Extract RankRevealingBase CRTP mixin to eliminate decomposition code duplication

libeigen/eigen!2272

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

Eigen/LU

@@ -25,6 +25,7 @@
 
 #include "src/misc/Kernel.h"
 #include "src/misc/Image.h"
+#include "src/misc/RankRevealingBase.h"
 
 // IWYU pragma: begin_exports
 #include "src/LU/FullPivLU.h"

Eigen/QR

@@ -31,6 +31,8 @@
  * \endcode
  */
 
+#include "src/misc/RankRevealingBase.h"
+
 // IWYU pragma: begin_exports
 #include "src/QR/HouseholderQR.h"
 #include "src/QR/FullPivHouseholderQR.h"

Eigen/src/LU/FullPivLU.h

@@ -60,11 +60,23 @@ struct traits<FullPivLU<MatrixType_, PermutationIndex_> > : traits<MatrixType_>
  * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()
  */
 template <typename MatrixType_, typename PermutationIndex_>
-class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> > {
+class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> >,
+                  public RankRevealingBase<FullPivLU<MatrixType_, PermutationIndex_> > {
  public:
   typedef MatrixType_ MatrixType;
   typedef SolverBase<FullPivLU> Base;
+  typedef RankRevealingBase<FullPivLU> RankRevealingBase_;
   friend class SolverBase<FullPivLU>;
+  friend class RankRevealingBase<FullPivLU>;
+  using RankRevealingBase_::dimensionOfKernel;
+  using RankRevealingBase_::isInjective;
+  using RankRevealingBase_::isInvertible;
+  using RankRevealingBase_::isSurjective;
+  using RankRevealingBase_::maxPivot;
+  using RankRevealingBase_::nonzeroPivots;
+  using RankRevealingBase_::rank;
+  using RankRevealingBase_::setThreshold;
+  using RankRevealingBase_::threshold;
 
   EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU)
   enum {
@@ -148,23 +160,6 @@ class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> >
     return m_lu;
   }
 
-  /** \returns the number of nonzero pivots in the LU 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(m_isInitialized && "LU is not initialized.");
-    return m_nonzero_pivots;
-  }
-
-  /** \returns the absolute value of the biggest pivot, i.e. the biggest
-   *          diagonal coefficient of U.
-   */
-  RealScalar maxPivot() const { return m_maxpivot; }
-
   /** \returns the permutation matrix P
    *
    * \sa permutationQ()
@@ -278,114 +273,10 @@ class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> >
    */
   typename internal::traits<MatrixType>::Scalar determinant() const;
 
-  /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+  /** \returns the absolute value of the i-th pivot coefficient (for RankRevealingBase). */
-   * who need to determine when pivots are to be considered nonzero. This is not used for the
+  RealScalar pivotCoeff(Index i) const {
-   * LU 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)
-   */
-  FullPivLU& setThreshold(const RealScalar& threshold) {
-    m_usePrescribedThreshold = true;
-    m_prescribedThreshold = threshold;
-    return *this;
-  }
-
-  /** 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 lu.setThreshold(Eigen::Default); \endcode
-   *
-   * See the documentation of setThreshold(const RealScalar&).
-   */
-  FullPivLU& setThreshold(Default_t) {
-    m_usePrescribedThreshold = false;
-    return *this;
-  }
-
-  /** 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(m_isInitialized || m_usePrescribedThreshold);
-    return m_usePrescribedThreshold ? m_prescribedThreshold
-                                    // Higham's backward error bound for Gaussian elimination with
-                                    // complete pivoting (Theorem 9.4) is ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂.
-                                    // The factor of 4 covers the constant c.
-                                    : NumTraits<Scalar>::epsilon() * RealScalar(4 * m_lu.diagonalSize());
-  }
-
-  /** \returns the rank of the matrix of which *this is the LU 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(m_isInitialized && "LU is not initialized.");
+    return abs(m_lu.coeff(i, i));
-    RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
-    Index result = 0;
-    for (Index i = 0; i < m_nonzero_pivots; ++i) result += (abs(m_lu.coeff(i, i)) > premultiplied_threshold);
-    return result;
-  }
-
-  /** \returns the dimension of the kernel of the matrix of which *this is the LU 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(m_isInitialized && "LU is not initialized.");
-    return cols() - rank();
-  }
-
-  /** \returns true if the matrix of which *this is the LU 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(m_isInitialized && "LU is not initialized.");
-    return rank() == cols();
-  }
-
-  /** \returns true if the matrix of which *this is the LU 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(m_isInitialized && "LU is not initialized.");
-    return rank() == rows();
-  }
-
-  /** \returns true if the matrix of which *this is the LU 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(m_isInitialized && "LU is not initialized.");
-    return isInjective() && (m_lu.rows() == m_lu.cols());
   }
 
   /** \returns the inverse of the matrix of which *this is the LU decomposition.
@@ -424,15 +315,13 @@ class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> >
   PermutationQType m_q;
   IntColVectorType m_rowsTranspositions;
   IntRowVectorType m_colsTranspositions;
-  Index m_nonzero_pivots;
   RealScalar m_l1_norm;
-  RealScalar m_maxpivot, m_prescribedThreshold;
   signed char m_det_pq;
-  bool m_isInitialized, m_usePrescribedThreshold;
+  bool m_isInitialized;
 };
 
 template <typename MatrixType, typename PermutationIndex>
-FullPivLU<MatrixType, PermutationIndex>::FullPivLU() : m_isInitialized(false), m_usePrescribedThreshold(false) {}
+FullPivLU<MatrixType, PermutationIndex>::FullPivLU() : m_isInitialized(false) {}
 
 template <typename MatrixType, typename PermutationIndex>
 FullPivLU<MatrixType, PermutationIndex>::FullPivLU(Index rows, Index cols)
@@ -441,8 +330,7 @@ FullPivLU<MatrixType, PermutationIndex>::FullPivLU(Index rows, Index cols)
       m_q(cols),
       m_rowsTranspositions(rows),
       m_colsTranspositions(cols),
-      m_isInitialized(false),
+      m_isInitialized(false) {}
-      m_usePrescribedThreshold(false) {}
 
 template <typename MatrixType, typename PermutationIndex>
 template <typename InputType>
@@ -452,8 +340,7 @@ FullPivLU<MatrixType, PermutationIndex>::FullPivLU(const EigenBase<InputType>& m
       m_q(matrix.cols()),
       m_rowsTranspositions(matrix.rows()),
       m_colsTranspositions(matrix.cols()),
-      m_isInitialized(false),
+      m_isInitialized(false) {
-      m_usePrescribedThreshold(false) {
   compute(matrix.derived());
 }
 
@@ -465,8 +352,7 @@ FullPivLU<MatrixType, PermutationIndex>::FullPivLU(EigenBase<InputType>& matrix)
       m_q(matrix.cols()),
       m_rowsTranspositions(matrix.rows()),
       m_colsTranspositions(matrix.cols()),
-      m_isInitialized(false),
+      m_isInitialized(false) {
-      m_usePrescribedThreshold(false) {
   computeInPlace();
 }
 
@@ -487,8 +373,8 @@ void FullPivLU<MatrixType, PermutationIndex>::computeInPlace() {
   m_colsTranspositions.resize(m_lu.cols());
   Index number_of_transpositions = 0;  // number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i
 
-  m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
+  this->m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
-  m_maxpivot = RealScalar(0);
+  this->m_maxpivot = RealScalar(0);
 
   for (Index k = 0; k < size; ++k) {
     // First, we need to find the pivot.
@@ -507,7 +393,7 @@ void FullPivLU<MatrixType, PermutationIndex>::computeInPlace() {
     if (numext::is_exactly_zero(biggest_in_corner)) {
       // before exiting, make sure to initialize the still uninitialized transpositions
       // in a sane state without destroying what we already have.
-      m_nonzero_pivots = k;
+      this->m_nonzero_pivots = k;
       for (Index i = k; i < size; ++i) {
         m_rowsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
         m_colsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
@@ -517,7 +403,7 @@ void FullPivLU<MatrixType, PermutationIndex>::computeInPlace() {
 
     RealScalar abs_pivot = internal::abs_knowing_score<Scalar>()(
         m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner);
-    if (abs_pivot > m_maxpivot) m_maxpivot = abs_pivot;
+    if (abs_pivot > this->m_maxpivot) this->m_maxpivot = abs_pivot;
 
     // Now that we've found the pivot, we need to apply the row/col swaps to
     // bring it to the location (k,k).

Eigen/src/QR/ColPivHouseholderQR.h

@@ -51,11 +51,23 @@ struct traits<ColPivHouseholderQR<MatrixType_, PermutationIndex_>> : traits<Matr
  * \sa MatrixBase::colPivHouseholderQr()
  */
 template <typename MatrixType_, typename PermutationIndex_>
-class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, PermutationIndex_>> {
+class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, PermutationIndex_>>,
+                            public RankRevealingBase<ColPivHouseholderQR<MatrixType_, PermutationIndex_>> {
  public:
   typedef MatrixType_ MatrixType;
   typedef SolverBase<ColPivHouseholderQR> Base;
+  typedef RankRevealingBase<ColPivHouseholderQR> RankRevealingBase_;
   friend class SolverBase<ColPivHouseholderQR>;
+  friend class RankRevealingBase<ColPivHouseholderQR>;
+  using RankRevealingBase_::dimensionOfKernel;
+  using RankRevealingBase_::isInjective;
+  using RankRevealingBase_::isInvertible;
+  using RankRevealingBase_::isSurjective;
+  using RankRevealingBase_::maxPivot;
+  using RankRevealingBase_::nonzeroPivots;
+  using RankRevealingBase_::rank;
+  using RankRevealingBase_::setThreshold;
+  using RankRevealingBase_::threshold;
   typedef PermutationIndex_ PermutationIndex;
   EIGEN_GENERIC_PUBLIC_INTERFACE(ColPivHouseholderQR)
 
@@ -82,7 +94,6 @@ class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, P
     m_colNormsUpdated.resize(cols);
     m_colNormsDirect.resize(cols);
     m_isInitialized = false;
-    m_usePrescribedThreshold = false;
   }
 
  public:
@@ -100,8 +111,7 @@ class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, P
         m_temp(),
         m_colNormsUpdated(),
         m_colNormsDirect(),
-        m_isInitialized(false),
+        m_isInitialized(false) {}
-        m_usePrescribedThreshold(false) {}
 
   /** \brief Default Constructor with memory preallocation
    *
@@ -252,65 +262,10 @@ class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, P
    */
   typename MatrixType::Scalar signDeterminant() const;
 
-  /** \returns the rank of the matrix of which *this is the QR decomposition.
+  /** \returns the absolute value of the i-th pivot coefficient (for RankRevealingBase). */
-   *
+  RealScalar pivotCoeff(Index i) const {
-   * \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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+    return abs(m_qr.coeff(i, i));
-    RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
-    Index result = 0;
-    for (Index i = 0; i < m_nonzero_pivots; ++i) result += (abs(m_qr.coeff(i, i)) > premultiplied_threshold);
-    return result;
-  }
-
-  /** \returns the dimension of the kernel of the matrix of which *this is the QR 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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-    return cols() - rank();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-    return rank() == cols();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-    return rank() == rows();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-    return isInjective() && isSurjective();
   }
 
   /** \returns the inverse of the matrix of which *this is the QR decomposition.
@@ -332,72 +287,6 @@ class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, P
    */
   const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
 
-  /** 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
-   * QR 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)
-   */
-  ColPivHouseholderQR& setThreshold(const RealScalar& threshold) {
-    m_usePrescribedThreshold = true;
-    m_prescribedThreshold = threshold;
-    return *this;
-  }
-
-  /** 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 qr.setThreshold(Eigen::Default); \endcode
-   *
-   * See the documentation of setThreshold(const RealScalar&).
-   */
-  ColPivHouseholderQR& setThreshold(Default_t) {
-    m_usePrescribedThreshold = false;
-    return *this;
-  }
-
-  /** 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(m_isInitialized || m_usePrescribedThreshold);
-    return m_usePrescribedThreshold ? m_prescribedThreshold
-                                    // Higham's backward error bound for Householder QR (Theorem 19.4) is
-                                    // ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂. The factor of 4 covers the
-                                    // constant c (typically 3–6 worst-case, ~1 probabilistically).
-                                    : NumTraits<Scalar>::epsilon() * RealScalar(4 * m_qr.diagonalSize());
-  }
-
-  /** \returns the number of nonzero pivots in the QR 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(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-    return m_nonzero_pivots;
-  }
-
-  /** \returns the absolute value of the biggest pivot, i.e. the biggest
-   *          diagonal coefficient of R.
-   */
-  RealScalar maxPivot() const { return m_maxpivot; }
-
   /** \brief Reports whether the QR factorization was successful.
    *
    * \note This function always returns \c Success. It is provided for compatibility
@@ -431,9 +320,7 @@ class ColPivHouseholderQR : public SolverBase<ColPivHouseholderQR<MatrixType_, P
   RowVectorType m_temp;
   RealRowVectorType m_colNormsUpdated;
   RealRowVectorType m_colNormsDirect;
-  bool m_isInitialized, m_usePrescribedThreshold;
+  bool m_isInitialized;
-  RealScalar m_prescribedThreshold, m_maxpivot;
-  Index m_nonzero_pivots;
   Index m_det_p;
 };
 
@@ -515,8 +402,8 @@ void ColPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
       numext::abs2<RealScalar>(m_colNormsUpdated.maxCoeff() * NumTraits<RealScalar>::epsilon()) / RealScalar(rows);
   RealScalar norm_downdate_threshold = numext::sqrt(NumTraits<RealScalar>::epsilon());
 
-  m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
+  this->m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
-  m_maxpivot = RealScalar(0);
+  this->m_maxpivot = RealScalar(0);
 
   for (Index k = 0; k < size; ++k) {
     // first, we look up in our table m_colNormsUpdated which column has the biggest norm
@@ -526,7 +413,8 @@ void ColPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
 
     // Track the number of meaningful pivots but do not stop the decomposition to make
     // sure that the initial matrix is properly reproduced. See bug 941.
-    if (m_nonzero_pivots == size && biggest_col_sq_norm < threshold_helper * RealScalar(rows - k)) m_nonzero_pivots = k;
+    if (this->m_nonzero_pivots == size && biggest_col_sq_norm < threshold_helper * RealScalar(rows - k))
+      this->m_nonzero_pivots = k;
 
     // apply the transposition to the columns
     m_colsTranspositions.coeffRef(k) = static_cast<PermutationIndex>(biggest_col_index);
@@ -545,7 +433,7 @@ void ColPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
     m_qr.coeffRef(k, k) = beta;
 
     // remember the maximum absolute value of diagonal coefficients
-    if (abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+    if (abs(beta) > this->m_maxpivot) this->m_maxpivot = abs(beta);
 
     // apply the householder transformation
     m_qr.bottomRightCorner(rows - k, cols - k - 1)

Eigen/src/QR/FullPivHouseholderQR.h

@@ -60,11 +60,23 @@ struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType, PermutationIndex
  * \sa MatrixBase::fullPivHouseholderQr()
  */
 template <typename MatrixType_, typename PermutationIndex_>
-class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_, PermutationIndex_> > {
+class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_, PermutationIndex_> >,
+                             public RankRevealingBase<FullPivHouseholderQR<MatrixType_, PermutationIndex_> > {
  public:
   typedef MatrixType_ MatrixType;
   typedef SolverBase<FullPivHouseholderQR> Base;
+  typedef RankRevealingBase<FullPivHouseholderQR> RankRevealingBase_;
   friend class SolverBase<FullPivHouseholderQR>;
+  friend class RankRevealingBase<FullPivHouseholderQR>;
+  using RankRevealingBase_::dimensionOfKernel;
+  using RankRevealingBase_::isInjective;
+  using RankRevealingBase_::isInvertible;
+  using RankRevealingBase_::isSurjective;
+  using RankRevealingBase_::maxPivot;
+  using RankRevealingBase_::nonzeroPivots;
+  using RankRevealingBase_::rank;
+  using RankRevealingBase_::setThreshold;
+  using RankRevealingBase_::threshold;
   typedef PermutationIndex_ PermutationIndex;
   EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivHouseholderQR)
 
@@ -105,8 +117,7 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
         m_cols_transpositions(),
         m_cols_permutation(),
         m_temp(),
-        m_isInitialized(false),
+        m_isInitialized(false) {}
-        m_usePrescribedThreshold(false) {}
 
   /** \brief Default Constructor with memory preallocation
    *
@@ -121,8 +132,7 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
         m_cols_transpositions((std::min)(rows, cols)),
         m_cols_permutation(cols),
         m_temp(cols),
-        m_isInitialized(false),
+        m_isInitialized(false) {}
-        m_usePrescribedThreshold(false) {}
 
   /** \brief Constructs a QR factorization from a given matrix
    *
@@ -144,8 +154,7 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
         m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
         m_cols_permutation(matrix.cols()),
         m_temp(matrix.cols()),
-        m_isInitialized(false),
+        m_isInitialized(false) {
-        m_usePrescribedThreshold(false) {
     compute(matrix.derived());
   }
 
@@ -164,8 +173,7 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
         m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
         m_cols_permutation(matrix.cols()),
         m_temp(matrix.cols()),
-        m_isInitialized(false),
+        m_isInitialized(false) {
-        m_usePrescribedThreshold(false) {
     computeInPlace();
   }
 
@@ -273,65 +281,10 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
    */
   typename MatrixType::Scalar signDeterminant() const;
 
-  /** \returns the rank of the matrix of which *this is the QR decomposition.
+  /** \returns the absolute value of the i-th pivot coefficient (for RankRevealingBase). */
-   *
+  RealScalar pivotCoeff(Index i) const {
-   * \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(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+    return abs(m_qr.coeff(i, i));
-    RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
-    Index result = 0;
-    for (Index i = 0; i < m_nonzero_pivots; ++i) result += (abs(m_qr.coeff(i, i)) > premultiplied_threshold);
-    return result;
-  }
-
-  /** \returns the dimension of the kernel of the matrix of which *this is the QR 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(m_isInitialized && "FullPivHouseholderQR is not initialized.");
-    return cols() - rank();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "FullPivHouseholderQR is not initialized.");
-    return rank() == cols();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "FullPivHouseholderQR is not initialized.");
-    return rank() == rows();
-  }
-
-  /** \returns true if the matrix of which *this is the QR 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(m_isInitialized && "FullPivHouseholderQR is not initialized.");
-    return isInjective() && isSurjective();
   }
 
   /** \returns the inverse of the matrix of which *this is the QR decomposition.
@@ -353,72 +306,6 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
    */
   const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
 
-  /** 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
-   * QR 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)
-   */
-  FullPivHouseholderQR& setThreshold(const RealScalar& threshold) {
-    m_usePrescribedThreshold = true;
-    m_prescribedThreshold = threshold;
-    return *this;
-  }
-
-  /** 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 qr.setThreshold(Eigen::Default); \endcode
-   *
-   * See the documentation of setThreshold(const RealScalar&).
-   */
-  FullPivHouseholderQR& setThreshold(Default_t) {
-    m_usePrescribedThreshold = false;
-    return *this;
-  }
-
-  /** 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(m_isInitialized || m_usePrescribedThreshold);
-    return m_usePrescribedThreshold ? m_prescribedThreshold
-                                    // Higham's backward error bound for Householder QR (Theorem 19.4) is
-                                    // ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂. The factor of 4 covers the
-                                    // constant c (typically 3–6 worst-case, ~1 probabilistically).
-                                    : NumTraits<Scalar>::epsilon() * RealScalar(4 * m_qr.diagonalSize());
-  }
-
-  /** \returns the number of nonzero pivots in the QR 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(m_isInitialized && "LU is not initialized.");
-    return m_nonzero_pivots;
-  }
-
-  /** \returns the absolute value of the biggest pivot, i.e. the biggest
-   *          diagonal coefficient of U.
-   */
-  RealScalar maxPivot() const { return m_maxpivot; }
-
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   template <typename RhsType, typename DstType>
   void _solve_impl(const RhsType& rhs, DstType& dst) const;
@@ -438,9 +325,7 @@ class FullPivHouseholderQR : public SolverBase<FullPivHouseholderQR<MatrixType_,
   IntDiagSizeVectorType m_cols_transpositions;
   PermutationType m_cols_permutation;
   RowVectorType m_temp;
-  bool m_isInitialized, m_usePrescribedThreshold;
+  bool m_isInitialized;
-  RealScalar m_prescribedThreshold, m_maxpivot;
-  Index m_nonzero_pivots;
   RealScalar m_precision;
   Index m_det_p;
 };
@@ -513,8 +398,8 @@ void FullPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
 
   RealScalar biggest(0);
 
-  m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
+  this->m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
-  m_maxpivot = RealScalar(0);
+  this->m_maxpivot = RealScalar(0);
 
   for (Index k = 0; k < size; ++k) {
     Index row_of_biggest_in_corner, col_of_biggest_in_corner;
@@ -532,7 +417,7 @@ void FullPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
 
     // if the corner is negligible, then we have less than full rank, and we can finish early
     if (internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision)) {
-      m_nonzero_pivots = k;
+      this->m_nonzero_pivots = k;
       for (Index i = k; i < size; i++) {
         m_rows_transpositions.coeffRef(i) = internal::convert_index<PermutationIndex>(i);
         m_cols_transpositions.coeffRef(i) = internal::convert_index<PermutationIndex>(i);
@@ -557,7 +442,7 @@ void FullPivHouseholderQR<MatrixType, PermutationIndex>::computeInPlace() {
     m_qr.coeffRef(k, k) = beta;
 
     // remember the maximum absolute value of diagonal coefficients
-    if (abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+    if (abs(beta) > this->m_maxpivot) this->m_maxpivot = abs(beta);
 
     m_qr.bottomRightCorner(rows - k, cols - k - 1)
         .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows - k - 1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k + 1));

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