otbTimeSeriesLeastSquareFittingFunctor.h

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/*
 * Copyright (C) 2005-2022 Centre National d'Etudes Spatiales (CNES)
 *
 * This file is part of Orfeo Toolbox
 *
 *     https://www.orfeo-toolbox.org/
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
 
#ifndef otbTimeSeriesLSFF_h
#define otbTimeSeriesLSFF_h
 
#include "vnl/algo/vnl_matrix_inverse.h"
#include "vnl/vnl_transpose.h"
#include "vnl/vnl_matrix.h"
 
namespace otb
{
namespace Functor
{
template <class TSeriesType, class TTimeFunction, class TDateType = TSeriesType, class TWeightType = TSeriesType>
class TimeSeriesLeastSquareFittingFunctor
{
public:
  typedef typename TTimeFunction::CoefficientsType CoefficientsType;
 
  TimeSeriesLeastSquareFittingFunctor()
  {
    for (unsigned int i = 0; i < m_WeightSeries.Size(); ++i)
      m_WeightSeries[i] = 1.0;
  }
  virtual ~TimeSeriesLeastSquareFittingFunctor()
  {
  }
 
  inline TSeriesType operator()(const TSeriesType& series)
  {
    TTimeFunction estFunction = this->EstimateTimeFunction(series);
    TSeriesType   outSeries;
    for (unsigned int i = 0; i < m_DoySeries.Size(); ++i)
      outSeries[i]      = estFunction.GetValue(m_DoySeries[i]);
    return outSeries;
  }
 
  inline void SetDates(const TDateType& doy)
  {
    for (unsigned int i = 0; i < doy.Size(); ++i)
      m_DoySeries[i]    = doy[i];
  }
 
  inline void SetWeights(const TWeightType& weights)
  {
    for (unsigned int i = 0; i < weights.Size(); ++i)
      m_WeightSeries[i] = weights[i];
  }
 
  inline CoefficientsType GetCoefficients(const TSeriesType& series) const
  {
    return (this->EstimateTimeFunction(series)).GetCoefficients();
  }
 
  inline TTimeFunction EstimateTimeFunction(const TSeriesType& series) const
  {
    TTimeFunction estFunction;
    unsigned int  nbDates = m_DoySeries.Size();
    unsigned int  nbCoefs = estFunction.GetCoefficients().Size();
 
    // b = A * c
    vnl_matrix<double> A(nbDates, nbCoefs);
    vnl_matrix<double> b(nbDates, 1);
 
    // fill the matrices
 
    typename TTimeFunction::CoefficientsType tmpCoefs;
    for (unsigned int j = 0; j < nbCoefs; ++j)
      tmpCoefs[j]       = 0.0;
 
    for (unsigned int i = 0; i < nbDates; ++i)
    {
      b.put(i, 0, series[i] / m_WeightSeries[i]);
      for (unsigned int j = 0; j < nbCoefs; ++j)
      {
        tmpCoefs[j] = 1.0;
        estFunction.SetCoefficients(tmpCoefs);
        A.put(i, j, estFunction.GetValue(m_DoySeries[i]) / m_WeightSeries[i]);
        tmpCoefs[j] = 0.0;
      }
    }
    // solve the problem c = (At * A)^-1*At*b
 
    vnl_matrix<double> atainv = vnl_matrix_inverse<double>(vnl_transpose(A) * A);
 
    vnl_matrix<double> atainvat = atainv * vnl_transpose(A);
    vnl_matrix<double> c        = atainvat * b;
 
    for (unsigned int j = 0; j < nbCoefs; ++j)
      tmpCoefs[j]       = c.get(j, 0);
    estFunction.SetCoefficients(tmpCoefs);
 
    return estFunction;
  }
 
private:
  TDateType   m_DoySeries;
  TWeightType m_WeightSeries;
};
}
} // namespace otb
#endif