diff options
author | Jitse Niesen <jitse@maths.leeds.ac.uk> | 2010-01-11 18:05:30 +0000 |
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committer | Jitse Niesen <jitse@maths.leeds.ac.uk> | 2010-01-11 18:05:30 +0000 |
commit | 65cd1c7639e6dab0416ecc440b01e7257554dfc0 (patch) | |
tree | 11e189a6ac1b738b8245798e3e5c9e88608b0fc0 /unsupported/Eigen | |
parent | a05d42616b6ae486e1329644355d2cd8a65739ad (diff) |
Add support for matrix sine, cosine, sinh and cosh.
Diffstat (limited to 'unsupported/Eigen')
-rw-r--r-- | unsupported/Eigen/MatrixFunctions | 9 | ||||
-rw-r--r-- | unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h | 4 | ||||
-rw-r--r-- | unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h | 129 | ||||
-rw-r--r-- | unsupported/Eigen/src/MatrixFunctions/StemFunction.h | 123 |
4 files changed, 243 insertions, 22 deletions
diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions index bf2223a6e..91790c8d2 100644 --- a/unsupported/Eigen/MatrixFunctions +++ b/unsupported/Eigen/MatrixFunctions @@ -41,6 +41,15 @@ namespace Eigen { * \brief This module aims to provide various methods for the computation of * matrix functions. * + * %Matrix functions are defined as follows. Suppose that \f$ f \f$ + * is an entire function (that is, a function on the complex plane + * that is everywhere complex differentiable). Then its Taylor + * series + * \f[ f(0) + f'(0) x + \frac{f''(0)}{2} x^2 + \frac{f'''(0)}{3!} x^3 + \cdots \f] + * converges to \f$ f(x) \f$. In this case, we can define the matrix + * function by the same series: + * \f[ f(M) = f(0) + f'(0) M + \frac{f''(0)}{2} M^2 + \frac{f'''(0)}{3!} M^3 + \cdots \f] + * * \code * #include <unsupported/Eigen/MatrixFunctions> * \endcode diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h index b5f4e2b6f..fd1938a87 100644 --- a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h @@ -33,8 +33,8 @@ * * \brief Compute the matrix exponential. * - * \param M matrix whose exponential is to be computed. - * \param result pointer to the matrix in which to store the result. + * \param[in] M matrix whose exponential is to be computed. + * \param[out] result pointer to the matrix in which to store the result. * * The matrix exponential of \f$ M \f$ is defined by * \f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f] diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h index 43539f549..49326cd0e 100644 --- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h @@ -1,7 +1,7 @@ // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // -// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk> +// Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public @@ -25,12 +25,8 @@ #ifndef EIGEN_MATRIX_FUNCTION #define EIGEN_MATRIX_FUNCTION -template <typename Scalar> -struct ei_stem_function -{ - typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; - typedef ComplexScalar type(ComplexScalar, int); -}; +#include "StemFunction.h" +#include "MatrixFunctionAtomic.h" /** \ingroup MatrixFunctions_Module * @@ -43,14 +39,15 @@ struct ei_stem_function * This function computes \f$ f(A) \f$ and stores the result in the * matrix pointed to by \p result. * - * %Matrix functions are defined as follows. Suppose that \f$ f \f$ - * is an entire function (that is, a function on the complex plane - * that is everywhere complex differentiable). Then its Taylor - * series - * \f[ f(0) + f'(0) x + \frac{f''(0)}{2} x^2 + \frac{f'''(0)}{3!} x^3 + \cdots \f] - * converges to \f$ f(x) \f$. In this case, we can define the matrix - * function by the same series: - * \f[ f(M) = f(0) + f'(0) M + \frac{f''(0)}{2} M^2 + \frac{f'''(0)}{3!} M^3 + \cdots \f] + * Suppose that \p M is a matrix whose entries have type \c Scalar. + * Then, the second argument, \p f, should be a function with prototype + * \code + * ComplexScalar f(ComplexScalar, int) + * \endcode + * where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is + * real (e.g., \c float or \c double) and \c ComplexScalar = + * \c Scalar if \c Scalar is complex. The return value of \c f(x,n) + * should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x. * * This routine uses the algorithm described in: * Philip Davies and Nicholas J. Higham, @@ -73,19 +70,21 @@ struct ei_stem_function * the z-axis. This is the same example as used in the documentation * of ei_matrix_exponential(). * - * Note that the function \c expfn is defined for complex numbers \c x, - * even though the matrix \c A is over the reals. - * * \include MatrixFunction.cpp * Output: \verbinclude MatrixFunction.out + * + * Note that the function \c expfn is defined for complex numbers + * \c x, even though the matrix \c A is over the reals. Instead of + * \c expfn, we could also have used StdStemFunctions::exp: + * \code + * ei_matrix_function(A, StdStemFunctions<std::complex<double> >::exp, &B); + * \endcode */ template <typename Derived> EIGEN_STRONG_INLINE void ei_matrix_function(const MatrixBase<Derived>& M, typename ei_stem_function<typename ei_traits<Derived>::Scalar>::type f, typename MatrixBase<Derived>::PlainMatrixType* result); -#include "MatrixFunctionAtomic.h" - /** \ingroup MatrixFunctions_Module * \brief Helper class for computing matrix functions. @@ -510,4 +509,94 @@ EIGEN_STRONG_INLINE void ei_matrix_function(const MatrixBase<Derived>& M, MatrixFunction<PlainMatrixType>(M, f, result); } +/** \ingroup MatrixFunctions_Module + * + * \brief Compute the matrix sine. + * + * \param[in] M a square matrix. + * \param[out] result pointer to matrix in which to store the result, \f$ \sin(M) \f$ + * + * This function calls ei_matrix_function() with StdStemFunctions::sin(). + * + * \include MatrixSine.cpp + * Output: \verbinclude MatrixSine.out + */ +template <typename Derived> +EIGEN_STRONG_INLINE void ei_matrix_sin(const MatrixBase<Derived>& M, + typename MatrixBase<Derived>::PlainMatrixType* result) +{ + ei_assert(M.rows() == M.cols()); + typedef typename MatrixBase<Derived>::PlainMatrixType PlainMatrixType; + typedef typename ei_traits<PlainMatrixType>::Scalar Scalar; + typedef typename ei_stem_function<Scalar>::ComplexScalar ComplexScalar; + MatrixFunction<PlainMatrixType>(M, StdStemFunctions<ComplexScalar>::sin, result); +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Compute the matrix cosine. + * + * \param[in] M a square matrix. + * \param[out] result pointer to matrix in which to store the result, \f$ \cos(M) \f$ + * + * This function calls ei_matrix_function() with StdStemFunctions::cos(). + * + * \sa ei_matrix_sin() for an example. + */ +template <typename Derived> +EIGEN_STRONG_INLINE void ei_matrix_cos(const MatrixBase<Derived>& M, + typename MatrixBase<Derived>::PlainMatrixType* result) +{ + ei_assert(M.rows() == M.cols()); + typedef typename MatrixBase<Derived>::PlainMatrixType PlainMatrixType; + typedef typename ei_traits<PlainMatrixType>::Scalar Scalar; + typedef typename ei_stem_function<Scalar>::ComplexScalar ComplexScalar; + MatrixFunction<PlainMatrixType>(M, StdStemFunctions<ComplexScalar>::cos, result); +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Compute the matrix hyperbolic sine. + * + * \param[in] M a square matrix. + * \param[out] result pointer to matrix in which to store the result, \f$ \sinh(M) \f$ + * + * This function calls ei_matrix_function() with StdStemFunctions::sinh(). + * + * \include MatrixSinh.cpp + * Output: \verbinclude MatrixSinh.out + */ +template <typename Derived> +EIGEN_STRONG_INLINE void ei_matrix_sinh(const MatrixBase<Derived>& M, + typename MatrixBase<Derived>::PlainMatrixType* result) +{ + ei_assert(M.rows() == M.cols()); + typedef typename MatrixBase<Derived>::PlainMatrixType PlainMatrixType; + typedef typename ei_traits<PlainMatrixType>::Scalar Scalar; + typedef typename ei_stem_function<Scalar>::ComplexScalar ComplexScalar; + MatrixFunction<PlainMatrixType>(M, StdStemFunctions<ComplexScalar>::sinh, result); +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Compute the matrix hyberpolic cosine. + * + * \param[in] M a square matrix. + * \param[out] result pointer to matrix in which to store the result, \f$ \cosh(M) \f$ + * + * This function calls ei_matrix_function() with StdStemFunctions::cosh(). + * + * \sa ei_matrix_sinh() for an example. + */ +template <typename Derived> +EIGEN_STRONG_INLINE void ei_matrix_cosh(const MatrixBase<Derived>& M, + typename MatrixBase<Derived>::PlainMatrixType* result) +{ + ei_assert(M.rows() == M.cols()); + typedef typename MatrixBase<Derived>::PlainMatrixType PlainMatrixType; + typedef typename ei_traits<PlainMatrixType>::Scalar Scalar; + typedef typename ei_stem_function<Scalar>::ComplexScalar ComplexScalar; + MatrixFunction<PlainMatrixType>(M, StdStemFunctions<ComplexScalar>::cosh, result); +} + #endif // EIGEN_MATRIX_FUNCTION diff --git a/unsupported/Eigen/src/MatrixFunctions/StemFunction.h b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h new file mode 100644 index 000000000..90965c7dd --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h @@ -0,0 +1,123 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_STEM_FUNCTION +#define EIGEN_STEM_FUNCTION + +template <typename Scalar> +struct ei_stem_function +{ + typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; + typedef ComplexScalar type(ComplexScalar, int); +}; + +/** \ingroup MatrixFunctions_Module + * \brief Stem functions corresponding to standard mathematical functions. + */ +template <typename Scalar> +class StdStemFunctions +{ + public: + + /** \brief The exponential function (and its derivatives). */ + static Scalar exp(Scalar x, int) + { + return std::exp(x); + } + + /** \brief Cosine (and its derivatives). */ + static Scalar cos(Scalar x, int n) + { + Scalar res; + switch (n % 4) { + case 0: + res = std::cos(x); + break; + case 1: + res = -std::sin(x); + break; + case 2: + res = -std::cos(x); + break; + case 3: + res = std::sin(x); + break; + } + return res; + } + + /** \brief Sine (and its derivatives). */ + static Scalar sin(Scalar x, int n) + { + Scalar res; + switch (n % 4) { + case 0: + res = std::sin(x); + break; + case 1: + res = std::cos(x); + break; + case 2: + res = -std::sin(x); + break; + case 3: + res = -std::cos(x); + break; + } + return res; + } + + /** \brief Hyperbolic cosine (and its derivatives). */ + static Scalar cosh(Scalar x, int n) + { + Scalar res; + switch (n % 2) { + case 0: + res = std::cosh(x); + break; + case 1: + res = std::sinh(x); + break; + } + return res; + } + + /** \brief Hyperbolic sine (and its derivatives). */ + static Scalar sinh(Scalar x, int n) + { + Scalar res; + switch (n % 2) { + case 0: + res = std::sinh(x); + break; + case 1: + res = std::cosh(x); + break; + } + return res; + } + +}; // end of class StdStemFunctions + +#endif // EIGEN_STEM_FUNCTION |