ColPivHouseholderQR_LAPACKE.h

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 ********************************************************************************
 *   Content : Eigen bindings to LAPACKe
 *    Householder QR decomposition of a matrix with column pivoting based on
 *    LAPACKE_?geqp3 function.
 ********************************************************************************
*/
// SPDX-License-Identifier: BSD-3-Clause
 
#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
#if defined(EIGEN_USE_LAPACKE)
 
template <typename Scalar>
inline lapack_int call_geqp3(int matrix_layout, lapack_int m, lapack_int n, Scalar* a, lapack_int lda, lapack_int* jpvt,
                             Scalar* tau);
template <>
inline lapack_int call_geqp3(int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, lapack_int* jpvt,
                             float* tau) {
  return LAPACKE_sgeqp3(matrix_layout, m, n, a, lda, jpvt, tau);
}
template <>
inline lapack_int call_geqp3(int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, lapack_int* jpvt,
                             double* tau) {
  return LAPACKE_dgeqp3(matrix_layout, m, n, a, lda, jpvt, tau);
}
template <>
inline lapack_int call_geqp3(int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda,
                             lapack_int* jpvt, lapack_complex_float* tau) {
  return LAPACKE_cgeqp3(matrix_layout, m, n, a, lda, jpvt, tau);
}
template <>
inline lapack_int call_geqp3(int matrix_layout, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda,
                             lapack_int* jpvt, lapack_complex_double* tau) {
  return LAPACKE_zgeqp3(matrix_layout, m, n, a, lda, jpvt, tau);
}
 
template <typename MatrixType>
struct ColPivHouseholderQR_LAPACKE_impl {
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename internal::lapacke_helpers::translate_type_imp<Scalar>::type LapackeType;
  static constexpr int LapackeStorage = MatrixType::IsRowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
 
  typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
  typedef PermutationMatrix<Dynamic, Dynamic, lapack_int> PermutationType;
 
  static void run(MatrixType& qr, HCoeffsType& hCoeffs, PermutationType& colsPermutation, Index& nonzero_pivots,
                  RealScalar& maxpivot, bool usePrescribedThreshold, RealScalar prescribedThreshold, Index& det_p,
                  bool& isInitialized) {
    isInitialized = false;
    hCoeffs.resize(qr.diagonalSize());
    nonzero_pivots = 0;
    maxpivot = RealScalar(0);
    colsPermutation.resize(qr.cols());
    colsPermutation.indices().setZero();
 
    lapack_int rows = internal::lapacke_helpers::to_lapack(qr.rows());
    lapack_int cols = internal::lapacke_helpers::to_lapack(qr.cols());
    LapackeType* qr_data = (LapackeType*)(qr.data());
    lapack_int lda = internal::lapacke_helpers::to_lapack(qr.outerStride());
    lapack_int* perm_data = colsPermutation.indices().data();
    LapackeType* hCoeffs_data = (LapackeType*)(hCoeffs.data());
 
    lapack_int info = call_geqp3(LapackeStorage, rows, cols, qr_data, lda, perm_data, hCoeffs_data);
    if (info != 0) return;
 
    maxpivot = qr.diagonal().cwiseAbs().maxCoeff();
    hCoeffs.adjointInPlace();
    // Higham's backward error bound (Theorem 19.4): ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂.
    // The factor of 4 covers the constant c (typically 3–6 worst-case).
    RealScalar defaultThreshold = NumTraits<RealScalar>::epsilon() * RealScalar(4 * qr.diagonalSize());
    RealScalar threshold = usePrescribedThreshold ? prescribedThreshold : defaultThreshold;
    RealScalar premultiplied_threshold = maxpivot * threshold;
    nonzero_pivots = (qr.diagonal().cwiseAbs().array() > premultiplied_threshold).count();
    colsPermutation.indices().array() -= 1;
    det_p = colsPermutation.determinant();
    isInitialized = true;
  }
 
  static void init(Index rows, Index cols, HCoeffsType& hCoeffs, PermutationType& colsPermutation,
                   bool& usePrescribedThreshold, bool& isInitialized) {
    Index diag = numext::mini(rows, cols);
    hCoeffs.resize(diag);
    colsPermutation.resize(cols);
    usePrescribedThreshold = false;
    isInitialized = false;
  }
};
 
#define COLPIVQR_LAPACKE_COMPUTEINPLACE(EIGTYPE)                                                                   \
  template <>                                                                                                      \
  inline void ColPivHouseholderQR<EIGTYPE, lapack_int>::computeInPlace() {                                         \
    ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_nonzero_pivots,        \
                                                      m_maxpivot, m_usePrescribedThreshold, m_prescribedThreshold, \
                                                      m_det_p, m_isInitialized);                                   \
  }
 
#define COLPIVQR_LAPACKE_INIT(EIGTYPE)                                                                            \
  template <>                                                                                                     \
  inline void ColPivHouseholderQR<EIGTYPE, lapack_int>::init(Index rows, Index cols) {                            \
    ColPivHouseholderQR_LAPACKE_impl<MatrixType>::init(rows, cols, m_hCoeffs, m_colsPermutation, m_isInitialized, \
                                                       m_usePrescribedThreshold);                                 \
  }
 
#define COLPIVQR_LAPACKE(EIGTYPE)               \
  COLPIVQR_LAPACKE_COMPUTEINPLACE(EIGTYPE)      \
  COLPIVQR_LAPACKE_INIT(EIGTYPE)                \
  COLPIVQR_LAPACKE_COMPUTEINPLACE(Ref<EIGTYPE>) \
  COLPIVQR_LAPACKE_INIT(Ref<EIGTYPE>)
 
typedef Matrix<float, Dynamic, Dynamic, ColMajor> MatrixXfC;
typedef Matrix<double, Dynamic, Dynamic, ColMajor> MatrixXdC;
typedef Matrix<std::complex<float>, Dynamic, Dynamic, ColMajor> MatrixXcfC;
typedef Matrix<std::complex<double>, Dynamic, Dynamic, ColMajor> MatrixXcdC;
typedef Matrix<float, Dynamic, Dynamic, RowMajor> MatrixXfR;
typedef Matrix<double, Dynamic, Dynamic, RowMajor> MatrixXdR;
typedef Matrix<std::complex<float>, Dynamic, Dynamic, RowMajor> MatrixXcfR;
typedef Matrix<std::complex<double>, Dynamic, Dynamic, RowMajor> MatrixXcdR;
 
COLPIVQR_LAPACKE(MatrixXfC)
COLPIVQR_LAPACKE(MatrixXdC)
COLPIVQR_LAPACKE(MatrixXcfC)
COLPIVQR_LAPACKE(MatrixXcdC)
COLPIVQR_LAPACKE(MatrixXfR)
COLPIVQR_LAPACKE(MatrixXdR)
COLPIVQR_LAPACKE(MatrixXcfR)
COLPIVQR_LAPACKE(MatrixXcdR)
 
#undef COLPIVQR_LAPACKE
#undef COLPIVQR_LAPACKE_INIT
#undef COLPIVQR_LAPACKE_COMPUTEINPLACE
 
#endif
}  // end namespace Eigen
 
#endif  // EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H