LUDecomposition.h

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//
// File: LUDecomposition.h
// Authors:
//   Julien Dutheil
// Created: 2004-04-07 16:24:00
//
 
/*
  Copyright or © or Copr. Bio++ Development Team, (November 17, 2004)
  
  This software is a computer program whose purpose is to provide classes
  for numerical calculus.
  
  This software is governed by the CeCILL license under French law and
  abiding by the rules of distribution of free software. You can use,
  modify and/ or redistribute the software under the terms of the CeCILL
  license as circulated by CEA, CNRS and INRIA at the following URL
  "http://www.cecill.info".
  
  As a counterpart to the access to the source code and rights to copy,
  modify and redistribute granted by the license, users are provided only
  with a limited warranty and the software's author, the holder of the
  economic rights, and the successive licensors have only limited
  liability.
  
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  software by the user in light of its specific status of free software,
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  therefore means that it is reserved for developers and experienced
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  knowledge of the CeCILL license and that you accept its terms.
*/
 
#ifndef BPP_NUMERIC_MATRIX_LUDECOMPOSITION_H
#define BPP_NUMERIC_MATRIX_LUDECOMPOSITION_H
 
 
#include "../../Exceptions.h"
#include "../NumTools.h"
#include "Matrix.h"
 
// From the STL:
#include <algorithm>
#include <vector>
// for min(), max() below
 
namespace bpp
{
template<class Real>
class LUDecomposition
{
private:
  /* Array for internal storage of decomposition.  */
  RowMatrix<Real> LU;
  RowMatrix<Real> L_;
  RowMatrix<Real> U_;
  size_t m, n;
  int pivsign;
  std::vector<size_t> piv;
 
private:
  static void permuteCopy(const Matrix<Real>& A, const std::vector<size_t>& piv, size_t j0, size_t j1, Matrix<Real>& X)
  {
    size_t piv_length = piv.size();
 
    X.resize(piv_length, j1 - j0 + 1);
 
    for (size_t i = 0; i < piv_length; i++)
    {
      for (size_t j = j0; j <= j1; j++)
      {
        X(i, j - j0) = A(piv[i], j);
      }
    }
  }
 
  static void permuteCopy(const std::vector<Real>& A, const std::vector<size_t>& piv, std::vector<Real>& X)
  {
    size_t piv_length = piv.size();
    if (piv_length != A.size())
      X.clean();
 
    X.resize(piv_length);
 
    for (size_t i = 0; i < piv_length; i++)
    {
      X[i] = A[piv[i]];
    }
  }
 
public:
  // This is the constructor in JAMA C++ port. However, it seems to have some bug...
  // We use the original JAMA's 'experimental' port, which gives good results instead.
  /*    LUDecomposition (const Matrix<Real> &A) : LU(A), m(A.getNumberOfRows()), n(A.getNumberOfColumns()), piv(A.getNumberOfRows())
        {
 
        // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
 
 
        for (size_t i = 0; i < m; i++) {
        piv[i] = i;
        }
        pivsign = 1;
        //Real *LUrowi = 0;;
        vector<Real> LUrowi;
        vector<Real> LUcolj;
 
        // Outer loop.
 
        for (size_t j = 0; j < n; j++) {
 
        // Make a copy of the j-th column to localize references.
 
        LUcolj = LU.col(j);
        //for (size_t i = 0; i < m; i++) {
      //  LUcolj[i] = LU(i,j);
      //}
 
      // Apply previous transformations.
 
      for (size_t i = 0; i < m; i++) {
        //LUrowi = LU[i];
        LUrowi = LU.row(i);
 
        // Most of the time is spent in the following dot product.
 
        size_t kmax = NumTools::min<size_t>(i,j);
        double s = 0.0;
        for (size_t k = 0; k < kmax; k++) {
        s += LUrowi[k] * LUcolj[k];
        }
 
        LUrowi[j] = LUcolj[i] -= s;
        }
 
        // Find pivot and exchange if necessary.
 
        size_t p = j;
        for (size_t i = j+1; i < m; i++) {
        if (NumTools::abs<Real>(LUcolj[i]) > NumTools::abs<Real>(LUcolj[p])) {
        p = i;
        }
        }
        if (p != j) {
        size_t k=0;
        for (k = 0; k < n; k++) {
        double t = LU(p,k);
        LU(p,k) = LU(j,k);
        LU(j,k) = t;
        }
        k = piv[p];
        piv[p] = piv[j];
        piv[j] = k;
        pivsign = -pivsign;
        }
 
        // Compute multipliers.
 
        if ((j < m) && (LU(j,j) != 0.0)) {
        for (size_t i = j+1; i < m; i++) {
        LU(i,j) /= LU(j,j);
        }
        }
        }
        }
   */
 
  LUDecomposition (const Matrix<Real>& A) :
    LU(A),
    L_(A.getNumberOfRows(), A.getNumberOfColumns()),
    U_(A.getNumberOfColumns(), A.getNumberOfColumns()),
    m(A.getNumberOfRows()),
    n(A.getNumberOfColumns()),
    pivsign(1),
    piv(A.getNumberOfRows())
  {
    for (size_t i = 0; i < m; i++)
    {
      piv[i] = i;
    }
    // Main loop.
    for (size_t k = 0; k < n; k++)
    {
      // Find pivot.
      size_t p = k;
      for (size_t i = k + 1; i < m; i++)
      {
        if (NumTools::abs<Real>(LU(i, k)) > NumTools::abs<Real>(LU(p, k)))
        {
          p = i;
        }
      }
      // Exchange if necessary.
      if (p != k)
      {
        for (size_t j = 0; j < n; j++)
        {
          double t = LU(p, j); LU(p, j) = LU(k, j); LU(k, j) = t;
        }
        size_t t = piv[p]; piv[p] = piv[k]; piv[k] = t;
        pivsign = -pivsign;
      }
      // Compute multipliers and eliminate k-th column.
      if (LU(k, k) != 0.0)
      {
        for (size_t i = k + 1; i < m; i++)
        {
          LU(i, k) /= LU(k, k);
          for (size_t j = k + 1; j < n; j++)
          {
            LU(i, j) -= LU(i, k) * LU(k, j);
          }
        }
      }
    }
  }
 
  const RowMatrix<Real>& getL()
  {
    for (size_t i = 0; i < m; i++)
    {
      for (size_t j = 0; j < n; j++)
      {
        if (i > j)
        {
          L_(i, j) = LU(i, j);
        }
        else if (i == j)
        {
          L_(i, j) = 1.0;
        }
        else
        {
          L_(i, j) = 0.0;
        }
      }
    }
    return L_;
  }
 
  const RowMatrix<Real>& getU ()
  {
    for (size_t i = 0; i < n; i++)
    {
      for (size_t j = 0; j < n; j++)
      {
        if (i <= j)
        {
          U_(i, j) = LU(i, j);
        }
        else
        {
          U_(i, j) = 0.0;
        }
      }
    }
    return U_;
  }
 
  std::vector<size_t> getPivot () const
  {
    return piv;
  }
 
 
  Real det() const
  {
    if (m != n)
    {
      return Real(0);
    }
    Real d = Real(pivsign);
    for (size_t j = 0; j < n; j++)
    {
      d *= LU(j, j);
    }
    return d;
  }
 
  Real solve (const Matrix<Real>& B, Matrix<Real>& X) const
  {
    /* Dimensions: A is mxn, X is nxk, B is mxk */
 
    if (B.getNumberOfRows() != m)
    {
      throw BadIntegerException("Wrong dimension in LU::solve", static_cast<int>(B.getNumberOfRows()));
    }
 
    Real minD = NumTools::abs<Real>(LU(0, 0));
    for (size_t i = 1; i < m; i++)
    {
      Real currentValue = NumTools::abs<Real>(LU(i, i));
      if (currentValue < minD)
        minD = currentValue;
    }
 
    if (minD < NumConstants::SMALL())
    {
      throw ZeroDivisionException("Singular matrix in LU::solve.");
    }
 
    // Copy right hand side with pivoting
    size_t nx = B.getNumberOfColumns();
 
    permuteCopy(B, piv, 0, nx - 1, X);
 
    // Solve L*Y = B(piv,:)
    for (size_t k = 0; k < n; k++)
    {
      for (size_t i = k + 1; i < n; i++)
      {
        for (size_t j = 0; j < nx; j++)
        {
          X(i, j) -= X(k, j) * LU(i, k);
        }
      }
    }
    // Solve U*X = Y;
    // !!! Do not use unsigned int with -- loop!!!
    // for (int k = n-1; k >= 0; k--) {
    size_t k = n;
 
    do
    {
      k--;
      for (size_t j = 0; j < nx; j++)
      {
        X(k, j) /= LU(k, k);
      }
      for (size_t i = 0; i < k; i++)
      {
        for (size_t j = 0; j < nx; j++)
        {
          X(i, j) -= X(k, j) * LU(i, k);
        }
      }
    }
    while (k > 0);
 
    return minD;
  }
 
 
  Real solve (const std::vector<Real>& b, std::vector<Real>& x)  const
  {
    /* Dimensions: A is mxn, X is nxk, B is mxk */
 
    if (b.dim1() != m)
    {
      throw BadIntegerException("Wrong dimension in LU::solve", b.dim1());
    }
 
    Real minD = NumTools::abs<Real>(LU(0, 0));
    for (size_t i = 1; i < m; i++)
    {
      Real currentValue = NumTools::abs<Real>(LU(i, i));
      if (currentValue < minD)
        minD = currentValue;
    }
 
    if (minD < NumConstants::SMALL())
    {
      throw ZeroDivisionException("Singular matrix in LU::solve.");
    }
 
    permuteCopy(b, piv, x);
 
    // Solve L*Y = B(piv)
    for (size_t k = 0; k < n; k++)
    {
      for (size_t i = k + 1; i < n; i++)
      {
        x[i] -= x[k] * LU(i, k);
      }
    }
 
    // Solve U*X = Y;
    // for (size_t k = n-1; k >= 0; k--) {
    size_t k = n;
    do
    {
      k--;
      x[k] /= LU(k, k);
      for (size_t i = 0; i < k; i++)
      {
        x[i] -= x[k] * LU(i, k);
      }
    }
    while (k > 0);
 
    return minD;
  }
}; /* class LU */
} // end of namespace bpp.
#endif // BPP_NUMERIC_MATRIX_LUDECOMPOSITION_H