make ColPivotingQR use HouseholderSequence

Eigen/src/Core/VectorBlock.h

@@ -77,11 +77,12 @@ template<typename VectorType, int Size, int PacketAccess> class VectorBlock
     typedef Block<VectorType,
                   ei_traits<VectorType>::RowsAtCompileTime==1 ? 1 : Size,
                   ei_traits<VectorType>::ColsAtCompileTime==1 ? 1 : Size,
-                  PacketAccess> Base;
+                  PacketAccess> _Base;
     enum {
       IsColVector = ei_traits<VectorType>::ColsAtCompileTime==1
     };
   public:
+    _EIGEN_GENERIC_PUBLIC_INTERFACE(VectorBlock, _Base)
 
     using Base::operator=;
     using Base::operator+=;

Eigen/src/Householder/HouseholderSequence.h

@@ -136,6 +136,22 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
       }
     }
 
+    template<typename OtherDerived>
+    typename OtherDerived::PlainMatrixType operator*(const MatrixBase<OtherDerived>& other) const
+    {
+      typename OtherDerived::PlainMatrixType res(other);
+      applyThisOnTheLeft(res);
+      return res;
+    }
+
+    template<typename OtherDerived> friend
+    typename OtherDerived::PlainMatrixType operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence& h)
+    {
+      typename OtherDerived::PlainMatrixType res(other);
+      h.applyThisOnTheRight(res);
+      return res;
+    }
+
   protected:
 
     typename VectorsType::Nested m_vectors;
@@ -143,4 +159,10 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
     bool m_trans;
 };
 
+template<typename VectorsType, typename CoeffsType>
+HouseholderSequence<VectorsType,CoeffsType> makeHouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans=false)
+{
+  return HouseholderSequence<VectorsType,CoeffsType>(v, h, trans);
+}
+
 #endif // EIGEN_HOUSEHOLDER_SEQUENCE_H

Eigen/src/QR/ColPivotingHouseholderQR.h

@@ -62,6 +62,7 @@ template<typename MatrixType> class ColPivotingHouseholderQR
     typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
     typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
     typedef Matrix<RealScalar, 1, ColsAtCompileTime> RealRowVectorType;
+    typedef typename HouseholderSequence<MatrixQType,HCoeffsType>::ConjugateReturnType HouseholderSequenceType;
 
     /**
     * \brief Default Constructor.
@@ -99,7 +100,7 @@ template<typename MatrixType> class ColPivotingHouseholderQR
     template<typename OtherDerived, typename ResultType>
     bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
 
-    MatrixQType matrixQ(void) const;
+    HouseholderSequenceType matrixQ(void) const;
 
     /** \returns a reference to the matrix where the Householder QR decomposition is stored
       */
@@ -355,13 +356,8 @@ bool ColPivotingHouseholderQR<MatrixType>::solve(
 
   typename OtherDerived::PlainMatrixType c(b);
 
-  Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
-  for (int k = 0; k < m_rank; ++k)
-  {
-    int remainingSize = rows-k;
-    c.corner(BottomRight, remainingSize, cols)
-     .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
-  }
+  // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
+  c.applyOnTheLeft(makeHouseholderSequence(m_qr.corner(TopLeft,rows,m_rank), m_hCoeffs.start(m_rank)).transpose());
 
   if(!isSurjective())
   {
@@ -381,25 +377,12 @@ bool ColPivotingHouseholderQR<MatrixType>::solve(
   return true;
 }
 
-/** \returns the matrix Q */
+/** \returns the matrix Q as a sequence of householder transformations */
 template<typename MatrixType>
-typename ColPivotingHouseholderQR<MatrixType>::MatrixQType ColPivotingHouseholderQR<MatrixType>::matrixQ() const
+typename ColPivotingHouseholderQR<MatrixType>::HouseholderSequenceType ColPivotingHouseholderQR<MatrixType>::matrixQ() const
 {
   ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized.");
-  // compute the product H'_0 H'_1 ... H'_n-1,
-  // where H_k is the k-th Householder transformation I - h_k v_k v_k'
-  // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
-  int rows = m_qr.rows();
-  int cols = m_qr.cols();
-  int size = std::min(rows,cols);
-  MatrixQType res = MatrixQType::Identity(rows, rows);
-  Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
-  for (int k = size-1; k >= 0; k--)
-  {
-    res.block(k, k, rows-k, rows-k)
-       .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
-  }
-  return res;
+  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
 }
 
 #endif // EIGEN_HIDE_HEAVY_CODE