oops::RPCGMinimizer< MODEL > Class Template Reference

RPCG Minimizer. More...

#include <RPCGMinimizer.h>

Inheritance diagram for oops::RPCGMinimizer< MODEL >:

Collaboration diagram for oops::RPCGMinimizer< MODEL >:

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

Private Types
typedef CostFunction< MODEL >	CostFct_
typedef DualVector< MODEL >	Dual_
typedef HBHtMatrix< MODEL >	HBHt_
typedef RinvMatrix< MODEL >	Rinv_

Private Member Functions
double	solve (Dual_ &, double &, Dual_ &, const HBHt_ &, const Rinv_ &, const int &, const double &, Dual_ &, const double &) override

Detailed Description

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

RPCG Minimizer.

Augmented Restricted Preconditioned Conjugate Gradients.

This solver is based on the algorithm proposed in Gratton and Tshimanga, QJRMS, 135: 1573-1585 (2009). It performs minimization in observation space.

It solves the linear system \( (I + R^{-1}HBH^T) lambda = H^T R^{-1}d \) with \( HBH^T \) inner-product in the augmented observation space.

Note that the traditional \( B\)-preconditioning in model space corresponds to \(I\) for this algorithm.

A second-level preconditioner, \( G \), must be symmetric and positive definite with respect to \( HBH^T \) inner-product. Possible preconditioning is detailed in S. Gurol, PhD Manuscript, 2013.

On entry:

• vv = starting point, \( v_0 \).
• vvp = starting point augmented part, \( vp_0 \)
• rr = right hand side.
• dy = \( H (xb - xk) \)
• sigma = \( (xb - xk)^T B^{-1} (xb - xk)\).
• HBHt = \( HBH^T \).
• Rinv = \( R^{-1} \).
• G = preconditioner \( G \).
• Gt = preconditioner transpose \( G^T \).

On exit, vv and vvp will contain the solution \( lambda = [vv; vp] \)

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 preconditioned residual norm reduces by a factor of "tolerance".

Definition at line 67 of file RPCGMinimizer.h.

Member Typedef Documentation

CostFct_

template<typename MODEL >

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

private

Definition at line 68 of file RPCGMinimizer.h.

Dual_

template<typename MODEL >

typedef DualVector<MODEL> oops::RPCGMinimizer< MODEL >::Dual_

private

Definition at line 69 of file RPCGMinimizer.h.

HBHt_

template<typename MODEL >

typedef HBHtMatrix<MODEL> oops::RPCGMinimizer< MODEL >::HBHt_

private

Definition at line 70 of file RPCGMinimizer.h.

Rinv_

template<typename MODEL >

typedef RinvMatrix<MODEL> oops::RPCGMinimizer< MODEL >::Rinv_

private

Definition at line 71 of file RPCGMinimizer.h.

Constructor & Destructor Documentation

RPCGMinimizer()

template<typename MODEL >

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

inline

Definition at line 75 of file RPCGMinimizer.h.

~RPCGMinimizer()

template<typename MODEL >

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

inline

Definition at line 76 of file RPCGMinimizer.h.

Member Function Documentation

classname()

template<typename MODEL >

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

inlineoverridevirtual

Implements oops::DualMinimizer< MODEL >.

Definition at line 74 of file RPCGMinimizer.h.

solve()

template<typename MODEL >

double oops::RPCGMinimizer< MODEL >::solve ( Dual_ &  vv, double &  vvp, Dual_ &  rr, const HBHt_ &  HBHt, const Rinv_ &  Rinv, const int &  maxiter, const double &  tolerance, Dual_ &  dy, const double &  sigma  )

overrideprivatevirtual

Implements oops::DualMinimizer< MODEL >.

Definition at line 86 of file RPCGMinimizer.h.

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

• RPCGMinimizer.h