* Fix a bug in HouseholderQR with mixed fixed/dynamic size: must use EIGEN_SIZE_MIN instead of EIGEN_ENUM_MIN, and there are many other occurences throughout Eigen!

* HouseholderSequence:
  - add shift parameter
  - add essentialVector() method to start abstracting the direction
  - add unit test in householder.cpp

Eigen/src/Householder/HouseholderSequence.h

@@ -65,32 +65,44 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
   : public AnyMatrixBase<HouseholderSequence<VectorsType,CoeffsType> >
 {
     typedef typename VectorsType::Scalar Scalar;
+    typedef Block<VectorsType, Dynamic, 1> EssentialVectorType;
+    
   public:
 
     typedef HouseholderSequence<VectorsType,
       typename ei_meta_if<NumTraits<Scalar>::IsComplex,
-        NestByValue<typename ei_cleantype<typename CoeffsType::ConjugateReturnType>::type >,
+        typename ei_cleantype<typename CoeffsType::ConjugateReturnType>::type,
         CoeffsType>::ret> ConjugateReturnType;
 
     HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans = false)
-      : m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(v.diagonalSize())
+      : m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(v.diagonalSize()),
-    {}
+        m_shift(0)
+    {
+    }
 
-    HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors)
+    HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors, int shift)
-      : m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(actualVectors)
+      : m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(actualVectors), m_shift(shift)
-    {}
+    {
+    }
 
     int rows() const { return m_vectors.rows(); }
     int cols() const { return m_vectors.rows(); }
 
+    const EssentialVectorType essentialVector(int k) const
+    {
+      ei_assert(k>= 0 && k < m_actualVectors);
+      const int start = k+1+m_shift;
+      return Block<VectorsType,Dynamic,1>(m_vectors, start, k, rows()-start, 1);
+    }
+
     HouseholderSequence transpose() const
-    { return HouseholderSequence(m_vectors, m_coeffs, !m_trans, m_actualVectors); }
+    { return HouseholderSequence(m_vectors, m_coeffs, !m_trans, m_actualVectors, m_shift); }
 
     ConjugateReturnType conjugate() const
-    { return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), m_trans, m_actualVectors); }
+    { return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), m_trans, m_actualVectors, m_shift); }
 
     ConjugateReturnType adjoint() const
-    { return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), !m_trans, m_actualVectors); }
+    { return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), !m_trans, m_actualVectors, m_shift); }
 
     ConjugateReturnType inverse() const { return adjoint(); }
 
@@ -98,45 +110,41 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
     template<typename DestType> void evalTo(DestType& dst) const
     {
       int vecs = m_actualVectors;
-      int length = m_vectors.rows();
+      dst.setIdentity(rows(), rows());
-      dst.setIdentity();
+      Matrix<Scalar,1,DestType::RowsAtCompileTime> temp(rows());
-      Matrix<Scalar,1,DestType::RowsAtCompileTime> temp(dst.rows());
       for(int k = vecs-1; k >= 0; --k)
       {
+        int cornerSize = rows() - k - m_shift;
         if(m_trans)
-          dst.corner(BottomRight, length-k, length-k)
+          dst.corner(BottomRight, cornerSize, cornerSize)
-          .applyHouseholderOnTheRight(m_vectors.col(k).tail(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(0));
+          .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
         else
-          dst.corner(BottomRight, length-k, length-k)
+          dst.corner(BottomRight, cornerSize, cornerSize)
-            .applyHouseholderOnTheLeft(m_vectors.col(k).tail(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(k));
+            .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
       }
     }
 
     /** \internal */
     template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
     {
-      int vecs = m_actualVectors; // number of householder vectors
-      int length = m_vectors.rows(); // size of the largest householder vector
       Matrix<Scalar,1,Dest::RowsAtCompileTime> temp(dst.rows());
-      for(int k = 0; k < vecs; ++k)
+      for(int k = 0; k < m_actualVectors; ++k)
       {
-        int actual_k = m_trans ? vecs-k-1 : k;
+        int actual_k = m_trans ? m_actualVectors-k-1 : k;
-        dst.corner(BottomRight, dst.rows(), length-actual_k)
+        dst.corner(BottomRight, dst.rows(), rows()-m_shift-actual_k)
-           .applyHouseholderOnTheRight(m_vectors.col(actual_k).tail(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
+           .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
       }
     }
 
     /** \internal */
     template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
     {
-      int vecs = m_actualVectors; // number of householder vectors
-      int length = m_vectors.rows(); // size of the largest householder vector
       Matrix<Scalar,1,Dest::ColsAtCompileTime> temp(dst.cols());
-      for(int k = 0; k < vecs; ++k)
+      for(int k = 0; k < m_actualVectors; ++k)
       {
-        int actual_k = m_trans ? k : vecs-k-1;
+        int actual_k = m_trans ? k : m_actualVectors-k-1;
-        dst.corner(BottomRight, length-actual_k, dst.cols())
+        dst.corner(BottomRight, rows()-m_shift-actual_k, dst.cols())
-           .applyHouseholderOnTheLeft(m_vectors.col(actual_k).tail(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
+           .applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
       }
     }
 
@@ -161,6 +169,7 @@ template<typename VectorsType, typename CoeffsType> class HouseholderSequence
     typename CoeffsType::Nested m_coeffs;
     bool m_trans;
     int m_actualVectors;
+    int m_shift;
 };
 
 template<typename VectorsType, typename CoeffsType>
@@ -170,9 +179,9 @@ HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsTyp
 }
 
 template<typename VectorsType, typename CoeffsType>
-HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors)
+HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors, int shift)
 {
-  return HouseholderSequence<VectorsType,CoeffsType>(v, h, trans, actualVectors);
+  return HouseholderSequence<VectorsType,CoeffsType>(v, h, trans, actualVectors, shift);
 }
 
 #endif // EIGEN_HOUSEHOLDER_SEQUENCE_H

Eigen/src/QR/ColPivHouseholderQR.h

@@ -448,7 +448,8 @@ struct ei_solve_retval<ColPivHouseholderQR<_MatrixType>, Rhs>
       dec().matrixQR(),
       dec().hCoeffs(),
       true,
-      dec().nonzeroPivots()
+      dec().nonzeroPivots(),
+      0
     ));
 
     dec().matrixQR()
@@ -475,7 +476,7 @@ typename ColPivHouseholderQR<MatrixType>::HouseholderSequenceType ColPivHousehol
   ::householderQ() const
 {
   ei_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
-  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate(), false, m_nonzero_pivots);
+  return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate(), false, m_nonzero_pivots, 0);
 }
 
 #endif // EIGEN_HIDE_HEAVY_CODE

Eigen/src/QR/HouseholderQR.h

@@ -55,11 +55,11 @@ template<typename _MatrixType> class HouseholderQR
       RowsAtCompileTime = MatrixType::RowsAtCompileTime,
       ColsAtCompileTime = MatrixType::ColsAtCompileTime,
       Options = MatrixType::Options,
-      DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,RowsAtCompileTime)
+      DiagSizeAtCompileTime = EIGEN_SIZE_MIN(ColsAtCompileTime,RowsAtCompileTime)
     };
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
-    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, AutoAlign | (ei_traits<MatrixType>::Flags&RowMajorBit ? RowMajor : ColMajor)> MatrixQType;
+    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, ei_traits<MatrixType>::Flags&RowMajorBit ? RowMajor : ColMajor> MatrixQType;
     typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType;
     typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
     typedef typename HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType HouseholderSequenceType;
@@ -191,7 +191,7 @@ HouseholderQR<MatrixType>& HouseholderQR<MatrixType>::compute(const MatrixType&
 
   RowVectorType temp(cols);
 
-  for (int k = 0; k < size; ++k)
+  for(int k = 0; k < size; ++k)
   {
     int remainingRows = rows - k;
     int remainingCols = cols - k - 1;

test/householder.cpp

@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
@@ -23,7 +23,7 @@
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
 #include "main.h"
-#include <Eigen/Householder>
+#include <Eigen/QR>
 
 template<typename MatrixType> void householder(const MatrixType& m)
 {
@@ -40,6 +40,12 @@ template<typename MatrixType> void householder(const MatrixType& m)
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
   typedef Matrix<Scalar, ei_decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
+  typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
+
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> RightSquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic> VBlockMatrixType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
   
   Matrix<Scalar, EIGEN_ENUM_MAX(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp(std::max(rows,cols));
   Scalar* tmp = &_tmp.coeffRef(0,0);
@@ -85,8 +91,42 @@ template<typename MatrixType> void householder(const MatrixType& m)
   VERIFY_IS_MUCH_SMALLER_THAN(ei_imag(m3(0,0)), ei_real(m3(0,0)));
   VERIFY_IS_APPROX(ei_real(m3(0,0)), alpha);
 
-  // test householder sequence
+  // test householder sequence on the left with a shift
-  // TODO test HouseholderSequence
+
+  int shift = ei_random(0, std::max(rows-2,0));
+  int brows = rows - shift;
+  m1.setRandom(rows, cols);
+  HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
+  HouseholderQR<HBlockMatrixType> qr(hbm);
+  m2 = m1;
+  m2.block(shift,0,brows,cols) = qr.matrixQR();
+  HCoeffsVectorType hc = qr.hCoeffs().conjugate();
+  HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc, false, hc.size(), 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
+
+#if 0
+  // test householder sequence on the right with a shift
+
+  TMatrixType tm1 = m1.transpose();
+  TMatrixType tm2 = m2.transpose();
+  
+  int bcols = cols - shift;
+  VBlockMatrixType vbm = 
+  HouseholderQR<HBlockMatrixType> qr(hbm);
+  m2 = m1;
+  m2.block(shift,0,brows,cols) = qr.matrixQR();
+  HCoeffsVectorType hc = qr.hCoeffs().conjugate();
+  HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc, false, hc.size(), 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
+#endif
 }
 
 void test_householder()
@@ -98,6 +138,6 @@ void test_householder()
     CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
     CALL_SUBTEST_5( householder(MatrixXd(10,12)) );
     CALL_SUBTEST_6( householder(MatrixXcf(16,17)) );
+    CALL_SUBTEST_7( householder(MatrixXf(25,7)) );
   }
-
 }

test/qr.cpp

@@ -36,14 +36,11 @@ template<typename MatrixType> void qr(const MatrixType& m)
 
   MatrixType a = MatrixType::Random(rows,cols);
   HouseholderQR<MatrixType> qrOfA(a);
-  MatrixType r = qrOfA.matrixQR();
   
   MatrixQType q = qrOfA.householderQ();
   VERIFY_IS_UNITARY(q);
   
-  // FIXME need better way to construct trapezoid
+  MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
-  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
-
   VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
 }
 
@@ -114,7 +111,7 @@ template<typename MatrixType> void qr_verify_assert()
 
 void test_qr()
 {
-  for(int i = 0; i < 1; i++) {
+  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1( qr(MatrixXf(47,40)) );
    CALL_SUBTEST_2( qr(MatrixXcd(17,7)) );
    CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));