| /* | |
| Copyright (c) 2011, Intel Corporation. All rights reserved. | |
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| are permitted provided that the following conditions are met: | |
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| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND | |
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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 |