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Re: NSolve keeps on running forever

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82695] Re: [mg82681] NSolve keeps on running forever
  • From: "Nabeel Butt" <nabeel.butt at gmail.com>
  • Date: Mon, 29 Oct 2007 05:29:15 -0500 (EST)
  • References: <18342578.1193602902297.JavaMail.root@m35>

Hi Bob,
        You are right!
      But I changed the problem from NSolve to optimisation.Its a weird
system of large equations and I would send it to you once I am finished.
        regards,
          Nabeel


On 10/28/07, DrMajorBob <drmajorbob at bigfoot.com> wrote:
>
> Here's an initial look at the size of your problem:
>
> Cases[{\!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(h = 2\), \(Length[y]\)]\(hca[A, c, h,
> y, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma], \[Gamma]]\)\),(\!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(s = 2\), \(Length[y]\)]\(hca[A, c, s,
> y, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma], \[Gamma]] .
> Transpose[hca[A, c, s, y, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3,
> \[Sigma], \[Gamma]]]\)\))},_Symbol,Infinity];
> %//Length
> %%//Union//Length
> 95139
> 43
>
> That's 95,139 mentions of 6 variables and 37 unknown parameters. In
> addition, you've equated matrices... which isn't legal syntax in NSolve,
> AFAIK. (Correct me if I'm wrong.) I'm surprised NSolve even tries.
>
> On top of that, the following:
>
> Sum[hca[A, c, h, y, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma],
> \[Gamma]], {h, 2, Length[y]}]
>
> when evaluated, involves terms such as
>
> 2[{1, 2, 3, 2, 1, 4, 5, 3, 2,
>   1}, 2, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma], \[Gamma]]
>
> 3[{1, 2, 3, 2, 1, 4, 5, 3, 2,
>   1}, 3, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma], \[Gamma]]
>
> and so forth. Probably that's not what you intended, right?
>
> Fix that, change the matrix equations into scalar equations (Thread might
> help), and try again.
>
> Bobby
>
> On Sun, 28 Oct 2007 04:03:50 -0500, Nabeel Butt <nabeel.butt at gmail.com>
> wrote:
>
> > Hi Guys,
> >            I have a system of equations that I want to solve.It has a
> > solution but NSolve seems to keep on running forever.I am pasting the
> > code
> > over here:
>
> >  h[y_,t_,\[Beta]0_,\[Beta]1_,\[Beta]2_,\[Beta]3_,\[Sigma]_,\[Gamma]_]:={{v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]]},{(y[[t-1]])*v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]]},{((y[[t-1]])^2)*v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]]},{(((v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]])^2)-\[Sigma]^2*((y[[t-1]])^3))},{(((v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]])^2)-\[Sigma]^2*((y[[t-1]])^3))*y[[t-1]]},{(((v[y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]])^2)-\[Sigma]^2*((y[[t-1]])^3))*((y[[t-1]])^3)}};
> >
> v[y_,t_,\[Beta]0_,\[Beta]1_,\[Beta]2_,\[Beta]3_,\[Sigma]_,\[Gamma]_]:=y[[t]]-y[[t-1]]-\[Beta]0-\[Beta]1*y[[t-1]]-\[Beta]2*((y[[t-1]])^2);
> >
> hca[A_,c_,t_,y_,\[Beta]0_,\[Beta]1_,\[Beta]2_,\[Beta]3_,\[Sigma]_,\[Gamma]_]:=(
> > A.h
> >
> [y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]])*w[A,c,t,y,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]];
> >
> w[A_,c_,t_,y_,\[Beta]0_,\[Beta]1_,\[Beta]2_,\[Beta]3_,\[Sigma]_,\[Gamma]_]:=
> > Min[1,c/Norm[A.h
> > [y,t,\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]]]];
> > *c=5.85;
> >
> A={{a11,a12,a13,a14,a15,a16},{a21,a22,a23,a24,a25,a26},{a31,a32,a33,a34,a35,a36},{a41,a42,a43,a44,a45,a46},{a51,a52,a53,a54,a55,a56},{a61,a62,a63,a64,a65,a66}};
> > y={1,2,3,2,1,4,5,3,2,1};
> > NSolve[{\!\(
> > \*UnderoverscriptBox[\(\[Sum]\), \(h = 2\), \(Length[y]\)]hca[A, c, h,
> y,
> > \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma],
> > \[Gamma]]\)=={{0},{0},{0},{0},{0},{0}},
> > 1/Length[y]*(\!\(
> > \*UnderoverscriptBox[\(\[Sum]\), \(s = 2\), \(Length[y]\)]hca[A, c, s,
> y,
> > \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3, \[Sigma], \[Gamma]] .
> > Transpose[hca[A, c, s, y, \[Beta]0, \[Beta]1, \[Beta]2, \[Beta]3,
> > \[Sigma],
> >
> \[Gamma]]]\))=={{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,0,1}}},{\[Beta]0,\[Beta]1,\[Beta]2,\[Beta]3,\[Sigma],\[Gamma]}]
> >
> > regards,
> >
> >  Nabeel*
>
>
>
> --
> DrMajorBob at bigfoot.com
>



-- 
Nabeel Butt
UWO,London
Ontario, Canada



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