DRMinimizer.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_DRMINIMIZER_H_
#define OOPS_ASSIMILATION_DRMINIMIZER_H_
 
#include <limits>
#include <memory>
#include <string>
#include <vector>
 
#include "eckit/config/Configuration.h"
#include "oops/assimilation/BMatrix.h"
#include "oops/assimilation/ControlIncrement.h"
#include "oops/assimilation/CostFunction.h"
#include "oops/assimilation/HtRinvHMatrix.h"
#include "oops/assimilation/Minimizer.h"
#include "oops/assimilation/RinvHMatrix.h"
 
#include "oops/util/dot_product.h"
#include "oops/util/FloatCompare.h"
#include "oops/util/formats.h"
#include "oops/util/Logger.h"
 
namespace oops {
 
/// DR (Derber and Rosati) Minimizers
/*!
 * DRMinimizer is the base class for all minimizers that use \f$ B\f$ to
 * precondition the variational minimisation problem and use the auxiliary
 * variable \f$ \hat{x}=B^{-1}x\f$ and to update it in parallel to \f$ x\f$
 * based on Derber and Rosati, 1989, J. Phys. Oceanog. 1333-1347.
 * \f$ J_b\f$ is then computed as \f$ x^T\hat{x}\f$ eliminating the need for
 * \f$ B^{-1}\f$ or \f$ B^{1/2}\f$.
 */
 
// -----------------------------------------------------------------------------
 
template<typename MODEL, typename OBS> class DRMinimizer : public Minimizer<MODEL, OBS> {
  typedef BMatrix<MODEL, OBS>             Bmat_;
  typedef CostFunction<MODEL, OBS>        CostFct_;
  typedef ControlIncrement<MODEL, OBS>    CtrlInc_;
  typedef HtRinvHMatrix<MODEL, OBS>       HtRinvH_;
  typedef Minimizer<MODEL, OBS>           Minimizer_;
  typedef RinvHMatrix<MODEL, OBS>         RinvH_;
 
 public:
  explicit DRMinimizer(const CostFct_ & J): Minimizer_(J), J_(J), gradJb_(), costJ0Jb_(0) {}
  ~DRMinimizer() {}
  const std::string classname() const override = 0;
 
 private:
  CtrlInc_ * doMinimize(const eckit::Configuration &) override;
  virtual double solve(CtrlInc_ &, CtrlInc_ &, CtrlInc_ &,
                       const Bmat_ &, const HtRinvH_ &,
                       const double, const double,
                       const int, const double) = 0;
 
  const CostFct_ & J_;
  std::unique_ptr<CtrlInc_> gradJb_;
  std::vector<CtrlInc_> dxh_;
  double costJ0Jb_;
};
 
// =============================================================================
 
template<typename MODEL, typename OBS>
ControlIncrement<MODEL, OBS> *
DRMinimizer<MODEL, OBS>::doMinimize(const eckit::Configuration & config) {
  int ninner = config.getInt("ninner");
  double gnreduc = config.getDouble("gradient norm reduction");
 
  bool runOnlineAdjTest = config.getBool("online diagnostics.online adj test", false);
 
  if (gradJb_) {
    gradJb_.reset(new CtrlInc_(J_.jb().resolution(), *gradJb_));
  } else {
    gradJb_.reset(new CtrlInc_(J_.jb()));
  }
 
  Log::info() << std::endl;
  Log::info() << classname() << ": max iter = " << ninner
              <<  ", requested norm reduction = " << gnreduc << std::endl;
 
// Define the matrices
  const Bmat_    B(J_);
  const HtRinvH_ HtRinvH(J_, runOnlineAdjTest);
 
// Define minimisation starting point
  // dx
  CtrlInc_ * dx = new CtrlInc_(J_.jb());
  // dxh = B^{-1} dx
  CtrlInc_ dxh(J_.jb());
 
// Compute RHS (sum B^{-1} dx_{i}) + H^T R^{-1} d
// dx_i = x_i - x_{i-1}; dx_1 = x_1 - x_b
  CtrlInc_ rhs(J_.jb());
  CtrlInc_ dx0(rhs);
  if (config.has("fsoi")) {
    const eckit::LocalConfiguration FcSensitivityConfig(config, "fsoi.input forecast sensitivity");
    rhs.read(FcSensitivityConfig);
    dx0 = rhs;
    dx0 *= -1.0;
    Log::info() << classname() << " rhs has forecast sensitivity" << std::endl;
  } else {
    J_.computeGradientFG(rhs);
    J_.jb().addGradientFG(rhs, *gradJb_);
  }
  rhs *= -1.0;
  Log::info() << classname() << " rhs" << rhs << std::endl;
 
// Check for zero gradient (for example if no obs)
  const double gnorm = dot_product(rhs, rhs);
  const double epsilon = config.getDouble("epsilon", std::numeric_limits<double>::epsilon());
  Log::info() << "Initial RHS squared norm = " << gnorm << std::endl;
  if (gnorm < epsilon) {
    Log::info() << "RHS smaller than " << epsilon << ", returning." << std::endl;
    return dx;
  }
 
// Set J[0] = 0.5 (x_i - x_b)^T B^{-1} (x_i - x_b) + 0.5 d^T R^{-1} d
  const double costJ0Jb = costJ0Jb_;
  const double costJ0JoJc = J_.getCostJoJc();
 
// Solve the linear system
  double reduc = this->solve(*dx, dxh, rhs, B, HtRinvH, costJ0Jb, costJ0JoJc, ninner, gnreduc);
 
  Log::test() << classname() << ": reduction in residual norm = " << reduc << std::endl;
  Log::info() << classname() << " output increment:" << *dx << std::endl;
 
// Update gradient Jb
  *gradJb_ += dxh;
  dxh_.push_back(dxh);
 
// Update Jb component of J[0]: 0.5 (x_i - x_b)^T B^-1 (x_i - x_b)
  costJ0Jb_ += 0.5 * dot_product(*dx, dxh);
  for (unsigned int jouter = 1; jouter < dxh_.size(); ++jouter) {
    CtrlInc_ dxhtmp(dx->geometry(), dxh_[jouter-1]);
    costJ0Jb_ += dot_product(*dx, dxhtmp);
  }
 
  if (config.has("fsoi")) {
    Log::info() << classname() << " Entering Observation Sensitivity Calculation" << std::endl;
 
    // Multiply result of solver by RinvH to get observation sensitivity (ys)
    DualVector<MODEL, OBS> ys;
    const RinvH_ RinvH(J_);
    RinvH.multiply(*dx, ys);
 
    // Write out observation sensitivity
    const std::string osensname = "ObsSensitivity";
    ys.saveDep(osensname);
 
    bool runFSOIincTest = config.getBool("fsoi.increment test", false);
    if (runFSOIincTest) {
      // Get departures
      DualVector<MODEL, OBS> dp;
      for (unsigned jj = 0; jj < J_.nterms(); ++jj) {
        std::unique_ptr<GeneralizedDepartures> ww(J_.jterm(jj).newGradientFG());
        dp.append(J_.jterm(jj).multiplyCovar(*ww));
      }
 
      // <K dp,  dx>, where dx = K dp
      double adj_tst_fwd = dot_product(dx0, dx0);
      // <dp, Kt dx>, where K = Hessian Ht Rinv; dp=departures
      double adj_tst_bwd = dot_product(ys, dp);
 
      Log::info() << "Online FSOI increment test: " << std::endl
                  << util::PrintAdjTest(adj_tst_fwd, adj_tst_bwd, "K") << std::endl;
 
      double fsoi_inctest_tolerance = config.getDouble("fsoi.increment test tolerance", 1.0e-5);
      bool passed = oops::is_close_absolute(adj_tst_fwd, adj_tst_bwd, fsoi_inctest_tolerance);
      if (passed) {
        Log::test() << "FSOI increment test within tolerance." << std::endl;
      } else {
        Log::test() << "FSOI increment test fails tolerance bound." << std::endl;
      }
    }
 
    // Make sure not to update state in FSOI mode
    dx->zero();
  }
 
  return dx;
}
 
// -----------------------------------------------------------------------------
 
}  // namespace oops
 
#endif  // OOPS_ASSIMILATION_DRMINIMIZER_H_