IterativeSolverBase.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_ITERATIVE_SOLVER_BASE_H
#define EIGEN_ITERATIVE_SOLVER_BASE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
template <typename T>
auto is_ref_compatible_test(T& matrix) -> decltype(Ref<const T>(matrix), std::true_type());
std::false_type is_ref_compatible_test(...);
 
template <typename MatrixType>
using is_ref_compatible = decltype(is_ref_compatible_test(std::declval<remove_all_t<MatrixType>&>()));
 
// Returns a \a rows x \a cols matrix whose columns are an orthonormal basis of a random subspace,
// obtained by QR-orthonormalizing a random matrix. The IDR(s)-type solvers use this to build the
// shadow space; the basis only has to be (almost surely) non-degenerate, so any random seed is fine.
template <typename MatrixType>
MatrixType random_orthonormal_basis(Index rows, Index cols) {
  HouseholderQR<MatrixType> qr(MatrixType::Random(rows, cols));
  return qr.householderQ() * MatrixType::Identity(rows, cols);
}
 
template <typename RealScalar>
EIGEN_DEVICE_FUNC RealScalar iterative_solver_scaling_factor(RealScalar norm) {
  // Scale only when forming a quadratic recurrence term from norm may underflow or overflow.
  const RealScalar sqrtMin = numext::sqrt((std::numeric_limits<RealScalar>::min)());
  const RealScalar sqrtMax = numext::sqrt((std::numeric_limits<RealScalar>::max)());
  return norm < sqrtMin || norm > sqrtMax ? norm : RealScalar(1);
}
 
template <typename MatrixType, bool MatrixFree = !internal::is_ref_compatible<MatrixType>::value>
class generic_matrix_wrapper;
 
// We have an explicit matrix at hand, compatible with Ref<>
template <typename MatrixType>
class generic_matrix_wrapper<MatrixType, false> {
 public:
  using ActualMatrixType = Ref<const MatrixType>;
  template <int UpLo>
  struct ConstSelfAdjointViewReturnType {
    using Type = typename ActualMatrixType::template ConstSelfAdjointViewReturnType<UpLo>::Type;
  };
 
  enum { MatrixFree = false };
 
  // Default-construct: passing (0,0) trips the size assertion for fixed-size MatrixType (#1704).
  generic_matrix_wrapper() : m_dummy(), m_matrix(m_dummy) {}
 
  template <typename InputType>
  generic_matrix_wrapper(const InputType& mat) : m_matrix(mat) {}
 
  const ActualMatrixType& matrix() const { return m_matrix; }
 
  template <typename MatrixDerived>
  void grab(const EigenBase<MatrixDerived>& mat) {
    internal::destroy_at(&m_matrix);
    internal::construct_at(&m_matrix, mat.derived());
  }
 
  void grab(const Ref<const MatrixType>& mat) {
    if (&(mat.derived()) != &m_matrix) {
      internal::destroy_at(&m_matrix);
      internal::construct_at(&m_matrix, mat);
    }
  }
 
 protected:
  MatrixType m_dummy;  // used to default initialize the Ref<> object
  ActualMatrixType m_matrix;
};
 
// MatrixType is not compatible with Ref<> -> matrix-free wrapper
template <typename MatrixType>
class generic_matrix_wrapper<MatrixType, true> {
 public:
  using ActualMatrixType = MatrixType;
  template <int UpLo>
  struct ConstSelfAdjointViewReturnType {
    using Type = ActualMatrixType;
  };
 
  enum { MatrixFree = true };
 
  generic_matrix_wrapper() = default;
 
  generic_matrix_wrapper(const MatrixType& mat) : mp_matrix(&mat) {}
 
  const ActualMatrixType& matrix() const { return *mp_matrix; }
 
  void grab(const MatrixType& mat) { mp_matrix = &mat; }
 
 protected:
  const ActualMatrixType* mp_matrix = nullptr;
};
 
}  // namespace internal

template <typename Derived>
class IterativeSolverBase : public SparseSolverBase<Derived> {
 protected:
  using Base = SparseSolverBase<Derived>;
  using Base::m_isInitialized;
 
 public:
  using MatrixType = typename internal::traits<Derived>::MatrixType;
  using Preconditioner = typename internal::traits<Derived>::Preconditioner;
  using Scalar = typename MatrixType::Scalar;
  using StorageIndex = typename MatrixType::StorageIndex;
  using RealScalar = typename MatrixType::RealScalar;
 
  enum { ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
 
 public:
  using Base::derived;

  IterativeSolverBase() { init(); }

  template <typename MatrixDerived>
  explicit IterativeSolverBase(const EigenBase<MatrixDerived>& A) : m_matrixWrapper(A.derived()) {
    init();
    compute(matrix());
  }
 
  IterativeSolverBase(IterativeSolverBase&&) = default;

  template <typename MatrixDerived>
  Derived& analyzePattern(const EigenBase<MatrixDerived>& A) {
    grab(A.derived());
    m_preconditioner.analyzePattern(matrix());
    m_isInitialized = true;
    m_analysisIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }

  template <typename MatrixDerived>
  Derived& factorize(const EigenBase<MatrixDerived>& A) {
    eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
    grab(A.derived());
    m_preconditioner.factorize(matrix());
    m_factorizationIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }

  template <typename MatrixDerived>
  Derived& compute(const EigenBase<MatrixDerived>& A) {
    grab(A.derived());
    m_preconditioner.compute(matrix());
    m_isInitialized = true;
    m_analysisIsOk = true;
    m_factorizationIsOk = true;
    m_info = m_preconditioner.info();
    return derived();
  }

  constexpr Index rows() const noexcept { return matrix().rows(); }

  constexpr Index cols() const noexcept { return matrix().cols(); }

  RealScalar tolerance() const { return m_tolerance; }

  Derived& setTolerance(const RealScalar& tolerance) {
    m_tolerance = tolerance;
    return derived();
  }

  Preconditioner& preconditioner() { return m_preconditioner; }

  const Preconditioner& preconditioner() const { return m_preconditioner; }

  Index maxIterations() const { return (m_maxIterations < 0) ? 2 * matrix().cols() : m_maxIterations; }

  Derived& setMaxIterations(Index maxIters) {
    m_maxIterations = maxIters;
    return derived();
  }

  Index iterations() const {
    eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
    return m_iterations;
  }

  RealScalar error() const {
    eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
    return m_error;
  }

  template <typename Rhs, typename Guess>
  inline const SolveWithGuess<Derived, Rhs, Guess> solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const {
    eigen_assert(m_isInitialized && "Solver is not initialized.");
    eigen_assert(derived().rows() == b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
    return SolveWithGuess<Derived, Rhs, Guess>(derived(), b.derived(), x0);
  }

  template <typename Rhs, typename Dest>
  void solveWithGuessInPlace(const Rhs& b, Dest& x) const {
    eigen_assert(m_isInitialized && "Solver is not initialized.");
    eigen_assert(derived().rows() == b.rows() &&
                 "solveWithGuessInPlace(): invalid number of rows of the right hand side b");
    derived()._solve_vector_with_guess_impl(b, x);
  }

  ComputationInfo info() const {
    eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
    return m_info;
  }

  template <typename Rhs, typename DestDerived>
  void _solve_with_guess_impl(const Rhs& b, SparseMatrixBase<DestDerived>& aDest) const {
    eigen_assert(rows() == b.rows());
 
    Index rhsCols = b.cols();
    Index size = b.rows();
    DestDerived& dest(aDest.derived());
    using DestScalar = typename DestDerived::Scalar;
    Eigen::Matrix<DestScalar, Dynamic, 1> tb(size);
    Eigen::Matrix<DestScalar, Dynamic, 1> tx(cols());
    // We do not directly fill dest because sparse expressions have to be free of aliasing issue.
    // For non square least-square problems, b and dest might not have the same size whereas they might alias
    // each-other.
    typename DestDerived::PlainObject tmp(cols(), rhsCols);
    ComputationInfo global_info = Success;
    for (Index k = 0; k < rhsCols; ++k) {
      tb = b.col(k);
      tx = dest.col(k);
      derived()._solve_vector_with_guess_impl(tb, tx);
      tmp.col(k) = tx.sparseView(0);
 
      // The call to _solve_vector_with_guess_impl updates m_info, so if it failed for a previous column
      // we need to restore it to the worst value.
      if (m_info == NumericalIssue)
        global_info = NumericalIssue;
      else if (m_info == NoConvergence)
        global_info = NoConvergence;
    }
    m_info = global_info;
    dest.swap(tmp);
  }
 
  template <typename Rhs, typename DestDerived>
  std::enable_if_t<Rhs::ColsAtCompileTime != 1 && DestDerived::ColsAtCompileTime != 1> _solve_with_guess_impl(
      const Rhs& b, MatrixBase<DestDerived>& aDest) const {
    eigen_assert(rows() == b.rows());
 
    Index rhsCols = b.cols();
    DestDerived& dest(aDest.derived());
    ComputationInfo global_info = Success;
    for (Index k = 0; k < rhsCols; ++k) {
      typename DestDerived::ColXpr xk(dest, k);
      typename Rhs::ConstColXpr bk(b, k);
      derived()._solve_vector_with_guess_impl(bk, xk);
 
      // The call to _solve_vector_with_guess_impl updates m_info, so if it failed for a previous column
      // we need to restore it to the worst value.
      if (m_info == NumericalIssue)
        global_info = NumericalIssue;
      else if (m_info == NoConvergence)
        global_info = NoConvergence;
    }
    m_info = global_info;
  }
 
  template <typename Rhs, typename DestDerived>
  std::enable_if_t<Rhs::ColsAtCompileTime == 1 || DestDerived::ColsAtCompileTime == 1> _solve_with_guess_impl(
      const Rhs& b, MatrixBase<DestDerived>& dest) const {
    derived()._solve_vector_with_guess_impl(b, dest.derived());
  }

  template <typename Rhs, typename Dest>
  void _solve_impl(const Rhs& b, Dest& x) const {
    x.setZero();
    derived()._solve_with_guess_impl(b, x);
  }
 
 protected:
  void init() {
    m_isInitialized = false;
    m_analysisIsOk = false;
    m_factorizationIsOk = false;
    m_maxIterations = -1;
    m_tolerance = NumTraits<Scalar>::epsilon();
  }
 
  using MatrixWrapper = internal::generic_matrix_wrapper<MatrixType>;
  using ActualMatrixType = typename MatrixWrapper::ActualMatrixType;
 
  const ActualMatrixType& matrix() const { return m_matrixWrapper.matrix(); }
 
  template <typename InputType>
  void grab(const InputType& A) {
    m_matrixWrapper.grab(A);
  }
 
  MatrixWrapper m_matrixWrapper;
  Preconditioner m_preconditioner;
 
  Index m_maxIterations;
  RealScalar m_tolerance;
 
  mutable RealScalar m_error;
  mutable Index m_iterations;
  mutable ComputationInfo m_info;
  mutable bool m_analysisIsOk, m_factorizationIsOk;
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_ITERATIVE_SOLVER_BASE_H