Extract RankRevealingBase CRTP mixin to eliminate decomposition code duplication

libeigen/eigen!2272

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>

Eigen/src/misc/RankRevealingBase.h

@@ -0,0 +1,178 @@
+// 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/.
+
+#ifndef EIGEN_RANK_REVEALING_BASE_H
+#define EIGEN_RANK_REVEALING_BASE_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \brief CRTP mixin providing threshold management, rank computation, and rank-derived queries
+ *         for rank-revealing decompositions (FullPivLU, ColPivHouseholderQR, FullPivHouseholderQR).
+ *
+ * \tparam Derived the concrete decomposition class (CRTP parameter)
+ *
+ * The derived class must provide:
+ *   - rows(), cols() (inherited from SolverBase)
+ *   - m_isInitialized (bool member, also used by SolverBase)
+ *   - pivotCoeff(Index i) returning the absolute value of the i-th pivot
+ */
+template <typename Derived>
+class RankRevealingBase {
+ public:
+  typedef typename internal::traits<Derived>::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+
+  RankRevealingBase()
+      : m_usePrescribedThreshold(false),
+        m_prescribedThreshold(RealScalar(0)),
+        m_maxpivot(RealScalar(0)),
+        m_nonzero_pivots(0) {}
+
+  /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+   * who need to determine when pivots are to be considered nonzero. This is not used for the
+   * decomposition itself.
+   *
+   * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+   * uses a formula to automatically determine a reasonable threshold.
+   * Once you have called the present method setThreshold(const RealScalar&),
+   * your value is used instead.
+   *
+   * \param threshold The new value to use as the threshold.
+   *
+   * A pivot will be considered nonzero if its absolute value is strictly greater than
+   *  \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+   * where maxpivot is the biggest pivot.
+   *
+   * If you want to come back to the default behavior, call setThreshold(Default_t)
+   */
+  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()));
+  }
+
+  /** \returns the rank of the matrix of which *this is the decomposition.
+   *
+   * \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 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;
+  }
+
+  /** \returns the dimension of the kernel of the matrix of which *this is the decomposition.
+   *
+   * \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 Index dimensionOfKernel() const {
+    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
+    return self().cols() - rank();
+  }
+
+  /** \returns true if the matrix of which *this is the decomposition represents an injective
+   *          linear map, i.e. has trivial kernel; false otherwise.
+   *
+   * \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 isInjective() const {
+    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
+    return rank() == self().cols();
+  }
+
+  /** \returns true if the matrix of which *this is the decomposition represents a surjective
+   *          linear map; false otherwise.
+   *
+   * \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 isSurjective() const {
+    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
+    return rank() == self().rows();
+  }
+
+  /** \returns true if the matrix of which *this is the decomposition is invertible.
+   *
+   * \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();
+  }
+
+  /** \returns the number of nonzero pivots in the decomposition.
+   * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+   * So that notion isn't really intrinsically interesting, but it is
+   * still useful when implementing algorithms.
+   *
+   * \sa rank()
+   */
+  inline Index nonzeroPivots() const {
+    eigen_assert(self().m_isInitialized && "Decomposition is not initialized.");
+    return m_nonzero_pivots;
+  }
+
+  /** \returns the absolute value of the biggest pivot, i.e. the biggest
+   *          diagonal coefficient of U (or R).
+   */
+  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