add reconstructedMatrix() to LLT, and LUs

=> they show that some improvements have still to be done
   for permutations, tr*tr, trapezoidal matrices

Eigen/src/Cholesky/LDLT.h

@@ -155,7 +155,7 @@ template<typename _MatrixType> class LDLT
       return m_matrix;
     }
 
-    const MatrixType reconstructedMatrix() const;
+    MatrixType reconstructedMatrix() const;
 
     inline int rows() const { return m_matrix.rows(); }
     inline int cols() const { return m_matrix.cols(); }
@@ -324,7 +324,7 @@ bool LDLT<MatrixType>::solveInPlace(MatrixBase<Derived> &bAndX) const
  * i.e., it returns the product: P^T L D L^* P.
  * This function is provided for debug purpose. */
 template<typename MatrixType>
-const MatrixType LDLT<MatrixType>::reconstructedMatrix() const
+MatrixType LDLT<MatrixType>::reconstructedMatrix() const
 {
   ei_assert(m_isInitialized && "LDLT is not initialized.");
   const int size = m_matrix.rows();

Eigen/src/Cholesky/LLT.h

@@ -133,6 +133,8 @@ template<typename _MatrixType, int _UpLo> class LLT
       return m_matrix;
     }
 
+    MatrixType reconstructedMatrix() const;
+
     inline int rows() const { return m_matrix.rows(); }
     inline int cols() const { return m_matrix.cols(); }
 
@@ -295,6 +297,16 @@ bool LLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
   return true;
 }
 
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: L L^*.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int _UpLo>
+MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
+{
+  ei_assert(m_isInitialized && "LLT is not initialized.");
+  return matrixL() * matrixL().adjoint().toDenseMatrix();
+}
+
 /** \cholesky_module
   * \returns the LLT decomposition of \c *this
   */

Eigen/src/LU/FullPivLU.h

@@ -361,6 +361,8 @@ template<typename _MatrixType> class FullPivLU
                (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()));
     }
 
+    MatrixType reconstructedMatrix() const;
+
     inline int rows() const { return m_lu.rows(); }
     inline int cols() const { return m_lu.cols(); }
 
@@ -487,6 +489,33 @@ typename ei_traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() cons
   return Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());
 }
 
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^{-1} L U Q^{-1}.
+ * This function is provided for debug purpose. */
+template<typename MatrixType>
+MatrixType FullPivLU<MatrixType>::reconstructedMatrix() const
+{
+  ei_assert(m_isInitialized && "LU is not initialized.");
+  const int smalldim = std::min(m_lu.rows(), m_lu.cols());
+  // LU
+  MatrixType res(m_lu.rows(),m_lu.cols());
+  // FIXME the .toDenseMatrix() should not be needed...
+  res = m_lu.corner(TopLeft,m_lu.rows(),smalldim)
+            .template triangularView<UnitLower>().toDenseMatrix()
+      * m_lu.corner(TopLeft,smalldim,m_lu.cols())
+            .template triangularView<Upper>().toDenseMatrix();
+
+  // P^{-1}(LU)
+  // FIXME implement inplace permutation
+  res = (m_p.inverse() * res).eval();
+
+  // (P^{-1}LU)Q^{-1}
+  // FIXME implement inplace permutation
+  res = (res * m_q.inverse()).eval();
+
+  return res;
+}
+
 /********* Implementation of kernel() **************************************************/
 
 template<typename _MatrixType>

Eigen/src/LU/PartialPivLU.h

@@ -165,6 +165,8 @@ template<typename _MatrixType> class PartialPivLU
       */
     typename ei_traits<MatrixType>::Scalar determinant() const;
 
+    MatrixType reconstructedMatrix() const;
+
     inline int rows() const { return m_lu.rows(); }
     inline int cols() const { return m_lu.cols(); }
 
@@ -400,6 +402,24 @@ typename ei_traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() c
   return Scalar(m_det_p) * m_lu.diagonal().prod();
 }
 
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^{-1} L U.
+ * This function is provided for debug purpose. */
+template<typename MatrixType>
+MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
+{
+  ei_assert(m_isInitialized && "LU is not initialized.");
+  // LU
+  MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()
+                 * m_lu.template triangularView<Upper>();
+  
+  // P^{-1}(LU)
+  // FIXME implement inplace permutation
+  res = (m_p.inverse() * res).eval();
+
+  return res;
+}
+
 /***** Implementation of solve() *****************************************************/
 
 template<typename _MatrixType, typename Rhs>

test/cholesky.cpp

@@ -95,7 +95,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
 
   {
     LLT<SquareMatrixType,Lower> chollo(symmLo);
-    VERIFY_IS_APPROX(symm, chollo.matrixL().toDenseMatrix() * chollo.matrixL().adjoint().toDenseMatrix());
+    VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
     vecX = chollo.solve(vecB);
     VERIFY_IS_APPROX(symm * vecX, vecB);
     matX = chollo.solve(matB);
@@ -103,7 +103,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
 
     // test the upper mode
     LLT<SquareMatrixType,Upper> cholup(symmUp);
-    VERIFY_IS_APPROX(symm, cholup.matrixL().toDenseMatrix() * cholup.matrixL().adjoint().toDenseMatrix());
+    VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix());
     vecX = cholup.solve(vecB);
     VERIFY_IS_APPROX(symm * vecX, vecB);
     matX = cholup.solve(matB);
@@ -119,8 +119,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
 
   {
     LDLT<SquareMatrixType> ldlt(symm);
-    // TODO(keir): This doesn't make sense now that LDLT pivots.
+    VERIFY_IS_APPROX(symm, ldlt.reconstructedMatrix());
-    //VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
     vecX = ldlt.solve(vecB);
     VERIFY_IS_APPROX(symm * vecX, vecB);
     matX = ldlt.solve(matB);

test/lu.cpp

@@ -91,6 +91,7 @@ template<typename MatrixType> void lu_non_invertible()
   KernelMatrixType m1kernel = lu.kernel();
   ImageMatrixType m1image = lu.image(m1);
 
+  VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
   VERIFY(rank == lu.rank());
   VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
   VERIFY(!lu.isInjective());
@@ -125,6 +126,7 @@ template<typename MatrixType> void lu_invertible()
     lu.compute(m1);
   } while(!lu.isInvertible());
 
+  VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
   VERIFY(0 == lu.dimensionOfKernel());
   VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
   VERIFY(size == lu.rank());
@@ -138,6 +140,23 @@ template<typename MatrixType> void lu_invertible()
   VERIFY_IS_APPROX(m2, lu.inverse()*m3);
 }
 
+template<typename MatrixType> void lu_partial_piv()
+{
+  /* this test covers the following files:
+     PartialPivLU.h
+  */
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  int rows = ei_random<int>(1,4);
+  int cols = rows;
+
+  MatrixType m1(cols, rows);
+  m1.setRandom();
+  PartialPivLU<MatrixType> plu(m1);
+
+  VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
+}
+
 template<typename MatrixType> void lu_verify_assert()
 {
   MatrixType tmp;
@@ -180,6 +199,7 @@ void test_lu()
     
     CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
     CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
+    CALL_SUBTEST_4( lu_partial_piv<MatrixXd>() );
     CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
     
     CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
@@ -188,6 +208,7 @@ void test_lu()
     
     CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
     CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
+    CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>() );
     CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
 
     CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));