11-28-2008
None over there to solve this??
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my input
a b c d e f g
k i m g i k l
b i n g o h m
a b c d e
b i n g o
my output
a b c d e f g
k i m g i k l
b i n g o h m
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LEARN ABOUT DEBIAN
solver
solver(2rheolef) rheolef-6.1 solver(2rheolef)
NAME
solver - direct or interative solver interface
DESCRIPTION
The class implements a matrix factorization:
LU factorization for an unsymmetric matrix and
Choleski fatorisation for a symmetric one.
Let a be a square invertible matrix in
csr format (see csr(2)).
csr<Float> a;
We get the factorization by:
solver<Float> sa (a);
Each call to the direct solver for a*x = b writes either:
vec<Float> x = sa.solve(b);
When the matrix is modified in a computation loop but
conserves its sparsity pattern, an efficient re-factorization
writes:
sa.update_values (new_a);
x = sa.solve(b);
This approach skip the long step of the symbolic factization step.
ITERATIVE SOLVER
The factorization can also be incomplete, i.e. a pseudo-inverse,
suitable for preconditionning iterative methods.
In that case, the sa.solve(b) call runs a conjugate gradient
when the matrix is symmetric, or a generalized minimum residual
algorithm when the matrix is unsymmetric.
AUTOMATIC CHOICE AND CUSTOMIZATION
The symmetry of the matrix is tested via the a.is_symmetric() property
(see csr(2)) while the choice between direct or iterative solver
is switched from the a.pattern_dimension() value. When the pattern
is 3D, an iterative method is faster and less memory consuming.
Otherwhise, for 1D or 2D problems, the direct method is prefered.
These default choices can be supersetted by using explicit options:
solver_option_type opt;
opt.iterative = true;
solver<Float> sa (a, opt);
See the solver.h header for the complete list of available options.
IMPLEMENTATION NOTE
The implementation bases on the pastix library.
IMPLEMENTATION
template <class T, class M = rheo_default_memory_model>
class solver_basic : public smart_pointer<solver_rep<T,M> > {
public:
// typedefs:
typedef solver_rep<T,M> rep;
typedef smart_pointer<rep> base;
// allocator:
solver_basic ();
explicit solver_basic (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
void update_values (const csr<T,M>& a);
// accessors:
vec<T,M> trans_solve (const vec<T,M>& b) const;
vec<T,M> solve (const vec<T,M>& b) const;
};
// factorizations:
template <class T, class M>
solver_basic<T,M> ldlt(const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
template <class T, class M>
solver_basic<T,M> lu (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
template <class T, class M>
solver_basic<T,M> ic0 (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
template <class T, class M>
solver_basic<T,M> ilu0(const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
typedef solver_basic<Float> solver;
SEE ALSO
csr(2), csr(2)
rheolef-6.1 rheolef-6.1 solver(2rheolef)