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Extract RankRevealingBase CRTP mixin to eliminate decomposition code duplication

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libeigen/eigen!2272

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
This commit is contained in:
Rasmus Munk Larsen
2026-03-28 19:12:23 -07:00
parent 5e521f3e45
commit 0fe8cdfa3b
6 changed files with 254 additions and 414 deletions
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164
Eigen/src/LU/FullPivLU.h
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@@ -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(),
* who need to determine when pivots are to be considered nonzero. This is not used for the
* 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 {
/** \returns the absolute value of the i-th pivot coefficient (for RankRevealingBase). */
RealScalar pivotCoeff(Index i) const {
using std::abs;
eigen_assert(m_isInitialized && "LU is not initialized.");
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());
return abs(m_lu.coeff(i, i));
}
/** \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_usePrescribedThreshold(false) {}
m_isInitialized(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_usePrescribedThreshold(false) {
m_isInitialized(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_usePrescribedThreshold(false) {
m_isInitialized(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)
m_maxpivot = RealScalar(0);
this->m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
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).