oops::DRGMRESRMinimizer< MODEL > Class Template Reference

Derber-Rosati GMRESR Minimizer. More...

#include <DRGMRESRMinimizer.h>

Inheritance diagram for oops::DRGMRESRMinimizer< MODEL >:

Collaboration diagram for oops::DRGMRESRMinimizer< MODEL >:

Public Member Functions
const std::string	classname () const override
	DRGMRESRMinimizer (const eckit::Configuration &, const CostFct_ &J)
	~DRGMRESRMinimizer ()
Public Member Functions inherited from oops::DRMinimizer< MODEL >
	DRMinimizer (const CostFct_ &J)
	~DRMinimizer ()
Public Member Functions inherited from oops::Minimizer< MODEL >
	Minimizer (const CostFct_ &J)
virtual	~Minimizer ()
ControlIncrement< MODEL > *	minimize (const eckit::Configuration &)

Private Types
typedef BMatrix< MODEL >	Bmat_
typedef CostFunction< MODEL >	CostFct_
typedef ControlIncrement< MODEL >	CtrlInc_
typedef HtRinvHMatrix< MODEL >	HtRinvH_

Private Member Functions
double	solve (CtrlInc_ &, CtrlInc_ &, CtrlInc_ &, const Bmat_ &, const HtRinvH_ &, const double, const double, const int, const double) override

Detailed Description

template<typename MODEL>
class oops::DRGMRESRMinimizer< MODEL >

Derber-Rosati GMRESR Minimizer.

Derber-Rosati GMRESR solver for Ax=b.

DRGMRESR solver for Ax=b. This is a "double" version of GMRESR (H.A. Van der Vorst and C. Vuik, 1994, Numerical Linear Algebra with Applications, 1(4), 369-386) following Derber and Rosati (J. Derber and A. Rosati, 1989, J. Phys. Oceanog. 1333-1347). It solves Ax=b for the particular case \( A=B^{-1}+C\), without requiring the application of \( B^{-1}\). A must be square, but need not be symmetric. (For a symmetric matrix, and constant preconditioner, DRGMRESR is simply Derber-Rosati PCG with full orthogonalisation.) A preconditioner must be supplied that, given a vector q, returns an approximate solution of \( (AB)^{-1} q\). The preconditioner can be variable. Note that the traditional \( B\)-preconditioning corresponds to precond= \(I\).

On entry:

• x = starting point, \( X_0 \).
• xh = \( B^{-1} x_0\).
• B = \( B \).
• C = \( C \).
• precond = preconditioner matrix \( F_k \approx (AB)^{-1} \).

On exit, x will contain the solution \( x \) and xh will contain \( B^{-1} x\).

Matrices must implement a method:

• void multiply(const VECTOR&, VECTOR&) const

which applies the matrix to the first argument, and returns the matrix-vector product in the second. (Note: the const is optional, but recommended.)

Iteration will stop if the maximum iteration limit "maxiter" is reached or if the residual norm reduces by a factor of "tolerance".

The return value is the achieved reduction in residual norm.

Definition at line 72 of file DRGMRESRMinimizer.h.

Member Typedef Documentation

Bmat_

template<typename MODEL >

typedef BMatrix<MODEL> oops::DRGMRESRMinimizer< MODEL >::Bmat_

private

Definition at line 73 of file DRGMRESRMinimizer.h.

CostFct_

template<typename MODEL >

typedef CostFunction<MODEL> oops::DRGMRESRMinimizer< MODEL >::CostFct_

private

Definition at line 74 of file DRGMRESRMinimizer.h.

CtrlInc_

template<typename MODEL >

typedef ControlIncrement<MODEL> oops::DRGMRESRMinimizer< MODEL >::CtrlInc_

private

Definition at line 75 of file DRGMRESRMinimizer.h.

HtRinvH_

template<typename MODEL >

typedef HtRinvHMatrix<MODEL> oops::DRGMRESRMinimizer< MODEL >::HtRinvH_

private

Definition at line 76 of file DRGMRESRMinimizer.h.

Constructor & Destructor Documentation

DRGMRESRMinimizer()

template<typename MODEL >

oops::DRGMRESRMinimizer< MODEL >::DRGMRESRMinimizer ( const eckit::Configuration &  , const CostFct_ &  J  )

inline

Definition at line 80 of file DRGMRESRMinimizer.h.

~DRGMRESRMinimizer()

template<typename MODEL >

oops::DRGMRESRMinimizer< MODEL >::~DRGMRESRMinimizer ( )

inline

Definition at line 81 of file DRGMRESRMinimizer.h.

Member Function Documentation

classname()

template<typename MODEL >

const std::string oops::DRGMRESRMinimizer< MODEL >::classname ( ) const

inlineoverridevirtual

Implements oops::DRMinimizer< MODEL >.

Definition at line 79 of file DRGMRESRMinimizer.h.

solve()

template<typename MODEL >

double oops::DRGMRESRMinimizer< MODEL >::solve ( CtrlInc_ &  xx, CtrlInc_ &  xh, CtrlInc_ &  rr, const Bmat_ &  B, const HtRinvH_ &  HtRinvH, const double  costJ0Jb, const double  costJ0JoJc, const int  maxiter, const double  tolerance  )

overrideprivatevirtual

Implements oops::DRMinimizer< MODEL >.

Definition at line 90 of file DRGMRESRMinimizer.h.

Here is the call graph for this function:

---

The documentation for this class was generated from the following file:

• DRGMRESRMinimizer.h