1,6]] == H[[1,6]],V[[1,7]] == H[[1,7]],V[[1,8]] == >H[[1,8]], > >V[[2,1]] == H[[2,1]],V[[2,2]] == H[[2,2]],V[[2,3]] == >H[[2,3]] > >,V[[2,4]] == H[[2,4]],V[[2,5]] == H[[2,5]],V[[2,6]] == >H[[2,6]], > >V[[2,7]] == H[[2,7]],V[[2,8]] == H[[2,8]],V[[3,1]] == >H[[3,1]] > >,V[[3,2]] == H[[3,2]],V[[3,3]] == H[[3,3]],V[[3,4]] == >H[[3,4]], > >V[[3,5]] == H[[3,5]],V[[3,6]] == H[[3,6]],V[[3,7]] == >H[[3,7]], > >V[[3,8]] == H[[3,8]],V[[4,1]] == H[[4,1]],V[[4,2]] == >H[[4,2]], > >V[[4,3]] == H[[4,3]],V[[4,4]] == H[[4,4]],V[[4,5]] == >H[[4,5]], > >V[[4,6]] == H[[4,6]],V[[4,7]] == H[[4,7]],V[[4,8]] == >H[[4,8]], > >V[[5,1]] == H[[5,1]],V[[5,2]] == H[[5,2]],V[[5,3]] == >H[[5,3]], > >V[[5,4]] == H[[5,4]],V[[5,5]] == H[[5,5]],V[[5,6]] == >H[[5,6]], > >V[[5,7]] == H[[5,7]],V[[5,8]] == H[[5,8]],V[[6,1]] == >H[[6,1]], > >V[[6,2]] == H[[6,2]],V[[6,3]] == H[[6,3]],V[[6,4]] == >H[[6,4]], > >V[[6,5]] == H[[6,5]],V[[6,6]] == H[[6,6]],V[[6,7]] == >H[[6,7]], > >V[[6,8]] = H[[6,8]],V[[7,1]] == H[[7,1]],V[[8,2]] == >H[[7,2]], > >V[[7,3]] == H[[7,3]],V[[7,4]] == H[[7,4]],V[[7,5]] == >H[[7,5]], > >V[[7,6]] == H[[7,6]],V[[7,7]] == H[[7,7]],V[[7,8]] == >H[[7,8]], > >V[[8,1]] == H[[8,1]],V[[8,2]] == H[[8,2]],V[[8,3]] == >H[[8,3]], > >V[[8,4]] == H[[8,4]],V[[8,5]] == H[[8,5]],V[[8,6]] == >H[[8,6]], > >V[[8,7]] == H[[8,7]],V[[8,8]] == >H[[8,8]]},{a[1,1],0.5},{a[1,2],0.6},{ > >a[1,3],0.5},{a[1,4],0.65},{a[1,5],0.5},{a[1,6],0.85},{a[1,7],0.5},{a[1,8] >, > >0.5},{a[2,1],0.35},{a[2,2],0.15},{a[2,3],0.55},{a[2,4], > >0.85},{a[2,5],0.95} > >{a[2,6],0.55},{a[2,7],0.5},{a[2,8],0.5},{a[3,1],0.5},{a[3,2],0.5},{a[3,3] >, > >0.5},{a[3,4],0.5},{a[3,5],0.5},{a[3,6],0.5},{a[3,7],0.5},{a[3,8],0.5},{ > >a[4,1],0.5},{a[4,2],0.5},{a[4,3],0.5},{a[4,4],0.5}, > >{a[4,5],0.5},{a[4,6],0.5},{a[4,7],0.5},{a[4,8],0.5},{a[5,1],0.5},{a[5,2], > > >0.5},{a[5,3],0.5},{a[5,4],0.5},{a[5,5],0.5},{a[5,6],0.5},{a[5,7],0.5},{ > >a[5,8],0.5},{a[6,1],0.5},{a[6,2],0.5},{a[6,3],0.5},{a[6,4],0.5},{a[6,5], > >0.5},{a[6,6],0.5},{a[6,7],0.5},{a[6,8],0.5},{a[7,1],0.5},{a[7,2],0.5},{ > >a[7,3],0.5},{a[7,4],0.5},{a[7,5],0.5},{a[7,6],0.5},{a[7,7],0.5},{a[7,8], > >0.5},{a[8,1],0.5},{a[8,2],0.5},{a[8,3],0.5},{a[8,4],0.5},{a[8,5],0.5},{ > >a[8,6],0.5},{a[8,7],0.5},{a[8,8],0.5}]; > >FindRoot::"write": "Tag Times in (a[2, 5] a[2, 6] is Protected. > >e/.% > >