Spectra
1.0.1
Headeronly C++ Library for Large Scale Eigenvalue Problems

#include <Spectra/SymGEigsShiftSolver.h>
Public Member Functions  
SymGEigsShiftSolver (OpType &op, BOpType &Bop, Index nev, Index ncv, const Scalar &sigma)  
Public Member Functions inherited from Spectra::SymEigsBase< SymGEigsCayleyOp< OpType, BOpType >, BOpType >  
void  init (const Scalar *init_resid) 
void  init () 
Index  compute (SortRule selection=SortRule::LargestMagn, Index maxit=1000, Scalar tol=1e10, SortRule sorting=SortRule::LargestAlge) 
CompInfo  info () const 
Index  num_iterations () const 
Index  num_operations () const 
Vector  eigenvalues () const 
virtual Matrix  eigenvectors (Index nvec) const 
virtual Matrix  eigenvectors () const 
This class implements the generalized eigen solver for real symmetric matrices using the Cayley spectral transformation. The original problem is to solve \(Ax=\lambda Bx\), where \(A\) is symmetric and \(B\) is positive definite. The transformed problem is \((A\sigma B)^{1}(A+\sigma B)x=\nu x\), where \(\nu=(\lambda+\sigma)/(\lambda\sigma)\), and \(\sigma\) is a userspecified shift.
This solver requires two matrix operation objects: one to compute \(y=(A\sigma B)^{1}x\) for any vector \(v\), and one for the matrix multiplication \(Bv\).
If \(A\) and \(B\) are stored as Eigen matrices, then the first operation object can be created using the SymShiftInvert class, and the second one can be created using the DenseSymMatProd or SparseSymMatProd classes. If the users need to define their own operation classes, then they should implement all the public member functions as in those builtin classes.
OpType  The type of the first operation object. Users could either use the wrapper class SymShiftInvert, or define their own that implements the type definition Scalar and all the public member functions as in SymShiftInvert. 
BOpType  The name of the matrix operation class for \(B\). Users could either use the wrapper classes such as DenseSymMatProd and SparseSymMatProd, or define their own that implements all the public member functions as in DenseSymMatProd. 
Mode  Mode of the generalized eigen solver. In this solver it is Spectra::GEigsMode::Cayley. 
Definition at line 399 of file SymGEigsShiftSolver.h.

inline 
Constructor to create a solver object.
op  The matrix operation object that computes \(y=(A\sigma B)^{1}v\) for any vector \(v\). Users could either create the object from the wrapper class SymShiftInvert, or define their own that implements all the public members as in SymShiftInvert. 
Bop  The \(B\) matrix operation object that implements the matrixvector multiplication \(Bv\). Users could either create the object from the wrapper classes such as DenseSymMatProd and SparseSymMatProd, or define their own that implements all the public member functions as in DenseSymMatProd. \(B\) needs to be positive definite. 
nev  Number of eigenvalues requested. This should satisfy \(1\le nev \le n1\), where \(n\) is the size of matrix. 
ncv  Parameter that controls the convergence speed of the algorithm. Typically a larger ncv means faster convergence, but it may also result in greater memory use and more matrix operations in each iteration. This parameter must satisfy \(nev < ncv \le n\), and is advised to take \(ncv \ge 2\cdot nev\). 
sigma  The value of the shift. 
Definition at line 455 of file SymGEigsShiftSolver.h.