MATLAB cannot cope with this Jacobian matrix?
in [Matlab]
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From: Merciadri Luca on 18 Feb 2010 12:21 -----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. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkt9dxwACgkQM0LLzLt8MhxihACfUI0au8Nrk8M6ggoe+pZjv1t0 FXcAn1/IHnOO6jjK7fSnAq7VqlU9LJkR =P5NT -----END PGP SIGNATURE-----
From: Alan Weiss on 18 Feb 2010 14:07 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. > -----BEGIN PGP SIGNATURE----- > Version: GnuPG v1.4.9 (GNU/Linux) > Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> > > iEYEARECAAYFAkt9dxwACgkQM0LLzLt8MhxihACfUI0au8Nrk8M6ggoe+pZjv1t0 > FXcAn1/IHnOO6jjK7fSnAq7VqlU9LJkR > =P5NT > -----END PGP SIGNATURE-----
From: John D'Errico on 18 Feb 2010 14:28 Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote in message <87tytejw83.fsf(a)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
From: Merciadri Luca on 18 Feb 2010 15:27 -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 "John D'Errico" <woodchips(a)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. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkt9oqsACgkQM0LLzLt8MhwAXwCfa1BaK5iYxhzyBFHruxMbb7LD QUYAmwZ8HJEgO7eUONvJvXU8e91DsFra =WOc6 -----END PGP SIGNATURE-----
From: Merciadri Luca on 18 Feb 2010 15:29 -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Alan Weiss <aweiss(a)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. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkt9o0EACgkQM0LLzLt8Mhx6SgCfWqHaNajvda4XSNZE8rOTolKY vkgAniVneA5bq1BgM5tLvVx9XJ4Ghp9Z =h5iv -----END PGP SIGNATURE-----
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