eigen/Eigen/src/SparseCore/SparseCompressedBase.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 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_SPARSE_COMPRESSED_BASE_H
#define EIGEN_SPARSE_COMPRESSED_BASE_H

#include "./InternalHeaderCheck.h"

namespace Eigen { 

template<typename Derived> class SparseCompressedBase;
  
namespace internal {

template<typename Derived>
struct traits<SparseCompressedBase<Derived> > : traits<Derived>
{};

template <typename Derived, class Comp, bool IsVector>
struct inner_sort_impl;

} // end namespace internal

/** \ingroup SparseCore_Module
  * \class SparseCompressedBase
  * \brief Common base class for sparse [compressed]-{row|column}-storage format.
  *
  * This class defines the common interface for all derived classes implementing the compressed sparse storage format, such as:
  *  - SparseMatrix
  *  - Ref<SparseMatrixType,Options>
  *  - Map<SparseMatrixType>
  *
  */
template<typename Derived>
class SparseCompressedBase
  : public SparseMatrixBase<Derived>
{
  public:
    typedef SparseMatrixBase<Derived> Base;
    EIGEN_SPARSE_PUBLIC_INTERFACE(SparseCompressedBase)
    using Base::operator=;
    using Base::IsRowMajor;
    
    class InnerIterator;
    class ReverseInnerIterator;
    
  protected:
    typedef typename Base::IndexVector IndexVector;
    Eigen::Map<IndexVector> innerNonZeros() { return Eigen::Map<IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }
    const  Eigen::Map<const IndexVector> innerNonZeros() const { return Eigen::Map<const IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }
        
  public:
    
    /** \returns the number of non zero coefficients */
    inline Index nonZeros() const
    {
     if (Derived::IsVectorAtCompileTime && outerIndexPtr() == 0)
       return derived().nonZeros();
     else if (derived().outerSize() == 0)
       return 0;
     else if (isCompressed())
       return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
     else
       return innerNonZeros().sum();
    }
    
    /** \returns a const pointer to the array of values.
      * This function is aimed at interoperability with other libraries.
      * \sa innerIndexPtr(), outerIndexPtr() */
    inline const Scalar* valuePtr() const { return derived().valuePtr(); }
    /** \returns a non-const pointer to the array of values.
      * This function is aimed at interoperability with other libraries.
      * \sa innerIndexPtr(), outerIndexPtr() */
    inline Scalar* valuePtr() { return derived().valuePtr(); }

    /** \returns a const pointer to the array of inner indices.
      * This function is aimed at interoperability with other libraries.
      * \sa valuePtr(), outerIndexPtr() */
    inline const StorageIndex* innerIndexPtr() const { return derived().innerIndexPtr(); }
    /** \returns a non-const pointer to the array of inner indices.
      * This function is aimed at interoperability with other libraries.
      * \sa valuePtr(), outerIndexPtr() */
    inline StorageIndex* innerIndexPtr() { return derived().innerIndexPtr(); }

    /** \returns a const pointer to the array of the starting positions of the inner vectors.
      * This function is aimed at interoperability with other libraries.
      * \warning it returns the null pointer 0 for SparseVector
      * \sa valuePtr(), innerIndexPtr() */
    inline const StorageIndex* outerIndexPtr() const { return derived().outerIndexPtr(); }
    /** \returns a non-const pointer to the array of the starting positions of the inner vectors.
      * This function is aimed at interoperability with other libraries.
      * \warning it returns the null pointer 0 for SparseVector
      * \sa valuePtr(), innerIndexPtr() */
    inline StorageIndex* outerIndexPtr() { return derived().outerIndexPtr(); }

    /** \returns a const pointer to the array of the number of non zeros of the inner vectors.
      * This function is aimed at interoperability with other libraries.
      * \warning it returns the null pointer 0 in compressed mode */
    inline const StorageIndex* innerNonZeroPtr() const { return derived().innerNonZeroPtr(); }
    /** \returns a non-const pointer to the array of the number of non zeros of the inner vectors.
      * This function is aimed at interoperability with other libraries.
      * \warning it returns the null pointer 0 in compressed mode */
    inline StorageIndex* innerNonZeroPtr() { return derived().innerNonZeroPtr(); }
    
    /** \returns whether \c *this is in compressed form. */
    inline bool isCompressed() const { return innerNonZeroPtr()==0; }

    /** \returns a read-only view of the stored coefficients as a 1D array expression.
      *
      * \warning this method is for \b compressed \b storage \b only, and it will trigger an assertion otherwise.
      *
      * \sa valuePtr(), isCompressed() */
    const Map<const Array<Scalar,Dynamic,1> > coeffs() const { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }

    /** \returns a read-write view of the stored coefficients as a 1D array expression
      *
      * \warning this method is for \b compressed \b storage \b only, and it will trigger an assertion otherwise.
      *
      * Here is an example:
      * \include SparseMatrix_coeffs.cpp
      * and the output is:
      * \include SparseMatrix_coeffs.out
      *
      * \sa valuePtr(), isCompressed() */
    Map<Array<Scalar,Dynamic,1> > coeffs() { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }
    
    /** sorts the inner vectors in the range [begin,end) with respect to `Comp`  
      * \sa innerIndicesAreSorted() */
    template <class Comp = std::less<>>
    inline void sortInnerIndices(Index begin, Index end) {
      eigen_assert(begin >= 0 && end <= derived().outerSize() && end >= begin);
      internal::inner_sort_impl<Derived, Comp, IsVectorAtCompileTime>::run(*this, begin, end);
    }
    
    /** \returns the index of the first inner vector in the range [begin,end) that is not sorted with respect to `Comp`, or `end` if the range is fully sorted
      * \sa sortInnerIndices() */
    template <class Comp = std::less<>>
    inline Index innerIndicesAreSorted(Index begin, Index end) const {
      eigen_assert(begin >= 0 && end <= derived().outerSize() && end >= begin);
      return internal::inner_sort_impl<Derived, Comp, IsVectorAtCompileTime>::check(*this, begin, end);
    }

    /** sorts the inner vectors in the range [0,outerSize) with respect to `Comp`
      * \sa innerIndicesAreSorted() */
    template <class Comp = std::less<>>
    inline void sortInnerIndices() {
      Index begin = 0;
      Index end = derived().outerSize();
      internal::inner_sort_impl<Derived, Comp, IsVectorAtCompileTime>::run(*this, begin, end);
    }

    /** \returns the index of the first inner vector in the range [0,outerSize) that is not sorted with respect to `Comp`, or `outerSize` if the range is fully sorted
      * \sa sortInnerIndices() */
    template<class Comp = std::less<>>
    inline Index innerIndicesAreSorted() const {
      Index begin = 0;
      Index end = derived().outerSize();
      return internal::inner_sort_impl<Derived, Comp, IsVectorAtCompileTime>::check(*this, begin, end);
    }

  protected:
    /** Default constructor. Do nothing. */
    SparseCompressedBase() {}

    /** \internal return the index of the coeff at (row,col) or just before if it does not exist.
      * This is an analogue of std::lower_bound.
      */
    internal::LowerBoundIndex lower_bound(Index row, Index col) const
    {
      eigen_internal_assert(row>=0 && row<this->rows() && col>=0 && col<this->cols());

      const Index outer = Derived::IsRowMajor ? row : col;
      const Index inner = Derived::IsRowMajor ? col : row;

      Index start = this->outerIndexPtr()[outer];
      Index end = this->isCompressed() ? this->outerIndexPtr()[outer+1] : this->outerIndexPtr()[outer] + this->innerNonZeroPtr()[outer];
      eigen_assert(end>=start && "you are using a non finalized sparse matrix or written coefficient does not exist");
      internal::LowerBoundIndex p;
      p.value = std::lower_bound(this->innerIndexPtr()+start, this->innerIndexPtr()+end,inner) - this->innerIndexPtr();
      p.found = (p.value<end) && (this->innerIndexPtr()[p.value]==inner);
      return p;
    }

    friend struct internal::evaluator<SparseCompressedBase<Derived> >;

  private:
    template<typename OtherDerived> explicit SparseCompressedBase(const SparseCompressedBase<OtherDerived>&);
};

template<typename Derived>
class SparseCompressedBase<Derived>::InnerIterator
{
  public:
    InnerIterator()
      : m_values(0), m_indices(0), m_outer(0), m_id(0), m_end(0)
    {}

    InnerIterator(const InnerIterator& other)
      : m_values(other.m_values), m_indices(other.m_indices), m_outer(other.m_outer), m_id(other.m_id), m_end(other.m_end)
    {}

    InnerIterator& operator=(const InnerIterator& other)
    {
      m_values = other.m_values;
      m_indices = other.m_indices;
      const_cast<OuterType&>(m_outer).setValue(other.m_outer.value());
      m_id = other.m_id;
      m_end = other.m_end;
      return *this;
    }

    InnerIterator(const SparseCompressedBase& mat, Index outer)
      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)
    {
      if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)
      {
        m_id = 0;
        m_end = mat.nonZeros();
      }
      else
      {
        m_id = mat.outerIndexPtr()[outer];
        if(mat.isCompressed())
          m_end = mat.outerIndexPtr()[outer+1];
        else
          m_end = m_id + mat.innerNonZeroPtr()[outer];
      }
    }

    explicit InnerIterator(const SparseCompressedBase& mat) : InnerIterator(mat, Index(0))
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
    }

    explicit InnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)
      : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_id(0), m_end(data.size())
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
    }

    inline InnerIterator& operator++() { m_id++; return *this; }
    inline InnerIterator& operator+=(Index i) { m_id += i ; return *this; }

    inline InnerIterator operator+(Index i) 
    { 
        InnerIterator result = *this;
        result += i;
        return result;
    }

    inline const Scalar& value() const { return m_values[m_id]; }
    inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id]); }

    inline StorageIndex index() const { return m_indices[m_id]; }
    inline Index outer() const { return m_outer.value(); }
    inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }
    inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }

    inline operator bool() const { return (m_id < m_end); }

  protected:
    const Scalar* m_values;
    const StorageIndex* m_indices;
    typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;
    const OuterType m_outer;
    Index m_id;
    Index m_end;
  private:
    // If you get here, then you're not using the right InnerIterator type, e.g.:
    //   SparseMatrix<double,RowMajor> A;
    //   SparseMatrix<double>::InnerIterator it(A,0);
    template<typename T> InnerIterator(const SparseMatrixBase<T>&, Index outer);
};

template<typename Derived>
class SparseCompressedBase<Derived>::ReverseInnerIterator
{
  public:
    ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)
    {
      if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)
      {
        m_start = 0;
        m_id = mat.nonZeros();
      }
      else
      {
        m_start = mat.outerIndexPtr()[outer];
        if(mat.isCompressed())
          m_id = mat.outerIndexPtr()[outer+1];
        else
          m_id = m_start + mat.innerNonZeroPtr()[outer];
      }
    }

    explicit ReverseInnerIterator(const SparseCompressedBase& mat)
      : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(0), m_start(0), m_id(mat.nonZeros())
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
    }

    explicit ReverseInnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)
      : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_start(0), m_id(data.size())
    {
      EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
    }

    inline ReverseInnerIterator& operator--() { --m_id; return *this; }
    inline ReverseInnerIterator& operator-=(Index i) { m_id -= i; return *this; }

    inline ReverseInnerIterator operator-(Index i) 
    {
        ReverseInnerIterator result = *this;
        result -= i;
        return result;
    }

    inline const Scalar& value() const { return m_values[m_id-1]; }
    inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id-1]); }

    inline StorageIndex index() const { return m_indices[m_id-1]; }
    inline Index outer() const { return m_outer.value(); }
    inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }
    inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }

    inline operator bool() const { return (m_id > m_start); }

  protected:
    const Scalar* m_values;
    const StorageIndex* m_indices;
    typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;
    const OuterType m_outer;
    Index m_start;
    Index m_id;
};

namespace internal {

// modified from https://artificial-mind.net/blog/2020/11/28/std-sort-multiple-ranges

template <typename Scalar, typename StorageIndex>
class StorageVal;
template <typename Scalar, typename StorageIndex>
class StorageRef;
template <typename Scalar, typename StorageIndex>
class CompressedStorageIterator;

// class to hold an index/value pair
template <typename Scalar, typename StorageIndex>
class StorageVal
{
public:
    
  StorageVal(const StorageIndex& innerIndex, const Scalar& value) : m_innerIndex(innerIndex), m_value(value) {}
  StorageVal(const StorageVal& other) : m_innerIndex(other.m_innerIndex), m_value(other.m_value) {}

  inline const StorageIndex& key() const { return m_innerIndex; }
  inline StorageIndex& key() { return m_innerIndex; }
  inline const Scalar& value() const { return m_value; }
  inline Scalar& value() { return m_value; }

  // enables StorageVal to be compared with respect to any type that is convertible to StorageIndex
  inline operator StorageIndex() const { return m_innerIndex; }

protected:
  StorageIndex m_innerIndex;
  Scalar m_value;
private:
  StorageVal() = delete;
};
// class to hold an index/value iterator pair
// used to define assignment, swap, and comparison operators for CompressedStorageIterator
template <typename Scalar, typename StorageIndex>
class StorageRef 
{
public:
  using value_type = StorageVal<Scalar, StorageIndex>;

  inline StorageRef& operator=(const StorageRef& other) {
    key() = other.key();
    value() = other.value();
    return *this;
  }
  inline StorageRef& operator=(const value_type& other) {
    key() = other.key();
    value() = other.value();
    return *this;
  }
  inline operator value_type() const { return value_type(key(), value()); }
  inline friend void swap(const StorageRef& a, const StorageRef& b) {
    std::iter_swap(a.keyPtr(), b.keyPtr());
    std::iter_swap(a.valuePtr(), b.valuePtr());
  }

  inline const StorageIndex& key() const { return *m_innerIndexIterator; }
  inline StorageIndex& key() { return *m_innerIndexIterator; }
  inline const Scalar& value() const { return *m_valueIterator; }
  inline Scalar& value() { return *m_valueIterator; }
  inline StorageIndex* keyPtr() const { return m_innerIndexIterator; }
  inline Scalar* valuePtr() const { return m_valueIterator; }

  // enables StorageRef to be compared with respect to any type that is convertible to StorageIndex
  inline operator StorageIndex() const { return *m_innerIndexIterator; }

protected:
  StorageIndex* m_innerIndexIterator;
  Scalar* m_valueIterator;
private:
  StorageRef() = delete;
  // these constructors are called by the CompressedStorageIterator constructors for convenience only
  StorageRef(StorageIndex* innerIndexIterator, Scalar* valueIterator) : m_innerIndexIterator(innerIndexIterator), m_valueIterator(valueIterator) {}
  StorageRef(const StorageRef& other) : m_innerIndexIterator(other.m_innerIndexIterator), m_valueIterator(other.m_valueIterator) {}

  friend class CompressedStorageIterator<Scalar, StorageIndex>;
};

// STL-compatible iterator class that operates on inner indices and values
template<typename Scalar, typename StorageIndex>
class CompressedStorageIterator
{
public:
  using iterator_category = std::random_access_iterator_tag;
  using reference = StorageRef<Scalar, StorageIndex>;
  using difference_type = Index;
  using value_type = typename reference::value_type;
  using pointer = value_type*;

  CompressedStorageIterator() = delete;
  CompressedStorageIterator(difference_type index, StorageIndex* innerIndexPtr, Scalar* valuePtr) : m_index(index), m_data(innerIndexPtr, valuePtr) {}
  CompressedStorageIterator(difference_type index, reference data) : m_index(index), m_data(data) {}
  CompressedStorageIterator(const CompressedStorageIterator& other) : m_index(other.m_index), m_data(other.m_data) {}
  inline CompressedStorageIterator& operator=(const CompressedStorageIterator& other) {
    m_index = other.m_index;
    m_data = other.m_data;
    return *this;
  }

  inline CompressedStorageIterator operator+(difference_type offset) const { return CompressedStorageIterator(m_index + offset, m_data); }
  inline CompressedStorageIterator operator-(difference_type offset) const { return CompressedStorageIterator(m_index - offset, m_data); }
  inline difference_type operator-(const CompressedStorageIterator& other) const { return m_index - other.m_index; }
  inline CompressedStorageIterator& operator++() { ++m_index; return *this; }
  inline CompressedStorageIterator& operator--() { --m_index; return *this; }
  inline CompressedStorageIterator& operator+=(difference_type offset) { m_index += offset; return *this; }
  inline CompressedStorageIterator& operator-=(difference_type offset) { m_index -= offset; return *this; }
  inline reference operator*() const { return reference(m_data.keyPtr() + m_index, m_data.valuePtr() + m_index); }

  #define MAKE_COMP(OP) inline bool operator OP(const CompressedStorageIterator& other) const { return m_index OP other.m_index; }
  MAKE_COMP(<)
  MAKE_COMP(>)
  MAKE_COMP(>=)
  MAKE_COMP(<=)
  MAKE_COMP(!=)
  MAKE_COMP(==)
  #undef MAKE_COMP

protected:
  difference_type m_index;
  reference m_data;
};

template <typename Derived, class Comp, bool IsVector>
struct inner_sort_impl {
  typedef typename Derived::Scalar Scalar;
  typedef typename Derived::StorageIndex StorageIndex;
  static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
    const bool is_compressed = obj.isCompressed();
    for (Index outer = begin; outer < end; outer++) {
      Index begin_offset = obj.outerIndexPtr()[outer];
      Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
      CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
      CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
      std::sort(begin_it, end_it, Comp());
    }
  }
  static inline Index check(const SparseCompressedBase<Derived>& obj, Index begin, Index end) {
    const bool is_compressed = obj.isCompressed();
    for (Index outer = begin; outer < end; outer++) {
      Index begin_offset = obj.outerIndexPtr()[outer];
      Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
      const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
      const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
      bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
      if (!is_sorted) return outer;
    }
    return end;
  }
};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
  typedef typename Derived::Scalar Scalar;
  typedef typename Derived::StorageIndex StorageIndex;
  static inline void run(SparseCompressedBase<Derived>& obj, Index, Index) {
    Index begin_offset = 0;
    Index end_offset = obj.nonZeros();
    CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
    CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
    std::sort(begin_it, end_it, Comp());
  }
  static inline Index check(const SparseCompressedBase<Derived>& obj, Index, Index) {
    Index begin_offset = 0;
    Index end_offset = obj.nonZeros();
    const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
    const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
    return std::is_sorted(begin_it, end_it, Comp()) ? 1 : 0;
  }
};

template<typename Derived>
struct evaluator<SparseCompressedBase<Derived> >
  : evaluator_base<Derived>
{
  typedef typename Derived::Scalar Scalar;
  typedef typename Derived::InnerIterator InnerIterator;
  
  enum {
    CoeffReadCost = NumTraits<Scalar>::ReadCost,
    Flags = Derived::Flags
  };
  
  evaluator() : m_matrix(0), m_zero(0)
  {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
  explicit evaluator(const Derived &mat) : m_matrix(&mat), m_zero(0)
  {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
  
  inline Index nonZerosEstimate() const {
    return m_matrix->nonZeros();
  }
  
  operator Derived&() { return m_matrix->const_cast_derived(); }
  operator const Derived&() const { return *m_matrix; }
  
  typedef typename DenseCoeffsBase<Derived,ReadOnlyAccessors>::CoeffReturnType CoeffReturnType;
  const Scalar& coeff(Index row, Index col) const
  {
    Index p = find(row,col);

    if(p==Dynamic)
      return m_zero;
    else
      return m_matrix->const_cast_derived().valuePtr()[p];
  }

  Scalar& coeffRef(Index row, Index col)
  {
    Index p = find(row,col);
    eigen_assert(p!=Dynamic && "written coefficient does not exist");
    return m_matrix->const_cast_derived().valuePtr()[p];
  }

protected:

  Index find(Index row, Index col) const
  {
    internal::LowerBoundIndex p = m_matrix->lower_bound(row,col);
    return p.found ? p.value : Dynamic;
  }

  const Derived *m_matrix;
  const Scalar m_zero;
};

}

} // end namespace Eigen

#endif // EIGEN_SPARSE_COMPRESSED_BASE_H