Fix HouseholderSequence::conjugate() and ::adjoint() and add respective unit tests.

Eigen/src/Eigenvalues/HessenbergDecomposition.h

@@ -82,7 +82,7 @@ template<typename _MatrixType> class HessenbergDecomposition
     typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
 
     /** \brief Return type of matrixQ() */
-    typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
     
     typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
 

Eigen/src/Eigenvalues/Tridiagonalization.h

@@ -96,7 +96,7 @@ template<typename _MatrixType> class Tridiagonalization
             >::type SubDiagonalReturnType;
 
     /** \brief Return type of matrixQ() */
-    typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
 
     /** \brief Default constructor.
       *

Eigen/src/Householder/HouseholderSequence.h

@@ -125,7 +125,9 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
     typedef typename VectorsType::Index Index;
 
     typedef HouseholderSequence<
-      VectorsType,
+      typename internal::conditional<NumTraits<Scalar>::IsComplex,
+        typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,
+        VectorsType>::type,
       typename internal::conditional<NumTraits<Scalar>::IsComplex,
         typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,
         CoeffsType>::type,
@@ -206,7 +208,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS
     /** \brief Complex conjugate of the Householder sequence. */
     ConjugateReturnType conjugate() const
     {
-      return ConjugateReturnType(m_vectors, m_coeffs.conjugate())
+      return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
              .setTrans(m_trans)
              .setLength(m_length)
              .setShift(m_shift);

Eigen/src/QR/ColPivHouseholderQR.h

@@ -55,7 +55,7 @@ template<typename _MatrixType> class ColPivHouseholderQR
     typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
     typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
     typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;
-    typedef typename HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
     
   private:
     

Eigen/src/QR/HouseholderQR.h

@@ -57,7 +57,7 @@ template<typename _MatrixType> class HouseholderQR
     typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;
     typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
     typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
-    typedef typename HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType HouseholderSequenceType;
+    typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;
 
     /**
       * \brief Default Constructor.

Eigen/src/SVD/UpperBidiagonalization.h

@@ -39,7 +39,7 @@ template<typename _MatrixType> class UpperBidiagonalization
               CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Diagonal<const MatrixType,0> >
             > HouseholderUSequenceType;
     typedef HouseholderSequence<
-              const MatrixType,
+              const typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type,
               Diagonal<const MatrixType,1>,
               OnTheRight
             > HouseholderVSequenceType;
@@ -74,7 +74,7 @@ template<typename _MatrixType> class UpperBidiagonalization
     const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
     {
       eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
-      return HouseholderVSequenceType(m_householder, m_householder.const_derived().template diagonal<1>())
+      return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
              .setLength(m_householder.cols()-1)
              .setShift(1);
     }

test/householder.cpp

@@ -89,12 +89,29 @@ template<typename MatrixType> void householder(const MatrixType& m)
   hseq.setLength(hc.size()).setShift(shift);
   VERIFY(hseq.length() == hc.size());
   VERIFY(hseq.shift() == shift);
-
+  
   MatrixType m5 = m2;
   m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
   VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
   m3 = hseq;
   VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
+  
+  SquareMatrixType hseq_mat = hseq;
+  SquareMatrixType hseq_mat_conj = hseq.conjugate();
+  SquareMatrixType hseq_mat_adj = hseq.adjoint();
+  SquareMatrixType hseq_mat_trans = hseq.transpose();
+  SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
+  VERIFY_IS_APPROX(hseq_mat.adjoint(),    hseq_mat_adj);
+  VERIFY_IS_APPROX(hseq_mat.conjugate(),  hseq_mat_conj);
+  VERIFY_IS_APPROX(hseq_mat.transpose(),  hseq_mat_trans);
+  VERIFY_IS_APPROX(hseq_mat * m6,             hseq_mat * m6);
+  VERIFY_IS_APPROX(hseq_mat.adjoint() * m6,   hseq_mat_adj * m6);
+  VERIFY_IS_APPROX(hseq_mat.conjugate() * m6, hseq_mat_conj * m6);
+  VERIFY_IS_APPROX(hseq_mat.transpose() * m6, hseq_mat_trans * m6);
+  VERIFY_IS_APPROX(m6 * hseq_mat,             m6 * hseq_mat);
+  VERIFY_IS_APPROX(m6 * hseq_mat.adjoint(),   m6 * hseq_mat_adj);
+  VERIFY_IS_APPROX(m6 * hseq_mat.conjugate(), m6 * hseq_mat_conj);
+  VERIFY_IS_APPROX(m6 * hseq_mat.transpose(), m6 * hseq_mat_trans);
 
   // test householder sequence on the right with a shift
 

test/upperbidiagonalization.cpp

@@ -16,6 +16,7 @@ template<typename MatrixType> void upperbidiag(const MatrixType& m)
   const typename MatrixType::Index cols = m.cols();
 
   typedef Matrix<typename MatrixType::RealScalar, MatrixType::RowsAtCompileTime,  MatrixType::ColsAtCompileTime> RealMatrixType;
+  typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime,  MatrixType::RowsAtCompileTime> TransposeMatrixType;
 
   MatrixType a = MatrixType::Random(rows,cols);
   internal::UpperBidiagonalization<MatrixType> ubd(a);
@@ -24,6 +25,8 @@ template<typename MatrixType> void upperbidiag(const MatrixType& m)
   b.block(0,0,cols,cols) = ubd.bidiagonal();
   MatrixType c = ubd.householderU() * b * ubd.householderV().adjoint();
   VERIFY_IS_APPROX(a,c);
+  TransposeMatrixType d = ubd.householderV() * b.adjoint() * ubd.householderU().adjoint();
+  VERIFY_IS_APPROX(a.adjoint(),d);
 }
 
 void test_upperbidiagonalization()