Thread Subject:

A question about the chebfun() function

Hi folks,

I am using the chebfun function to find the eigenvalues and eigenfunctions of the following boundary value problem

D^4 y=lambda*y, y''(0)=y'''(0)=y''(1)=y'''(1)=0,

where D is the differential operator, lambda is the eigenvalue and the solution y is the corresponding eigenfunction.

I used the following code in chebfun:

L = chebop(@(x,u) diff(u,4), [0,1]);
L.lbc = @(u) diff(u,2);
L.lbc =@(u) diff(u,3);
L.rbc = @(u) diff(u,2);
L.rbc =@(u) diff(u,3);
[V,D] = eigs(L,trunc);
disp(diag(D)), toc

HOWEVER, the below error was reported

Error using eig
Matrix must be square.

Error in linop/eigs>bc_eig (line 288)
    [V,D] = eig(full(Amat),full(Pmat));

Error in linop/eigs (line 94)
    [V1,D1] = bc_eig(A,B,33,33,0,map,breaks);

Error in chebop/eigs (line 57)
[varargout{1:nargout}] = eigs(L,varargin{:});

Looks like I am on the right track but some nonsquare matrix caused that error. Sincerely appreciate your comments and suggestions.

Thanks.
Jeff

On 6/30/2012 10:04 PM, Jeff wrote:
> Hi folks,
>
> I am using the chebfun function to find the eigenvalues and eigenfunctions
>of the following boundary value problem
>
> D^4 y=lambda*y, y''(0)=y'''(0)=y''(1)=y'''(1)=0,
>
> where D is the differential operator, lambda is the eigenvalue and
>the solution y is the corresponding eigenfunction.
>
> I used the following code in chebfun:
>
> L = chebop(@(x,u) diff(u,4), [0,1]);
> L.lbc = @(u) diff(u,2);
> L.lbc =@(u) diff(u,3);
> L.rbc = @(u) diff(u,2);
> L.rbc =@(u) diff(u,3);
> [V,D] = eigs(L,trunc);
> disp(diag(D)), toc
>
> HOWEVER, the below error was reported
>
> Error using eig
> Matrix must be square.
>


what is trunc ? Please post complete code that can be run.

non square matrix does not have eigenvalues by definition.

" E = eig(X) is a vector containing the eigenvalues of a square
     matrix X."

note the words "square matrix" above.

try eig(sqrt(L*L')) instead and see if this helps in your problem.

--Nasser

Thanks Nasser!

The complete code is as follows:

trunc=30;
tic
L = chebop(@(x,u) diff(u,4), [0,1]);
L.lbc = @(u) diff(u,2);
L.lbc =@(u) diff(u,3);
L.rbc = @(u) diff(u,2);
L.rbc =@(u) diff(u,3);
[V,D] = eigs(L,trunc);
disp(diag(D)), toc

where trunc means how many eigenvalues I am asking for. In the above code, trunc=30 means I am asking chebfun() to find the first 30 eigenvalues.

I agree with you that the above code produces some nonsquare matrix, which causes this error. But presumably the above code should present some square matrix, right? I have no idea what causes such nonsquare matrix. I tested the examples included in the chebfun document, which all produce square matrices.

Thanks again for your kind help!
Jeff


"Nasser M. Abbasi" <nma@12000.org> wrote in message <jsofp0$996$1@speranza.aioe.org>...
> On 6/30/2012 10:04 PM, Jeff wrote:
> > Hi folks,
> >
> > I am using the chebfun function to find the eigenvalues and eigenfunctions
> >of the following boundary value problem
> >
> > D^4 y=lambda*y, y''(0)=y'''(0)=y''(1)=y'''(1)=0,
> >
> > where D is the differential operator, lambda is the eigenvalue and
> >the solution y is the corresponding eigenfunction.
> >
> > I used the following code in chebfun:
> >
> > L = chebop(@(x,u) diff(u,4), [0,1]);
> > L.lbc = @(u) diff(u,2);
> > L.lbc =@(u) diff(u,3);
> > L.rbc = @(u) diff(u,2);
> > L.rbc =@(u) diff(u,3);
> > [V,D] = eigs(L,trunc);
> > disp(diag(D)), toc
> >
> > HOWEVER, the below error was reported
> >
> > Error using eig
> > Matrix must be square.
> >
>
>
> what is trunc ? Please post complete code that can be run.
>
> non square matrix does not have eigenvalues by definition.
>
> " E = eig(X) is a vector containing the eigenvalues of a square
> matrix X."
>
> note the words "square matrix" above.
>
> try eig(sqrt(L*L')) instead and see if this helps in your problem.
>
> --Nasser

On 6/30/2012 10:49 PM, Jeff wrote:

> The complete code is as follows:
>
> trunc=30;
> tic
> L = chebop(@(x,u) diff(u,4), [0,1]);
> L.lbc = @(u) diff(u,2);
> L.lbc =@(u) diff(u,3);
> L.rbc = @(u) diff(u,2);
> L.rbc =@(u) diff(u,3);
> [V,D] = eigs(L,trunc);
> disp(diag(D)), toc
>

I do not use chebop. But I noticed you are using 'L.lbc=' on 2 lines.
would this not overwrite the previous line?
same with 'L.rbc=' ?

Isn't this like writing

x=4
x=5

?

Sorry, do not know use chebop. may be chebop does things
differently here.

Can't you extract the system matrix from the object L? Then
you can use eig on A*A' and sqrt() the result.

--Nasser

"Jeff " <jeffirish63@yahoo.com> wrote in message
news:jsoeno$qjv$1@newscl01ah.mathworks.com...
> Hi folks,
>
> I am using the chebfun function to find the eigenvalues and eigenfunctions
> of the following boundary value problem

*snip*

> HOWEVER, the below error was reported
> Error using eig
> Matrix must be square.
>
> Error in linop/eigs>bc_eig (line 288)
> [V,D] = eig(full(Amat),full(Pmat));

You'll probably need to contact the Chebfun team for help determining the
cause of this error.

http://www.mathworks.com/matlabcentral/fileexchange/23972-chebfun

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
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