[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_BANDMATRIX_H
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| 11 | #define EIGEN_BANDMATRIX_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | namespace internal {
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| 16 |
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| 17 | template<typename Derived>
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| 18 | class BandMatrixBase : public EigenBase<Derived>
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| 19 | {
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| 20 | public:
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| 21 |
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| 22 | enum {
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| 23 | Flags = internal::traits<Derived>::Flags,
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| 24 | CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
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| 25 | RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
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| 26 | ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
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| 27 | MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
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| 28 | MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
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| 29 | Supers = internal::traits<Derived>::Supers,
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| 30 | Subs = internal::traits<Derived>::Subs,
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| 31 | Options = internal::traits<Derived>::Options
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| 32 | };
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| 33 | typedef typename internal::traits<Derived>::Scalar Scalar;
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| 34 | typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
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| 35 | typedef typename DenseMatrixType::Index Index;
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| 36 | typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
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| 37 | typedef EigenBase<Derived> Base;
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| 38 |
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| 39 | protected:
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| 40 | enum {
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| 41 | DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
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| 42 | ? 1 + Supers + Subs
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| 43 | : Dynamic,
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| 44 | SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
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| 45 | };
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| 46 |
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| 47 | public:
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| 48 |
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| 49 | using Base::derived;
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| 50 | using Base::rows;
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| 51 | using Base::cols;
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| 52 |
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| 53 | /** \returns the number of super diagonals */
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| 54 | inline Index supers() const { return derived().supers(); }
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| 55 |
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| 56 | /** \returns the number of sub diagonals */
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| 57 | inline Index subs() const { return derived().subs(); }
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| 58 |
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| 59 | /** \returns an expression of the underlying coefficient matrix */
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| 60 | inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
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| 61 |
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| 62 | /** \returns an expression of the underlying coefficient matrix */
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| 63 | inline CoefficientsType& coeffs() { return derived().coeffs(); }
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| 64 |
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| 65 | /** \returns a vector expression of the \a i -th column,
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| 66 | * only the meaningful part is returned.
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| 67 | * \warning the internal storage must be column major. */
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| 68 | inline Block<CoefficientsType,Dynamic,1> col(Index i)
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| 69 | {
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| 70 | EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
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| 71 | Index start = 0;
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| 72 | Index len = coeffs().rows();
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| 73 | if (i<=supers())
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| 74 | {
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| 75 | start = supers()-i;
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| 76 | len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
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| 77 | }
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| 78 | else if (i>=rows()-subs())
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| 79 | len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
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| 80 | return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
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| 81 | }
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| 82 |
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| 83 | /** \returns a vector expression of the main diagonal */
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| 84 | inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
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| 85 | { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
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| 86 |
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| 87 | /** \returns a vector expression of the main diagonal (const version) */
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| 88 | inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
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| 89 | { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
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| 90 |
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| 91 | template<int Index> struct DiagonalIntReturnType {
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| 92 | enum {
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| 93 | ReturnOpposite = (Options&SelfAdjoint) && (((Index)>0 && Supers==0) || ((Index)<0 && Subs==0)),
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| 94 | Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
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| 95 | ActualIndex = ReturnOpposite ? -Index : Index,
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| 96 | DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
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| 97 | ? Dynamic
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| 98 | : (ActualIndex<0
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| 99 | ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
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| 100 | : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
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| 101 | };
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| 102 | typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
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| 103 | typedef typename internal::conditional<Conjugate,
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| 104 | CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
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| 105 | BuildType>::type Type;
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| 106 | };
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| 107 |
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| 108 | /** \returns a vector expression of the \a N -th sub or super diagonal */
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| 109 | template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
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| 110 | {
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| 111 | return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
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| 112 | }
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| 113 |
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| 114 | /** \returns a vector expression of the \a N -th sub or super diagonal */
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| 115 | template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
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| 116 | {
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| 117 | return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
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| 118 | }
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| 119 |
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| 120 | /** \returns a vector expression of the \a i -th sub or super diagonal */
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| 121 | inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
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| 122 | {
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| 123 | eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
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| 124 | return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
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| 125 | }
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| 126 |
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| 127 | /** \returns a vector expression of the \a i -th sub or super diagonal */
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| 128 | inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
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| 129 | {
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| 130 | eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
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| 131 | return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
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| 132 | }
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| 133 |
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| 134 | template<typename Dest> inline void evalTo(Dest& dst) const
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| 135 | {
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| 136 | dst.resize(rows(),cols());
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| 137 | dst.setZero();
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| 138 | dst.diagonal() = diagonal();
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| 139 | for (Index i=1; i<=supers();++i)
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| 140 | dst.diagonal(i) = diagonal(i);
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| 141 | for (Index i=1; i<=subs();++i)
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| 142 | dst.diagonal(-i) = diagonal(-i);
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| 143 | }
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| 144 |
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| 145 | DenseMatrixType toDenseMatrix() const
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| 146 | {
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| 147 | DenseMatrixType res(rows(),cols());
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| 148 | evalTo(res);
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| 149 | return res;
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| 150 | }
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| 151 |
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| 152 | protected:
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| 153 |
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| 154 | inline Index diagonalLength(Index i) const
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| 155 | { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
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| 156 | };
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| 157 |
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| 158 | /**
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| 159 | * \class BandMatrix
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| 160 | * \ingroup Core_Module
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| 161 | *
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| 162 | * \brief Represents a rectangular matrix with a banded storage
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| 163 | *
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| 164 | * \param _Scalar Numeric type, i.e. float, double, int
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| 165 | * \param Rows Number of rows, or \b Dynamic
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| 166 | * \param Cols Number of columns, or \b Dynamic
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| 167 | * \param Supers Number of super diagonal
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| 168 | * \param Subs Number of sub diagonal
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| 169 | * \param _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
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| 170 | * The former controls \ref TopicStorageOrders "storage order", and defaults to
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| 171 | * column-major. The latter controls whether the matrix represents a selfadjoint
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| 172 | * matrix in which case either Supers of Subs have to be null.
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| 173 | *
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| 174 | * \sa class TridiagonalMatrix
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| 175 | */
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| 176 |
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| 177 | template<typename _Scalar, int _Rows, int _Cols, int _Supers, int _Subs, int _Options>
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| 178 | struct traits<BandMatrix<_Scalar,_Rows,_Cols,_Supers,_Subs,_Options> >
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| 179 | {
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| 180 | typedef _Scalar Scalar;
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| 181 | typedef Dense StorageKind;
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| 182 | typedef DenseIndex Index;
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| 183 | enum {
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| 184 | CoeffReadCost = NumTraits<Scalar>::ReadCost,
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| 185 | RowsAtCompileTime = _Rows,
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| 186 | ColsAtCompileTime = _Cols,
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| 187 | MaxRowsAtCompileTime = _Rows,
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| 188 | MaxColsAtCompileTime = _Cols,
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| 189 | Flags = LvalueBit,
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| 190 | Supers = _Supers,
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| 191 | Subs = _Subs,
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| 192 | Options = _Options,
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| 193 | DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
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| 194 | };
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| 195 | typedef Matrix<Scalar,DataRowsAtCompileTime,ColsAtCompileTime,Options&RowMajor?RowMajor:ColMajor> CoefficientsType;
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| 196 | };
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| 197 |
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| 198 | template<typename _Scalar, int Rows, int Cols, int Supers, int Subs, int Options>
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| 199 | class BandMatrix : public BandMatrixBase<BandMatrix<_Scalar,Rows,Cols,Supers,Subs,Options> >
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| 200 | {
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| 201 | public:
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| 202 |
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| 203 | typedef typename internal::traits<BandMatrix>::Scalar Scalar;
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| 204 | typedef typename internal::traits<BandMatrix>::Index Index;
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| 205 | typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
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| 206 |
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| 207 | inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
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| 208 | : m_coeffs(1+supers+subs,cols),
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| 209 | m_rows(rows), m_supers(supers), m_subs(subs)
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| 210 | {
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| 211 | }
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| 212 |
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| 213 | /** \returns the number of columns */
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| 214 | inline Index rows() const { return m_rows.value(); }
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| 215 |
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| 216 | /** \returns the number of rows */
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| 217 | inline Index cols() const { return m_coeffs.cols(); }
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| 218 |
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| 219 | /** \returns the number of super diagonals */
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| 220 | inline Index supers() const { return m_supers.value(); }
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| 221 |
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| 222 | /** \returns the number of sub diagonals */
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| 223 | inline Index subs() const { return m_subs.value(); }
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| 224 |
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| 225 | inline const CoefficientsType& coeffs() const { return m_coeffs; }
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| 226 | inline CoefficientsType& coeffs() { return m_coeffs; }
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| 227 |
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| 228 | protected:
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| 229 |
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| 230 | CoefficientsType m_coeffs;
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| 231 | internal::variable_if_dynamic<Index, Rows> m_rows;
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| 232 | internal::variable_if_dynamic<Index, Supers> m_supers;
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| 233 | internal::variable_if_dynamic<Index, Subs> m_subs;
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| 234 | };
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| 235 |
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| 236 | template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
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| 237 | class BandMatrixWrapper;
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| 238 |
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| 239 | template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
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| 240 | struct traits<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
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| 241 | {
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| 242 | typedef typename _CoefficientsType::Scalar Scalar;
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| 243 | typedef typename _CoefficientsType::StorageKind StorageKind;
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| 244 | typedef typename _CoefficientsType::Index Index;
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| 245 | enum {
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| 246 | CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost,
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| 247 | RowsAtCompileTime = _Rows,
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| 248 | ColsAtCompileTime = _Cols,
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| 249 | MaxRowsAtCompileTime = _Rows,
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| 250 | MaxColsAtCompileTime = _Cols,
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| 251 | Flags = LvalueBit,
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| 252 | Supers = _Supers,
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| 253 | Subs = _Subs,
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| 254 | Options = _Options,
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| 255 | DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
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| 256 | };
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| 257 | typedef _CoefficientsType CoefficientsType;
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| 258 | };
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| 259 |
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| 260 | template<typename _CoefficientsType,int _Rows, int _Cols, int _Supers, int _Subs,int _Options>
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| 261 | class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsType,_Rows,_Cols,_Supers,_Subs,_Options> >
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| 262 | {
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| 263 | public:
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| 264 |
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| 265 | typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
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| 266 | typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
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| 267 | typedef typename internal::traits<BandMatrixWrapper>::Index Index;
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| 268 |
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| 269 | inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=_Rows, Index cols=_Cols, Index supers=_Supers, Index subs=_Subs)
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| 270 | : m_coeffs(coeffs),
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| 271 | m_rows(rows), m_supers(supers), m_subs(subs)
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| 272 | {
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| 273 | EIGEN_UNUSED_VARIABLE(cols);
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| 274 | //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
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| 275 | }
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| 276 |
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| 277 | /** \returns the number of columns */
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| 278 | inline Index rows() const { return m_rows.value(); }
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| 279 |
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| 280 | /** \returns the number of rows */
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| 281 | inline Index cols() const { return m_coeffs.cols(); }
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| 282 |
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| 283 | /** \returns the number of super diagonals */
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| 284 | inline Index supers() const { return m_supers.value(); }
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| 285 |
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| 286 | /** \returns the number of sub diagonals */
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| 287 | inline Index subs() const { return m_subs.value(); }
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| 288 |
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| 289 | inline const CoefficientsType& coeffs() const { return m_coeffs; }
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| 290 |
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| 291 | protected:
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| 292 |
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| 293 | const CoefficientsType& m_coeffs;
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| 294 | internal::variable_if_dynamic<Index, _Rows> m_rows;
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| 295 | internal::variable_if_dynamic<Index, _Supers> m_supers;
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| 296 | internal::variable_if_dynamic<Index, _Subs> m_subs;
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| 297 | };
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| 298 |
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| 299 | /**
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| 300 | * \class TridiagonalMatrix
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| 301 | * \ingroup Core_Module
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| 302 | *
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| 303 | * \brief Represents a tridiagonal matrix with a compact banded storage
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| 304 | *
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| 305 | * \param _Scalar Numeric type, i.e. float, double, int
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| 306 | * \param Size Number of rows and cols, or \b Dynamic
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| 307 | * \param _Options Can be 0 or \b SelfAdjoint
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| 308 | *
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| 309 | * \sa class BandMatrix
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| 310 | */
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| 311 | template<typename Scalar, int Size, int Options>
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| 312 | class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
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| 313 | {
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| 314 | typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
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| 315 | typedef typename Base::Index Index;
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| 316 | public:
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| 317 | TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
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| 318 |
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| 319 | inline typename Base::template DiagonalIntReturnType<1>::Type super()
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| 320 | { return Base::template diagonal<1>(); }
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| 321 | inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
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| 322 | { return Base::template diagonal<1>(); }
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| 323 | inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
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| 324 | { return Base::template diagonal<-1>(); }
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| 325 | inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
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| 326 | { return Base::template diagonal<-1>(); }
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| 327 | protected:
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| 328 | };
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| 329 |
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| 330 | } // end namespace internal
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| 331 |
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| 332 | } // end namespace Eigen
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| 333 |
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| 334 | #endif // EIGEN_BANDMATRIX_H
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