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Re: NSolve keeps on running forever

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82702] Re: [mg82681] NSolve keeps on running forever
  • From: "Nabeel Butt" <nabeel.butt at gmail.com>
  • Date: Mon, 29 Oct 2007 05:32:52 -0500 (EST)
  • References: <18342578.1193602902297.JavaMail.root@m35>

Hi Bob,
        I have some problem and it would really help save my time.Say I have
a matrix of variables that is 6 by 6.I also have an identity matrix that is
6 by 6.I want to create an expression that takes the coressponding entries
in the matrices subtracts them and then takes their square.I will have 36
new variables and create an algebraic expression by adding them all.
       THanks .
            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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