Eigen/src/CholmodSupport/CholmodSupport.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 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_CHOLMODSUPPORT_H
#define EIGEN_CHOLMODSUPPORT_H

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

namespace Eigen {

namespace internal {

template <typename Scalar>
struct cholmod_configure_matrix;

template <>
struct cholmod_configure_matrix<double> {
  template <typename CholmodType>
  static void run(CholmodType& mat) {
    mat.xtype = CHOLMOD_REAL;
    mat.dtype = CHOLMOD_DOUBLE;
  }
};

template <>
struct cholmod_configure_matrix<std::complex<double> > {
  template <typename CholmodType>
  static void run(CholmodType& mat) {
    mat.xtype = CHOLMOD_COMPLEX;
    mat.dtype = CHOLMOD_DOUBLE;
  }
};

// Other scalar types are not yet supported by Cholmod
// template<> struct cholmod_configure_matrix<float> {
//   template<typename CholmodType>
//   static void run(CholmodType& mat) {
//     mat.xtype = CHOLMOD_REAL;
//     mat.dtype = CHOLMOD_SINGLE;
//   }
// };
//
// template<> struct cholmod_configure_matrix<std::complex<float> > {
//   template<typename CholmodType>
//   static void run(CholmodType& mat) {
//     mat.xtype = CHOLMOD_COMPLEX;
//     mat.dtype = CHOLMOD_SINGLE;
//   }
// };

}  // namespace internal

/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
 * Note that the data are shared.
 */
template <typename Scalar_, int Options_, typename StorageIndex_>
cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, StorageIndex_> > mat) {
  cholmod_sparse res;
  res.nzmax = mat.nonZeros();
  res.nrow = mat.rows();
  res.ncol = mat.cols();
  res.p = mat.outerIndexPtr();
  res.i = mat.innerIndexPtr();
  res.x = mat.valuePtr();
  res.z = 0;
  res.sorted = 1;
  if (mat.isCompressed()) {
    res.packed = 1;
    res.nz = 0;
  } else {
    res.packed = 0;
    res.nz = mat.innerNonZeroPtr();
  }

  res.dtype = 0;
  res.stype = -1;

  if (internal::is_same<StorageIndex_, int>::value) {
    res.itype = CHOLMOD_INT;
  } else if (internal::is_same<StorageIndex_, SuiteSparse_long>::value) {
    res.itype = CHOLMOD_LONG;
  } else {
    eigen_assert(false && "Index type not supported yet");
  }

  // setup res.xtype
  internal::cholmod_configure_matrix<Scalar_>::run(res);

  res.stype = 0;

  return res;
}

template <typename Scalar_, int Options_, typename Index_>
const cholmod_sparse viewAsCholmod(const SparseMatrix<Scalar_, Options_, Index_>& mat) {
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
  return res;
}

template <typename Scalar_, int Options_, typename Index_>
const cholmod_sparse viewAsCholmod(const SparseVector<Scalar_, Options_, Index_>& mat) {
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.const_cast_derived()));
  return res;
}

/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
 * The data are not copied but shared. */
template <typename Scalar_, int Options_, typename Index_, unsigned int UpLo>
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<Scalar_, Options_, Index_>, UpLo>& mat) {
  cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_, Options_, Index_> >(mat.matrix().const_cast_derived()));

  if (UpLo == Upper) res.stype = 1;
  if (UpLo == Lower) res.stype = -1;
  // swap stype for rowmajor matrices (only works for real matrices)
  EIGEN_STATIC_ASSERT((Options_ & RowMajorBit) == 0 || NumTraits<Scalar_>::IsComplex == 0,
                      THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
  if (Options_ & RowMajorBit) res.stype *= -1;

  return res;
}

/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
 * The data are not copied but shared. */
template <typename Derived>
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat) {
  EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags & RowMajorBit) == 0,
                      THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
  typedef typename Derived::Scalar Scalar;

  cholmod_dense res;
  res.nrow = mat.rows();
  res.ncol = mat.cols();
  res.nzmax = res.nrow * res.ncol;
  res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
  res.x = (void*)(mat.derived().data());
  res.z = 0;

  internal::cholmod_configure_matrix<Scalar>::run(res);

  return res;
}

/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
 * The data are not copied but shared. */
template <typename Scalar, typename StorageIndex>
Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_sparse& cm) {
  return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
      cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol], static_cast<StorageIndex*>(cm.p),
      static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
}

/** Returns a view of the Cholmod sparse matrix factor \a cm as an Eigen sparse matrix.
 * The data are not copied but shared. */
template <typename Scalar, typename StorageIndex>
Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> > viewAsEigen(cholmod_factor& cm) {
  return Map<const SparseMatrix<Scalar, ColMajor, StorageIndex> >(
      cm.n, cm.n, static_cast<StorageIndex*>(cm.p)[cm.n], static_cast<StorageIndex*>(cm.p),
      static_cast<StorageIndex*>(cm.i), static_cast<Scalar*>(cm.x));
}

namespace internal {

// template specializations for int and long that call the correct cholmod method

#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name)                        \
  template <typename StorageIndex_>                                 \
  inline ret cm_##name(cholmod_common& Common) {                    \
    return cholmod_##name(&Common);                                 \
  }                                                                 \
  template <>                                                       \
  inline ret cm_##name<SuiteSparse_long>(cholmod_common & Common) { \
    return cholmod_l_##name(&Common);                               \
  }

#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1)                         \
  template <typename StorageIndex_>                                          \
  inline ret cm_##name(t1& a1, cholmod_common& Common) {                     \
    return cholmod_##name(&a1, &Common);                                     \
  }                                                                          \
  template <>                                                                \
  inline ret cm_##name<SuiteSparse_long>(t1 & a1, cholmod_common & Common) { \
    return cholmod_l_##name(&a1, &Common);                                   \
  }

EIGEN_CHOLMOD_SPECIALIZE0(int, start)
EIGEN_CHOLMOD_SPECIALIZE0(int, finish)

EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)

EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
EIGEN_CHOLMOD_SPECIALIZE1(cholmod_sparse*, factor_to_sparse, cholmod_factor, L)

template <typename StorageIndex_>
inline cholmod_dense* cm_solve(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
  return cholmod_solve(sys, &L, &B, &Common);
}
template <>
inline cholmod_dense* cm_solve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common& Common) {
  return cholmod_l_solve(sys, &L, &B, &Common);
}

template <typename StorageIndex_>
inline cholmod_sparse* cm_spsolve(int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common& Common) {
  return cholmod_spsolve(sys, &L, &B, &Common);
}
template <>
inline cholmod_sparse* cm_spsolve<SuiteSparse_long>(int sys, cholmod_factor& L, cholmod_sparse& B,
                                                    cholmod_common& Common) {
  return cholmod_l_spsolve(sys, &L, &B, &Common);
}

template <typename StorageIndex_>
inline int cm_factorize_p(cholmod_sparse* A, double beta[2], StorageIndex_* fset, std::size_t fsize, cholmod_factor* L,
                          cholmod_common& Common) {
  return cholmod_factorize_p(A, beta, fset, fsize, L, &Common);
}
template <>
inline int cm_factorize_p<SuiteSparse_long>(cholmod_sparse* A, double beta[2], SuiteSparse_long* fset,
                                            std::size_t fsize, cholmod_factor* L, cholmod_common& Common) {
  return cholmod_l_factorize_p(A, beta, fset, fsize, L, &Common);
}

#undef EIGEN_CHOLMOD_SPECIALIZE0
#undef EIGEN_CHOLMOD_SPECIALIZE1

}  // namespace internal

enum CholmodMode { CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt };

/** \ingroup CholmodSupport_Module
 * \class CholmodBase
 * \brief The base class for the direct Cholesky factorization of Cholmod
 * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
 */
template <typename MatrixType_, int UpLo_, typename Derived>
class CholmodBase : public SparseSolverBase<Derived> {
 protected:
  typedef SparseSolverBase<Derived> Base;
  using Base::derived;
  using Base::m_isInitialized;

 public:
  typedef MatrixType_ MatrixType;
  enum { UpLo = UpLo_ };
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef MatrixType CholMatrixType;
  typedef typename MatrixType::StorageIndex StorageIndex;
  enum { ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };

 public:
  CholmodBase() : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
    EIGEN_STATIC_ASSERT((internal::is_same<double, RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
    m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
    internal::cm_start<StorageIndex>(m_cholmod);
  }

  explicit CholmodBase(const MatrixType& matrix)
      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) {
    EIGEN_STATIC_ASSERT((internal::is_same<double, RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
    m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
    internal::cm_start<StorageIndex>(m_cholmod);
    compute(matrix);
  }

  ~CholmodBase() {
    if (m_cholmodFactor) internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
    internal::cm_finish<StorageIndex>(m_cholmod);
  }

  inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
  inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }

  /** \brief Reports whether previous computation was successful.
   *
   * \returns \c Success if computation was successful,
   *          \c NumericalIssue if the matrix.appears to be negative.
   */
  ComputationInfo info() const {
    eigen_assert(m_isInitialized && "Decomposition is not initialized.");
    return m_info;
  }

  /** Computes the sparse Cholesky decomposition of \a matrix */
  Derived& compute(const MatrixType& matrix) {
    analyzePattern(matrix);
    factorize(matrix);
    return derived();
  }

  /** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
   *
   * This function is particularly useful when solving for several problems having the same structure.
   *
   * \sa factorize()
   */
  void analyzePattern(const MatrixType& matrix) {
    if (m_cholmodFactor) {
      internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
      m_cholmodFactor = 0;
    }
    cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
    m_cholmodFactor = internal::cm_analyze<StorageIndex>(A, m_cholmod);

    this->m_isInitialized = true;
    this->m_info = Success;
    m_analysisIsOk = true;
    m_factorizationIsOk = false;
  }

  /** Performs a numeric decomposition of \a matrix
   *
   * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been
   * performed.
   *
   * \sa analyzePattern()
   */
  void factorize(const MatrixType& matrix) {
    eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
    cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
    internal::cm_factorize_p<StorageIndex>(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod);

    // If the factorization failed, either the input matrix was zero (so m_cholmodFactor == nullptr), or minor is the
    // column at which it failed. On success minor == n.
    this->m_info =
        (m_cholmodFactor != nullptr && m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
    m_factorizationIsOk = true;
  }

  /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
   *  See the Cholmod user guide for details. */
  cholmod_common& cholmod() { return m_cholmod; }

#ifndef EIGEN_PARSED_BY_DOXYGEN
  /** \internal */
  template <typename Rhs, typename Dest>
  void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const {
    eigen_assert(m_factorizationIsOk &&
                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
                 "symbolic()/numeric()");
    const Index size = m_cholmodFactor->n;
    EIGEN_UNUSED_VARIABLE(size);
    eigen_assert(size == b.rows());

    // Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
    Ref<const Matrix<typename Rhs::Scalar, Dynamic, Dynamic, ColMajor> > b_ref(b.derived());

    cholmod_dense b_cd = viewAsCholmod(b_ref);
    cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod);
    if (!x_cd) {
      this->m_info = NumericalIssue;
      return;
    }
    // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
    // NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
    dest = Matrix<Scalar, Dest::RowsAtCompileTime, Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),
                                                                                 b.rows(), b.cols());
    internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
  }

  /** \internal */
  template <typename RhsDerived, typename DestDerived>
  void _solve_impl(const SparseMatrixBase<RhsDerived>& b, SparseMatrixBase<DestDerived>& dest) const {
    eigen_assert(m_factorizationIsOk &&
                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
                 "symbolic()/numeric()");
    const Index size = m_cholmodFactor->n;
    EIGEN_UNUSED_VARIABLE(size);
    eigen_assert(size == b.rows());

    // note: cs stands for Cholmod Sparse
    Ref<SparseMatrix<typename RhsDerived::Scalar, ColMajor, typename RhsDerived::StorageIndex> > b_ref(
        b.const_cast_derived());
    cholmod_sparse b_cs = viewAsCholmod(b_ref);
    cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod);
    if (!x_cs) {
      this->m_info = NumericalIssue;
      return;
    }
    // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
    // NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's
    // sparse solver)
    dest.derived() = viewAsEigen<typename DestDerived::Scalar, typename DestDerived::StorageIndex>(*x_cs);
    internal::cm_free_sparse<StorageIndex>(x_cs, m_cholmod);
  }
#endif  // EIGEN_PARSED_BY_DOXYGEN

  /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
   *
   * During the numerical factorization, an offset term is added to the diagonal coefficients:\n
   * \c d_ii = \a offset + \c d_ii
   *
   * The default is \a offset=0.
   *
   * \returns a reference to \c *this.
   */
  Derived& setShift(const RealScalar& offset) {
    m_shiftOffset[0] = double(offset);
    return derived();
  }

  /** \returns the determinant of the underlying matrix from the current factorization */
  Scalar determinant() const {
    using std::exp;
    return exp(logDeterminant());
  }

  /** \returns the log determinant of the underlying matrix from the current factorization */
  Scalar logDeterminant() const {
    using numext::real;
    using std::log;
    eigen_assert(m_factorizationIsOk &&
                 "The decomposition is not in a valid state for solving, you must first call either compute() or "
                 "symbolic()/numeric()");

    RealScalar logDet = 0;
    Scalar* x = static_cast<Scalar*>(m_cholmodFactor->x);
    if (m_cholmodFactor->is_super) {
      // Supernodal factorization stored as a packed list of dense column-major blocks,
      // as described by the following structure:

      // super[k] == index of the first column of the j-th super node
      StorageIndex* super = static_cast<StorageIndex*>(m_cholmodFactor->super);
      // pi[k] == offset to the description of row indices
      StorageIndex* pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
      // px[k] == offset to the respective dense block
      StorageIndex* px = static_cast<StorageIndex*>(m_cholmodFactor->px);

      Index nb_super_nodes = m_cholmodFactor->nsuper;
      for (Index k = 0; k < nb_super_nodes; ++k) {
        StorageIndex ncols = super[k + 1] - super[k];
        StorageIndex nrows = pi[k + 1] - pi[k];

        Map<const Array<Scalar, 1, Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows + 1));
        logDet += sk.real().log().sum();
      }
    } else {
      // Simplicial factorization stored as standard CSC matrix.
      StorageIndex* p = static_cast<StorageIndex*>(m_cholmodFactor->p);
      Index size = m_cholmodFactor->n;
      for (Index k = 0; k < size; ++k) logDet += log(real(x[p[k]]));
    }
    if (m_cholmodFactor->is_ll) logDet *= 2.0;
    return logDet;
  }

  template <typename Stream>
  void dumpMemory(Stream& /*s*/) {}

 protected:
  mutable cholmod_common m_cholmod;
  cholmod_factor* m_cholmodFactor;
  double m_shiftOffset[2];
  mutable ComputationInfo m_info;
  int m_factorizationIsOk;
  int m_analysisIsOk;
};

/** \ingroup CholmodSupport_Module
 * \class CholmodSimplicialLLT
 * \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
 *
 * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
 * using the Cholmod library.
 * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical
 * interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
 * either dense or sparse.
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
 *               or Upper. Default is Lower.
 *
 * \implsparsesolverconcept
 *
 * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
 * compressed.
 *
 * \warning Only double precision real and complex scalar types are supported by Cholmod.
 *
 * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
 */
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSimplicialLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT<MatrixType_, UpLo_> > {
  typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT> Base;
  using Base::m_cholmod;

 public:
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef TriangularView<const MatrixType, Eigen::Lower> MatrixL;
  typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::Upper> MatrixU;

  CholmodSimplicialLLT() : Base() { init(); }

  CholmodSimplicialLLT(const MatrixType& matrix) : Base() {
    init();
    this->compute(matrix);
  }

  ~CholmodSimplicialLLT() {}

  /** \returns an expression of the factor L */
  inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }

  /** \returns an expression of the factor U (= L^*) */
  inline MatrixU matrixU() const { return matrixL().adjoint(); }

 protected:
  void init() {
    m_cholmod.final_asis = 0;
    m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
    m_cholmod.final_ll = 1;
  }
};

/** \ingroup CholmodSupport_Module
 * \class CholmodSimplicialLDLT
 * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
 *
 * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
 * using the Cholmod library.
 * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical
 * interest. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices X and B can be
 * either dense or sparse.
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
 *               or Upper. Default is Lower.
 *
 * \implsparsesolverconcept
 *
 * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
 * compressed.
 *
 * \warning Only double precision real and complex scalar types are supported by Cholmod.
 *
 * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
 */
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSimplicialLDLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT<MatrixType_, UpLo_> > {
  typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT> Base;
  using Base::m_cholmod;

 public:
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef Matrix<Scalar, Dynamic, 1> VectorType;
  typedef TriangularView<const MatrixType, Eigen::UnitLower> MatrixL;
  typedef TriangularView<const typename MatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;

  CholmodSimplicialLDLT() : Base() { init(); }

  CholmodSimplicialLDLT(const MatrixType& matrix) : Base() {
    init();
    this->compute(matrix);
  }

  ~CholmodSimplicialLDLT() {}

  /** \returns a vector expression of the diagonal D */
  inline VectorType vectorD() const {
    auto cholmodL = viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor);

    VectorType D{cholmodL.rows()};

    for (Index k = 0; k < cholmodL.outerSize(); ++k) {
      typename decltype(cholmodL)::InnerIterator it{cholmodL, k};
      D(k) = it.value();
    }

    return D;
  }

  /** \returns an expression of the factor L */
  inline MatrixL matrixL() const { return viewAsEigen<Scalar, StorageIndex>(*Base::m_cholmodFactor); }

  /** \returns an expression of the factor U (= L^*) */
  inline MatrixU matrixU() const { return matrixL().adjoint(); }

 protected:
  void init() {
    m_cholmod.final_asis = 1;
    m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
  }
};

/** \ingroup CholmodSupport_Module
 * \class CholmodSupernodalLLT
 * \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
 *
 * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
 * using the Cholmod library.
 * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
 * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
 * X and B can be either dense or sparse.
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
 *               or Upper. Default is Lower.
 *
 * \implsparsesolverconcept
 *
 * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
 * compressed.
 *
 * \warning Only double precision real and complex scalar types are supported by Cholmod.
 *
 * \sa \ref TutorialSparseSolverConcept
 */
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodSupernodalLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT<MatrixType_, UpLo_> > {
  typedef CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT> Base;
  using Base::m_cholmod;

 public:
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;

  CholmodSupernodalLLT() : Base() { init(); }

  CholmodSupernodalLLT(const MatrixType& matrix) : Base() {
    init();
    this->compute(matrix);
  }

  ~CholmodSupernodalLLT() {}

  /** \returns an expression of the factor L */
  inline MatrixType matrixL() const {
    // Convert Cholmod factor's supernodal storage format to Eigen's CSC storage format
    cholmod_sparse* cholmodL = internal::cm_factor_to_sparse(*Base::m_cholmodFactor, m_cholmod);
    MatrixType L = viewAsEigen<Scalar, StorageIndex>(*cholmodL);
    internal::cm_free_sparse<StorageIndex>(cholmodL, m_cholmod);

    return L;
  }

  /** \returns an expression of the factor U (= L^*) */
  inline MatrixType matrixU() const { return matrixL().adjoint(); }

 protected:
  void init() {
    m_cholmod.final_asis = 1;
    m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
  }
};

/** \ingroup CholmodSupport_Module
 * \class CholmodDecomposition
 * \brief A general Cholesky factorization and solver based on Cholmod
 *
 * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
 * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
 * X and B can be either dense or sparse.
 *
 * This variant permits to change the underlying Cholesky method at runtime.
 * On the other hand, it does not provide access to the result of the factorization.
 * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
 *
 * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
 * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
 *               or Upper. Default is Lower.
 *
 * \implsparsesolverconcept
 *
 * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non
 * compressed.
 *
 * \warning Only double precision real and complex scalar types are supported by Cholmod.
 *
 * \sa \ref TutorialSparseSolverConcept
 */
template <typename MatrixType_, int UpLo_ = Lower>
class CholmodDecomposition : public CholmodBase<MatrixType_, UpLo_, CholmodDecomposition<MatrixType_, UpLo_> > {
  typedef CholmodBase<MatrixType_, UpLo_, CholmodDecomposition> Base;
  using Base::m_cholmod;

 public:
  typedef MatrixType_ MatrixType;

  CholmodDecomposition() : Base() { init(); }

  CholmodDecomposition(const MatrixType& matrix) : Base() {
    init();
    this->compute(matrix);
  }

  ~CholmodDecomposition() {}

  void setMode(CholmodMode mode) {
    switch (mode) {
      case CholmodAuto:
        m_cholmod.final_asis = 1;
        m_cholmod.supernodal = CHOLMOD_AUTO;
        break;
      case CholmodSimplicialLLt:
        m_cholmod.final_asis = 0;
        m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
        m_cholmod.final_ll = 1;
        break;
      case CholmodSupernodalLLt:
        m_cholmod.final_asis = 1;
        m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
        break;
      case CholmodLDLt:
        m_cholmod.final_asis = 1;
        m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
        break;
      default:
        break;
    }
  }

 protected:
  void init() {
    m_cholmod.final_asis = 1;
    m_cholmod.supernodal = CHOLMOD_AUTO;
  }
};

}  // end namespace Eigen

#endif  // EIGEN_CHOLMODSUPPORT_H