Thread Subject: MATLAB cannot cope with this Jacobian matrix?

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Hi,

I have a 5 * 5 Jacobian matrix whose eigenvalues need to be
found. Let's call J this Jacobian matrix. I then do eig(J) in MATLAB,
and, after some minutes (~40 min.), I receive the so-magic message
==
Error, (in expand/bigprod) integer too large in context (in `sym')
==

I then tried, before typing eig(J), to type `clear maplemex.' But it
then never uses any of the processors on my machine.

Any idea? I need to find these eigenvalues... Okay, J is only composed
with `syms' variables, but it should work with it, shouldn't it?

Thanks!


- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- --

In the land of the blind, the one-eyed man is king.
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In general there is no symbolic solution to the eigenvalue problem in
dimensions 5 or higher.

For a numerical solution, convert your matrix to floating-point. You can
use the subs command to convert a variable to a floating-point value.
Then use the eig or eigs command.

Alan Weiss
MATLAB mathematical toolbox documentation

Merciadri Luca wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Hi,
>
> I have a 5 * 5 Jacobian matrix whose eigenvalues need to be
> found. Let's call J this Jacobian matrix. I then do eig(J) in MATLAB,
> and, after some minutes (~40 min.), I receive the so-magic message
> ==
> Error, (in expand/bigprod) integer too large in context (in `sym')
> ==
>
> I then tried, before typing eig(J), to type `clear maplemex.' But it
> then never uses any of the processors on my machine.
>
> Any idea? I need to find these eigenvalues... Okay, J is only composed
> with `syms' variables, but it should work with it, shouldn't it?
>
> Thanks!
>
>
> - --
> Merciadri Luca
> See http://www.student.montefiore.ulg.ac.be/~merciadri/
> - --
>
> In the land of the blind, the one-eyed man is king.
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Merciadri Luca <Luca.Merciadri@student.ulg.ac.be> wrote in message <87tytejw83.fsf@merciadriluca-station.MERCIADRILUCA>...
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Hi,
>
> I have a 5 * 5 Jacobian matrix whose eigenvalues need to be
> found. Let's call J this Jacobian matrix. I then do eig(J) in MATLAB,
> and, after some minutes (~40 min.), I receive the so-magic message
> ==
> Error, (in expand/bigprod) integer too large in context (in `sym')
> ==
>
> I then tried, before typing eig(J), to type `clear maplemex.' But it
> then never uses any of the processors on my machine.
>
> Any idea? I need to find these eigenvalues... Okay, J is only composed
> with `syms' variables, but it should work with it, shouldn't it?

If your matrix is symbolic, then go back to the
definition of what an eigenvalue means. The
eigenvalues are solutions to the characteristic
polynomial. But here that polynomial will be
a 5th order polynomial, with general symbolic
coefficients. Since we know that such a
polynomial has NO general solution for a 5th
or higher order polynomial, then this explains
why matlab failed.

It matters not how big or fast is your computer,
it still cannot solve the impossible.

John

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"John D'Errico" <woodchips@rochester.rr.com> writes:

> If your matrix is symbolic, then go back to the
> definition of what an eigenvalue means. The
> eigenvalues are solutions to the characteristic
> polynomial. But here that polynomial will be
> a 5th order polynomial, with general symbolic
> coefficients. Since we know that such a
> polynomial has NO general solution for a 5th
> or higher order polynomial, then this explains
> why matlab failed.
>
> It matters not how big or fast is your computer,
> it still cannot solve the impossible.
I totally agree with you and I had already thought about this, but it
is however possible for MATLAB to express a solution in analytical
form, i.e. give me eigenvalues with square roots, etc.

Okay, it is not guaranteed, but there are plenty of cases where it
happens to be possible.

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- --

It pays to pay attention.
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Alan Weiss <aweiss@mathworks.com> writes:

> In general there is no symbolic solution to the eigenvalue problem in
> dimensions 5 or higher.
Okay.

> For a numerical solution, convert your matrix to floating-point. You
> can use the subs command to convert a variable to a floating-point
> value. Then use the eig or eigs command.
Thanks, I did not know this command.

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- --

It takes two to tango.
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