Re: [ublas] Size problem in operations on sparse matrices

From: Sourabh (sourabh_at_[hidden])
Date: 2007-03-02 07:34:18

On Fri, 2 Mar 2007, Gunter Winkler wrote:

> On Friday 02 March 2007 12:17, Sourabh wrote:
> > The following program aborts when I am trying to use assign.
> > What is the proper way of dealing with matrices of size 1e7, which are
> > sparse and lower triangular. 
> 
> see below.

Thanks. using compressed_matrix allowed me bigger sizes.

 
> > The question I have is, how costly is it to 
> > take inverse of such matrices ? 
> 
> Don't do this. The inverse of a sparse matrix is usually dense, the 
> computation time grows like n^3 (or even worse) and the error can be as large 
> as n^2 * 1.0e-14 ... I order to solve sparse linear systems you can either 
> use a direct method (provided by UMFPACK or CXSparse) or an iterative method 
> (provided by my examples or the Iterative Template Library). Solver for 
> triangular systems are also available.
> 
> (Or wait a few days/weeks until my native ublas sparse LU decomposition is 
> finished.)

Is it true even if the matrix (which I want inverse of) is lower 
triangular and sparse ? Actually I have a decision to make. I have a 
matrix of constant values, If I don't 
take inverse of that matrix, I have to solve the set of linear equations 
many 
times. On the other hand, if I take inverse of the matrix, I can compute 
the values (A * inv (X) + Y) once and store the matrix. (The size of X is 
1e7).  I am unable to decide which way will be faster or feasible in terms 
of storage and run time complexity ?

Could you please help me in deciding this ? 

> > I also have to do multiplication and 
> > addition of such matrices. 
> 
> multiplication is done by sparse_prod (operation_sparse.hpp) or simply by 
> prod(). Addition uses operator + () or operator += ().
> 
> > The improper way, as mentioned in the program 
> > below causes abortion of program.
> > The exact assertion used was :
> >
> > boost/numeric/ublas/functional.hpp at line 1406:
> > size2 == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size2
> > Aborted (core dumped)
> 
> mapped_matrix has the size limit 
> (size1*size2) < std::numeric_limits<size_type>::max
> 
> try compressed_matrix and have a look at the list archives at [2]
> 
> mfg
> Gunter
> 
> [1] http://www.bauv.unibw-muenchen.de/~winkler/ublas/examples/
> [2] http://dir.gmane.org/gmane.comp.lib.boost.ublas
> 
> 
> 

-- 
-- Sourabh