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Add support for matrix sine, cosine, sinh and cosh.

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This commit is contained in:
Jitse Niesen
2010-01-11 18:05:30 +00:00
parent a05d42616b
commit 65cd1c7639
8 changed files with 401 additions and 22 deletions
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129
unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
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@@ -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