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/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_least_squares_h__
#define __math_least_squares_h__
#include <Eigen/Cholesky>
#include "types.h"
namespace MR
{
namespace Math
{
/** @addtogroup linalg
@{ */
/** @defgroup ls Least-squares & Moore-Penrose pseudo-inverse
@{ */
//! return Moore-Penrose pseudo-inverse of M
template <class MatrixType>
inline Eigen::Matrix<typename MatrixType::Scalar,Eigen::Dynamic, Eigen::Dynamic> pinv (const MatrixType& M)
{
if (M.rows() >= M.cols())
return (M.transpose()*M).ldlt().solve (M.transpose());
else
return (M*M.transpose()).ldlt().solve (M).transpose();
}
template <class MatrixType>
inline size_t rank (const MatrixType& M)
{
Eigen::FullPivLU<MatrixType> lu_decomp (M);
return lu_decomp.rank();
}
/** @} */
/** @} */
}
}
#endif
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