Eigen/src/Core/Transpositions.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#ifndef EIGEN_TRANSPOSITIONS_H
#define EIGEN_TRANSPOSITIONS_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

template <typename Derived>
class TranspositionsBase {
  using Traits = internal::traits<Derived>;

 public:
  using IndicesType = typename Traits::IndicesType;
  using StorageIndex = typename IndicesType::Scalar;
  using Index = Eigen::Index;  ///< \deprecated since Eigen 3.3

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

  /** Copies the \a other transpositions into \c *this */
  template <typename OtherDerived>
  Derived& operator=(const TranspositionsBase<OtherDerived>& other) {
    indices() = other.indices();
    return derived();
  }

  /** \returns the number of transpositions */
  EIGEN_DEVICE_FUNC Index size() const { return indices().size(); }
  /** \returns the number of rows of the equivalent permutation matrix */
  EIGEN_DEVICE_FUNC Index rows() const { return indices().size(); }
  /** \returns the number of columns of the equivalent permutation matrix */
  EIGEN_DEVICE_FUNC Index cols() const { return indices().size(); }

  /** Direct access to the underlying index vector */
  EIGEN_DEVICE_FUNC inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
  /** Direct access to the underlying index vector */
  inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }
  /** Direct access to the underlying index vector */
  inline const StorageIndex& operator()(Index i) const { return indices()(i); }
  /** Direct access to the underlying index vector */
  inline StorageIndex& operator()(Index i) { return indices()(i); }
  /** Direct access to the underlying index vector */
  inline const StorageIndex& operator[](Index i) const { return indices()(i); }
  /** Direct access to the underlying index vector */
  inline StorageIndex& operator[](Index i) { return indices()(i); }

  /** const version of indices(). */
  EIGEN_DEVICE_FUNC const IndicesType& indices() const { return derived().indices(); }
  /** \returns a reference to the stored array representing the transpositions. */
  EIGEN_DEVICE_FUNC IndicesType& indices() { return derived().indices(); }

  /** Resizes to given size. */
  inline void resize(Index newSize) { indices().resize(newSize); }

  /** Sets \c *this to represents an identity transformation */
  void setIdentity() {
    for (StorageIndex i = 0; i < indices().size(); ++i) coeffRef(i) = i;
  }

  // FIXME: do we want such methods ?
  // might be useful when the target matrix expression is complex, e.g.:
  // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
  /*
  template<typename MatrixType>
  void applyForwardToRows(MatrixType& mat) const
  {
    for(Index k=0 ; k<size() ; ++k)
      if(m_indices(k)!=k)
        mat.row(k).swap(mat.row(m_indices(k)));
  }

  template<typename MatrixType>
  void applyBackwardToRows(MatrixType& mat) const
  {
    for(Index k=size()-1 ; k>=0 ; --k)
      if(m_indices(k)!=k)
        mat.row(k).swap(mat.row(m_indices(k)));
  }
  */

  /** \returns the inverse transformation */
  inline Transpose<TranspositionsBase> inverse() const { return Transpose<TranspositionsBase>(derived()); }

  /** \returns the transpose transformation */
  inline Transpose<TranspositionsBase> transpose() const { return Transpose<TranspositionsBase>(derived()); }

  /** \returns the adjoint transformation. Its matrix is a real permutation, so this equals transpose() and inverse().
   */
  Transpose<TranspositionsBase> adjoint() const { return Transpose<TranspositionsBase>(derived()); }
};

namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
struct traits<Transpositions<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
    : traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
  using IndicesType = Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>;
  using StorageKind = TranspositionsStorage;
};
}  // namespace internal

/** \class Transpositions
 * \ingroup Core_Module
 *
 * \brief Represents a sequence of transpositions (row/column interchange)
 *
 * \tparam SizeAtCompileTime the number of transpositions, or Dynamic
 * \tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to
 * SizeAtCompileTime. Most of the time, you should not have to specify it.
 *
 * This class represents a permutation transformation as a sequence of \em n transpositions
 * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
 * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
 * the rows \c i and \c indices[i] of the matrix \c M.
 * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
 *
 * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
 * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
 *
 * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
 * \code
 * Transpositions tr;
 * MatrixXf mat;
 * mat = tr * mat;
 * \endcode
 * In this example, we detect that the matrix appears on both side, and so the transpositions
 * are applied in-place without any temporary or extra copy.
 *
 * \sa class PermutationMatrix
 */

template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
class Transpositions
    : public TranspositionsBase<Transpositions<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
  using Traits = internal::traits<Transpositions>;

 public:
  using Base = TranspositionsBase<Transpositions>;
  using IndicesType = typename Traits::IndicesType;
  using StorageIndex = typename IndicesType::Scalar;

  inline Transpositions() {}

  /** Copy constructor. */
  template <typename OtherDerived>
  inline Transpositions(const TranspositionsBase<OtherDerived>& other) : m_indices(other.indices()) {}

  /** Generic constructor from expression of the transposition indices. */
  template <typename Other>
  explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices) {}

  /** Copies the \a other transpositions into \c *this */
  template <typename OtherDerived>
  Transpositions& operator=(const TranspositionsBase<OtherDerived>& other) {
    return Base::operator=(other);
  }

  /** Constructs an uninitialized permutation matrix of given size.
   */
  inline Transpositions(Index size) : m_indices(size) {}

  /** const version of indices(). */
  EIGEN_DEVICE_FUNC const IndicesType& indices() const { return m_indices; }
  /** \returns a reference to the stored array representing the transpositions. */
  EIGEN_DEVICE_FUNC IndicesType& indices() { return m_indices; }

 protected:
  IndicesType m_indices;
};

namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
struct traits<Map<Transpositions<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> >
    : traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
  using IndicesType = Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_>;
  using StorageIndex = StorageIndex_;
  using StorageKind = TranspositionsStorage;
};
}  // namespace internal

template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess>
class Map<Transpositions<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess>
    : public TranspositionsBase<
          Map<Transpositions<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess> > {
  using Traits = internal::traits<Map>;

 public:
  using Base = TranspositionsBase<Map>;
  using IndicesType = typename Traits::IndicesType;
  using StorageIndex = typename IndicesType::Scalar;

  explicit inline Map(const StorageIndex* indicesPtr) : m_indices(indicesPtr) {}

  inline Map(const StorageIndex* indicesPtr, Index size) : m_indices(indicesPtr, size) {}

  /** Copies the \a other transpositions into \c *this */
  template <typename OtherDerived>
  Map& operator=(const TranspositionsBase<OtherDerived>& other) {
    return Base::operator=(other);
  }

#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=.
   */
  Map& operator=(const Map& other) {
    m_indices = other.m_indices;
    return *this;
  }
#endif

  /** const version of indices(). */
  EIGEN_DEVICE_FUNC const IndicesType& indices() const { return m_indices; }

  /** \returns a reference to the stored array representing the transpositions. */
  EIGEN_DEVICE_FUNC IndicesType& indices() { return m_indices; }

 protected:
  IndicesType m_indices;
};

namespace internal {
template <typename IndicesType_>
struct traits<TranspositionsWrapper<IndicesType_> > : traits<PermutationWrapper<IndicesType_> > {
  using StorageKind = TranspositionsStorage;
};
}  // namespace internal

template <typename IndicesType_>
class TranspositionsWrapper : public TranspositionsBase<TranspositionsWrapper<IndicesType_> > {
  using Traits = internal::traits<TranspositionsWrapper>;

 public:
  using Base = TranspositionsBase<TranspositionsWrapper>;
  using IndicesType = typename Traits::IndicesType;
  using StorageIndex = typename IndicesType::Scalar;

  explicit inline TranspositionsWrapper(IndicesType& indices) : m_indices(indices) {}

  /** Copies the \a other transpositions into \c *this */
  template <typename OtherDerived>
  TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other) {
    return Base::operator=(other);
  }

  /** const version of indices(). */
  EIGEN_DEVICE_FUNC const IndicesType& indices() const { return m_indices; }

  /** \returns a reference to the stored array representing the transpositions. */
  EIGEN_DEVICE_FUNC IndicesType& indices() { return m_indices; }

 protected:
  typename IndicesType::Nested m_indices;
};

/** \returns the \a matrix with the \a transpositions applied to the columns.
 */
template <typename MatrixDerived, typename TranspositionsDerived>
EIGEN_DEVICE_FUNC const Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct> operator*(
    const MatrixBase<MatrixDerived>& matrix, const TranspositionsBase<TranspositionsDerived>& transpositions) {
  return Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct>(matrix.derived(), transpositions.derived());
}

/** \returns the \a matrix with the \a transpositions applied to the rows.
 */
template <typename TranspositionsDerived, typename MatrixDerived>
EIGEN_DEVICE_FUNC const Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct> operator*(
    const TranspositionsBase<TranspositionsDerived>& transpositions, const MatrixBase<MatrixDerived>& matrix) {
  return Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct>(transpositions.derived(), matrix.derived());
}

// Template partial specialization for transposed/inverse transpositions

namespace internal {

template <typename Derived>
struct traits<Transpose<TranspositionsBase<Derived> > > : traits<Derived> {};

}  // end namespace internal

template <typename TranspositionsDerived>
class Transpose<TranspositionsBase<TranspositionsDerived> > {
  using TranspositionType = TranspositionsDerived;
  using IndicesType = typename TranspositionType::IndicesType;

 public:
  explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}

  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return m_transpositions.size(); }
  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_transpositions.size(); }
  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_transpositions.size(); }

  /** \returns the \a matrix with the inverse transpositions applied to the columns.
   */
  template <typename OtherDerived>
  friend const Product<OtherDerived, Transpose, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix,
                                                                            const Transpose& trt) {
    return Product<OtherDerived, Transpose, AliasFreeProduct>(matrix.derived(), trt);
  }

  /** \returns the \a matrix with the inverse transpositions applied to the rows.
   */
  template <typename OtherDerived>
  const Product<Transpose, OtherDerived, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
    return Product<Transpose, OtherDerived, AliasFreeProduct>(*this, matrix.derived());
  }

  EIGEN_DEVICE_FUNC const TranspositionType& nestedExpression() const { return m_transpositions; }

 protected:
  const TranspositionType& m_transpositions;
};

}  // end namespace Eigen

#endif  // EIGEN_TRANSPOSITIONS_H