Classes | |
struct | AdditionalData |
Public Member Functions | |
SolverQMRS (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData()) | |
SolverQMRS (SolverControl &cn, const AdditionalData &data=AdditionalData()) | |
template<class MATRIX , class PRECONDITIONER > | |
void | solve (const MATRIX &A, VECTOR &x, const VECTOR &b, const PRECONDITIONER &precondition) |
virtual void | print_vectors (const unsigned int step, const VECTOR &x, const VECTOR &r, const VECTOR &d) const |
Protected Member Functions | |
virtual double | criterion () |
Protected Attributes | |
VECTOR * | Vv |
VECTOR * | Vp |
VECTOR * | Vq |
VECTOR * | Vt |
VECTOR * | Vd |
VECTOR * | Vx |
const VECTOR * | Vb |
double | res2 |
AdditionalData | additional_data |
Private Member Functions | |
template<class MATRIX , class PRECONDITIONER > | |
bool | iterate (const MATRIX &A, const PRECONDITIONER &precondition) |
Private Attributes | |
unsigned int | step |
Quasi-minimal residual method for symmetric matrices.
The QMRS method is supposed to solve symmetric indefinite linear systems with symmetric, not necessarily definite preconditioners. This version of QMRS is adapted from Freund/Nachtigal: Software for simplified Lanczos and QMR algorithms, Appl. Num. Math. 19 (1995), pp. 319-341
This version is for right preconditioning only, since then only the preconditioner is used: left preconditioning seems to require the inverse.
For the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class.
Like all other solver classes, this class has a local structure called AdditionalData
which is used to pass additional parameters to the solver, like damping parameters or the number of temporary vectors. We use this additional structure instead of passing these values directly to the constructor because this makes the use of the SolverSelector
and other classes much easier and guarantees that these will continue to work even if number or type of the additional parameters for a certain solver changes.
However, since the QMRS method does not need additional data, the respective structure is empty and does not offer any functionality. The constructor has a default argument, so you may call it without the additional parameter.
SolverQMRS< VECTOR >::SolverQMRS | ( | SolverControl & | cn, | |
VectorMemory< VECTOR > & | mem, | |||
const AdditionalData & | data = AdditionalData() | |||
) |
Constructor.
SolverQMRS< VECTOR >::SolverQMRS | ( | SolverControl & | cn, | |
const AdditionalData & | data = AdditionalData() | |||
) |
Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
void SolverQMRS< VECTOR >::solve | ( | const MATRIX & | A, | |
VECTOR & | x, | |||
const VECTOR & | b, | |||
const PRECONDITIONER & | precondition | |||
) | [inline] |
Solve the linear system for x.
virtual void SolverQMRS< VECTOR >::print_vectors | ( | const unsigned int | step, | |
const VECTOR & | x, | |||
const VECTOR & | r, | |||
const VECTOR & | d | |||
) | const [virtual] |
Interface for derived class. This function gets the current iteration vector, the residual and the update vector in each step. It can be used for a graphical output of the convergence history.
virtual double SolverQMRS< VECTOR >::criterion | ( | ) | [protected, virtual] |
Implementation of the computation of the norm of the residual.
bool SolverQMRS< VECTOR >::iterate | ( | const MATRIX & | A, | |
const PRECONDITIONER & | precondition | |||
) | [inline, private] |
The iteration loop itself.
VECTOR* SolverQMRS< VECTOR >::Vv [protected] |
Temporary vectors, allocated through the VectorMemory
object at the start of the actual solution process and deallocated at the end.
VECTOR* SolverQMRS< VECTOR >::Vp [protected] |
VECTOR* SolverQMRS< VECTOR >::Vq [protected] |
VECTOR* SolverQMRS< VECTOR >::Vt [protected] |
VECTOR* SolverQMRS< VECTOR >::Vd [protected] |
VECTOR* SolverQMRS< VECTOR >::Vx [protected] |
Iteration vector.
const VECTOR* SolverQMRS< VECTOR >::Vb [protected] |
RHS vector.
double SolverQMRS< VECTOR >::res2 [protected] |
Within the iteration loop, the square of the residual vector is stored in this variable. The function criterion
uses this variable to compute the convergence value, which in this class is the norm of the residual vector and thus the square root of the res2
value.
AdditionalData SolverQMRS< VECTOR >::additional_data [protected] |
Additional parameters..
unsigned int SolverQMRS< VECTOR >::step [private] |
The current iteration step.