MatCreateBSE#

Create a matrix that can be used to define a structured eigenvalue problem of type BSE (Bethe-Salpeter Equation).

Synopsis#

#include "slepcsys.h" 
PetscErrorCode MatCreateBSE(Mat R,Mat C,Mat *H)

Collective

Input Parameters#

  • R - matrix for the diagonal block (resonant)

  • C - matrix for the off-diagonal block (coupling)

Output Parameter#

  • H - the resulting matrix

Notes#

The resulting matrix has the block form

\[\begin{split}H = \begin{bmatrix} R & C \\ -C^* & -R^T \end{bmatrix},\end{split}\]
where \(R\) is assumed to be (complex) Hermitian and \(C\) complex symmetric. Note that this function does not check these properties, so if the matrices provided by the user do not satisfy them, then the solver will not behave as expected.

The obtained matrix can be used as an input matrix to EPS eigensolvers via EPSSetOperators() for the case that the problem type is EPS_BSE. Note that the user cannot just build a matrix with the required structure, it must be done via this function.

In the current implementation, H is a MATNEST matrix, where R and C form the top block row, while the bottom block row is composed of matrices of type MATTRANSPOSEVIRTUAL and MATHERMITIANTRANSPOSEVIRTUAL scaled by -1.

See Also#

Structured Eigenvalue Problems, MatCreateNest(), EPSSetOperators(), EPSSetProblemType(), MatCreateHamiltonian()

Level#

intermediate

Location#

src/sys/mat/matstruct.c

Examples#

src/eps/tutorials/ex55.c

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