SaddlePointPrecondMatrix.h

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/*
 * (C) Copyright 2009-2016 ECMWF.
 * 
 * This software is licensed under the terms of the Apache Licence Version 2.0
 * which can be obtained at http://www.apache.org/licenses/LICENSE-2.0. 
 * In applying this licence, ECMWF does not waive the privileges and immunities 
 * granted to it by virtue of its status as an intergovernmental organisation nor
 * does it submit to any jurisdiction.
 */
 
#ifndef OOPS_ASSIMILATION_SADDLEPOINTPRECONDMATRIX_H_
#define OOPS_ASSIMILATION_SADDLEPOINTPRECONDMATRIX_H_
 
#include <boost/noncopyable.hpp>
 
#include "oops/assimilation/ControlIncrement.h"
#include "oops/assimilation/CostFctWeak.h"
#include "oops/assimilation/CostFunction.h"
#include "oops/assimilation/DualVector.h"
#include "oops/assimilation/SaddlePointVector.h"
 
namespace oops {
 
  /// The preconditioner for the saddle-point minimizer.
  /*!
   *  The solvers represent matrices as objects that implement a "multiply"
   *  method. This class defines objects that apply the saddle-point matrix.
   */
 
// -----------------------------------------------------------------------------
template<typename MODEL, typename OBS>
class SaddlePointPrecondMatrix : private boost::noncopyable {
  typedef ControlIncrement<MODEL, OBS>    CtrlInc_;
  typedef CostFctWeak<MODEL, OBS>         CostFctWeak_;
  typedef CostFunction<MODEL, OBS>        CostFct_;
  typedef SaddlePointVector<MODEL, OBS>   SPVector_;
 
 public:
  explicit SaddlePointPrecondMatrix(const CostFct_ & j);
  void multiply(const SPVector_ &, SPVector_ &) const;
 
 private:
  void Lhatinv(const CtrlInc_ &, CtrlInc_ &, const int) const;
  void Lhatinvt(const CtrlInc_ &, CtrlInc_ &, const int) const;
 
  const CostFctWeak_ & j_;
  const bool idmodel_;
};
 
// =============================================================================
 
template<typename MODEL, typename OBS>
SaddlePointPrecondMatrix<MODEL, OBS>::SaddlePointPrecondMatrix(const CostFct_ & j)
  : j_(dynamic_cast<const CostFctWeak_ &>(j)),
    idmodel_(false)
{}
 
// -----------------------------------------------------------------------------
 
template<typename MODEL, typename OBS>
void SaddlePointPrecondMatrix<MODEL, OBS>::multiply(const SPVector_ & x, SPVector_ & z) const {
  z.lambda().clear();
  z.lambda().dx(new CtrlInc_(j_.jb()));
  z.dx(new CtrlInc_(j_.jb()));
 
  int norder = 1;  // truncation order for Lhatinv and Lhatinvt
 
  Lhatinvt(x.dx(), z.lambda().dx(), norder);
 
  CtrlInc_ l(z.lambda().dx());
  j_.jb().multiplyB(z.lambda().dx(), l);
  l *= -1.0;
  l += x.lambda().dx();
 
  Lhatinv(l, z.dx(), norder);
 
  for (unsigned jj = 0; jj < j_.nterms(); ++jj) {
    z.lambda().append(j_.jterm(jj).multiplyCoInv(*x.lambda().getv(jj)));
  }
}
 
// -----------------------------------------------------------------------------
 
template<typename MODEL, typename OBS>
void SaddlePointPrecondMatrix<MODEL, OBS>::Lhatinv(const CtrlInc_ & xx, CtrlInc_ & zz,
                                                   const int norder) const {
// Approximate L=I + (I-L) + (I-L)^2 + ... + (I-L)^norder
  CtrlInc_ ww(xx);
 
  zz = xx;
  for (int jj = 0; jj < norder; ++jj) {
    j_.runTLM(ww, idmodel_);
    ww.shift_forward();
    zz += ww;
  }
}
 
// -----------------------------------------------------------------------------
 
template<typename MODEL, typename OBS>
void SaddlePointPrecondMatrix<MODEL, OBS>::Lhatinvt(const CtrlInc_ & xx, CtrlInc_ & zz,
                                                    const int norder) const {
// Approximate L'=I + (I-L') + (I-L')^2 + ... + (I-L')^norder
  CtrlInc_ ww(xx);
 
  zz = xx;
  for (int jj = 0; jj < norder; ++jj) {
    ww.shift_backward();
    j_.runADJ(ww, idmodel_);
    zz += ww;
  }
}
 
// -----------------------------------------------------------------------------
}  // namespace oops
 
#endif  // OOPS_ASSIMILATION_SADDLEPOINTPRECONDMATRIX_H_