diff options
author | Gael Guennebaud <g.gael@free.fr> | 2010-06-10 16:39:46 +0200 |
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committer | Gael Guennebaud <g.gael@free.fr> | 2010-06-10 16:39:46 +0200 |
commit | 469382407ca5d730f23788c593e71e91d24e9b89 (patch) | |
tree | 7c5423e63a9c4b01a25b0edded15cae4d7efb88c /Eigen/src/Eigenvalues/Tridiagonalization.h | |
parent | d2d7465bcfcfc60e2b7350f4e4ae44d809182d39 (diff) |
* Make HouseholderSequence::evalTo works in place
* Clean a bit the Triadiagonalization making sure it the inplace
function really works inplace ;), and that only the lower
triangular part of the matrix is referenced.
* Remove the Tridiagonalization member object of SelfAdjointEigenSolver
exploiting the in place capability of HouseholdeSequence.
* Update unit test to check SelfAdjointEigenSolver only consider
the lower triangular part.
Diffstat (limited to 'Eigen/src/Eigenvalues/Tridiagonalization.h')
-rw-r--r-- | Eigen/src/Eigenvalues/Tridiagonalization.h | 236 |
1 files changed, 143 insertions, 93 deletions
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h index 62a607176..af970e94d 100644 --- a/Eigen/src/Eigenvalues/Tridiagonalization.h +++ b/Eigen/src/Eigenvalues/Tridiagonalization.h @@ -154,7 +154,7 @@ template<typename _MatrixType> class Tridiagonalization { m_matrix = matrix; m_hCoeffs.resize(matrix.rows()-1, 1); - _compute(m_matrix, m_hCoeffs); + ei_tridiagonalization_inplace(m_matrix, m_hCoeffs); m_isInitialized = true; return *this; } @@ -285,43 +285,6 @@ template<typename _MatrixType> class Tridiagonalization */ const SubDiagonalReturnType subDiagonal() const; - /** \brief Performs a full decomposition in place - * - * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal - * decomposition is to be computed. On output, the orthogonal matrix Q - * in the decomposition if \p extractQ is true. - * \param[out] diag The diagonal of the tridiagonal matrix T in the - * decomposition. - * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in - * the decomposition. - * \param[in] extractQ If true, the orthogonal matrix Q in the - * decomposition is computed and stored in \p mat. - * - * Compute the tridiagonal matrix of \p mat in place. The tridiagonal - * matrix T is passed to the output parameters \p diag and \p subdiag. If - * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. - * - * The vectors \p diag and \p subdiag are not resized. The function - * assumes that they are already of the correct size. The length of the - * vector \p diag should equal the number of rows in \p mat, and the - * length of the vector \p subdiag should be one left. - * - * This implementation contains an optimized path for real 3-by-3 matrices - * which is especially useful for plane fitting. - * - * \note Notwithstanding the name, the current implementation copies - * \p mat to a temporary matrix and uses that matrix to compute the - * decomposition. - * - * Example (this uses the same matrix as the example in - * Tridiagonalization(const MatrixType&)): - * \include Tridiagonalization_decomposeInPlace.cpp - * Output: \verbinclude Tridiagonalization_decomposeInPlace.out - * - * \sa Tridiagonalization(const MatrixType&), compute() - */ - static void decomposeInPlace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ = true); - protected: static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs); @@ -368,21 +331,36 @@ Tridiagonalization<MatrixType>::matrixT() const } /** \internal - * Performs a tridiagonal decomposition of \a matA in place. + * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place. * - * \param matA the input selfadjoint matrix - * \param hCoeffs returned Householder coefficients + * \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced. + * On output, the strict upper part is left unchanged, and the lower triangular part + * represents the T and Q matrices in packed format has detailed below. + * \param[out] hCoeffs returned Householder coefficients (see below) * - * The result is written in the lower triangular part of \a matA. + * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal + * and lower sub-diagonal of the matrix \a matA. + * The unitary matrix Q is represented in a compact way as a product of + * Householder reflectors \f$ H_i \f$ such that: + * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$. + * The Householder reflectors are defined as + * \f$ H_i = (I - h_i v_i v_i^T) \f$ + * where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and + * \f$ v_i \f$ is the Householder vector defined by + * \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$. * * Implemented from Golub's "Matrix Computations", algorithm 8.3.1. * - * \sa packedMatrix() + * \sa Tridiagonalization::packedMatrix() */ -template<typename MatrixType> -void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs) +template<typename MatrixType, typename CoeffVectorType> +void ei_tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs) { - assert(matA.rows()==matA.cols()); + ei_assert(matA.rows()==matA.cols()); + ei_assert(matA.rows()==hCoeffs.size()+1); + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; Index n = matA.rows(); for (Index i = 0; i<n-1; ++i) { @@ -408,67 +386,139 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& } } -template<typename MatrixType> -void Tridiagonalization<MatrixType>::decomposeInPlace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) +// forward declaration, implementation at the end of this file +template<typename MatrixType, int Size=MatrixType::ColsAtCompileTime> +struct ei_tridiagonalization_inplace_selector; + +/** \brief Performs a full tridiagonalization in place + * + * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal + * decomposition is to be computed. Only the lower triangular part referenced. + * The rest is left unchanged. On output, the orthogonal matrix Q + * in the decomposition if \p extractQ is true. + * \param[out] diag The diagonal of the tridiagonal matrix T in the + * decomposition. + * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in + * the decomposition. + * \param[in] extractQ If true, the orthogonal matrix Q in the + * decomposition is computed and stored in \p mat. + * + * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place + * such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real + * symmetric tridiagonal matrix. + * + * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If + * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower + * part of the matrix \p mat is destroyed. + * + * The vectors \p diag and \p subdiag are not resized. The function + * assumes that they are already of the correct size. The length of the + * vector \p diag should equal the number of rows in \p mat, and the + * length of the vector \p subdiag should be one left. + * + * This implementation contains an optimized path for 3-by-3 matrices + * which is especially useful for plane fitting. + * + * \note Currently, it requires two temporary vectors to hold the intermediate + * Householder coefficients, and to reconstruct the matrix Q from the Householder + * reflectors. + * + * Example (this uses the same matrix as the example in + * Tridiagonalization::Tridiagonalization(const MatrixType&)): + * \include Tridiagonalization_decomposeInPlace.cpp + * Output: \verbinclude Tridiagonalization_decomposeInPlace.out + * + * \sa class Tridiagonalization + */ +template<typename MatrixType, typename DiagonalType, typename SubDiagonalType> +void ei_tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) { + typedef typename MatrixType::Index Index; Index n = mat.rows(); ei_assert(mat.cols()==n && diag.size()==n && subdiag.size()==n-1); - if (n==3 && (!NumTraits<Scalar>::IsComplex) ) - { - _decomposeInPlace3x3(mat, diag, subdiag, extractQ); - } - else + ei_tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ); +} + +/** \internal + * General full tridiagonalization + */ +template<typename MatrixType, int Size> +struct ei_tridiagonalization_inplace_selector +{ + typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType; + typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType; + typedef typename MatrixType::Index Index; + template<typename DiagonalType, typename SubDiagonalType> + static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) { - Tridiagonalization tridiag(mat); - diag = tridiag.diagonal(); - subdiag = tridiag.subDiagonal(); - if (extractQ) - mat = tridiag.matrixQ(); + CoeffVectorType hCoeffs(mat.cols()-1); + ei_tridiagonalization_inplace(mat,hCoeffs); + diag = mat.diagonal().real(); + subdiag = mat.template diagonal<-1>().real(); + if(extractQ) + mat = HouseholderSequenceType(mat, hCoeffs.conjugate(), false, mat.rows() - 1, 1); } -} +}; /** \internal - * Optimized path for 3x3 matrices. + * Specialization for 3x3 matrices. * Especially useful for plane fitting. */ template<typename MatrixType> -void Tridiagonalization<MatrixType>::_decomposeInPlace3x3(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) +struct ei_tridiagonalization_inplace_selector<MatrixType,3> { - diag[0] = ei_real(mat(0,0)); - RealScalar v1norm2 = ei_abs2(mat(0,2)); - if (ei_isMuchSmallerThan(v1norm2, RealScalar(1))) - { - diag[1] = ei_real(mat(1,1)); - diag[2] = ei_real(mat(2,2)); - subdiag[0] = ei_real(mat(0,1)); - subdiag[1] = ei_real(mat(1,2)); - if (extractQ) - mat.setIdentity(); - } - else + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + + template<typename DiagonalType, typename SubDiagonalType> + static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) { - RealScalar beta = ei_sqrt(ei_abs2(mat(0,1))+v1norm2); - RealScalar invBeta = RealScalar(1)/beta; - Scalar m01 = mat(0,1) * invBeta; - Scalar m02 = mat(0,2) * invBeta; - Scalar q = RealScalar(2)*m01*mat(1,2) + m02*(mat(2,2) - mat(1,1)); - diag[1] = ei_real(mat(1,1) + m02*q); - diag[2] = ei_real(mat(2,2) - m02*q); - subdiag[0] = beta; - subdiag[1] = ei_real(mat(1,2) - m01 * q); - if (extractQ) + diag[0] = ei_real(mat(0,0)); + RealScalar v1norm2 = ei_abs2(mat(2,0)); + if (ei_isMuchSmallerThan(v1norm2, RealScalar(1))) { - mat(0,0) = 1; - mat(0,1) = 0; - mat(0,2) = 0; - mat(1,0) = 0; - mat(1,1) = m01; - mat(1,2) = m02; - mat(2,0) = 0; - mat(2,1) = m02; - mat(2,2) = -m01; + diag[1] = ei_real(mat(1,1)); + diag[2] = ei_real(mat(2,2)); + subdiag[0] = ei_real(mat(1,0)); + subdiag[1] = ei_real(mat(2,1)); + if (extractQ) + mat.setIdentity(); + } + else + { + RealScalar beta = ei_sqrt(ei_abs2(mat(1,0)) + v1norm2); + RealScalar invBeta = RealScalar(1)/beta; + Scalar m01 = ei_conj(mat(1,0)) * invBeta; + Scalar m02 = ei_conj(mat(2,0)) * invBeta; + Scalar q = RealScalar(2)*m01*ei_conj(mat(2,1)) + m02*(mat(2,2) - mat(1,1)); + diag[1] = ei_real(mat(1,1) + m02*q); + diag[2] = ei_real(mat(2,2) - m02*q); + subdiag[0] = beta; + subdiag[1] = ei_real(ei_conj(mat(2,1)) - m01 * q); + if (extractQ) + { + mat << 1, 0, 0, + 0, m01, m02, + 0, m02, -m01; + } } } -} +}; +/** \internal + * Trivial specialization for 1x1 matrices + */ +template<typename MatrixType> +struct ei_tridiagonalization_inplace_selector<MatrixType,1> +{ + typedef typename MatrixType::Scalar Scalar; + + template<typename DiagonalType, typename SubDiagonalType> + static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ) + { + diag(0,0) = ei_real(mat(0,0)); + if(extractQ) + mat(0,0) = Scalar(1); + } +}; #endif // EIGEN_TRIDIAGONALIZATION_H |