HCL_IRArnoldi

class HCL_IRArnoldi_d : public HCL_ItEigSolver_d

HCL_IRArnoldi_d implements the implicitly restarted Arnoldi algorithm for solving the (generalized) eigenvalue problem

Inheritance:

Public

Inherited from HCL_ItEigSolver_d:

Inherited from HCL_Base:

Public Methods
int Count()
void DecCount()
void IncCount()

Private Fields
int ReferenceCount

Documentation

HCL_IRArnoldi_d implements the implicitly restarted Arnoldi algorithm for solving the (generalized) eigenvalue problem. The algorithm computes approximations to a few eigenpairs of of a linear operator. Optionally, this can be done with respect to the semi-inner prouct defined by a positive semi-definite linear operator B. This is an adaptation of the algorithm inplemented in ARPACK.
References:
R.B. Lehoucq, D.C. Sorensen & C. Yang, "ARPACK Users Guide"

Methods

virtual Table& Parameters()
Access to parameter table. Algorithmic parameters can be accessed with Parameters().GetValue("NAME",val) or changed with Parameters().PutValue("NAME",val).

int Solve( int &nev, HCL_LinearOp_d &A, HCL_Vector_d &x )
Solve A*x = lambda*x
Returns:
The value of TermCode (See the Parameters section of this document.)
Parameters:
nev - Number of eigenvalues wanted. On output this contains the number of eigenvalues actually computed.
A - Linear operator.
x - Vector to start Arnoldi iteration. This is changed by the function, and does not have a meaningful value on return.

int Solve( int &nev, HCL_LinearOp_d &OP, double sigmar, HCL_Vector_d &resid )
Solve A*x = lambda*x using shift-and-invert mode. Eigenvalues near the real shift 'sigmar' will be emphasized during the iteration. Note that the user must supply the linear operator 'OP', rather than 'A'.
Returns:
The value of TermCode (See the Parameters section of this document.)
Parameters:
nev - Number of eigenvalues wanted. On output this contains the number of eigenvalues actually computed.
OP - Linear operator Inv[A-sigmar*I].
sigmar - Real shift to apply.
x - Vector to start Arnoldi iteration. This is changed by the function, and does not have a meaningful value on return.

int Solve( int &nev, HCL_LinearOp_d &OP, HCL_LinearOp_d &M, HCL_Vector_d &x )
Solve A*x = lambda*M*x, with M symmetric positive semi-definite. Note that the user must supply the linear operator 'OP', rather than 'A'.
Returns:
The value of TermCode (See the Parameters section of this document.)
Parameters:
nev - Number of eigenvalues wanted. On output this contains the number of eigenvalues actually computed.
OP - Linear operator Inv[M]*A.
x - Vector to start Arnoldi iteration. This is changed by the function, and does not have a meaningful value on return.

int Solve( int &nev, HCL_LinearOp_d &OP, HCL_LinearOp_d &M, double sigmar, HCL_Vector_d &x)
Solve A*x = lambda*M*x with M symmetric positive semi-definite, and using shift-and-invert mode. Eigenvalues near the real shift 'sigmar' will be emphasized during the iteration. Note that the user must supply the linear operator 'OP', rather than 'A'.
Returns:
The value of TermCode (See the Parameters section of this document.)
Parameters:
nev - Number of eigenvalues wanted. On output this contains the number of eigenvalues actually computed.
OP - Linear operator Inv[A-sigmar*M]*M.
sigmar - Real shift to apply.
x - Vector to start Arnoldi iteration. This is changed by the function, and does not have a meaningful value on return.

virtual int Eigenvalue( int i, double &eigr, double &eigi )
Access to eigenvalues computed by Solve()
Returns:
Nonzero if 'i' is not valid or if Solve() has not been called.
Parameters:
i - Which eigenvalue to return. (Must be between 1 and the number of eigenvalues computed in Solve())
eigr - Returns the real part of the ith eigenvalue.
eigi - Returns the imaginary part of the ith eigenvalue.

virtual int Eigenvalue( int i, double &eigr )
Access to (real part of) eigenvalues computed by Solve()
Returns:
Nonzero if 'i' is not valid or if Solve() has not been called.
Parameters:
i - Which eigenvalue to return. (Must be between 1 and the number of eigenvalues computed in Solve())
eigr - Returns the real part of the ith eigenvalue.

int EigPair(int i, double &eigr, double &eigi, HCL_Vector_d *vr, HCL_Vector_d *vi)
Access to eigenvalues and eigenvectors computed by Solve()
Returns:
Nonzero if 'i' is not valid or if Solve() has not been called.
Parameters:
i - Which eigenpair to return. (Must be between 1 and the number of eigenvalues computed in Solve())
eigr - Returns the real part of the ith eigenvalue.
eigi - Returns the imaginary part of the ith eigenvalue.
eigr - Returns the real part of the ith eigenvector.
eigi - Returns the imaginary part of the ith eigenvector.

Input Parameters

In a parameter file, these names may be prepended by "ItEigSolver::" or "IRArnoldi::"

int SubspaceDim

Dimension of Krylov subspace. The algorithm will allocate roughly this many vectors in the domain of the problem. Increasing this value will generally improve convergence. SubspaceDim must satisfy 2*nev < SubspaceDim < Dim(A).
Default = 2*nev + 1

char Which[2]