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Re: NSolve keeps on running forever

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82729] Re: [mg82681] NSolve keeps on running forever
  • From: DrMajorBob <drmajorbob at bigfoot.com>
  • Date: Tue, 30 Oct 2007 03:23:01 -0500 (EST)
  • References: <18342578.1193602902297.JavaMail.root@m35> <op.t0xemrpkqu6oor@monster.gateway.2wire.net> <2111825.1193666327269.JavaMail.root@m35>
  • Reply-to: drmajorbob at bigfoot.com

Something like

#.#&[Flatten[matrix1-matrix2]]

Bobby

On Sun, 28 Oct 2007 20:43:36 -0500, Nabeel Butt <nabeel.butt at gmail.com> 
wrote:

> 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]_,\[G=
amma]_]:=(
>> > 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]_,\[Gam=
ma]_]:=
>> > 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,a=
62,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
>>
>
>
>



-- =

DrMajorBob at bigfoot.com


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