BDCSVD_LAPACKE.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2022 Melven Roehrig-Zoellner <Melven.Roehrig-Zoellner@DLR.de>
// Copyright (c) 2011, Intel Corporation. All rights reserved.
//
// This file is based on the JacobiSVD_LAPACKE.h originally from Intel -
// see license notice below:
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 ********************************************************************************
 *   Content : Eigen bindings to LAPACKe
 *    Singular Value Decomposition - SVD (divide and conquer variant)
 ********************************************************************************
*/
#ifndef EIGEN_BDCSVD_LAPACKE_H
#define EIGEN_BDCSVD_LAPACKE_H

namespace Eigen {

namespace internal {

namespace lapacke_helpers {

// defining a derived class to allow access to protected members
template <typename MatrixType_, int Options>
class BDCSVD_LAPACKE : public BDCSVD<MatrixType_, Options> {
  typedef BDCSVD<MatrixType_, Options> SVD;
  typedef typename SVD::MatrixType MatrixType;
  typedef typename SVD::Scalar Scalar;
  typedef typename SVD::RealScalar RealScalar;

 public:
  // construct this by moving from a parent object
  BDCSVD_LAPACKE(SVD&& svd) : SVD(std::move(svd)) {}

  template <typename Derived>
  void compute_impl_lapacke(const MatrixBase<Derived>& matrix, unsigned int computationOptions) {
    SVD::allocate(matrix.rows(), matrix.cols(), computationOptions);

    SVD::m_nonzeroSingularValues = SVD::m_diagSize;

    // prepare arguments to ?gesdd
    const lapack_int matrix_order = lapack_storage_of(matrix);
    const char jobz = (SVD::m_computeFullU || SVD::m_computeFullV)   ? 'A'
                      : (SVD::m_computeThinU || SVD::m_computeThinV) ? 'S'
                                                                     : 'N';
    const lapack_int u_cols = (jobz == 'A') ? to_lapack(SVD::rows()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
    const lapack_int vt_rows = (jobz == 'A') ? to_lapack(SVD::cols()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
    lapack_int ldu, ldvt;
    Scalar *u, *vt, dummy;
    MatrixType localU;
    if (SVD::computeU() && !(SVD::m_computeThinU && SVD::m_computeFullV)) {
      ldu = to_lapack(SVD::m_matrixU.outerStride());
      u = SVD::m_matrixU.data();
    } else if (SVD::computeV()) {
      localU.resize(SVD::rows(), u_cols);
      ldu = to_lapack(localU.outerStride());
      u = localU.data();
    } else {
      ldu = 1;
      u = &dummy;
    }
    MatrixType localV;
    if (SVD::computeU() || SVD::computeV()) {
      localV.resize(vt_rows, SVD::cols());
      ldvt = to_lapack(localV.outerStride());
      vt = localV.data();
    } else {
      ldvt = 1;
      vt = &dummy;
    }
    MatrixType temp;
    temp = matrix;

    // actual call to ?gesdd
    lapack_int info = gesdd(matrix_order, jobz, to_lapack(SVD::rows()), to_lapack(SVD::cols()), to_lapack(temp.data()),
                            to_lapack(temp.outerStride()), (RealScalar*)SVD::m_singularValues.data(), to_lapack(u), ldu,
                            to_lapack(vt), ldvt);

    // Check the result of the LAPACK call
    if (info < 0 || !SVD::m_singularValues.allFinite()) {
      // this includes info == -4 => NaN entry in A
      SVD::m_info = InvalidInput;
    } else if (info > 0) {
      SVD::m_info = NoConvergence;
    } else {
      SVD::m_info = Success;
      if (SVD::m_computeThinU && SVD::m_computeFullV) {
        SVD::m_matrixU = localU.leftCols(SVD::m_matrixU.cols());
      }
      if (SVD::computeV()) {
        SVD::m_matrixV = localV.adjoint().leftCols(SVD::m_matrixV.cols());
      }
    }
    SVD::m_isInitialized = true;
  }
};

template <typename MatrixType_, int Options, typename Derived>
BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd, const MatrixBase<Derived>& matrix,
                                             int computationOptions) {
  // we need to move to the wrapper type and back
  BDCSVD_LAPACKE<MatrixType_, Options> tmpSvd(std::move(svd));
  tmpSvd.compute_impl_lapacke(matrix, computationOptions);
  svd = std::move(tmpSvd);
  return svd;
}

}  // end namespace lapacke_helpers

}  // end namespace internal

#define EIGEN_LAPACKE_SDD(EIGTYPE, EIGCOLROW, OPTIONS)                                           \
  template <>                                                                                    \
  template <typename Derived>                                                                    \
  inline BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>&        \
  BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl( \
      const MatrixBase<Derived>& matrix, unsigned int computationOptions) {                      \
    return internal::lapacke_helpers::BDCSVD_wrapper(*this, matrix, computationOptions);         \
  }

#define EIGEN_LAPACK_SDD_OPTIONS(OPTIONS)        \
  EIGEN_LAPACKE_SDD(double, ColMajor, OPTIONS)   \
  EIGEN_LAPACKE_SDD(float, ColMajor, OPTIONS)    \
  EIGEN_LAPACKE_SDD(dcomplex, ColMajor, OPTIONS) \
  EIGEN_LAPACKE_SDD(scomplex, ColMajor, OPTIONS) \
                                                 \
  EIGEN_LAPACKE_SDD(double, RowMajor, OPTIONS)   \
  EIGEN_LAPACKE_SDD(float, RowMajor, OPTIONS)    \
  EIGEN_LAPACKE_SDD(dcomplex, RowMajor, OPTIONS) \
  EIGEN_LAPACKE_SDD(scomplex, RowMajor, OPTIONS)

EIGEN_LAPACK_SDD_OPTIONS(0)
EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU)
EIGEN_LAPACK_SDD_OPTIONS(ComputeThinV)
EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU)
EIGEN_LAPACK_SDD_OPTIONS(ComputeFullV)
EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeThinV)
EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeFullV)
EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeFullV)
EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeThinV)

#undef EIGEN_LAPACK_SDD_OPTIONS

#undef EIGEN_LAPACKE_SDD

}  // end namespace Eigen

#endif  // EIGEN_BDCSVD_LAPACKE_H