itkQRDecomposition.h

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 *  Copyright NumFOCUS
 *
 *  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
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 *  distributed under the License is distributed on an "AS IS" BASIS,
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 *  See the License for the specific language governing permissions and
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#ifndef itkQRDecomposition_h
#define itkQRDecomposition_h
 
#include "itkMacro.h"
#include "vnl/vnl_matrix.h"
#include "vnl/vnl_vector.h"
#include "itk_eigen.h"
#include ITK_EIGEN(Dense)
 
namespace itk
{

template <typename T>
class QRDecomposition
{
public:
  using MatrixType = vnl_matrix<T>;
  using VectorType = vnl_vector<T>;
 
  explicit QRDecomposition(const MatrixType & A)
  {
    itkAssertOrThrowMacro(A.rows() > 0 && A.cols() > 0, "QRDecomposition requires a non-empty matrix");
    using RowMajor = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
    using ColMajor = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>;
    const unsigned int rows = A.rows();
    const unsigned int cols = A.cols();
 
    Eigen::Map<const RowMajor>           aMap(A.data_block(), rows, cols);
    const Eigen::HouseholderQR<ColMajor> qr(aMap);
 
    const ColMajor qFull = qr.householderQ();
    const ColMajor rFull = qr.matrixQR().template triangularView<Eigen::Upper>();
 
    m_Q.set_size(rows, rows);
    Eigen::Map<RowMajor>(m_Q.data_block(), rows, rows) = qFull;
    m_R.set_size(rows, cols);
    Eigen::Map<RowMajor>(m_R.data_block(), rows, cols) = rFull;
 
    m_Square = (rows == cols);
    m_Determinant = m_Square ? static_cast<T>(aMap.determinant()) : T{};
  }

  const MatrixType &
  GetQ() const
  {
    return m_Q;
  }

  const MatrixType &
  GetR() const
  {
    return m_R;
  }

  VectorType
  Solve(const VectorType & b) const
  {
    using RowMajor = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
    using Vector = Eigen::Matrix<T, Eigen::Dynamic, 1>;
    const unsigned int rows = m_Q.rows();
    const unsigned int cols = m_R.cols();
    itkAssertOrThrowMacro(b.size() == rows, "QRDecomposition::Solve requires b length to match the row count");
    if (cols > rows)
    {
      itkGenericExceptionMacro("QRDecomposition::Solve supports square or overdetermined systems only (rows >= cols)");
    }
 
    Eigen::Map<const RowMajor> qMap(m_Q.data_block(), rows, rows);
    Eigen::Map<const RowMajor> rMap(m_R.data_block(), rows, cols);
    Eigen::Map<const Vector>   bMap(b.data_block(), rows);
 
    const Vector qtb = qMap.adjoint() * bMap;
    const Vector x = rMap.topLeftCorner(cols, cols).template triangularView<Eigen::Upper>().solve(qtb.head(cols));
 
    VectorType out(cols);
    Eigen::Map<Vector>(out.data_block(), cols) = x;
    return out;
  }

  T
  GetDeterminant() const
  {
    return m_Determinant;
  }
 
private:
  MatrixType m_Q;
  MatrixType m_R;
  T          m_Determinant{};
  bool       m_Square{ false };
};
 
} // namespace itk
 
#endif // itkQRDecomposition_h