belfem::fem::dofmgr::EigenValues Class Reference

#include <cl_FEM_DofMgr_EigenValues.hpp>

Public Member Functions
	EigenValues (DofManager *aParent)
	~EigenValues ()
	EigenValues (const EigenValues &)=delete
	EigenValues (EigenValues &&)=delete
EigenValues &	operator= (const EigenValues &)=delete
EigenValues &	operator= (EigenValues &&)=delete
void	set_num_minvals (const index_t aNumMinVals)
void	set_num_maxvals (const index_t aNumMaxVals)
void	set_tolerance (const real aTolerance)
	relative accuracy demanded of each Ritz value.
void	set_subspace_size (const index_t aSubspaceSize)
	floor for the Krylov subspace.
void	set_max_iterations (const index_t aNumMaxIter)
	restart budget handed to ( p )dnaupd.
void	set_symmetric (const bool aSymmetric)
	declare the matrix symmetric, selecting dsaupd / dseupd over dnaupd / dneupd.
bool	is_symmetric () const
	whether the spectral ratio this object returns may be called kappa_2.
real	compute_conditioning ()
real	compute_lambda_max ()
real	compute_smallest_eigenvalues ()
	compute the eigenvalues at one end of the spectrum and return the extremal magnitude found there.
real	compute_largest_eigenvalues ()
const Vector< real > &	lambda_real () const
	real and imaginary parts of the values found by the last call above.
const Vector< real > &	lambda_imag () const
int_t	number_of_converged_values () const
	how many of the requested values actually converged
const string &	backend_label () const
	"ARPACK" or "PARPACK", whichever drove the last call
EigenOutcome	outcome () const
	how the last compute_conditioning() ended.
void	reset ()

Constructor & Destructor Documentation

EigenValues() [1/3]

belfem::fem::dofmgr::EigenValues::EigenValues

(

DofManager *

aParent

)

~EigenValues()

belfem::fem::dofmgr::EigenValues::~EigenValues

(

)

EigenValues() [2/3]

belfem::fem::dofmgr::EigenValues::EigenValues ( const EigenValues & )

delete

EigenValues() [3/3]

belfem::fem::dofmgr::EigenValues::EigenValues ( EigenValues && )

delete

Member Function Documentation

backend_label()

const string & belfem::fem::dofmgr::EigenValues::backend_label ( ) const

inline

"ARPACK" or "PARPACK", whichever drove the last call

compute_conditioning()

real belfem::fem::dofmgr::EigenValues::compute_conditioning

(

)

compute_lambda_max()

real belfem::fem::dofmgr::EigenValues::compute_lambda_max

(

)

compute_largest_eigenvalues()

real belfem::fem::dofmgr::EigenValues::compute_largest_eigenvalues

(

)

compute_smallest_eigenvalues()

real belfem::fem::dofmgr::EigenValues::compute_smallest_eigenvalues

(

)

compute the eigenvalues at one end of the spectrum and return the extremal magnitude found there.

how many are computed is set by set_num_minvals / set_num_maxvals ; the full set is exposed through lambda_real / lambda_imag

is_symmetric()

bool belfem::fem::dofmgr::EigenValues::is_symmetric ( ) const

inline

whether the spectral ratio this object returns may be called kappa_2.

That needs symmetry AND a positive definite spectrum – real eigenvalues alone are not enough

lambda_imag()

const Vector< real > & belfem::fem::dofmgr::EigenValues::lambda_imag ( ) const

inline

lambda_real()

const Vector< real > & belfem::fem::dofmgr::EigenValues::lambda_real ( ) const

inline

real and imaginary parts of the values found by the last call above.

Which ranks hold them depends on the build:

• serial, or PARPACK: valid on every rank. pdneupd returns the same spectrum everywhere
• multi-rank without PARPACK: valid on the MASTER ONLY. The master computes alone and only the scalar extremum is broadcast, so a worker's buffers stay stale

The same split applies to number_of_converged_values().

number_of_converged_values()

int_t belfem::fem::dofmgr::EigenValues::number_of_converged_values ( ) const

inline

how many of the requested values actually converged

operator=() [1/2]

EigenValues & belfem::fem::dofmgr::EigenValues::operator= ( const EigenValues & )

delete

operator=() [2/2]

EigenValues & belfem::fem::dofmgr::EigenValues::operator= ( EigenValues && )

delete

outcome()

EigenOutcome belfem::fem::dofmgr::EigenValues::outcome ( ) const

inline

how the last compute_conditioning() ended.

Identical on every rank – it is broadcast before it is stored

reset()

void belfem::fem::dofmgr::EigenValues::reset

(

)

set_max_iterations()

void belfem::fem::dofmgr::EigenValues::set_max_iterations

(

const index_t

aNumMaxIter

)

restart budget handed to ( p )dnaupd.

There is no matvec budget: one restart does NOT cost ncv - nev products ( ARPACK boosts nev internally between restarts, so np shrinks; measured 10.1 and 12.2 products per restart at ncv - nev = 19 ), so this bounds the restart count and the achieved product count is REPORTED rather than modeled

set_num_maxvals()

void belfem::fem::dofmgr::EigenValues::set_num_maxvals

(

const index_t

aNumMaxVals

)

set_num_minvals()

void belfem::fem::dofmgr::EigenValues::set_num_minvals

(

const index_t

aNumMinVals

)

set_subspace_size()

void belfem::fem::dofmgr::EigenValues::set_subspace_size

(

const index_t

aSubspaceSize

)

floor for the Krylov subspace.

Larger usually means fewer matrix-vector products but a bigger basis ( n x ncv )

set_symmetric()

void belfem::fem::dofmgr::EigenValues::set_symmetric

(

const bool

aSymmetric

)

declare the matrix symmetric, selecting dsaupd / dseupd over dnaupd / dneupd.

Lanczos is cheaper and its workspace is smaller, and for a symmetric matrix the spectral ratio IS kappa_2 – which the nonsymmetric driver cannot promise.

This is an ASSERTION BY THE CALLER, not a measurement. A matrix wrongly declared symmetric gives a wrong answer with no diagnostic: dsaupd only ever references one triangle's worth of information through the matvec, so an unsymmetric part is silently ignored rather than detected

set_tolerance()

void belfem::fem::dofmgr::EigenValues::set_tolerance

(

const real

aTolerance

)

relative accuracy demanded of each Ritz value.

The small end of the spectrum is only reachable while this stays above eps_mach * kappa – see the note at mEpsilon before lowering it. Non-positive values are rejected: ARPACK reads <= 0 as "use machine precision", which is exactly the unreachable setting on an ill conditioned matrix

---

The documentation for this class was generated from the following files:

• src/fem/kernel/cl_FEM_DofMgr_EigenValues.hpp
• src/fem/kernel/cl_FEM_DofMgr_EigenValues.cpp