[Getfem-users] Re: gmm 2.0.2, sub index question

[Yves Renard]

Le Jeudi 01 Mars 2007 10:33, vous avez écrit :

>   Is it possible to obtain a sparse matrix from a larger one, removing
> only a specified column/row?  So far I use the sub_index (collection)
> syntax, but my matrices are really really large (2*10^6 times 2*10^6)
> and this makes it really slow, in the order of one minute to remove just
> one row/column in a gmm::copy.

Hi Sebastian,

Yes, there should be some more appropriate procedure to suppress a line or a 
column to a large sparse matrix.

First other method, you can use two copy with a sub_interval. For instance if 
you want to suppress the line of index i :

M of size n x n, M2 of size (n-1) x n

gmm::copy(gmm::sub_matrix(M, gmm::sub_interval(0, i), gmm::sub_interval(0, n), 
gmm::sub_matrix(M2, gmm::sub_interval(0, i), gmm::sub_interval(0, n));

gmm::copy(gmm::sub_matrix(M, gmm::sub_interval(i+1, n-i-1), 
gmm::sub_interval(0, n), gmm::sub_matrix(M2, gmm::sub_interval(i, n-i-1), 
gmm::sub_interval(0, n));

May be a faster method is to build an appropriate sparse matrix H having only 
a "1" on each line and apply a matrix multiplication:

M of size n x n, M2 of size (n-1) x n, H of size (n-1) x n,
For (unsigned k = 0; k < i; ++k) H(k, k) = 1.0;
For (unsigned k = i+1; k < n; ++k) H(k-1, k) = 1.0;
gmm::mult(H, M, M2);

But, dont forget the following rule : If M is a row matrix, then H can be 
either a row or a column matrix but if M is a column matrix then H should be 
a column matrix too.

Of course, an even faster method should be to adapt a particular algorithm to 
supress a line or a column to a particular sparse matrix implementation. What 
kind of matrix do you use ?

-- 
Yves.

-------------------------------------------------------------------------
  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
  Institut Camille Jordan - CNRS UMR 5208
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard
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