bug #1493: Make representation of HouseholderSequence consistent and working for complex numbers. Made corresponding unit test actually test that. Also simplify implementation of QR decompositions

Eigen/src/Eigenvalues/HessenbergDecomposition.h

@@ -315,7 +315,7 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
 
     // A = A H'
     matA.rightCols(remainingSize)
-        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));
+        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1), numext::conj(h), &temp.coeffRef(0));
   }
 }
 

Eigen/src/Householder/Householder.h

@@ -103,7 +103,7 @@ void MatrixBase<Derived>::makeHouseholder(
   * \param essential the essential part of the vector \c v
   * \param tau the scaling factor of the Householder transformation
   * \param workspace a pointer to working space with at least
-  *                  this->cols() * essential.size() entries
+  *                  this->cols() entries
   *
   * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 
   *     MatrixBase::applyHouseholderOnTheRight()
@@ -140,7 +140,7 @@ void MatrixBase<Derived>::applyHouseholderOnTheLeft(
   * \param essential the essential part of the vector \c v
   * \param tau the scaling factor of the Householder transformation
   * \param workspace a pointer to working space with at least
-  *                  this->cols() * essential.size() entries
+  *                  this->rows() entries
   *
   * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), 
   *     MatrixBase::applyHouseholderOnTheLeft()
@@ -160,10 +160,10 @@ void MatrixBase<Derived>::applyHouseholderOnTheRight(
   {
     Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
     Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
-    tmp.noalias() = right * essential.conjugate();
+    tmp.noalias() = right * essential;
     tmp += this->col(0);
     this->col(0) -= tau * tmp;
-    right.noalias() -= tau * tmp * essential.transpose();
+    right.noalias() -= tau * tmp * essential.adjoint();
   }
 }
 

Eigen/src/Householder/HouseholderSequence.h

@@ -140,6 +140,22 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
       Side
     > ConjugateReturnType;
 
+    typedef HouseholderSequence<
+      VectorsType,
+      typename internal::conditional<NumTraits<Scalar>::IsComplex,
+        typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,
+        CoeffsType>::type,
+      Side
+    > AdjointReturnType;
+
+    typedef HouseholderSequence<
+      typename internal::conditional<NumTraits<Scalar>::IsComplex,
+        typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,
+        VectorsType>::type,
+      CoeffsType,
+      Side
+    > TransposeReturnType;
+
     /** \brief Constructor.
       * \param[in]  v      %Matrix containing the essential parts of the Householder vectors
       * \param[in]  h      Vector containing the Householder coefficients
@@ -206,9 +222,12 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
     }
 
     /** \brief %Transpose of the Householder sequence. */
-    HouseholderSequence transpose() const
+    TransposeReturnType transpose() const
     {
-      return HouseholderSequence(*this).setTrans(!m_trans);
+      return TransposeReturnType(m_vectors.conjugate(), m_coeffs)
+              .setTrans(!m_trans)
+              .setLength(m_length)
+              .setShift(m_shift);
     }
 
     /** \brief Complex conjugate of the Householder sequence. */
@@ -221,13 +240,16 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
     }
 
     /** \brief Adjoint (conjugate transpose) of the Householder sequence. */
-    ConjugateReturnType adjoint() const
+    AdjointReturnType adjoint() const
     {
-      return conjugate().setTrans(!m_trans);
+      return AdjointReturnType(m_vectors, m_coeffs.conjugate())
+              .setTrans(!m_trans)
+              .setLength(m_length)
+              .setShift(m_shift);
     }
 
     /** \brief Inverse of the Householder sequence (equals the adjoint). */
-    ConjugateReturnType inverse() const { return adjoint(); }
+    AdjointReturnType inverse() const { return adjoint(); }
 
     /** \internal */
     template<typename DestType> inline void evalTo(DestType& dst) const
@@ -273,10 +295,10 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
           Index cornerSize = rows() - k - m_shift;
           if(m_trans)
             dst.bottomRightCorner(cornerSize, cornerSize)
-               .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
+               .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
           else
             dst.bottomRightCorner(cornerSize, cornerSize)
-               .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
+               .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
         }
       }
     }

Eigen/src/QR/ColPivHouseholderQR.h

@@ -595,11 +595,7 @@ void ColPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &
 
   typename RhsType::PlainObject c(rhs);
 
-  // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
-  c.applyOnTheLeft(householderSequence(m_qr, m_hCoeffs)
-                    .setLength(nonzero_pivots)
-                    .transpose()
-    );
+  c.applyOnTheLeft(householderQ().setLength(nonzero_pivots).adjoint() );
 
   m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
       .template triangularView<Upper>()

Eigen/src/QR/CompleteOrthogonalDecomposition.h

@@ -452,7 +452,7 @@ void CompleteOrthogonalDecomposition<MatrixType>::computeInPlace()
         // Apply Z(k) to the first k rows of X_k
         m_cpqr.m_qr.topRightCorner(k, cols - rank + 1)
             .applyHouseholderOnTheRight(
-                m_cpqr.m_qr.row(k).tail(cols - rank).transpose(), m_zCoeffs(k),
+                m_cpqr.m_qr.row(k).tail(cols - rank).adjoint(), m_zCoeffs(k),
                 &m_temp(0));
       }
       if (k != rank - 1) {
@@ -500,11 +500,8 @@ void CompleteOrthogonalDecomposition<_MatrixType>::_solve_impl(
   }
 
   // Compute c = Q^* * rhs
-  // Note that the matrix Q = H_0^* H_1^*... so its inverse is
-  // Q^* = (H_0 H_1 ...)^T
   typename RhsType::PlainObject c(rhs);
-  c.applyOnTheLeft(
-      householderSequence(matrixQTZ(), hCoeffs()).setLength(rank).transpose());
+  c.applyOnTheLeft(matrixQ().setLength(rank).adjoint());
 
   // Solve T z = c(1:rank, :)
   dst.topRows(rank) = matrixT()

Eigen/src/QR/HouseholderQR.h

@@ -353,11 +353,7 @@ void HouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) c
 
   typename RhsType::PlainObject c(rhs);
 
-  // Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T
-  c.applyOnTheLeft(householderSequence(
-    m_qr.leftCols(rank),
-    m_hCoeffs.head(rank)).transpose()
-  );
+  c.applyOnTheLeft(householderQ().setLength(rank).adjoint() );
 
   m_qr.topLeftCorner(rank, rank)
       .template triangularView<Upper>()

Eigen/src/SVD/UpperBidiagonalization.h

@@ -127,7 +127,7 @@ void upperbidiagonalization_inplace_unblocked(MatrixType& mat,
        .makeHouseholderInPlace(mat.coeffRef(k,k+1), upper_diagonal[k]);
     // apply householder transform to remaining part of mat on the left
     mat.bottomRightCorner(remainingRows-1, remainingCols)
-       .applyHouseholderOnTheRight(mat.row(k).tail(remainingCols-1).transpose(), mat.coeff(k,k+1), tempData);
+       .applyHouseholderOnTheRight(mat.row(k).tail(remainingCols-1).adjoint(), mat.coeff(k,k+1), tempData);
   }
 }