xlifepp::internalEigenSolver – Functions#

applyBlockHouseholderOnTheLeft#

template<typename MatrixType, typename VectorsType, typename CoeffsType> void xlifepp::internalEigenSolver::applyBlockHouseholderOnTheLeft(MatrixType &mat, VectorsType &vectors, const CoeffsType &hCoeffs)#

directSwapping#

template<typename MatrixType> MatrixType xlifepp::internalEigenSolver::directSwapping(MatrixType &matT, unsigned int p, unsigned int q, real_t gamma)#

doComputeEigenvectorsComplexSolverInPlace#

template<typename MatrixType> void xlifepp::internalEigenSolver::doComputeEigenvectorsComplexSolverInPlace(const real_t matrixnorm, const MatrixType &schurT, const MatrixType &schurU, MatrixType &eigVec)#

doComputeEigenvectorsRealSolverInPlace#

template<typename MatrixType> void xlifepp::internalEigenSolver::doComputeEigenvectorsRealSolverInPlace(const real_t matrixnorm, const MatrixType &schurT, const MatrixType &schurU, MatrixType &eigVec)#

householderQRinplaceBlocked#

template<typename MatrixQR, typename HCoeffs> void xlifepp::internalEigenSolver::householderQRinplaceBlocked(MatrixQR &mat, HCoeffs &hCoeffs, Index maxBlockSize = 32)#

householderQRinplaceUnblocked#

template<typename MatrixQR, typename HCoeffs> void xlifepp::internalEigenSolver::householderQRinplaceUnblocked(MatrixQR &mat, HCoeffs &hCoeffs)#

makeBlockHouseholderTriangularFactor#

template<typename TriangularFactorType, typename VectorsType, typename CoeffsType> void xlifepp::internalEigenSolver::makeBlockHouseholderTriangularFactor(TriangularFactorType &triFactor, VectorsType &vectors, const CoeffsType &hCoeffs)#

printOutDebugInfoEigenProblem#

inline void xlifepp::internalEigenSolver::printOutDebugInfoEigenProblem(const string_t &nameOfClass, const string_t &message)#

swapComplexSchurInPlace#

template<typename MatrixType> void xlifepp::internalEigenSolver::swapComplexSchurInPlace(MatrixType &matrixT, const std::vector<int> &order)#

template<typename MatrixType> void xlifepp::internalEigenSolver::swapComplexSchurInPlace(MatrixType &matrixT, MatrixType &matrixQ, const std::vector<int> &order)#

swapRealSchurInPlace#

template<typename MatrixType> void xlifepp::internalEigenSolver::swapRealSchurInPlace(MatrixType &matrixT, MatrixType &matrixQ, unsigned int ifst, unsigned int ilst)#

Given the quasi-triangular matrix T and orthogonal matrix Q obtained from the real Schur decomposition, this function reorders the eigenvalues appearing on the (block) diagonal of matrix T The diagonal element of block of T with row index ifst is moved to row ilst.

This is implemented from “On Swapping Diagonal Blocks in Real Schur Form”

Parameters:

matrixT – [inout] quasi-triangular matrix of real Schur decomposition
matrixQ – [inout] orthogonal of real Schur decomposition
ifst – [in] index of row needs moving
ilst – [in] index of destination row

testErrorEigenProblem#

inline void xlifepp::internalEigenSolver::testErrorEigenProblem(bool condition, const string_t &s)#

testErrorEigenProblemMultVec#

inline void xlifepp::internalEigenSolver::testErrorEigenProblemMultVec(bool condition, const string_t &s)#

testWarningEigenProblem#

inline void xlifepp::internalEigenSolver::testWarningEigenProblem(bool condition, const string_t &s)#

tridiagonalizationInplace#

template<typename MatrixType, typename DiagonalType, typename SubDiagonalType> void xlifepp::internalEigenSolver::tridiagonalizationInplace(MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ)#

Performs a full tridiagonalization in place.

Computes the tridiagonal decomposition of the selfadjoint matrix mat in place such that \( mat = Q T Q^* \) where \( Q \) is unitary and \( T \) a real symmetric tridiagonal matrix.

The tridiagonal matrix T is passed to the output parameters diag and subdiag. If extractQ is true, then the orthogonal matrix Q is passed to mat. Otherwise the lower part of the matrix mat is destroyed.

The vectors diag and subdiag are not resized. The function assumes that they are already of the correct size. The length of the vector diag should equal the number of rows in mat, and the length of the vector subdiag should be one left.

See also

class Tridiagonalization

Parameters:

mat – [inout] On input, the selfadjoint matrix whose tridiagonal decomposition is to be computed. Only the lower triangular part referenced. The rest is left unchanged. On output, the orthogonal matrix Q in the decomposition if extractQ is true.
diag – [out] The diagonal of the tridiagonal matrix T in the decomposition.
subdiag – [out] The subdiagonal of the tridiagonal matrix T in the decomposition.
extractQ – [in] If true, the orthogonal matrix Q in the decomposition is computed and stored in mat.

Note

Currently, it requires two temporary vectors to hold the intermediate Householder coefficients, and to reconstruct the matrix Q from the Householder reflectors.

template<typename MatrixType, typename CoeffVectorType> void xlifepp::internalEigenSolver::tridiagonalizationInplace(MatrixType &matA, CoeffVectorType &hCoeffs)#

Performs a tridiagonal decomposition of the selfadjoint matrix matA in-place.

On output, the tridiagonal selfadjoint matrix T is stored in the diagonal and lower sub-diagonal of the matrix matA. The unitary matrix Q is represented in a compact way as a product of Householder reflectors \( H_i \) such that: \( Q = H_{N-1} \ldots H_1 H_0 \). The Householder reflectors are defined as \( H_i = (I - h_i v_i v_i^T) \) where \( h_i = hCoeffs[i]\) is the \( i \)th Householder coefficient and \( v_i \) is the Householder vector defined by \( v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \).

Implemented from Golub’s “Matrix Computations”, algorithm 8.3.1.

tridiagonalizationUpperInplace#

template<typename MatrixType, typename CoeffVectorType> void xlifepp::internalEigenSolver::tridiagonalizationUpperInplace(MatrixType &matA, CoeffVectorType &hCoeffs)#