New scoring functor to select the pivot.

This is can be useful for non-floating point scalars, where choosing the biggest element is generally not the best choice.

Eigen/src/Core/functors/UnaryFunctors.h

@@ -55,6 +55,34 @@ struct functor_traits<scalar_abs_op<Scalar> >
   };
 };
 
+/** \internal
+  * \brief Template functor to compute the score of a scalar, to chose a pivot
+  *
+  * \sa class CwiseUnaryOp
+  */
+template<typename Scalar> struct scalar_score_coeff_op : scalar_abs_op<Scalar>
+{
+  typedef void Score_is_abs;
+};
+template<typename Scalar>
+struct functor_traits<scalar_score_coeff_op<Scalar> > : functor_traits<scalar_abs_op<Scalar> > {};
+
+/* Avoid recomputing abs when we know the score and they are the same. Not a true Eigen functor.  */
+template<typename Scalar, typename=void> struct abs_knowing_score
+{
+  EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)
+  typedef typename NumTraits<Scalar>::Real result_type;
+  template<typename Score>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { using std::abs; return abs(a); }
+};
+template<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>
+{
+  EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)
+  typedef typename NumTraits<Scalar>::Real result_type;
+  template<typename Scal>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scal&, const result_type& a) const { return a; }
+};
+
 /** \internal
   * \brief Template functor to compute the squared absolute value of a scalar
   *

Eigen/src/LU/FullPivLU.h

@@ -459,14 +459,16 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
 
     // biggest coefficient in the remaining bottom-right corner (starting at row k, col k)
     Index row_of_biggest_in_corner, col_of_biggest_in_corner;
-    RealScalar biggest_in_corner;
+    typedef internal::scalar_score_coeff_op<Scalar> Scoring;
+    typedef typename Scoring::result_type Score;
+    Score biggest_in_corner;
     biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)
-                        .cwiseAbs()
+                        .unaryExpr(Scoring())
                         .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
     row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner,
     col_of_biggest_in_corner += k; // need to add k to them.
 
-    if(biggest_in_corner==RealScalar(0))
+    if(biggest_in_corner==Score(0))
     {
       // before exiting, make sure to initialize the still uninitialized transpositions
       // in a sane state without destroying what we already have.
@@ -479,7 +481,8 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
       break;
     }
 
-    if(biggest_in_corner > m_maxpivot) m_maxpivot = biggest_in_corner;
+    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;
 
     // 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/LU/PartialPivLU.h

@@ -275,6 +275,8 @@ struct partial_lu_impl
     */
   static Index unblocked_lu(MatrixType& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)
   {
+    typedef scalar_score_coeff_op<Scalar> Scoring;
+    typedef typename Scoring::result_type Score;
     const Index rows = lu.rows();
     const Index cols = lu.cols();
     const Index size = (std::min)(rows,cols);
@@ -286,13 +288,13 @@ struct partial_lu_impl
       Index rcols = cols-k-1;
         
       Index row_of_biggest_in_col;
-      RealScalar biggest_in_corner
-        = lu.col(k).tail(rows-k).cwiseAbs().maxCoeff(&row_of_biggest_in_col);
+      Score biggest_in_corner
+        = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);
       row_of_biggest_in_col += k;
 
       row_transpositions[k] = PivIndex(row_of_biggest_in_col);
 
-      if(biggest_in_corner != RealScalar(0))
+      if(biggest_in_corner != Score(0))
       {
         if(k != row_of_biggest_in_col)
         {

Eigen/src/QR/FullPivHouseholderQR.h

@@ -443,13 +443,15 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
   for (Index k = 0; k < size; ++k)
   {
     Index row_of_biggest_in_corner, col_of_biggest_in_corner;
-    RealScalar biggest_in_corner;
+    typedef internal::scalar_score_coeff_op<Scalar> Scoring;
+    typedef typename Scoring::result_type Score;
 
-    biggest_in_corner = m_qr.bottomRightCorner(rows-k, cols-k)
-                            .cwiseAbs()
-                            .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+    Score score = m_qr.bottomRightCorner(rows-k, cols-k)
+                      .unaryExpr(Scoring())
+                      .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
     row_of_biggest_in_corner += k;
     col_of_biggest_in_corner += k;
+    RealScalar biggest_in_corner = internal::abs_knowing_score<Scalar>()(m_qr(row_of_biggest_in_corner, col_of_biggest_in_corner), score);
     if(k==0) biggest = biggest_in_corner;
 
     // if the corner is negligible, then we have less than full rank, and we can finish early