DiagonalMatrix.h 11.3 KB
Newer Older
LM's avatar
LM committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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_DIAGONALMATRIX_H
#define EIGEN_DIAGONALMATRIX_H

#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
class DiagonalBase : public EigenBase<Derived>
{
  public:
    typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
    typedef typename DiagonalVectorType::Scalar Scalar;
    typedef typename internal::traits<Derived>::StorageKind StorageKind;
    typedef typename internal::traits<Derived>::Index Index;

    enum {
      RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
      ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
      MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
      MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
      IsVectorAtCompileTime = 0,
      Flags = 0
    };

    typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
    typedef DenseMatrixType DenseType;
    typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;

    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
    inline Derived& derived() { return *static_cast<Derived*>(this); }

    DenseMatrixType toDenseMatrix() const { return derived(); }
    template<typename DenseDerived>
    void evalTo(MatrixBase<DenseDerived> &other) const;
    template<typename DenseDerived>
    void addTo(MatrixBase<DenseDerived> &other) const
    { other.diagonal() += diagonal(); }
    template<typename DenseDerived>
    void subTo(MatrixBase<DenseDerived> &other) const
    { other.diagonal() -= diagonal(); }

    inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
    inline DiagonalVectorType& diagonal() { return derived().diagonal(); }

    inline Index rows() const { return diagonal().size(); }
    inline Index cols() const { return diagonal().size(); }

    template<typename MatrixDerived>
    const DiagonalProduct<MatrixDerived, Derived, OnTheLeft>
    operator*(const MatrixBase<MatrixDerived> &matrix) const;

    inline const DiagonalWrapper<CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> >
    inverse() const
    {
      return diagonal().cwiseInverse();
    }
    
    #ifdef EIGEN2_SUPPORT
    template<typename OtherDerived>
    bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
    {
      return diagonal().isApprox(other.diagonal(), precision);
    }
    template<typename OtherDerived>
    bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const
    {
      return toDenseMatrix().isApprox(other, precision);
    }
    #endif
};

template<typename Derived>
template<typename DenseDerived>
void DiagonalBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
{
  other.setZero();
  other.diagonal() = diagonal();
}
#endif

/** \class DiagonalMatrix
  * \ingroup Core_Module
  *
  * \brief Represents a diagonal matrix with its storage
  *
  * \param _Scalar the type of coefficients
  * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
  * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
  *        to SizeAtCompileTime. Most of the time, you do not need to specify it.
  *
  * \sa class DiagonalWrapper
  */

namespace internal {
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
 : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
  typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
  typedef Dense StorageKind;
  typedef DenseIndex Index;
  enum {
    Flags = LvalueBit
  };
};
}
template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
class DiagonalMatrix
  : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
{
  public:
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
    typedef const DiagonalMatrix& Nested;
    typedef _Scalar Scalar;
    typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
    typedef typename internal::traits<DiagonalMatrix>::Index Index;
    #endif

  protected:

    DiagonalVectorType m_diagonal;

  public:

    /** const version of diagonal(). */
    inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
    /** \returns a reference to the stored vector of diagonal coefficients. */
    inline DiagonalVectorType& diagonal() { return m_diagonal; }

    /** Default constructor without initialization */
    inline DiagonalMatrix() {}

    /** Constructs a diagonal matrix with given dimension  */
    inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}

    /** 2D constructor. */
    inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}

    /** 3D constructor. */
    inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}

    /** Copy constructor. */
    template<typename OtherDerived>
    inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}

    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
    inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
    #endif

    /** generic constructor from expression of the diagonal coefficients */
    template<typename OtherDerived>
    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
    {}

    /** Copy operator. */
    template<typename OtherDerived>
    DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }

    #ifndef EIGEN_PARSED_BY_DOXYGEN
    /** This is a special case of the templated operator=. Its purpose is to
      * prevent a default operator= from hiding the templated operator=.
      */
    DiagonalMatrix& operator=(const DiagonalMatrix& other)
    {
      m_diagonal = other.diagonal();
      return *this;
    }
    #endif

    /** Resizes to given size. */
    inline void resize(Index size) { m_diagonal.resize(size); }
    /** Sets all coefficients to zero. */
    inline void setZero() { m_diagonal.setZero(); }
    /** Resizes and sets all coefficients to zero. */
    inline void setZero(Index size) { m_diagonal.setZero(size); }
    /** Sets this matrix to be the identity matrix of the current size. */
    inline void setIdentity() { m_diagonal.setOnes(); }
    /** Sets this matrix to be the identity matrix of the given size. */
    inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
};

/** \class DiagonalWrapper
  * \ingroup Core_Module
  *
  * \brief Expression of a diagonal matrix
  *
  * \param _DiagonalVectorType the type of the vector of diagonal coefficients
  *
  * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
  * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
  * and most of the time this is the only way that it is used.
  *
  * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
  */

namespace internal {
template<typename _DiagonalVectorType>
struct traits<DiagonalWrapper<_DiagonalVectorType> >
{
  typedef _DiagonalVectorType DiagonalVectorType;
  typedef typename DiagonalVectorType::Scalar Scalar;
  typedef typename DiagonalVectorType::Index Index;
  typedef typename DiagonalVectorType::StorageKind StorageKind;
  enum {
    RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    MaxRowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    MaxColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
    Flags =  traits<DiagonalVectorType>::Flags & LvalueBit
  };
};
}

template<typename _DiagonalVectorType>
class DiagonalWrapper
  : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
{
  public:
    #ifndef EIGEN_PARSED_BY_DOXYGEN
    typedef _DiagonalVectorType DiagonalVectorType;
    typedef DiagonalWrapper Nested;
    #endif

    /** Constructor from expression of diagonal coefficients to wrap. */
    inline DiagonalWrapper(const DiagonalVectorType& diagonal) : m_diagonal(diagonal) {}

    /** \returns a const reference to the wrapped expression of diagonal coefficients. */
    const DiagonalVectorType& diagonal() const { return m_diagonal; }

  protected:
    const typename DiagonalVectorType::Nested m_diagonal;
};

/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
  *
  * \only_for_vectors
  *
  * Example: \include MatrixBase_asDiagonal.cpp
  * Output: \verbinclude MatrixBase_asDiagonal.out
  *
  * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
  **/
template<typename Derived>
inline const DiagonalWrapper<const Derived>
MatrixBase<Derived>::asDiagonal() const
{
  return derived();
}

/** \returns true if *this is approximately equal to a diagonal matrix,
  *          within the precision given by \a prec.
  *
  * Example: \include MatrixBase_isDiagonal.cpp
  * Output: \verbinclude MatrixBase_isDiagonal.out
  *
  * \sa asDiagonal()
  */
template<typename Derived>
bool MatrixBase<Derived>::isDiagonal(RealScalar prec) const
{
  if(cols() != rows()) return false;
  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
  for(Index j = 0; j < cols(); ++j)
  {
    RealScalar absOnDiagonal = internal::abs(coeff(j,j));
    if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
  }
  for(Index j = 0; j < cols(); ++j)
    for(Index i = 0; i < j; ++i)
    {
      if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
      if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
    }
  return true;
}

#endif // EIGEN_DIAGONALMATRIX_H