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 ********************************************************************************
 *   Content : Eigen bindings to LAPACKe
 *    Householder QR decomposition of a matrix with column pivoting based on
 *    LAPACKE_?geqp3 function.
 ********************************************************************************
*/

#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H

#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;
      typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;

      static void run(MatrixType& qr, HCoeffsType& hCoeffs, PermutationType& colsPermutation,
                      IntRowVectorType& colsTranspositions, Index& nonzero_pivots, RealScalar& maxpivot,
                      bool usePrescribedThreshold, RealScalar prescribedThreshold, Index& det_p, bool& isInitialized) {
        using std::abs;
        
        isInitialized = false;
        hCoeffs.resize(qr.diagonalSize());
        colsTranspositions.resize(qr.cols());
        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();
        RealScalar defaultThreshold = NumTraits<RealScalar>::epsilon() * RealScalar(qr.diagonalSize());
        RealScalar threshold = usePrescribedThreshold ? prescribedThreshold : defaultThreshold;
        RealScalar premultiplied_threshold = abs(maxpivot) * threshold;
        nonzero_pivots = (qr.diagonal().cwiseAbs().array() > premultiplied_threshold).count();
        colsPermutation.indices().array() -= 1;
        det_p = colsPermutation.determinant();
        isInitialized = true;
      };
    };

    typedef Matrix<float, Dynamic, Dynamic, RowMajor> MatrixXfR;
    typedef Matrix<double, Dynamic, Dynamic, RowMajor> MatrixXdR;
    typedef Matrix<scomplex, Dynamic, Dynamic, RowMajor> MatrixXcfR;
    typedef Matrix<dcomplex, Dynamic, Dynamic, RowMajor> MatrixXcdR;

    template <> inline void ColPivHouseholderQR<MatrixXf, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXd, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXcf, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXcd, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXfR, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXdR, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXcfR, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }
    template <> inline void ColPivHouseholderQR<MatrixXcdR, lapack_int>::computeInPlace() {
      ColPivHouseholderQR_LAPACKE_impl<MatrixType>::run(m_qr, m_hCoeffs, m_colsPermutation, m_colsTranspositions,
                                                        m_nonzero_pivots, m_maxpivot, m_usePrescribedThreshold,
                                                        m_prescribedThreshold, m_det_p, m_isInitialized); }

#endif
}  // end namespace Eigen

#endif  // EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H