RankRevealingBase.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// 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-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_RANK_REVEALING_BASE_H
#define EIGEN_RANK_REVEALING_BASE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {

template <typename Derived>
class RankRevealingBase {
 public:
  using Scalar = typename internal::traits<Derived>::Scalar;
  using RealScalar = typename NumTraits<Scalar>::Real;
 
  RankRevealingBase()
      : m_usePrescribedThreshold(false),
        m_prescribedThreshold(RealScalar(0)),
        m_maxpivot(RealScalar(0)),
        m_nonzero_pivots(0) {}

  Derived& setThreshold(const RealScalar& threshold) {
    m_usePrescribedThreshold = true;
    m_prescribedThreshold = threshold;
    return self();
  }

  /** Allows to come back to the default behavior, letting Eigen use its default formula for
   * determining the threshold.
   *
   * You should pass the special object Eigen::Default as parameter here.
   * \code dec.setThreshold(Eigen::Default); \endcode
   *
   * See the documentation of setThreshold(const RealScalar&).
   */
  Derived& setThreshold(Default_t) {
    m_usePrescribedThreshold = false;
    return self();
  }

  /** Returns the threshold that will be used by certain methods such as rank().
   *
   * See the documentation of setThreshold(const RealScalar&).
   */
  RealScalar threshold() const {
    eigen_assert(self().m_isInitialized || m_usePrescribedThreshold);
    // Higham's backward error bound: ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂.
    // The factor of 4 covers the constant c.
    return m_usePrescribedThreshold
               ? m_prescribedThreshold
               : NumTraits<Scalar>::epsilon() * RealScalar(4 * (std::min)(self().rows(), self().cols()));
  }

  inline Index rank() const {
    using std::abs;
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
    Index result = 0;
    for (Index i = 0; i < m_nonzero_pivots; ++i) result += (self().pivotCoeff(i) > premultiplied_threshold);
    return result;
  }

  inline Index dimensionOfKernel() const {
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    return self().cols() - rank();
  }

  inline bool isInjective() const {
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    return rank() == self().cols();
  }

  inline bool isSurjective() const {
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    return rank() == self().rows();
  }

   * \note This method has to determine which pivots should be considered nonzero.
   *       For that, it uses the threshold value that you can control by calling
   *       setThreshold(const RealScalar&).
   */
  inline bool isInvertible() const {
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    return isInjective() && isSurjective();
  }

  inline Index nonzeroPivots() const {
    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
    return m_nonzero_pivots;
  }

  RealScalar maxPivot() const { return m_maxpivot; }
 
 protected:
  bool m_usePrescribedThreshold;
  RealScalar m_prescribedThreshold;
  RealScalar m_maxpivot;
  Index m_nonzero_pivots;
 
 private:
  Derived& self() { return static_cast<Derived&>(*this); }
  const Derived& self() const { return static_cast<const Derived&>(*this); }
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_RANK_REVEALING_BASE_H