Eigen/src/Core/PermutationMatrix.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2015 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/.

#ifndef EIGEN_PERMUTATIONMATRIX_H
#define EIGEN_PERMUTATIONMATRIX_H

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

namespace Eigen {

namespace internal {

enum PermPermProduct_t { PermPermProduct };

}  // end namespace internal

/** \class PermutationBase
 * \ingroup Core_Module
 *
 * \brief Base class for permutations
 *
 * \tparam Derived the derived class
 *
 * This class is the base class for all expressions representing a permutation matrix,
 * internally stored as a vector of integers.
 * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
 * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
 *  \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
 * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
 *  \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
 *
 * Permutation matrices are square and invertible.
 *
 * Notice that in addition to the member functions and operators listed here, there also are non-member
 * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
 * on either side.
 *
 * \sa class PermutationMatrix, class PermutationWrapper
 */
template <typename Derived>
class PermutationBase : public EigenBase<Derived> {
  typedef internal::traits<Derived> Traits;
  typedef EigenBase<Derived> Base;

 public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
  typedef typename Traits::IndicesType IndicesType;
  enum {
    Flags = Traits::Flags,
    RowsAtCompileTime = Traits::RowsAtCompileTime,
    ColsAtCompileTime = Traits::ColsAtCompileTime,
    MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
  };
  typedef typename Traits::StorageIndex StorageIndex;
  typedef Matrix<StorageIndex, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
      DenseMatrixType;
  typedef PermutationMatrix<IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, StorageIndex>
      PlainPermutationType;
  typedef PlainPermutationType PlainObject;
  using Base::derived;
  typedef Inverse<Derived> InverseReturnType;
  typedef void Scalar;
#endif

  /** Copies the other permutation into *this */
  template <typename OtherDerived>
  Derived& operator=(const PermutationBase<OtherDerived>& other) {
    indices() = other.indices();
    return derived();
  }

  /** Assignment from the Transpositions \a tr */
  template <typename OtherDerived>
  Derived& operator=(const TranspositionsBase<OtherDerived>& tr) {
    setIdentity(tr.size());
    for (Index k = size() - 1; k >= 0; --k) applyTranspositionOnTheRight(k, tr.coeff(k));
    return derived();
  }

  /** \returns the number of rows */
  inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }

  /** \returns the number of columns */
  inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }

  /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
  inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }

#ifndef EIGEN_PARSED_BY_DOXYGEN
  template <typename DenseDerived>
  void evalTo(MatrixBase<DenseDerived>& other) const {
    other.setZero();
    for (Index i = 0; i < rows(); ++i) other.coeffRef(indices().coeff(i), i) = typename DenseDerived::Scalar(1);
  }
#endif

  /** \returns a Matrix object initialized from this permutation matrix. Notice that it
   * is inefficient to return this Matrix object by value. For efficiency, favor using
   * the Matrix constructor taking EigenBase objects.
   */
  DenseMatrixType toDenseMatrix() const { return derived(); }

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

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

  /** Sets *this to be the identity permutation matrix */
  void setIdentity() {
    StorageIndex n = StorageIndex(size());
    for (StorageIndex i = 0; i < n; ++i) indices().coeffRef(i) = i;
  }

  /** Sets *this to be the identity permutation matrix of given size.
   */
  void setIdentity(Index newSize) {
    resize(newSize);
    setIdentity();
  }

  /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
   *
   * \returns a reference to *this.
   *
   * \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
   * this has linear complexity and requires a lot of branching.
   *
   * \sa applyTranspositionOnTheRight(Index,Index)
   */
  Derived& applyTranspositionOnTheLeft(Index i, Index j) {
    eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
    for (Index k = 0; k < size(); ++k) {
      if (indices().coeff(k) == i)
        indices().coeffRef(k) = StorageIndex(j);
      else if (indices().coeff(k) == j)
        indices().coeffRef(k) = StorageIndex(i);
    }
    return derived();
  }

  /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
   *
   * \returns a reference to *this.
   *
   * This is a fast operation, it only consists in swapping two indices.
   *
   * \sa applyTranspositionOnTheLeft(Index,Index)
   */
  Derived& applyTranspositionOnTheRight(Index i, Index j) {
    eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
    std::swap(indices().coeffRef(i), indices().coeffRef(j));
    return derived();
  }

  /** \returns the inverse permutation matrix.
   *
   * \note \blank \note_try_to_help_rvo
   */
  inline InverseReturnType inverse() const { return InverseReturnType(derived()); }
  /** \returns the transpose permutation matrix.
   *
   * \note \blank \note_try_to_help_rvo
   */
  inline InverseReturnType transpose() const { return InverseReturnType(derived()); }

  /**** multiplication helpers to hopefully get RVO ****/

#ifndef EIGEN_PARSED_BY_DOXYGEN
 protected:
  template <typename OtherDerived>
  void assignTranspose(const PermutationBase<OtherDerived>& other) {
    for (Index i = 0; i < rows(); ++i) indices().coeffRef(other.indices().coeff(i)) = i;
  }
  template <typename Lhs, typename Rhs>
  void assignProduct(const Lhs& lhs, const Rhs& rhs) {
    eigen_assert(lhs.cols() == rhs.rows());
    for (Index i = 0; i < rows(); ++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
  }
#endif

 public:
  /** \returns the product permutation matrix.
   *
   * \note \blank \note_try_to_help_rvo
   */
  template <typename Other>
  inline PlainPermutationType operator*(const PermutationBase<Other>& other) const {
    return PlainPermutationType(internal::PermPermProduct, derived(), other.derived());
  }

  /** \returns the product of a permutation with another inverse permutation.
   *
   * \note \blank \note_try_to_help_rvo
   */
  template <typename Other>
  inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other) const {
    return PlainPermutationType(internal::PermPermProduct, *this, other.eval());
  }

  /** \returns the product of an inverse permutation with another permutation.
   *
   * \note \blank \note_try_to_help_rvo
   */
  template <typename Other>
  friend inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other,
                                               const PermutationBase& perm) {
    return PlainPermutationType(internal::PermPermProduct, other.eval(), perm);
  }

  /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the
   * permutation.
   *
   * This function is O(\c n) procedure allocating a buffer of \c n booleans.
   */
  Index determinant() const {
    Index res = 1;
    Index n = size();
    Matrix<bool, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime> mask(n);
    mask.fill(false);
    Index r = 0;
    while (r < n) {
      // search for the next seed
      while (r < n && mask[r]) r++;
      if (r >= n) break;
      // we got one, let's follow it until we are back to the seed
      Index k0 = r++;
      mask.coeffRef(k0) = true;
      for (Index k = indices().coeff(k0); k != k0; k = indices().coeff(k)) {
        mask.coeffRef(k) = true;
        res = -res;
      }
    }
    return res;
  }

 protected:
};

namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
    : traits<
          Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
  typedef PermutationStorage StorageKind;
  typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
  typedef StorageIndex_ StorageIndex;
  typedef void Scalar;
};
}  // namespace internal

/** \class PermutationMatrix
 * \ingroup Core_Module
 *
 * \brief Permutation matrix
 *
 * \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
 * \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to
 * SizeAtCompileTime. Most of the time, you should not have to specify it. \tparam StorageIndex_ the integer type of the
 * indices
 *
 * This class represents a permutation matrix, internally stored as a vector of integers.
 *
 * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
 */
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
class PermutationMatrix
    : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
  typedef PermutationBase<PermutationMatrix> Base;
  typedef internal::traits<PermutationMatrix> Traits;

 public:
  typedef const PermutationMatrix& Nested;

#ifndef EIGEN_PARSED_BY_DOXYGEN
  typedef typename Traits::IndicesType IndicesType;
  typedef typename Traits::StorageIndex StorageIndex;
#endif

  inline PermutationMatrix() {}

  /** Constructs an uninitialized permutation matrix of given size.
   */
  explicit inline PermutationMatrix(Index size) : m_indices(size) {
    eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
  }

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

  /** Generic constructor from expression of the indices. The indices
   * array has the meaning that the permutations sends each integer i to indices[i].
   *
   * \warning It is your responsibility to check that the indices array that you passes actually
   * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
   * array's size.
   */
  template <typename Other>
  explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices) {}

  /** Convert the Transpositions \a tr to a permutation matrix */
  template <typename Other>
  explicit PermutationMatrix(const TranspositionsBase<Other>& tr) : m_indices(tr.size()) {
    *this = tr;
  }

  /** Copies the other permutation into *this */
  template <typename Other>
  PermutationMatrix& operator=(const PermutationBase<Other>& other) {
    m_indices = other.indices();
    return *this;
  }

  /** Assignment from the Transpositions \a tr */
  template <typename Other>
  PermutationMatrix& operator=(const TranspositionsBase<Other>& tr) {
    return Base::operator=(tr.derived());
  }

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

  /**** multiplication helpers to hopefully get RVO ****/

#ifndef EIGEN_PARSED_BY_DOXYGEN
  template <typename Other>
  PermutationMatrix(const InverseImpl<Other, PermutationStorage>& other)
      : m_indices(other.derived().nestedExpression().size()) {
    eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
    StorageIndex end = StorageIndex(m_indices.size());
    for (StorageIndex i = 0; i < end; ++i)
      m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
  }
  template <typename Lhs, typename Rhs>
  PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs) : m_indices(lhs.indices().size()) {
    Base::assignProduct(lhs, rhs);
  }
#endif

 protected:
  IndicesType m_indices;
};

namespace internal {
template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> >
    : traits<
          Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
  typedef PermutationStorage StorageKind;
  typedef Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_> IndicesType;
  typedef StorageIndex_ StorageIndex;
  typedef void Scalar;
};
}  // namespace internal

template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_>
    : public PermutationBase<
          Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> > {
  typedef PermutationBase<Map> Base;
  typedef internal::traits<Map> Traits;

 public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
  typedef typename Traits::IndicesType IndicesType;
  typedef typename IndicesType::Scalar StorageIndex;
#endif

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

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

  /** Copies the other permutation into *this */
  template <typename Other>
  Map& operator=(const PermutationBase<Other>& other) {
    return Base::operator=(other.derived());
  }

  /** Assignment from the Transpositions \a tr */
  template <typename Other>
  Map& operator=(const TranspositionsBase<Other>& tr) {
    return Base::operator=(tr.derived());
  }

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

 protected:
  IndicesType m_indices;
};

template <typename IndicesType_>
class TranspositionsWrapper;
namespace internal {
template <typename IndicesType_>
struct traits<PermutationWrapper<IndicesType_> > {
  typedef PermutationStorage StorageKind;
  typedef void Scalar;
  typedef typename IndicesType_::Scalar StorageIndex;
  typedef IndicesType_ IndicesType;
  enum {
    RowsAtCompileTime = IndicesType_::SizeAtCompileTime,
    ColsAtCompileTime = IndicesType_::SizeAtCompileTime,
    MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
    MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
    Flags = 0
  };
};
}  // namespace internal

/** \class PermutationWrapper
 * \ingroup Core_Module
 *
 * \brief Class to view a vector of integers as a permutation matrix
 *
 * \tparam IndicesType_ the type of the vector of integer (can be any compatible expression)
 *
 * This class allows to view any vector expression of integers as a permutation matrix.
 *
 * \sa class PermutationBase, class PermutationMatrix
 */
template <typename IndicesType_>
class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType_> > {
  typedef PermutationBase<PermutationWrapper> Base;
  typedef internal::traits<PermutationWrapper> Traits;

 public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
  typedef typename Traits::IndicesType IndicesType;
#endif

  inline PermutationWrapper(const IndicesType& indices) : m_indices(indices) {}

  /** const version of indices(). */
  const internal::remove_all_t<typename IndicesType::Nested>& indices() const { return m_indices; }

 protected:
  typename IndicesType::Nested m_indices;
};

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

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

template <typename PermutationType>
class InverseImpl<PermutationType, PermutationStorage> : public EigenBase<Inverse<PermutationType> > {
  typedef typename PermutationType::PlainPermutationType PlainPermutationType;
  typedef internal::traits<PermutationType> PermTraits;

 protected:
  InverseImpl() {}

 public:
  typedef Inverse<PermutationType> InverseType;
  using EigenBase<Inverse<PermutationType> >::derived;

#ifndef EIGEN_PARSED_BY_DOXYGEN
  typedef typename PermutationType::DenseMatrixType DenseMatrixType;
  enum {
    RowsAtCompileTime = PermTraits::RowsAtCompileTime,
    ColsAtCompileTime = PermTraits::ColsAtCompileTime,
    MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
  };
#endif

#ifndef EIGEN_PARSED_BY_DOXYGEN
  template <typename DenseDerived>
  void evalTo(MatrixBase<DenseDerived>& other) const {
    other.setZero();
    for (Index i = 0; i < derived().rows(); ++i)
      other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
  }
#endif

  /** \return the equivalent permutation matrix */
  PlainPermutationType eval() const { return derived(); }

  DenseMatrixType toDenseMatrix() const { return derived(); }

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

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

template <typename Derived>
const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const {
  return derived();
}

namespace internal {

template <>
struct AssignmentKind<DenseShape, PermutationShape> {
  typedef EigenBase2EigenBase Kind;
};

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_PERMUTATIONMATRIX_H