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

DRPCG Minimizer. More...

#include <DRPCGMinimizer.h>

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

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

Public Member Functions
const std::string	classname () const override
	DRPCGMinimizer (const eckit::Configuration &, const CostFct_ &)
	~DRPCGMinimizer ()
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::DRPCGMinimizer< MODEL, OBS >

DRPCG Minimizer.

Derber-Rosati Preconditioned Conjugate Gradients solver.

This solver is based on the standard Preconditioned Conjugate Gradients solver for Ax=b (G. H. Golub and C. F. Van Loan, Matrix Computations), and on the Derber and Rosati double PCG algorithm (J. Derber and A. Rosati, 1989, J. Phys. Oceanog. 1333-1347). For details see S. Gurol, PhD Manuscript, 2013. It solves \( Ax=b\) for the particular case \( A=B^{-1}+C\), without requiring the application of \( B^{-1}\). This algorithm is similar to DRIPCG except it includes standard PCG instead IPCG and stopping criteria is based on the preconditioner norm.

A must be square, symmetric, positive definite.

A preconditioner must be supplied that, given a vector q, returns an approximation to \( (AB)^{-1} q\). Possible preconditioning is detailed in S. Gurol, PhD Manuscript, 2013. Note that the traditional \( B\)-preconditioning corresponds to precond= \(I\).

On entry:

• dx = starting point, \( dx_{0} \).
• dxh = \( B^{-1} dx_{0} \).
• rr = \( (sum B^-1 dx^{b}_{i} + ) H^T R^{-1} d \)
• B = \( B \).
• C = \( C \).
• precond = preconditioner \( F_k \approx (AB)^{-1} \).

On exit, dx will contain the solution \( dx \) and dxh will contain \( B^{-1} dx\). The return value is the achieved reduction in preconditioned 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 matrix 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.)

Definition at line 79 of file DRPCGMinimizer.h.

Member Typedef Documentation

Bmat_

template<typename MODEL , typename OBS >

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

private

Definition at line 80 of file DRPCGMinimizer.h.

CostFct_

template<typename MODEL , typename OBS >

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

private

Definition at line 81 of file DRPCGMinimizer.h.

CtrlInc_

template<typename MODEL , typename OBS >

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

private

Definition at line 82 of file DRPCGMinimizer.h.

HtRinvH_

template<typename MODEL , typename OBS >

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

private

Definition at line 83 of file DRPCGMinimizer.h.

Constructor & Destructor Documentation

DRPCGMinimizer()

template<typename MODEL , typename OBS >

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

Definition at line 100 of file DRPCGMinimizer.h.

~DRPCGMinimizer()

template<typename MODEL , typename OBS >

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

inline

Definition at line 88 of file DRPCGMinimizer.h.

Member Function Documentation

classname()

template<typename MODEL , typename OBS >

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

inlineoverridevirtual

Implements oops::DRMinimizer< MODEL, OBS >.

Definition at line 86 of file DRPCGMinimizer.h.

solve()

template<typename MODEL , typename OBS >

double oops::DRPCGMinimizer< MODEL, OBS >::solve ( CtrlInc_ &  dx, CtrlInc_ &  dxh, 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 107 of file DRPCGMinimizer.h.

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Member Data Documentation

lmp_

template<typename MODEL , typename OBS >

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

private

Definition at line 94 of file DRPCGMinimizer.h.

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

• DRPCGMinimizer.h