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

// IWYU pragma: private
#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) {}
  StorageVal(StorageVal&& other) = default;

  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>;

  // StorageRef Needs to be move-able for sort on macos.
  StorageRef(StorageRef&& other) = default;

  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) {}
  CompressedStorageIterator(CompressedStorageIterator&& other) = default;
  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;
};

}  // namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SPARSE_COMPRESSED_BASE_H