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Diffstat (limited to 'eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h')
| -rw-r--r-- | eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h | 709 |
1 files changed, 0 insertions, 709 deletions
diff --git a/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h b/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h deleted file mode 100644 index a3273da..0000000 --- a/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h +++ /dev/null @@ -1,709 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -#ifndef EIGEN_MATRIX_POWER -#define EIGEN_MATRIX_POWER - -namespace Eigen { - -template<typename MatrixType> class MatrixPower; - -/** - * \ingroup MatrixFunctions_Module - * - * \brief Proxy for the matrix power of some matrix. - * - * \tparam MatrixType type of the base, a matrix. - * - * This class holds the arguments to the matrix power until it is - * assigned or evaluated for some other reason (so the argument - * should not be changed in the meantime). It is the return type of - * MatrixPower::operator() and related functions and most of the - * time this is the only way it is used. - */ -/* TODO This class is only used by MatrixPower, so it should be nested - * into MatrixPower, like MatrixPower::ReturnValue. However, my - * compiler complained about unused template parameter in the - * following declaration in namespace internal. - * - * template<typename MatrixType> - * struct traits<MatrixPower<MatrixType>::ReturnValue>; - */ -template<typename MatrixType> -class MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParenthesesReturnValue<MatrixType> > -{ - public: - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::Index Index; - - /** - * \brief Constructor. - * - * \param[in] pow %MatrixPower storing the base. - * \param[in] p scalar, the exponent of the matrix power. - */ - MatrixPowerParenthesesReturnValue(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p) - { } - - /** - * \brief Compute the matrix power. - * - * \param[out] result - */ - template<typename ResultType> - inline void evalTo(ResultType& result) const - { m_pow.compute(result, m_p); } - - Index rows() const { return m_pow.rows(); } - Index cols() const { return m_pow.cols(); } - - private: - MatrixPower<MatrixType>& m_pow; - const RealScalar m_p; -}; - -/** - * \ingroup MatrixFunctions_Module - * - * \brief Class for computing matrix powers. - * - * \tparam MatrixType type of the base, expected to be an instantiation - * of the Matrix class template. - * - * This class is capable of computing triangular real/complex matrices - * raised to a power in the interval \f$ (-1, 1) \f$. - * - * \note Currently this class is only used by MatrixPower. One may - * insist that this be nested into MatrixPower. This class is here to - * faciliate future development of triangular matrix functions. - */ -template<typename MatrixType> -class MatrixPowerAtomic : internal::noncopyable -{ - private: - enum { - RowsAtCompileTime = MatrixType::RowsAtCompileTime, - MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime - }; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef std::complex<RealScalar> ComplexScalar; - typedef typename MatrixType::Index Index; - typedef Block<MatrixType,Dynamic,Dynamic> ResultType; - - const MatrixType& m_A; - RealScalar m_p; - - void computePade(int degree, const MatrixType& IminusT, ResultType& res) const; - void compute2x2(ResultType& res, RealScalar p) const; - void computeBig(ResultType& res) const; - static int getPadeDegree(float normIminusT); - static int getPadeDegree(double normIminusT); - static int getPadeDegree(long double normIminusT); - static ComplexScalar computeSuperDiag(const ComplexScalar&, const ComplexScalar&, RealScalar p); - static RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p); - - public: - /** - * \brief Constructor. - * - * \param[in] T the base of the matrix power. - * \param[in] p the exponent of the matrix power, should be in - * \f$ (-1, 1) \f$. - * - * The class stores a reference to T, so it should not be changed - * (or destroyed) before evaluation. Only the upper triangular - * part of T is read. - */ - MatrixPowerAtomic(const MatrixType& T, RealScalar p); - - /** - * \brief Compute the matrix power. - * - * \param[out] res \f$ A^p \f$ where A and p are specified in the - * constructor. - */ - void compute(ResultType& res) const; -}; - -template<typename MatrixType> -MatrixPowerAtomic<MatrixType>::MatrixPowerAtomic(const MatrixType& T, RealScalar p) : - m_A(T), m_p(p) -{ - eigen_assert(T.rows() == T.cols()); - eigen_assert(p > -1 && p < 1); -} - -template<typename MatrixType> -void MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const -{ - using std::pow; - switch (m_A.rows()) { - case 0: - break; - case 1: - res(0,0) = pow(m_A(0,0), m_p); - break; - case 2: - compute2x2(res, m_p); - break; - default: - computeBig(res); - } -} - -template<typename MatrixType> -void MatrixPowerAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, ResultType& res) const -{ - int i = 2*degree; - res = (m_p-degree) / (2*i-2) * IminusT; - - for (--i; i; --i) { - res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res).template triangularView<Upper>() - .solve((i==1 ? -m_p : i&1 ? (-m_p-i/2)/(2*i) : (m_p-i/2)/(2*i-2)) * IminusT).eval(); - } - res += MatrixType::Identity(IminusT.rows(), IminusT.cols()); -} - -// This function assumes that res has the correct size (see bug 614) -template<typename MatrixType> -void MatrixPowerAtomic<MatrixType>::compute2x2(ResultType& res, RealScalar p) const -{ - using std::abs; - using std::pow; - res.coeffRef(0,0) = pow(m_A.coeff(0,0), p); - - for (Index i=1; i < m_A.cols(); ++i) { - res.coeffRef(i,i) = pow(m_A.coeff(i,i), p); - if (m_A.coeff(i-1,i-1) == m_A.coeff(i,i)) - res.coeffRef(i-1,i) = p * pow(m_A.coeff(i,i), p-1); - else if (2*abs(m_A.coeff(i-1,i-1)) < abs(m_A.coeff(i,i)) || 2*abs(m_A.coeff(i,i)) < abs(m_A.coeff(i-1,i-1))) - res.coeffRef(i-1,i) = (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_A.coeff(i,i)-m_A.coeff(i-1,i-1)); - else - res.coeffRef(i-1,i) = computeSuperDiag(m_A.coeff(i,i), m_A.coeff(i-1,i-1), p); - res.coeffRef(i-1,i) *= m_A.coeff(i-1,i); - } -} - -template<typename MatrixType> -void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const -{ - using std::ldexp; - const int digits = std::numeric_limits<RealScalar>::digits; - const RealScalar maxNormForPade = digits <= 24? 4.3386528e-1L // single precision - : digits <= 53? 2.789358995219730e-1L // double precision - : digits <= 64? 2.4471944416607995472e-1L // extended precision - : digits <= 106? 1.1016843812851143391275867258512e-1L // double-double - : 9.134603732914548552537150753385375e-2L; // quadruple precision - MatrixType IminusT, sqrtT, T = m_A.template triangularView<Upper>(); - RealScalar normIminusT; - int degree, degree2, numberOfSquareRoots = 0; - bool hasExtraSquareRoot = false; - - for (Index i=0; i < m_A.cols(); ++i) - eigen_assert(m_A(i,i) != RealScalar(0)); - - while (true) { - IminusT = MatrixType::Identity(m_A.rows(), m_A.cols()) - T; - normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff(); - if (normIminusT < maxNormForPade) { - degree = getPadeDegree(normIminusT); - degree2 = getPadeDegree(normIminusT/2); - if (degree - degree2 <= 1 || hasExtraSquareRoot) - break; - hasExtraSquareRoot = true; - } - matrix_sqrt_triangular(T, sqrtT); - T = sqrtT.template triangularView<Upper>(); - ++numberOfSquareRoots; - } - computePade(degree, IminusT, res); - - for (; numberOfSquareRoots; --numberOfSquareRoots) { - compute2x2(res, ldexp(m_p, -numberOfSquareRoots)); - res = res.template triangularView<Upper>() * res; - } - compute2x2(res, m_p); -} - -template<typename MatrixType> -inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(float normIminusT) -{ - const float maxNormForPade[] = { 2.8064004e-1f /* degree = 3 */ , 4.3386528e-1f }; - int degree = 3; - for (; degree <= 4; ++degree) - if (normIminusT <= maxNormForPade[degree - 3]) - break; - return degree; -} - -template<typename MatrixType> -inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(double normIminusT) -{ - const double maxNormForPade[] = { 1.884160592658218e-2 /* degree = 3 */ , 6.038881904059573e-2, 1.239917516308172e-1, - 1.999045567181744e-1, 2.789358995219730e-1 }; - int degree = 3; - for (; degree <= 7; ++degree) - if (normIminusT <= maxNormForPade[degree - 3]) - break; - return degree; -} - -template<typename MatrixType> -inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(long double normIminusT) -{ -#if LDBL_MANT_DIG == 53 - const int maxPadeDegree = 7; - const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L, - 1.999045567181744e-1L, 2.789358995219730e-1L }; -#elif LDBL_MANT_DIG <= 64 - const int maxPadeDegree = 8; - const long double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L, - 6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L }; -#elif LDBL_MANT_DIG <= 106 - const int maxPadeDegree = 10; - const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ , - 1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L, - 2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L, - 1.1016843812851143391275867258512e-1L }; -#else - const int maxPadeDegree = 10; - const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ , - 6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L, - 9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L, - 3.908166513900489428442993794761185e-2L, 6.266780814639442865832535460550138e-2L, - 9.134603732914548552537150753385375e-2L }; -#endif - int degree = 3; - for (; degree <= maxPadeDegree; ++degree) - if (normIminusT <= maxNormForPade[degree - 3]) - break; - return degree; -} - -template<typename MatrixType> -inline typename MatrixPowerAtomic<MatrixType>::ComplexScalar -MatrixPowerAtomic<MatrixType>::computeSuperDiag(const ComplexScalar& curr, const ComplexScalar& prev, RealScalar p) -{ - using std::ceil; - using std::exp; - using std::log; - using std::sinh; - - ComplexScalar logCurr = log(curr); - ComplexScalar logPrev = log(prev); - int unwindingNumber = ceil((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI)); - ComplexScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2) + ComplexScalar(0, EIGEN_PI*unwindingNumber); - return RealScalar(2) * exp(RealScalar(0.5) * p * (logCurr + logPrev)) * sinh(p * w) / (curr - prev); -} - -template<typename MatrixType> -inline typename MatrixPowerAtomic<MatrixType>::RealScalar -MatrixPowerAtomic<MatrixType>::computeSuperDiag(RealScalar curr, RealScalar prev, RealScalar p) -{ - using std::exp; - using std::log; - using std::sinh; - - RealScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2); - return 2 * exp(p * (log(curr) + log(prev)) / 2) * sinh(p * w) / (curr - prev); -} - -/** - * \ingroup MatrixFunctions_Module - * - * \brief Class for computing matrix powers. - * - * \tparam MatrixType type of the base, expected to be an instantiation - * of the Matrix class template. - * - * This class is capable of computing real/complex matrices raised to - * an arbitrary real power. Meanwhile, it saves the result of Schur - * decomposition if an non-integral power has even been calculated. - * Therefore, if you want to compute multiple (>= 2) matrix powers - * for the same matrix, using the class directly is more efficient than - * calling MatrixBase::pow(). - * - * Example: - * \include MatrixPower_optimal.cpp - * Output: \verbinclude MatrixPower_optimal.out - */ -template<typename MatrixType> -class MatrixPower : internal::noncopyable -{ - private: - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::Index Index; - - public: - /** - * \brief Constructor. - * - * \param[in] A the base of the matrix power. - * - * The class stores a reference to A, so it should not be changed - * (or destroyed) before evaluation. - */ - explicit MatrixPower(const MatrixType& A) : - m_A(A), - m_conditionNumber(0), - m_rank(A.cols()), - m_nulls(0) - { eigen_assert(A.rows() == A.cols()); } - - /** - * \brief Returns the matrix power. - * - * \param[in] p exponent, a real scalar. - * \return The expression \f$ A^p \f$, where A is specified in the - * constructor. - */ - const MatrixPowerParenthesesReturnValue<MatrixType> operator()(RealScalar p) - { return MatrixPowerParenthesesReturnValue<MatrixType>(*this, p); } - - /** - * \brief Compute the matrix power. - * - * \param[in] p exponent, a real scalar. - * \param[out] res \f$ A^p \f$ where A is specified in the - * constructor. - */ - template<typename ResultType> - void compute(ResultType& res, RealScalar p); - - Index rows() const { return m_A.rows(); } - Index cols() const { return m_A.cols(); } - - private: - typedef std::complex<RealScalar> ComplexScalar; - typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, - MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> ComplexMatrix; - - /** \brief Reference to the base of matrix power. */ - typename MatrixType::Nested m_A; - - /** \brief Temporary storage. */ - MatrixType m_tmp; - - /** \brief Store the result of Schur decomposition. */ - ComplexMatrix m_T, m_U; - - /** \brief Store fractional power of m_T. */ - ComplexMatrix m_fT; - - /** - * \brief Condition number of m_A. - * - * It is initialized as 0 to avoid performing unnecessary Schur - * decomposition, which is the bottleneck. - */ - RealScalar m_conditionNumber; - - /** \brief Rank of m_A. */ - Index m_rank; - - /** \brief Rank deficiency of m_A. */ - Index m_nulls; - - /** - * \brief Split p into integral part and fractional part. - * - * \param[in] p The exponent. - * \param[out] p The fractional part ranging in \f$ (-1, 1) \f$. - * \param[out] intpart The integral part. - * - * Only if the fractional part is nonzero, it calls initialize(). - */ - void split(RealScalar& p, RealScalar& intpart); - - /** \brief Perform Schur decomposition for fractional power. */ - void initialize(); - - template<typename ResultType> - void computeIntPower(ResultType& res, RealScalar p); - - template<typename ResultType> - void computeFracPower(ResultType& res, RealScalar p); - - template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> - static void revertSchur( - Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, - const ComplexMatrix& T, - const ComplexMatrix& U); - - template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> - static void revertSchur( - Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, - const ComplexMatrix& T, - const ComplexMatrix& U); -}; - -template<typename MatrixType> -template<typename ResultType> -void MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p) -{ - using std::pow; - switch (cols()) { - case 0: - break; - case 1: - res(0,0) = pow(m_A.coeff(0,0), p); - break; - default: - RealScalar intpart; - split(p, intpart); - - res = MatrixType::Identity(rows(), cols()); - computeIntPower(res, intpart); - if (p) computeFracPower(res, p); - } -} - -template<typename MatrixType> -void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart) -{ - using std::floor; - using std::pow; - - intpart = floor(p); - p -= intpart; - - // Perform Schur decomposition if it is not yet performed and the power is - // not an integer. - if (!m_conditionNumber && p) - initialize(); - - // Choose the more stable of intpart = floor(p) and intpart = ceil(p). - if (p > RealScalar(0.5) && p > (1-p) * pow(m_conditionNumber, p)) { - --p; - ++intpart; - } -} - -template<typename MatrixType> -void MatrixPower<MatrixType>::initialize() -{ - const ComplexSchur<MatrixType> schurOfA(m_A); - JacobiRotation<ComplexScalar> rot; - ComplexScalar eigenvalue; - - m_fT.resizeLike(m_A); - m_T = schurOfA.matrixT(); - m_U = schurOfA.matrixU(); - m_conditionNumber = m_T.diagonal().array().abs().maxCoeff() / m_T.diagonal().array().abs().minCoeff(); - - // Move zero eigenvalues to the bottom right corner. - for (Index i = cols()-1; i>=0; --i) { - if (m_rank <= 2) - return; - if (m_T.coeff(i,i) == RealScalar(0)) { - for (Index j=i+1; j < m_rank; ++j) { - eigenvalue = m_T.coeff(j,j); - rot.makeGivens(m_T.coeff(j-1,j), eigenvalue); - m_T.applyOnTheRight(j-1, j, rot); - m_T.applyOnTheLeft(j-1, j, rot.adjoint()); - m_T.coeffRef(j-1,j-1) = eigenvalue; - m_T.coeffRef(j,j) = RealScalar(0); - m_U.applyOnTheRight(j-1, j, rot); - } - --m_rank; - } - } - - m_nulls = rows() - m_rank; - if (m_nulls) { - eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero() - && "Base of matrix power should be invertible or with a semisimple zero eigenvalue."); - m_fT.bottomRows(m_nulls).fill(RealScalar(0)); - } -} - -template<typename MatrixType> -template<typename ResultType> -void MatrixPower<MatrixType>::computeIntPower(ResultType& res, RealScalar p) -{ - using std::abs; - using std::fmod; - RealScalar pp = abs(p); - - if (p<0) - m_tmp = m_A.inverse(); - else - m_tmp = m_A; - - while (true) { - if (fmod(pp, 2) >= 1) - res = m_tmp * res; - pp /= 2; - if (pp < 1) - break; - m_tmp *= m_tmp; - } -} - -template<typename MatrixType> -template<typename ResultType> -void MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p) -{ - Block<ComplexMatrix,Dynamic,Dynamic> blockTp(m_fT, 0, 0, m_rank, m_rank); - eigen_assert(m_conditionNumber); - eigen_assert(m_rank + m_nulls == rows()); - - MatrixPowerAtomic<ComplexMatrix>(m_T.topLeftCorner(m_rank, m_rank), p).compute(blockTp); - if (m_nulls) { - m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank).template triangularView<Upper>() - .solve(blockTp * m_T.topRightCorner(m_rank, m_nulls)); - } - revertSchur(m_tmp, m_fT, m_U); - res = m_tmp * res; -} - -template<typename MatrixType> -template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> -inline void MatrixPower<MatrixType>::revertSchur( - Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, - const ComplexMatrix& T, - const ComplexMatrix& U) -{ res.noalias() = U * (T.template triangularView<Upper>() * U.adjoint()); } - -template<typename MatrixType> -template<int Rows, int Cols, int Options, int MaxRows, int MaxCols> -inline void MatrixPower<MatrixType>::revertSchur( - Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, - const ComplexMatrix& T, - const ComplexMatrix& U) -{ res.noalias() = (U * (T.template triangularView<Upper>() * U.adjoint())).real(); } - -/** - * \ingroup MatrixFunctions_Module - * - * \brief Proxy for the matrix power of some matrix (expression). - * - * \tparam Derived type of the base, a matrix (expression). - * - * This class holds the arguments to the matrix power until it is - * assigned or evaluated for some other reason (so the argument - * should not be changed in the meantime). It is the return type of - * MatrixBase::pow() and related functions and most of the - * time this is the only way it is used. - */ -template<typename Derived> -class MatrixPowerReturnValue : public ReturnByValue< MatrixPowerReturnValue<Derived> > -{ - public: - typedef typename Derived::PlainObject PlainObject; - typedef typename Derived::RealScalar RealScalar; - typedef typename Derived::Index Index; - - /** - * \brief Constructor. - * - * \param[in] A %Matrix (expression), the base of the matrix power. - * \param[in] p real scalar, the exponent of the matrix power. - */ - MatrixPowerReturnValue(const Derived& A, RealScalar p) : m_A(A), m_p(p) - { } - - /** - * \brief Compute the matrix power. - * - * \param[out] result \f$ A^p \f$ where \p A and \p p are as in the - * constructor. - */ - template<typename ResultType> - inline void evalTo(ResultType& result) const - { MatrixPower<PlainObject>(m_A.eval()).compute(result, m_p); } - - Index rows() const { return m_A.rows(); } - Index cols() const { return m_A.cols(); } - - private: - const Derived& m_A; - const RealScalar m_p; -}; - -/** - * \ingroup MatrixFunctions_Module - * - * \brief Proxy for the matrix power of some matrix (expression). - * - * \tparam Derived type of the base, a matrix (expression). - * - * This class holds the arguments to the matrix power until it is - * assigned or evaluated for some other reason (so the argument - * should not be changed in the meantime). It is the return type of - * MatrixBase::pow() and related functions and most of the - * time this is the only way it is used. - */ -template<typename Derived> -class MatrixComplexPowerReturnValue : public ReturnByValue< MatrixComplexPowerReturnValue<Derived> > -{ - public: - typedef typename Derived::PlainObject PlainObject; - typedef typename std::complex<typename Derived::RealScalar> ComplexScalar; - typedef typename Derived::Index Index; - - /** - * \brief Constructor. - * - * \param[in] A %Matrix (expression), the base of the matrix power. - * \param[in] p complex scalar, the exponent of the matrix power. - */ - MatrixComplexPowerReturnValue(const Derived& A, const ComplexScalar& p) : m_A(A), m_p(p) - { } - - /** - * \brief Compute the matrix power. - * - * Because \p p is complex, \f$ A^p \f$ is simply evaluated as \f$ - * \exp(p \log(A)) \f$. - * - * \param[out] result \f$ A^p \f$ where \p A and \p p are as in the - * constructor. - */ - template<typename ResultType> - inline void evalTo(ResultType& result) const - { result = (m_p * m_A.log()).exp(); } - - Index rows() const { return m_A.rows(); } - Index cols() const { return m_A.cols(); } - - private: - const Derived& m_A; - const ComplexScalar m_p; -}; - -namespace internal { - -template<typename MatrixPowerType> -struct traits< MatrixPowerParenthesesReturnValue<MatrixPowerType> > -{ typedef typename MatrixPowerType::PlainObject ReturnType; }; - -template<typename Derived> -struct traits< MatrixPowerReturnValue<Derived> > -{ typedef typename Derived::PlainObject ReturnType; }; - -template<typename Derived> -struct traits< MatrixComplexPowerReturnValue<Derived> > -{ typedef typename Derived::PlainObject ReturnType; }; - -} - -template<typename Derived> -const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(const RealScalar& p) const -{ return MatrixPowerReturnValue<Derived>(derived(), p); } - -template<typename Derived> -const MatrixComplexPowerReturnValue<Derived> MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const -{ return MatrixComplexPowerReturnValue<Derived>(derived(), p); } - -} // namespace Eigen - -#endif // EIGEN_MATRIX_POWER |