Re: [Getfem-users] GMM - orthonormals basis for range of matrix

[Yves Renard]

Dear P. Berger,

No, there is no specific function in Gmm to compute the orthonormal basis for the range of a matrix. (There is a function which is range_basis in gmm_range_basis.h but it is for large sparse matrices and this extract only a basis, it do not perform an orthogonalization).

The class in gmm_modified_gram_schmidt.h header is mainly used by gmres algorithm. It works on a dense matrix.
The function "orthogonalize" performs the ortogonalization of the vector number i, storing the scalar  products in a vector Hi. This means that before calling "orthogonalize" you need to fill the vectors V[i] of the object  modified_gram_schmidt. This is really adapted to the gmres algorithm. Probably, in your case, it is simpler to just copy the loop of the function orthogonalize than using the modified_gram_schmidt object.

Yves.


Le 18/09/2013 18:26, Philipp Berger a écrit :

To whom it may concern,

sorry for asking something of such simple nature, but I can not figure it out on my own.

Is GMM able to calculate the orthonormal basis for the range of a matrix? Something like "orth()" in Matlab ( http://www.mathworks.de/help/matlab/ref/orth.html ).
I found the gmm_modified_gram_schmidt header, which seems to be what I want but since there is no documentation on the functions I find myself unable to understand how they are meant to be applied.

For example, given a matrix M:
gmm::row_matrix<gmm::wsvector<double>> M1;
M1.resize(4,4);
// Insert some data

And now I would like to get a matrix containg the orthonormal base of M1.

Thank you for your time,

P. Berger

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  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
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