ssk(3)

NAME

ssk - symmetric skyline matrix format

DESCRIPTION

The class implements a symmetric matrix Choleski factorization.
Let a be a square invertible matrix in
csr format (see csr(3)).

csr<Float> a;

We get the factorization by:

ssk<Float> m = ldlt(a);

Each call to the direct solver for a*x = b writes either:

vec<Float> x = m.solve(b);

or

m.solve(b,x);

DATA STRUCTURE

The storage is either skyline, multi-file or
chevron.
This alternative depends upon the configuration
(see . Installing}').
The chevron data structure is related to the multifrontal
algorithm and is implemented by using the spooles library.
The multi-file data structure refers to the out-of-core
algorithm and is implemented by using the taucs library.
If such a library is not available, the ssk class
implements a skyline storage scheme and the profil storage of the
ssk matrix is optimized by optimizing the renumbering,
by using the Gibbs, Pooles and Stockmeyer algorithm available
via the permutation class
(see permutation(3)).
@quotation Algorithm 582, collected Algorithms from ACM. Algorithm

appeared in ACM-Trans. Math. Software, vol.8, no. 2, Jun., 1982, p. 190.

@end quotation
When implementing the skyline data structure,
we can go back to the csr format, for the
pupose of pretty-printing:

cout << ps << color << logscale << csr<Float>(m);

IMPLEMENTATION

template<class T>
class ssk : smart_pointer<spooles_rep<T> > {
public:
// typedefs:

typedef T element_type;
typedef typename spooles_rep<T>::size_type size_type;

// allocators/deallocators:

ssk ();
explicit ssk<T> (const csr<T>&);

// accessors:

size_type nrow () const;
size_type ncol () const;
size_type nnz () const;

// factorisation and solver:

void solve(const vec<T>& b, vec<T>& x) const;
vec<T> solve(const vec<T>& b) const;
void factorize_ldlt();

protected:

const spooles_rep<T>& data() const {

return smart_pointer<spooles_rep<T> >::data();

}
spooles_rep<T>& data() {

return smart_pointer<spooles_rep<T> >::data();

}

};
template <class T>
ssk<T> ldlt (const csr<T>& m);

IMPLEMENTATION

template<class T>
class ssk : smart_pointer<umfpack_rep<T> > {
public:
// typedefs:

typedef T element_type;
typedef typename umfpack_rep<T>::size_type size_type;

// allocators/deallocators:

ssk ();
explicit ssk<T> (const csr<T>&);

// accessors:

size_type nrow () const;
size_type ncol () const;
size_type nnz () const;

// factorisation and solver:

void solve(const vec<T>& b, vec<T>& x) const;
vec<T> solve(const vec<T>& b) const;
void factorize_ldlt();
void factorize_lu();

protected:

const umfpack_rep<T>& data() const {

return smart_pointer<umfpack_rep<T> >::data();

}
umfpack_rep<T>& data() {

return smart_pointer<umfpack_rep<T> >::data();

}

};
template <class T>
ssk<T> ldlt (const csr<T>& m);

SEE ALSO

csr(3), permutation(3)

rheolef-5.89 ssk(3)