Move IncompleteCholesky to official modules

1 files changed, 0 insertions, 358 deletions

diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
deleted file mode 100644
index 2cad1cec6..000000000
--- a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
+++ /dev/null
@@ -1,358 +0,0 @@
-// 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>
-// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@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 is advised to give a row-oriented sparse matrix
-  * \tparam _UpLo The triangular part that will be used for the computations. It can be Lower
-    *               or Upper. Default is Lower.
-  * \tparam _OrderingType The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
-  *
-  * \implsparsesolverconcept
-  *
-  * It performs the following incomplete factorization: \f$ S P A P' S \approx L L' \f$
-  * where L is a lower triangular factor, S is a diagonal scaling matrix, and P is a
-  * fill-in reducing permutation as computed by the ordering method.
-  *
-  * \b Shifting \b strategy: Let \f$ B = S P A P' S \f$  be the scaled matrix on which the factorization is carried out,
-  * and \f$ \beta \f$ be the minimum value of the diagonal. If \f$ \beta > 0 \f$ then, the factorization is directly performed
-  * on the matrix B. Otherwise, the factorization is performed on the shifted matrix \f$ B + (\sigma+|\beta| I \f$ where
-  * \f$ \sigma \f$ is the initial shift value as returned and set by setInitialShift() method. The default value is \f$ \sigma = 10^{-3} \f$.
-  *
-  */
-template <typename Scalar, int _UpLo = Lower, typename _OrderingType = AMDOrdering<int> >
-class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> >
-{
-  protected:
-    typedef SparseSolverBase<IncompleteCholesky<Scalar,_UpLo,_OrderingType> > Base;
-    using Base::m_isInitialized;
-  public:
-    typedef typename NumTraits<Scalar>::Real RealScalar; 
-    typedef _OrderingType OrderingType;
-    typedef typename OrderingType::PermutationType PermutationType;
-    typedef typename PermutationType::StorageIndex StorageIndex; 
-    typedef SparseMatrix<Scalar,ColMajor,StorageIndex> FactorType;
-    typedef FactorType MatrixType;
-    typedef Matrix<Scalar,Dynamic,1> VectorSx;
-    typedef Matrix<RealScalar,Dynamic,1> VectorRx;
-    typedef Matrix<StorageIndex,Dynamic, 1> VectorIx;
-    typedef std::vector<std::list<StorageIndex> > VectorList; 
-    enum { UpLo = _UpLo };
-  public:
-
-    /** Default constructor leaving the object in a partly non-initialized stage.
-      *
-      * You must call compute() or the pair analyzePattern()/factorize() to make it valid.
-      *
-      * \sa IncompleteCholesky(const MatrixType&)
-      */
-    IncompleteCholesky() : m_initialShift(1e-3),m_factorizationIsOk(false) {}
-    
-    /** Constructor computing the incomplete factorization for the given matrix \a matrix.
-      */
-    template<typename MatrixType>
-    IncompleteCholesky(const MatrixType& matrix) : m_initialShift(1e-3),m_factorizationIsOk(false)
-    {
-      compute(matrix);
-    }
-    
-    /** \returns number of rows of the factored matrix */
-    Index rows() const { return m_L.rows(); }
-    
-    /** \returns number of columns of the factored matrix */
-    Index cols() const { return m_L.cols(); }
-    
-
-    /** \brief Reports whether previous computation was successful.
-      *
-      * It triggers an assertion if \c *this has not been initialized through the respective constructor,
-      * or a call to compute() or analyzePattern().
-      *
-      * \returns \c Success if computation was successful,
-      *          \c NumericalIssue if the matrix appears to be negative.
-      */
-    ComputationInfo info() const
-    {
-      eigen_assert(m_isInitialized && "IncompleteCholesky is not initialized.");
-      return m_info;
-    }
-    
-    /** \brief Set the initial shift parameter \f$ \sigma \f$.
-      */
-    void setInitialShift(RealScalar shift) { m_initialShift = shift; }
-    
-    /** \brief Computes the fill reducing permutation vector using the sparsity pattern of \a mat
-      */
-    template<typename MatrixType>
-    void analyzePattern(const MatrixType& mat)
-    {
-      OrderingType ord; 
-      PermutationType pinv;
-      ord(mat.template selfadjointView<UpLo>(), pinv); 
-      if(pinv.size()>0) m_perm = pinv.inverse();
-      else              m_perm.resize(0);
-      m_L.resize(mat.rows(), mat.cols());
-      m_analysisIsOk = true;
-      m_isInitialized = true;
-      m_info = Success;
-    }
-    
-    /** \brief Performs the numerical factorization of the input matrix \a mat
-      *
-      * The method analyzePattern() or compute() must have been called beforehand
-      * with a matrix having the same pattern.
-      *
-      * \sa compute(), analyzePattern()
-      */
-    template<typename MatrixType>
-    void factorize(const MatrixType& mat);
-    
-    /** Computes or re-computes the incomplete Cholesky factorization of the input matrix \a mat
-      *
-      * It is a shortcut for a sequential call to the analyzePattern() and factorize() methods.
-      *
-      * \sa analyzePattern(), factorize()
-      */
-    template<typename MatrixType>
-    void compute(const MatrixType& mat)
-    {
-      analyzePattern(mat);
-      factorize(mat);
-    }
-    
-    // internal
-    template<typename Rhs, typename Dest>
-    void _solve_impl(const Rhs& b, Dest& x) const
-    {
-      eigen_assert(m_factorizationIsOk && "factorize() should be called first");
-      if (m_perm.rows() == b.rows())  x = m_perm * b;
-      else                            x = b;
-      x = m_scale.asDiagonal() * x;
-      x = m_L.template triangularView<Lower>().solve(x);
-      x = m_L.adjoint().template triangularView<Upper>().solve(x);
-      x = m_scale.asDiagonal() * x;
-      if (m_perm.rows() == b.rows())
-        x = m_perm.inverse() * x;
-    }
-
-    /** \returns the sparse lower triangular factor L */
-    const FactorType& matrixL() const { eigen_assert("m_factorizationIsOk"); return m_L; }
-
-    /** \returns a vector representing the scaling factor S */
-    const VectorRx& scalingS() const { eigen_assert("m_factorizationIsOk"); return m_scale; }
-
-    /** \returns the fill-in reducing permutation P (can be empty for a natural ordering) */
-    const PermutationType& permutationP() const { eigen_assert("m_analysisIsOk"); return m_perm; }
-
-  protected:
-    FactorType m_L;              // The lower part stored in CSC
-    VectorRx m_scale;            // The vector for scaling the matrix 
-    RealScalar m_initialShift;   // The initial shift parameter
-    bool m_analysisIsOk; 
-    bool m_factorizationIsOk; 
-    ComputationInfo m_info;
-    PermutationType m_perm; 
-
-  private:
-    inline void updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol); 
-}; 
-
-template<typename Scalar, int _UpLo, typename OrderingType>
-template<typename _MatrixType>
-void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)
-{
-  using std::sqrt;
-  eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); 
-    
-  // Dropping strategy : 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() ) // To detect the null permutation
-  {
-    // The temporary is needed to make sure that the diagonal entry is properly sorted
-    FactorType tmp(mat.rows(), mat.cols());
-    tmp = mat.template selfadjointView<_UpLo>().twistedBy(m_perm);
-    m_L.template selfadjointView<Lower>() = tmp.template selfadjointView<Lower>();
-  }
-  else
-  {
-    m_L.template selfadjointView<Lower>() = mat.template selfadjointView<_UpLo>();
-  }
-  
-  Index n = m_L.cols(); 
-  Index nnz = m_L.nonZeros();
-  Map<VectorSx> vals(m_L.valuePtr(), nnz);         //values
-  Map<VectorIx> rowIdx(m_L.innerIndexPtr(), nnz);  //Row indices
-  Map<VectorIx> colPtr( m_L.outerIndexPtr(), n+1); // Pointer to the beginning of each row
-  VectorIx firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization
-  VectorList listCol(n);  // listCol(j) is a linked list of columns to update column j
-  VectorSx col_vals(n);   // Store a  nonzero values in each column
-  VectorIx col_irow(n);   // Row indices of nonzero elements in each column
-  VectorIx col_pattern(n);
-  col_pattern.fill(-1);
-  StorageIndex col_nnz;
-  
-  
-  // Computes the scaling factors 
-  m_scale.resize(n);
-  m_scale.setZero();
-  for (Index j = 0; j < n; j++)
-    for (Index k = colPtr[j]; k < colPtr[j+1]; k++)
-    {
-      m_scale(j) += numext::abs2(vals(k));
-      if(rowIdx[k]!=j)
-        m_scale(rowIdx[k]) += numext::abs2(vals(k));
-    }
-  
-  m_scale = m_scale.cwiseSqrt().cwiseSqrt();
-
-  for (Index j = 0; j < n; ++j)
-    if(m_scale(j)>(std::numeric_limits<RealScalar>::min)())
-      m_scale(j) = RealScalar(1)/m_scale(j);
-    else
-      m_scale(j) = 1;
-
-  // FIXME disable scaling if not needed, i.e., if it is roughly uniform? (this will make solve() faster)
-  
-  // Scale and compute the shift for the matrix 
-  RealScalar mindiag = NumTraits<RealScalar>::highest();
-  for (Index j = 0; j < n; j++)
-  {
-    for (Index k = colPtr[j]; k < colPtr[j+1]; k++)
-      vals[k] *= (m_scale(j)*m_scale(rowIdx[k]));
-    eigen_internal_assert(rowIdx[colPtr[j]]==j && "IncompleteCholesky: only the lower triangular part must be stored");
-    mindiag = numext::mini(numext::real(vals[colPtr[j]]), mindiag);
-  }
-  
-  RealScalar shift = 0;
-  if(mindiag <= RealScalar(0.))
-    shift = m_initialShift - mindiag;
-
-  // Apply the shift to the diagonal elements of the matrix
-  for (Index j = 0; j < n; j++)
-    vals[colPtr[j]] += shift;
-  
-  // jki version of the Cholesky factorization 
-  for (Index j=0; j < n; ++j)
-  {  
-    // Left-looking factorization of the j-th column
-    // First, load the j-th column into col_vals 
-    Scalar diag = vals[colPtr[j]];  // It is assumed that only the lower part is stored
-    col_nnz = 0;
-    for (Index i = colPtr[j] + 1; i < colPtr[j+1]; i++)
-    {
-      StorageIndex l = rowIdx[i];
-      col_vals(col_nnz) = vals[i];
-      col_irow(col_nnz) = l;
-      col_pattern(l) = col_nnz;
-      col_nnz++;
-    }
-    {
-      typename std::list<StorageIndex>::iterator k; 
-      // Browse all previous columns that will update column j
-      for(k = listCol[j].begin(); k != listCol[j].end(); k++) 
-      {
-        Index jk = firstElt(*k); // First element to use in the column 
-        eigen_internal_assert(rowIdx[jk]==j);
-        Scalar v_j_jk = numext::conj(vals[jk]);
-        
-        jk += 1; 
-        for (Index i = jk; i < colPtr[*k+1]; i++)
-        {
-          StorageIndex l = rowIdx[i];
-          if(col_pattern[l]<0)
-          {
-            col_vals(col_nnz) = vals[i] * v_j_jk;
-            col_irow[col_nnz] = l;
-            col_pattern(l) = col_nnz;
-            col_nnz++;
-          }
-          else
-            col_vals(col_pattern[l]) -= vals[i] * v_j_jk;
-        }
-        updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);
-      }
-    }
-    
-    // Scale the current column
-    if(numext::real(diag) <= 0) 
-    {
-      m_info = NumericalIssue; 
-      return; 
-    }
-    
-    RealScalar rdiag = sqrt(numext::real(diag));
-    vals[colPtr[j]] = rdiag;
-    for (Index k = 0; k<col_nnz; ++k)
-    {
-      Index i = col_irow[k];
-      //Scale
-      col_vals(k) /= rdiag;
-      //Update the remaining diagonals with col_vals
-      vals[colPtr[i]] -= numext::abs2(col_vals(k));
-    }
-    // Select the largest p elements
-    // p is the original number of elements in the column (without the diagonal)
-    Index p = colPtr[j+1] - colPtr[j] - 1 ; 
-    Ref<VectorSx> cvals = col_vals.head(col_nnz);
-    Ref<VectorIx> cirow = col_irow.head(col_nnz);
-    internal::QuickSplit(cvals,cirow, p); 
-    // Insert the largest p elements in the matrix
-    Index cpt = 0; 
-    for (Index i = colPtr[j]+1; i < colPtr[j+1]; i++)
-    {
-      vals[i] = col_vals(cpt); 
-      rowIdx[i] = col_irow(cpt);
-      // restore col_pattern:
-      col_pattern(col_irow(cpt)) = -1;
-      cpt++; 
-    }
-    // Get the first smallest row index and put it after the diagonal element
-    Index jk = colPtr(j)+1;
-    updateList(colPtr,rowIdx,vals,j,jk,firstElt,listCol); 
-  }
-  m_factorizationIsOk = true; 
-  m_info = Success;
-}
-
-template<typename Scalar, int _UpLo, typename OrderingType>
-inline void IncompleteCholesky<Scalar,_UpLo, OrderingType>::updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol)
-{
-  if (jk < colPtr(col+1) )
-  {
-    Index p = colPtr(col+1) - jk;
-    Index minpos; 
-    rowIdx.segment(jk,p).minCoeff(&minpos);
-    minpos += jk;
-    if (rowIdx(minpos) != rowIdx(jk))
-    {
-      //Swap
-      std::swap(rowIdx(jk),rowIdx(minpos));
-      std::swap(vals(jk),vals(minpos));
-    }
-    firstElt(col) = internal::convert_index<StorageIndex,Index>(jk);
-    listCol[rowIdx(jk)].push_back(internal::convert_index<StorageIndex,Index>(col));
-  }
-}
-
-} // end namespace Eigen 
-
-#endif