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Decouple MatrixFunction and MatrixFunctionAtomic
in preparation for implementation of matrix log.
This commit is contained in:
Jitse Niesen
parent
86ca35ccff
commit
a6d42e28fe
@ -1,7 +1,7 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
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// Copyright (C) 2009-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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@ -30,30 +30,36 @@
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/** \ingroup MatrixFunctions_Module
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* \brief Class for computing matrix exponentials.
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* \brief Class for computing matrix functions.
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* \tparam MatrixType type of the argument of the matrix function,
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* expected to be an instantiation of the Matrix class template.
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* \tparam AtomicType type for computing matrix function of atomic blocks.
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* \tparam IsComplex used internally to select correct specialization.
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*
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* This class implements the Schur-Parlett algorithm for computing matrix functions. The spectrum of the
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* matrix is divided in clustered of eigenvalues that lies close together. This class delegates the
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* computation of the matrix function on every block corresponding to these clusters to an object of type
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* \p AtomicType and uses these results to compute the matrix function of the whole matrix. The class
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* \p AtomicType should have a \p compute() member function for computing the matrix function of a block.
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*
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* \sa class MatrixFunctionAtomic, class MatrixLogarithmAtomic
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*/
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template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
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template <typename MatrixType,
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typename AtomicType,
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int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
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class MatrixFunction
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{
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private:
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typedef typename internal::traits<MatrixType>::Index Index;
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef typename internal::stem_function<Scalar>::type StemFunction;
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public:
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/** \brief Constructor.
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*
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* \param[in] A argument of matrix function, should be a square matrix.
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* \param[in] f an entire function; \c f(x,n) should compute the n-th derivative of f at x.
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* \param[in] atomic class for computing matrix function of atomic blocks.
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*
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* The class stores a reference to \p A, so it should not be
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* The class stores references to \p A and \p atomic, so they should not be
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* changed (or destroyed) before compute() is called.
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*/
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MatrixFunction(const MatrixType& A, StemFunction f);
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MatrixFunction(const MatrixType& A, AtomicType& atomic);
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/** \brief Compute the matrix function.
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*
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@ -71,8 +77,8 @@ class MatrixFunction
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/** \internal \ingroup MatrixFunctions_Module
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* \brief Partial specialization of MatrixFunction for real matrices
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*/
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template <typename MatrixType>
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class MatrixFunction<MatrixType, 0>
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template <typename MatrixType, typename AtomicType>
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class MatrixFunction<MatrixType, AtomicType, 0>
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{
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private:
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@ -86,16 +92,15 @@ class MatrixFunction<MatrixType, 0>
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typedef std::complex<Scalar> ComplexScalar;
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typedef Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols> ComplexMatrix;
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typedef typename internal::stem_function<Scalar>::type StemFunction;
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public:
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/** \brief Constructor.
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*
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* \param[in] A argument of matrix function, should be a square matrix.
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* \param[in] f an entire function; \c f(x,n) should compute the n-th derivative of f at x.
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* \param[in] atomic class for computing matrix function of atomic blocks.
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*/
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MatrixFunction(const MatrixType& A, StemFunction f) : m_A(A), m_f(f) { }
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MatrixFunction(const MatrixType& A, AtomicType& atomic) : m_A(A), m_atomic(atomic) { }
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/** \brief Compute the matrix function.
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*
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@ -111,14 +116,14 @@ class MatrixFunction<MatrixType, 0>
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{
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ComplexMatrix CA = m_A.template cast<ComplexScalar>();
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ComplexMatrix Cresult;
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MatrixFunction<ComplexMatrix> mf(CA, m_f);
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MatrixFunction<ComplexMatrix, AtomicType> mf(CA, m_atomic);
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mf.compute(Cresult);
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result = Cresult.real();
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}
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private:
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typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
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StemFunction *m_f; /**< \brief Stem function for matrix function under consideration */
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AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */
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MatrixFunction& operator=(const MatrixFunction&);
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};
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@ -127,8 +132,8 @@ class MatrixFunction<MatrixType, 0>
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/** \internal \ingroup MatrixFunctions_Module
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* \brief Partial specialization of MatrixFunction for complex matrices
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*/
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template <typename MatrixType>
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class MatrixFunction<MatrixType, 1>
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template <typename MatrixType, typename AtomicType>
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class MatrixFunction<MatrixType, AtomicType, 1>
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{
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private:
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@ -139,7 +144,6 @@ class MatrixFunction<MatrixType, 1>
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static const int ColsAtCompileTime = Traits::ColsAtCompileTime;
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static const int Options = MatrixType::Options;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef typename internal::stem_function<Scalar>::type StemFunction;
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typedef Matrix<Scalar, Traits::RowsAtCompileTime, 1> VectorType;
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typedef Matrix<Index, Traits::RowsAtCompileTime, 1> IntVectorType;
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typedef Matrix<Index, Dynamic, 1> DynamicIntVectorType;
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@ -149,7 +153,7 @@ class MatrixFunction<MatrixType, 1>
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public:
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MatrixFunction(const MatrixType& A, StemFunction f);
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MatrixFunction(const MatrixType& A, AtomicType& atomic);
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template <typename ResultType> void compute(ResultType& result);
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private:
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@ -168,7 +172,7 @@ class MatrixFunction<MatrixType, 1>
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DynMatrixType solveTriangularSylvester(const DynMatrixType& A, const DynMatrixType& B, const DynMatrixType& C);
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typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */
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StemFunction *m_f; /**< \brief Stem function for matrix function under consideration */
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AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */
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MatrixType m_T; /**< \brief Triangular part of Schur decomposition */
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MatrixType m_U; /**< \brief Unitary part of Schur decomposition */
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MatrixType m_fT; /**< \brief %Matrix function applied to #m_T */
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@ -192,11 +196,11 @@ class MatrixFunction<MatrixType, 1>
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/** \brief Constructor.
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*
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* \param[in] A argument of matrix function, should be a square matrix.
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* \param[in] f an entire function; \c f(x,n) should compute the n-th derivative of f at x.
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* \param[in] atomic class for computing matrix function of atomic blocks.
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*/
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template <typename MatrixType>
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MatrixFunction<MatrixType,1>::MatrixFunction(const MatrixType& A, StemFunction f) :
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m_A(A), m_f(f)
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template <typename MatrixType, typename AtomicType>
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MatrixFunction<MatrixType,AtomicType,1>::MatrixFunction(const MatrixType& A, AtomicType& atomic)
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: m_A(A), m_atomic(atomic)
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{
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/* empty body */
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}
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@ -206,9 +210,9 @@ MatrixFunction<MatrixType,1>::MatrixFunction(const MatrixType& A, StemFunction f
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* \param[out] result the function \p f applied to \p A, as
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* specified in the constructor.
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*/
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template <typename MatrixType>
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template <typename MatrixType, typename AtomicType>
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template <typename ResultType>
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void MatrixFunction<MatrixType,1>::compute(ResultType& result)
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void MatrixFunction<MatrixType,AtomicType,1>::compute(ResultType& result)
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{
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computeSchurDecomposition();
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partitionEigenvalues();
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@ -222,8 +226,8 @@ void MatrixFunction<MatrixType,1>::compute(ResultType& result)
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}
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/** \brief Store the Schur decomposition of #m_A in #m_T and #m_U */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::computeSchurDecomposition()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition()
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{
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const ComplexSchur<MatrixType> schurOfA(m_A);
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m_T = schurOfA.matrixT();
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@ -241,8 +245,8 @@ void MatrixFunction<MatrixType,1>::computeSchurDecomposition()
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* The implementation follows Algorithm 4.1 in the paper of Davies
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* and Higham.
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*/
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::partitionEigenvalues()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
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{
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const Index rows = m_T.rows();
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VectorType diag = m_T.diagonal(); // contains eigenvalues of A
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@ -278,8 +282,8 @@ void MatrixFunction<MatrixType,1>::partitionEigenvalues()
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* \returns Iterator to cluster containing \c key, or
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* \c m_clusters.end() if no cluster in m_clusters contains \c key.
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*/
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template <typename MatrixType>
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typename MatrixFunction<MatrixType,1>::ListOfClusters::iterator MatrixFunction<MatrixType,1>::findCluster(Scalar key)
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template <typename MatrixType, typename AtomicType>
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typename MatrixFunction<MatrixType,AtomicType,1>::ListOfClusters::iterator MatrixFunction<MatrixType,AtomicType,1>::findCluster(Scalar key)
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{
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typename Cluster::iterator j;
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for (typename ListOfClusters::iterator i = m_clusters.begin(); i != m_clusters.end(); ++i) {
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@ -291,8 +295,8 @@ typename MatrixFunction<MatrixType,1>::ListOfClusters::iterator MatrixFunction<M
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}
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/** \brief Compute #m_clusterSize and #m_eivalToCluster using #m_clusters */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::computeClusterSize()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::computeClusterSize()
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{
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const Index rows = m_T.rows();
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VectorType diag = m_T.diagonal();
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@ -313,8 +317,8 @@ void MatrixFunction<MatrixType,1>::computeClusterSize()
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}
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/** \brief Compute #m_blockStart using #m_clusterSize */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::computeBlockStart()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::computeBlockStart()
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{
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m_blockStart.resize(m_clusterSize.rows());
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m_blockStart(0) = 0;
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@ -324,8 +328,8 @@ void MatrixFunction<MatrixType,1>::computeBlockStart()
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}
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/** \brief Compute #m_permutation using #m_eivalToCluster and #m_blockStart */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::constructPermutation()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::constructPermutation()
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{
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DynamicIntVectorType indexNextEntry = m_blockStart;
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m_permutation.resize(m_T.rows());
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@ -337,8 +341,8 @@ void MatrixFunction<MatrixType,1>::constructPermutation()
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}
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/** \brief Permute Schur decomposition in #m_U and #m_T according to #m_permutation */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::permuteSchur()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::permuteSchur()
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{
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IntVectorType p = m_permutation;
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for (Index i = 0; i < p.rows() - 1; i++) {
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@ -355,8 +359,8 @@ void MatrixFunction<MatrixType,1>::permuteSchur()
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}
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/** \brief Swap rows \a index and \a index+1 in Schur decomposition in #m_U and #m_T */
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::swapEntriesInSchur(Index index)
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::swapEntriesInSchur(Index index)
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{
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JacobiRotation<Scalar> rotation;
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rotation.makeGivens(m_T(index, index+1), m_T(index+1, index+1) - m_T(index, index));
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@ -367,25 +371,23 @@ void MatrixFunction<MatrixType,1>::swapEntriesInSchur(Index index)
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/** \brief Compute block diagonal part of #m_fT.
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*
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* This routine computes the matrix function #m_f applied to the block
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* diagonal part of #m_T, with the blocking given by #m_blockStart. The
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* result is stored in #m_fT. The off-diagonal parts of #m_fT are set
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* to zero.
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* This routine computes the matrix function applied to the block diagonal part of #m_T, with the blocking
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* given by #m_blockStart. The matrix function of each diagonal block is computed by #m_atomic. The
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* off-diagonal parts of #m_fT are set to zero.
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*/
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::computeBlockAtomic()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::computeBlockAtomic()
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{
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m_fT.resize(m_T.rows(), m_T.cols());
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m_fT.setZero();
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MatrixFunctionAtomic<DynMatrixType> mfa(m_f);
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for (Index i = 0; i < m_clusterSize.rows(); ++i) {
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block(m_fT, i, i) = mfa.compute(block(m_T, i, i));
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block(m_fT, i, i) = m_atomic.compute(block(m_T, i, i));
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}
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}
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/** \brief Return block of matrix according to blocking given by #m_blockStart */
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template <typename MatrixType>
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Block<MatrixType> MatrixFunction<MatrixType,1>::block(MatrixType& A, Index i, Index j)
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template <typename MatrixType, typename AtomicType>
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Block<MatrixType> MatrixFunction<MatrixType,AtomicType,1>::block(MatrixType& A, Index i, Index j)
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{
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return A.block(m_blockStart(i), m_blockStart(j), m_clusterSize(i), m_clusterSize(j));
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}
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@ -393,12 +395,12 @@ Block<MatrixType> MatrixFunction<MatrixType,1>::block(MatrixType& A, Index i, In
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/** \brief Compute part of #m_fT above block diagonal.
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*
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* This routine assumes that the block diagonal part of #m_fT (which
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* equals #m_f applied to #m_T) has already been computed and computes
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* equals the matrix function applied to #m_T) has already been computed and computes
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* the part above the block diagonal. The part below the diagonal is
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* zero, because #m_T is upper triangular.
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*/
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template <typename MatrixType>
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void MatrixFunction<MatrixType,1>::computeOffDiagonal()
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template <typename MatrixType, typename AtomicType>
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void MatrixFunction<MatrixType,AtomicType,1>::computeOffDiagonal()
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{
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for (Index diagIndex = 1; diagIndex < m_clusterSize.rows(); diagIndex++) {
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for (Index blockIndex = 0; blockIndex < m_clusterSize.rows() - diagIndex; blockIndex++) {
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@ -439,8 +441,8 @@ void MatrixFunction<MatrixType,1>::computeOffDiagonal()
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* solution). In that case, these equations can be evaluated in the
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* order \f$ i=m,\ldots,1 \f$ and \f$ j=1,\ldots,n \f$.
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*/
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template <typename MatrixType>
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typename MatrixFunction<MatrixType,1>::DynMatrixType MatrixFunction<MatrixType,1>::solveTriangularSylvester(
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template <typename MatrixType, typename AtomicType>
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typename MatrixFunction<MatrixType,AtomicType,1>::DynMatrixType MatrixFunction<MatrixType,AtomicType,1>::solveTriangularSylvester(
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const DynMatrixType& A,
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const DynMatrixType& B,
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const DynMatrixType& C)
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@ -520,8 +522,18 @@ template<typename Derived> class MatrixFunctionReturnValue
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template <typename ResultType>
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inline void evalTo(ResultType& result) const
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{
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const typename Derived::PlainObject Aevaluated = m_A.eval();
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MatrixFunction<typename Derived::PlainObject> mf(Aevaluated, m_f);
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typedef typename Derived::PlainObject PlainObject;
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typedef internal::traits<PlainObject> Traits;
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static const int RowsAtCompileTime = Traits::RowsAtCompileTime;
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static const int ColsAtCompileTime = Traits::ColsAtCompileTime;
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static const int Options = PlainObject::Options;
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typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
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typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;
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typedef MatrixFunctionAtomic<DynMatrixType> AtomicType;
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AtomicType atomic(m_f);
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const PlainObject Aevaluated = m_A.eval();
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MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic);
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mf.compute(result);
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}
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