itkCholeskySolve.h

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 *  Copyright NumFOCUS
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 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
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#ifndef itkCholeskySolve_h
#define itkCholeskySolve_h
 
#include "itkMacro.h"
#include "vnl/vnl_matrix.h"
#include "vnl/vnl_vector.h"
#include "itk_eigen.h"
#include ITK_EIGEN(Dense)
 
namespace itk
{
namespace Math
{

namespace detail
{
// vnl storage is row-major and contiguous, so map the data block directly
// (no copy). For a symmetric A the storage order is immaterial; b/x map as
// plain contiguous vectors.
template <typename TReal>
using CholeskyRowMajor = Eigen::Matrix<TReal, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
template <typename TReal>
using CholeskyVector = Eigen::Matrix<TReal, Eigen::Dynamic, 1>;
} // namespace detail

template <typename T>
vnl_vector<T>
SolveSymmetricPositiveDefinite(const vnl_matrix<T> & A, const vnl_vector<T> & b)
{
  itkAssertOrThrowMacro(A.rows() == A.cols(), "SolveSymmetricPositiveDefinite requires a square matrix");
  itkAssertOrThrowMacro(A.rows() == b.size(), "SolveSymmetricPositiveDefinite requires matching b length");
  const unsigned int                            n = A.rows();
  Eigen::Map<const detail::CholeskyRowMajor<T>> aMap(A.data_block(), n, n);
  Eigen::Map<const detail::CholeskyVector<T>>   bMap(b.data_block(), n);
  vnl_vector<T>                                 x(n);
  Eigen::Map<detail::CholeskyVector<T>>         xMap(x.data_block(), n);
  xMap = aMap.template selfadjointView<Eigen::Lower>().ldlt().solve(bMap);
  return x;
}

template <typename T>
vnl_matrix<T>
CholeskyLowerTriangle(const vnl_matrix<T> & A)
{
  itkAssertOrThrowMacro(A.rows() == A.cols(), "CholeskyLowerTriangle requires a square matrix");
  const unsigned int                            n = A.rows();
  Eigen::Map<const detail::CholeskyRowMajor<T>> aMap(A.data_block(), n, n);
  const auto                                    llt = aMap.template selfadjointView<Eigen::Lower>().llt();
  if (llt.info() != Eigen::Success)
  {
    itkGenericExceptionMacro("CholeskyLowerTriangle requires a positive-definite matrix");
  }
  const detail::CholeskyRowMajor<T>       lower = llt.matrixL();
  vnl_matrix<T>                           result(n, n);
  Eigen::Map<detail::CholeskyRowMajor<T>> rMap(result.data_block(), n, n);
  rMap = lower;
  return result;
}
 
} // namespace Math
} // namespace itk
 
#endif // itkCholeskySolve_h