Merge

3 files changed, 224 insertions, 2 deletions

diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers
index 6c6946d91..c3cc97cd2 100644
--- a/unsupported/Eigen/IterativeSolvers
+++ b/unsupported/Eigen/IterativeSolvers
@@ -33,6 +33,7 @@
 #include "../../Eigen/Jacobi"
 #include "../../Eigen/Householder"
 #include "src/IterativeSolvers/GMRES.h"
+#include "src/IterativeSolvers/IncompleteCholesky.h"
 //#include "src/IterativeSolvers/SSORPreconditioner.h"
 
 //@}
diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
new file mode 100644
index 000000000..5bc41c0f8
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
@@ -0,0 +1,221 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INCOMPLETE_CHOlESKY_H
+#define EIGEN_INCOMPLETE_CHOlESKY_H
+#include "Eigen/src/IterativeLinearSolvers/IncompleteLUT.h" 
+#include <Eigen/OrderingMethods>
+#include <list>
+
+namespace Eigen {  
+/** 
+ * \brief Modified Incomplete Cholesky with dual threshold
+ * 
+ * References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with
+ *              Limited memory, SIAM J. Sci. Comput.  21(1), pp. 24-45, 1999
+ * 
+ * \tparam _MatrixType The type of the sparse matrix. It should be a symmetric 
+ *                     matrix. It is advised to give  a row-oriented sparse matrix 
+ * \tparam _UpLo The triangular part of the matrix to reference. 
+ * \tparam _OrderingType 
+ */
+
+template <typename Scalar, int _UpLo = Lower, typename _OrderingType = NaturalOrdering<int> >
+class IncompleteCholesky : internal::noncopyable
+{
+  public:
+    typedef SparseMatrix<Scalar,ColMajor> MatrixType;
+    typedef _OrderingType OrderingType;
+    typedef typename MatrixType::RealScalar RealScalar; 
+    typedef typename MatrixType::Index Index; 
+    typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
+    typedef Matrix<Scalar,Dynamic,1> VectorType; 
+    typedef Matrix<Index,Dynamic, 1> IndexType; 
+
+  public:
+    IncompleteCholesky() {}
+    IncompleteCholesky(const MatrixType& matrix)
+    {
+      compute(matrix);
+    }
+    
+    Index rows() const { return m_L.rows(); }
+    
+    Index cols() const { return m_L.cols(); }
+    
+
+    /** \brief Reports whether previous computation was successful.
+      *
+      * \returns \c Success if computation was succesful,
+      *          \c NumericalIssue if the matrix appears to be negative.
+      */
+    ComputationInfo info() const
+    {
+      eigen_assert(m_isInitialized && "IncompleteLLT is not initialized.");
+      return m_info;
+    }
+    /**
+    * \brief Computes the fill reducing permutation vector. 
+    */
+    template<typename MatrixType>
+    void analyzePattern(const MatrixType& mat)
+    {
+      OrderingType ord; 
+      ord(mat, m_perm); 
+      m_analysisIsOk = true; 
+    }
+    
+    template<typename MatrixType>
+    void factorize(const MatrixType& amat);
+    
+    template<typename MatrixType>
+    void compute (const MatrixType& matrix)
+    {
+      analyzePattern(matrix); 
+      factorize(matrix);
+    }
+    
+    template<typename Rhs, typename Dest>
+    void _solve(const Rhs& b, Dest& x) const
+    {
+      eigen_assert(m_factorizationIsOk && "factorize() should be called first");
+      if (m_perm.rows() == b.rows())
+        x = m_perm.inverse() * b; 
+      else 
+        x = b; 
+      x = m_L.template triangularView<UnitLower>().solve(x); 
+      x = m_L.adjoint().template triangularView<Upper>().solve(x); 
+      if (m_perm.rows() == b.rows())
+        x = m_perm * x;
+    }
+    template<typename Rhs> inline const internal::solve_retval<IncompleteCholesky, Rhs>
+    solve(const MatrixBase<Rhs>& b) const
+    {
+      eigen_assert(m_isInitialized && "IncompleteLLT is not initialized.");
+      eigen_assert(cols()==b.rows()
+                && "IncompleteLLT::solve(): invalid number of rows of the right hand side matrix b");
+      return internal::solve_retval<IncompleteCholesky, Rhs>(*this, b.derived());
+    }
+  protected:
+    SparseMatrix<Scalar,ColMajor> m_L;  // The lower part stored in CSC
+    bool m_analysisIsOk; 
+    bool m_factorizationIsOk; 
+    bool m_isInitialized;
+    ComputationInfo m_info;
+    PermutationType m_perm; 
+    
+}; 
+
+template<typename Scalar, int _UpLo, typename OrderingType>
+template<typename _MatrixType>
+void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)
+{
+  eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); 
+  
+  // FIXME Stability: We should probably compute the scaling factors and the shifts that are needed to ensure a succesful LLT factorization and an efficient preconditioner. 
+  
+  // Dropping strategies : Keep only the p largest elements per column, where p is the number of elements in the column of the original matrix. Other strategies will be added
+  
+  // Apply the fill-reducing permutation computed in analyzePattern()
+  if (m_perm.rows() == mat.rows() )
+    m_L.template selfadjointView<Lower>() = mat.template selfadjointView<_UpLo>().twistedBy(m_perm);
+  else
+    m_L.template selfadjointView<Lower>() = mat.template selfadjointView<_UpLo>();
+  
+  int n = mat.cols(); 
+  
+  Scalar *vals = m_L.valuePtr(); //Values 
+  Index *rowIdx = m_L.innerIndexPtr(); //Row indices 
+  Index *colPtr = m_L.outerIndexPtr(); // Pointer to the beginning of each row
+  VectorType firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization
+  // Initialize firstElt; 
+  for (int j = 0; j < n-1; j++) firstElt(j) = colPtr[j]+1; 
+  std::vector<std::list<Index> > listCol(n); // listCol(j) is a linked list of columns to update column j
+  VectorType curCol(n); // Store a  nonzero values in each column
+  VectorType irow(n); // Row indices of nonzero elements in each column
+  // jki version of the Cholesky factorization 
+  for (int j=0; j < n; j++)
+  {
+     //Left-looking factorize the column j 
+     // First, load the jth column into curCol 
+     Scalar diag = vals[colPtr[j]];  // Lower diagonal matrix with 
+     curCol.setZero();
+     irow.setLinSpaced(n,0,n-1); 
+     for (int i = colPtr[j] + 1; i < colPtr[j+1]; i++)
+     {
+       curCol(rowIdx[i]) = vals[i]; 
+       irow(rowIdx[i]) = rowIdx[i]; 
+     }
+     
+     std::list<int>::iterator k; 
+     // Browse all previous columns that will update column j
+     for(k = listCol[j].begin(); k != listCol[j].end(); k++) 
+     {
+       int jk = firstElt(*k); // First element to use in the column 
+       Scalar a_jk = vals[jk]; 
+       diag -= a_jk * a_jk; 
+       jk += 1; 
+       for (int i = jk; i < colPtr[*k]; i++)
+       {
+         curCol(rowIdx[i]) -= vals[i] * a_jk ;
+       }
+       firstElt(*k) = jk; 
+       if (jk < colPtr[*k+1]) 
+       {
+         // Add this column to the updating columns list for column *k+1
+         listCol[rowIdx[jk]].push_back(*k); 
+       }
+     }
+     
+     // Select the largest p elements
+     //  p is the original number of elements in the column (without the diagonal)
+     int p = colPtr[j+1] - colPtr[j] - 2 ; 
+     internal::QuickSplit(curCol, irow, p); 
+     if(RealScalar(diag) <= 0) 
+     { //FIXME We can use heuristics (Kershaw, 1978 or above reference ) to get a dynamic shift
+       m_info = NumericalIssue; 
+       return; 
+     }
+     RealScalar rdiag = internal::sqrt(RealScalar(diag));
+     Scalar scal = Scalar(1)/rdiag; 
+     vals[colPtr[j]] = rdiag;
+     // Insert the largest p elements in the matrix and scale them meanwhile  
+     int cpt = 0; 
+     for (int i = colPtr[j]+1; i < colPtr[j+1]; i++)
+     {
+       vals[i] = curCol(cpt) * scal; 
+       rowIdx[i] = irow(cpt); 
+       cpt ++; 
+     }
+  }
+  m_factorizationIsOk = true; 
+  m_isInitialized = true;
+  m_info = Success; 
+}
+
+namespace internal {
+
+template<typename _MatrixType, typename Rhs>
+struct solve_retval<IncompleteCholesky<_MatrixType>, Rhs>
+  : solve_retval_base<IncompleteCholesky<_MatrixType>, Rhs>
+{
+  typedef IncompleteCholesky<_MatrixType> Dec;
+  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    dec()._solve(rhs(),dst);
+  }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen 
+
+#endif
\ No newline at end of file
diff --git a/unsupported/test/matrix_power.cpp b/unsupported/test/matrix_power.cpp
index db356450a..95c63c574 100644
--- a/unsupported/test/matrix_power.cpp
+++ b/unsupported/test/matrix_power.cpp
@@ -34,8 +34,8 @@ template<typename T>
 void test2dHyperbolicRotation(double tol)
 {
   Matrix<std::complex<T>,2,2> A, B, C;
-  T angle, ch = std::cosh(1);
-  std::complex<T> ish(0, std::sinh(1));
+  T angle, ch = std::cosh((T)1);
+  std::complex<T> ish(0, std::sinh((T)1));
 
   A << ch, ish, -ish, ch;
   MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);