m_mform_eigensolver Module Reference

Module that provides an interface to SLEPc for solving (generalized) eigenvalue problems. More...

Data Types
interface	eigeninitoptions
type	eigensolver
	Type that wraps SLEPc functionality for solving (generalized) eigenvalue problems. More...

Functions/Subroutines
type(eigeninitoptions) function	init_eigeninitoptions (ksp_type, pc_type, hypre_type, rtol, atol, max_iter, verbosity, which, target, target_interval, eps_type)
	Initialize an EigenInitOptions object.
subroutine	init_eigen_options_from_traits (this, traits)
	Select solver options for eigenvalue problems, favouring direct solvers (MUMPS)
subroutine	eigensolver_init (this, amat, bmat, constraint1, constraint2, constraint3, coord_transform, options)
	Initialize the eigensolver.
subroutine	eigensolver_solve (this, rtol, max_iter, nr_pairs, verbosity)
	Solve the eigenvalue problem.
subroutine	eigensolver_get_eigenpair (this, index, val_r, fun_r, val_i, fun_i, err_est)
	Get an eigenpair.
subroutine	eigensolver_get_eigenvalues (this, vals_r, vals_i)
	Get all computed eigenvalues.
subroutine	eigensolver_destroy (this)
	Destroy the eigensolver and free associated resources.

Detailed Description

Module that provides an interface to SLEPc for solving (generalized) eigenvalue problems.

Function/Subroutine Documentation

eigensolver_destroy()

subroutine m_mform_eigensolver::eigensolver_destroy

(

class(eigensolver), intent(inout)

this

)

Destroy the eigensolver and free associated resources.

Parameters

this	The EigenSolver object

eigensolver_get_eigenpair()

subroutine m_mform_eigensolver::eigensolver_get_eigenpair	(	class(eigensolver), intent(in)	this,
		integer, intent(in)	index,
		real(wp), intent(out)	val_r,
		type(mformfun), intent(out)	fun_r,
		real(wp), intent(out), optional	val_i,
		type(mformfun), intent(out), optional	fun_i,
		real(wp), intent(out), optional	err_est )

Get an eigenpair.

Parameters

this	The EigenSolver object
index	The index of the eigenpair to get (1-based)
val_r	The real part of the eigenvalue
fun_r	The real part of the eigenfunction
val_i	_(optional)_ The imaginary part of the eigenvalue
fun_i	_(optional)_ The imaginary part of the eigenfunction
err_est	_(optional)_ The error estimate for the eigenpair

eigensolver_get_eigenvalues()

subroutine m_mform_eigensolver::eigensolver_get_eigenvalues	(	class(eigensolver), intent(in)	this,
		real(wp), dimension(:), intent(out), allocatable	vals_r,
		real(wp), dimension(:), intent(out), optional, allocatable	vals_i )

Get all computed eigenvalues.

Parameters

this	The EigenSolver object
vals_r	The real parts of the eigenvalues
vals_i	_(optional)_ The imaginary parts of the eigenvalues

eigensolver_init()

subroutine m_mform_eigensolver::eigensolver_init	(	class(eigensolver), intent(inout)	this,
		class(abstractmatrix), intent(in)	amat,
		class(abstractmatrix), intent(in), optional	bmat,
		class(mformconstraintlocal), intent(in), optional	constraint1,
		class(mformconstraintlocal), intent(in), optional	constraint2,
		class(mformconstraintlocal), intent(in), optional	constraint3,
		class(coordtransformabstract), intent(in), optional	coord_transform,
		type(eigeninitoptions), intent(in), optional	options )

Initialize the eigensolver.

Parameters

	this	The EigenSolver object
	amat	The matrix A in the eigenvalue problem: $A x = \lambda x$
	bmat	_(optional)_ The matrix B in the eigenvalue problem: $A x = \lambda B x$
[in]	constraint1	_(optional)_ An optional constraint to be applied to the solution
[in]	constraint2	_(optional)_ An optional constraint to be applied to the solution
[in]	constraint3	_(optional)_ An optional constraint to be applied to the solution
[in]	coord_transform	_(optional)_ The coordinate transformation associated with the m-form spaces
	options	_(optional)_ The options for initializing the eigensolver (default: auto-select based on traits)

eigensolver_solve()

subroutine m_mform_eigensolver::eigensolver_solve	(	class(eigensolver), intent(inout)	this,
		real(wp), intent(in), optional	rtol,
		integer, intent(in), optional	max_iter,
		integer, intent(in), optional	nr_pairs,
		integer, intent(in), optional	verbosity )

Solve the eigenvalue problem.

Parameters

this	The EigenSolver object
rtol	_(optional)_ The relative tolerance (default: 1.e-8)
max_iter	_(optional)_ The maximum number of iterations (default: size of the space)
nr_pairs	_(optional)_ The number of eigenpairs to compute (default: 6)
verbosity	_(optional)_ The verbosity level (default: VERBOSITY_WARN_ON_FAILURE) VERBOSITY_WARN_NEVER VERBOSITY_WARN_ON_FAILURE VERBOSITY_WARN_ALWAYS VERBOSITY_ERROR_ON_FAILURE

init_eigen_options_from_traits()

subroutine m_mform_eigensolver::init_eigen_options_from_traits	(	class(eigeninitoptions), intent(inout)	this,
		type(solverinittraits), intent(in)	traits )

Select solver options for eigenvalue problems, favouring direct solvers (MUMPS)

Eigenvalue solvers require highly accurate linear solves inside the spectral transform. Iterative methods with standard preconditioners often lack the accuracy needed for convergence of multiple eigenpairs. This override defaults to a direct solver (PREONLY + Cholesky/LU with MUMPS) which works both in serial and parallel.

Parameters

this	The EigenInitOptions object
traits	The solver traits derived from matrix properties

init_eigeninitoptions()

type(eigeninitoptions) function m_mform_eigensolver::init_eigeninitoptions	(	character(*), intent(in), optional	ksp_type,
		character(*), intent(in), optional	pc_type,
		character(*), intent(in), optional	hypre_type,
		real(wp), intent(in), optional	rtol,
		real(wp), intent(in), optional	atol,
		integer, intent(in), optional	max_iter,
		character(len=80), intent(in), optional	verbosity,
		character(*), intent(in), optional	which,
		real(wp), intent(in), optional	target,
		real(wp), dimension(2), intent(in), optional	target_interval,
		character(*), intent(in), optional	eps_type )

Initialize an EigenInitOptions object.

Parameters

ksp_type	_(optional)_ The KSP type to use (default: auto-select based on traits)
pc_type	_(optional)_ The PC type to use (default: auto-select based on traits)
hypre_type	_(optional)_ The HYPRE preconditioner type to use (default: auto-select based on traits)
rtol	_(optional)_ The relative tolerance (default: 1.e-10)
atol	_(optional)_ The absolute tolerance (default: 1.e-20)
max_iter	_(optional)_ The maximum number of iterations (default: size of the space)
verbosity	_(optional)_ The verbosity level (default: 'warn on failure') 'warn never' 'warn on failure' 'warn always' 'error on failure'
which	_(optional)_ Which part of the spectrum to compute. Possible values are:
which	_(optional)_ Which part of the spectrum to compute. Possible values are: 'largest magnitude' or 'lm' (default) 'smallest magnitude' or 'sm' 'largest real' or 'lr' 'smallest real' or 'sr' 'largest imaginary' or 'li' 'smallest imaginary' or 'si' 'target magnitude' or 'tm' 'target real' or 'tr' 'target imaginary' or 'ti' 'target interval' or 'all'
target	_(optional)_ The target value if 'which' is a target option
target_interval	_(optional)_ The target interval if 'which' is 'all'
eps_type	_(optional)_ The type of eigensolver to use (default: 'krylovschur'). Possible values are: 'power' 'subspace' 'arnoldi' 'lanczos' 'krylovschur' 'gd' 'jd' or 'jacobi davidson' 'rqcg' 'lobpcg' 'ciss' 'lyapii' 'lapack' 'arpack' 'blopex' 'primme' 'feast' 'scalapack' 'elpa' 'elemental' 'evsl' 'chase'