Eigensolver Class Reference

Collaboration diagram for Eigensolver:

Static Public Member Functions
static void	solveGeneralizedEigenvalues (Matrix< Real > &A, Matrix< Real > &B, std::vector< Real > &eigenvals, Matrix< Real > &eigenvectors)
	Use generalized eigenvalue solver. More...
static void	solveGeneralizedEigenvalues_Inv (Matrix< Real > &A, Matrix< Real > &B, std::vector< Real > &eigenvals, Matrix< Real > &eigenvectors)
	Solve by explicitly inverting the overlap matrix. More...

Private Types
using	Real = QMCTraits::RealType

Detailed Description

Definition at line 28 of file Eigensolver.h.

Member Typedef Documentation

Real

using Real = QMCTraits::RealType

private

Definition at line 30 of file Eigensolver.h.

Member Function Documentation

solveGeneralizedEigenvalues()

void solveGeneralizedEigenvalues ( Matrix< Real > &  A, Matrix< Real > &  B, std::vector< Real > &  eigenvals, Matrix< Real > &  eigenvectors  )

static

Use generalized eigenvalue solver.

Parameters

[in]	A	Hamiltonian matrix
[in]	B	Overlap matrix
[out]	eigenvals	Eigenvalues
[out]	eigenvectors	Eigenvectors corresponding to the eigenvalues

Definition at line 32 of file Eigensolver.cpp.

References qmcplusplus::Units::distance::A, B(), Matrix< T, Alloc >::cols(), Matrix< T, Alloc >::data(), LAPACK::ggev(), and Matrix< T, Alloc >::rows().

Referenced by LinearMethod::getLowestEigenvector_Gen(), and qmcplusplus::TEST_CASE().

{
  int Nl = A.rows();
  assert(A.rows() == A.cols());
  assert(Nl == eigenvals.size());
  assert(Nl == eigenvectors.rows());
  assert(Nl == eigenvectors.cols());

  // transpose the A and B (row-major vs. column-major)
  for (int i = 0; i < Nl; i++)
    for (int j = i + 1; j < Nl; j++)
    {
      std::swap(A(i, j), A(j, i));
      std::swap(B(i, j), B(j, i));
    }

  //   Getting the optimal worksize
  char jl('N');
  char jr('V');
  std::vector<Real> alphar(Nl), alphai(Nl), beta(Nl);
  //Matrix<Real> eigenT(Nl, Nl);
  int info;
  int lwork(-1);
  std::vector<Real> work(1);
  Real tt(0);
  int t(1);
  LAPACK::ggev(&jl, &jr, &Nl, A.data(), &Nl, B.data(), &Nl, alphar.data(), alphai.data(), beta.data(), &tt, &t,
               eigenvectors.data(), &Nl, work.data(), &lwork, &info);
  lwork = int(work[0]);
  work.resize(lwork);

  LAPACK::ggev(&jl, &jr, &Nl, A.data(), &Nl, B.data(), &Nl, alphar.data(), alphai.data(), beta.data(), &tt, &t,
               eigenvectors.data(), &Nl, work.data(), &lwork, &info);
  if (info != 0)
    throw std::runtime_error("Invalid Matrix Diagonalization Function, ggev info = " + std::to_string(info));

  for (int i = 0; i < Nl; i++)
    eigenvals[i] = alphar[i] / beta[i];
}

solveGeneralizedEigenvalues_Inv()

void solveGeneralizedEigenvalues_Inv ( Matrix< Real > &  A, Matrix< Real > &  B, std::vector< Real > &  eigenvals, Matrix< Real > &  eigenvectors  )

static

Solve by explicitly inverting the overlap matrix.

Parameters

[in]	A	Hamiltonian matrix
[in]	B	Overlap matrix
[out]	eigenvals	Eigenvalues
[out]	eigenvectors	Eigenvectors corresponding to the eigenvalues

Definition at line 78 of file Eigensolver.cpp.

References qmcplusplus::Units::distance::A, B(), Matrix< T, Alloc >::cols(), Matrix< T, Alloc >::data(), LAPACK::geev(), qmcplusplus::invert_matrix(), qmcplusplus::MatrixOperators::product(), and Matrix< T, Alloc >::rows().

Referenced by LinearMethod::getLowestEigenvector_Inv(), and qmcplusplus::TEST_CASE().

{
  int Nl = A.rows();
  assert(A.rows() == A.cols());
  assert(Nl == eigenvals.size());
  assert(Nl == eigenvectors.rows());
  assert(Nl == eigenvectors.cols());

  invert_matrix(B, false);

  Matrix<Real> prdMat(Nl, Nl);

  MatrixOperators::product(B, A, prdMat);

  // transpose the result (why?)
  for (int i = 0; i < Nl; i++)
    for (int j = i + 1; j < Nl; j++)
      std::swap(prdMat(i, j), prdMat(j, i));

  //   Getting the optimal worksize
  char jl('N');
  char jr('V');
  std::vector<Real> alphai(Nl);
  Matrix<Real> eigenD(Nl, Nl);
  int info;
  int lwork(-1);
  std::vector<Real> work(1);
  LAPACK::geev(&jl, &jr, &Nl, prdMat.data(), &Nl, eigenvals.data(), alphai.data(), eigenD.data(), &Nl,
               eigenvectors.data(), &Nl, work.data(), &lwork, &info);
  lwork = int(work[0]);
  work.resize(lwork);

  LAPACK::geev(&jl, &jr, &Nl, prdMat.data(), &Nl, eigenvals.data(), alphai.data(), eigenD.data(), &Nl,
               eigenvectors.data(), &Nl, work.data(), &lwork, &info);
  if (info != 0)
    throw std::runtime_error("Invalid Matrix Diagonalization Function, geev info = " + std::to_string(info));
}

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The documentation for this class was generated from the following files:

• /home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/QMCDrivers/WFOpt/Eigensolver.h
• /home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/QMCDrivers/WFOpt/Eigensolver.cpp