oops::DRIPCGMinimizer< MODEL, OBS > Class Template Reference

Derber-Rosati IPCG Minimizer. More...

#include <DRIPCGMinimizer.h>

Inheritance diagram for oops::DRIPCGMinimizer< MODEL, OBS >:

Collaboration diagram for oops::DRIPCGMinimizer< MODEL, OBS >:

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

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

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

Private Attributes
QNewtonLMP< CtrlInc_, Bmat_ >	lmp_

Detailed Description

template<typename MODEL, typename OBS>
class oops::DRIPCGMinimizer< MODEL, OBS >

Derber-Rosati IPCG Minimizer.

Derber-Rosati Inexact-Preconditioned Conjugate Gradients solver.

This solver is based on the Golub-Ye Inexact-Preconditioned Conjugate Gradients solver for Ax=b (G.H. Golub and Q. Ye 1999/00, SIAM J. Sci. Comput. 21(4) 1305-1320), and on the Derber and Rosati double PCG algorithm (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, symmetric, positive definite.

A preconditioner must be supplied that, given a vector q, returns an approximation to \( (AB)^{-1} q\). 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 = right hand side.
• B = \( B \).
• C = \( C \).
• precond = preconditioner \( F_k \approx (AB)^{-1} \).

On exit, x will contain the solution \( x \) and xh will contain \( B^{-1} x\). The return value is the achieved reduction in residual norm.

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

Each of BMATRIX, CMATRIX and PMATRIX 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 optonal, but recommended.)

Definition at line 75 of file DRIPCGMinimizer.h.

Member Typedef Documentation

Bmat_

template<typename MODEL , typename OBS >

typedef BMatrix<MODEL, OBS> oops::DRIPCGMinimizer< MODEL, OBS >::Bmat_

private

Definition at line 76 of file DRIPCGMinimizer.h.

CostFct_

template<typename MODEL , typename OBS >

typedef CostFunction<MODEL, OBS> oops::DRIPCGMinimizer< MODEL, OBS >::CostFct_

private

Definition at line 77 of file DRIPCGMinimizer.h.

CtrlInc_

template<typename MODEL , typename OBS >

typedef ControlIncrement<MODEL, OBS> oops::DRIPCGMinimizer< MODEL, OBS >::CtrlInc_

private

Definition at line 78 of file DRIPCGMinimizer.h.

HtRinvH_

template<typename MODEL , typename OBS >

typedef HtRinvHMatrix<MODEL, OBS> oops::DRIPCGMinimizer< MODEL, OBS >::HtRinvH_

private

Definition at line 79 of file DRIPCGMinimizer.h.

Constructor & Destructor Documentation

DRIPCGMinimizer()

template<typename MODEL , typename OBS >

oops::DRIPCGMinimizer< MODEL, OBS >::DRIPCGMinimizer	(	const eckit::Configuration &	conf,
		const CostFct_ &	J
	)

Definition at line 96 of file DRIPCGMinimizer.h.

~DRIPCGMinimizer()

template<typename MODEL , typename OBS >

oops::DRIPCGMinimizer< MODEL, OBS >::~DRIPCGMinimizer ( )

inline

Definition at line 84 of file DRIPCGMinimizer.h.

Member Function Documentation

classname()

template<typename MODEL , typename OBS >

const std::string oops::DRIPCGMinimizer< MODEL, OBS >::classname ( ) const

inlineoverridevirtual

Implements oops::DRMinimizer< MODEL, OBS >.

Definition at line 82 of file DRIPCGMinimizer.h.

solve()

template<typename MODEL , typename OBS >

double oops::DRIPCGMinimizer< MODEL, OBS >::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, OBS >.

Definition at line 103 of file DRIPCGMinimizer.h.

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Member Data Documentation

lmp_

template<typename MODEL , typename OBS >

QNewtonLMP<CtrlInc_, Bmat_> oops::DRIPCGMinimizer< MODEL, OBS >::lmp_

private

Definition at line 90 of file DRIPCGMinimizer.h.

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

• DRIPCGMinimizer.h