CholeskyDecomposition.hpp

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 *
 * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [4] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [5] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [6] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [7] Lamichhane, Newman & Gezelter, J. Chem. Phys. 141, 134110 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 */
 
#include "math/Vector.hpp"
 
#ifndef MATH_CHOLESKYDECOMPOSITION_HPP
#define MATH_CHOLESKYDECOMPOSITION_HPP
 
using namespace std;
namespace OpenMD {
 
  template<class MatrixType>
  void CholeskyDecomposition(MatrixType& A, MatrixType& L) {
    unsigned int n = A.getNRow();
    assert(n == A.getNCol() && n == L.getNRow() && n == L.getNCol());
 
    bool isspd(true);
    RealType eps =
        A.diagonals().abs().max() * (numeric_limits<RealType>::epsilon()) / 100;
 
    for (unsigned int j = 0; j < n; j++) {
      RealType d(0.0);
      for (unsigned int k = 0; k < j; k++) {
        RealType s(0.0);
 
        for (unsigned int i = 0; i < k; i++) {
          s += L(k, i) * L(j, i);
        }
 
        // if L(k,k) != 0
        if (std::abs(L(k, k)) > eps) {
          s = (A(j, k) - s) / L(k, k);
        } else {
          s     = (A(j, k) - s);
          isspd = false;
        }
        L(j, k) = s;
        d       = d + s * s;
 
        // this is approximately doing: isspd = isspd && ( A(k,j) == A(j,k) )
        isspd = isspd && (abs(A(k, j) - A(j, k)) < eps);
      }
      d       = A(j, j) - d;
      isspd   = isspd && (d > eps);
      L(j, j) = sqrt(d > 0.0 ? d : 0.0);
      for (unsigned int k = j + 1; k < n; k++) {
        L(j, k) = 0.0;
      }
    }
  }
}  // namespace OpenMD
 
#endif