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# EPSLyapIISetRanks

Set the ranks used in the solution of the Lyapunov equation.

## Synopsis

    #include "slepceps.h"
    PetscErrorCode EPSLyapIISetRanks(EPS eps,PetscInt rkc,PetscInt rkl)

Logically Collective

## Input Parameters

- eps - the linear eigensolver context

- rkc - the compressed rank

- rkl - the Lyapunov rank

## Options Database Key

- -eps_lyapii_ranks <rkc,rkl> - sets the rank parameters

## Notes

`PETSC_CURRENT` can be used to preserve the current value of any of the arguments, and `PETSC_DETERMINE` to set them to a default value.

Lyapunov inverse iteration needs to solve a large-scale Lyapunov equation at each iteration of the eigensolver. For this, an iterative solver (`LME`) is used, which requires to prescribe the rank of the solution matrix \(X\). This is the meaning of parameter `rkl`. Later, this matrix is compressed into another matrix of rank `rkc`. If not provided, `rkl` is a small multiple of `rkc`.

## See Also

EPS: Eigenvalue Problem Solver, `EPSLYAPII`, `EPSLyapIIGetRanks()`

## Level

intermediate

## Location

src/eps/impls/lyapii/lyapii.c

## Implementations

EPSLyapIISetRanks_LyapII() in src/eps/impls/lyapii/lyapii.c

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