Re: Finding unknown parameters

• To: mathgroup at smc.vnet.net
• Subject: [mg75166] Re: [mg75154] Finding unknown parameters
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Thu, 19 Apr 2007 04:30:30 -0400 (EDT)
• References: <200704180911.FAA08709@smc.vnet.net>

```I don't know if this will help you, but I fed the solution of each
iteration as the starting point for the successive iterations.

(MMA 5.2 Kernel) In[1]:=
x1:={1.3,1.33,1.28,1.25,1.29,1.32,1.38,1.24,1.26,1.24,1.25,1.3,1.27,1.3,1.32,
1.31,1.3,1.26,1.28,1.31,1.33,1.29,1.3,1.32,1.26,1.3,1.32,1.35,1.32,1.29}
(MMA 5.2 Kernel) In[2]:=
x2:={1.25,1.32,1.25,1.3,1.38,1.32,1.25,1.29,1.32,1.35,1.29,1.33,1.32,1.26,1.3,
1.25,1.25,1.29,1.31,1.31,1.27,1.26,1.29,1.31,1.28,1.33,1.27,1.26,1.29,
1.32}
(MMA 5.2 Kernel) In[3]:=
LMN[r1_,r2_,b1_,b2_,p_]=
Module[{n=Length[x1]},
n*Log[p]+n*Log[p+1]+n*Log[b1]+n*Log[r1]+n*Log[b2]+
n*Log[r2]+(b1-1)*Sum[Log[x1[[j]]],{j,1,n}]+(b2-1)*
Sum[Log[x2[[j]]],{j,1,n}]-(p+2)*
Sum[Log[1+r1*x1[[j]]^b1+r2*x2[[j]]^b2],{j,1,n}]];
(MMA 5.2 Kernel) In[4]:=
rr:=z_Complex\[Rule]{Re[z],Im[z]}
(MMA 5.2 Kernel) In[5]:=
eqns=Thread[D[LMN[r1,r2,b1,b2,p],{{b1,b2,p}}]\[Equal]0];
(MMA 5.2 Kernel) In[6]:=
rMatrix=Table[{r1,r2},{r2,0.001,1,0.15},{r1,0.001,1,0.15}];
(MMA 5.2 Kernel) In[7]:=
(*make each input domain point close to its neighbors*)

rList=Flatten[MapIndexed[If[EvenQ[#2[[1]]],Reverse@#1,#1]&,rMatrix],1];
(MMA 5.2 Kernel) In[8]:=
f=Block[{r1=#2[[1]],r2=#2[[2]],FindRoot},FindRoot[eqns,List@@@#1]]&
(MMA 5.2 Kernel) In[9]:=
ansList=Rest@FoldList[f,{b1\[Rule]20,b2\[Rule]20,p\[Rule]2},rList];
(MMA 5.2 Kernel) In[10]:=
MapThread[Join[Thread[{r1,r2}\[Rule]#1],#2]&,{rList,ansList}]

On 4/18/07, Shafiq Ahmad <shafiq.ahmad at rmit.edu.au> wrote:
> Hi,
>
> Below are the codes to solve the non-linear equations that I could
> furnished with help of Mr Jeans-Marc.  After running the codes, I got
> this error message (FindRoot::cvmit: "Failed to converge to the
> requested accuracy or precision \within 100 iterations) when run some
> real data of sample size 30. I did try to increase # of interations but
> could not get success. Any one has any clue?
>
> ====================================
>
>  In[115]:=
> LMN[r1_, r2_, b1_, b2_, p_] := Module[{n = Length[x1]}, n*Log[p] +
> n*Log[p + 1] + n*Log[b1] + n*Log[r1] + n*Log[b2] + n*Log[r2] +
>     (b1 - 1)*Sum[Log[x1[[j]]], {j, 1, n}] + (b2 - 1)*Sum[Log[x2[[j]]],
> {j, 1, n}] - (p + 2)*Sum[Log[1 + r1*x1[[j]]^b1 + r2*x2[[j]]^b2], {j, 1,
> n}]]
> x1 = {1.3, 1.33, 1.28, 1.25, 1.29, 1.32, 1.38, 1.24, 1.26, 1.24, 1.25,
> 1.3, 1.27, 1.3, 1.32, 1.31, 1.3, 1.26, 1.28, 1.31, 1.33, 1.29, 1.3,
> 1.32, 1.26, 1.3, 1.32,
>    1.35, 1.32, 1.29}
> x2 = {1.25, 1.32, 1.25, 1.3, 1.38, 1.32, 1.25, 1.29, 1.32, 1.35, 1.29,
> 1.33, 1.32, 1.26, 1.3, 1.25, 1.25, 1.29, 1.31, 1.31, 1.27, 1.26, 1.29,
> 1.31, 1.28, 1.33, 1.27,
>    1.26, 1.29, 1.32}
> rr = z_Complex -> {Re[z], Im[z]}
> sols = Table[Block[{b1, b2, p, Eqn1, Eqn2, Eqn3}, Eqn1 = D[LMN[r1, r2,
> b1, b2, p], b1] == 0; Eqn2 = D[LMN[r1, r2, b1, b2, p], b2] == 0;
>        Eqn3 = D[LMN[r1, r2, b1, b2, p], p] == 0; Join[{a -> r1, b ->
> r2}, FindRoot[{Eqn1, Eqn2, Eqn3}, {b1, 10}, {b2, 10}, {p, 10}]]], {r1,
> 0.001, 1, 0.15},
>      {r2, 0.001, 1, 0.15}] /. a -> r1 /. b -> r2
> pts = LMN[r1, r2, b1, b2, p] /. sols
>
> In[121]:=
> % /. rr
>
> =======================================
>
> Regards
> Shafiq
>
>
>

--
http://chris.chiasson.name/

```

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