Package slepc4py :: Module SLEPc :: Class PEP
[hide private]
[frames] | no frames]

Class PEP


PEP
Nested Classes [hide private]
  Basis
  Conv
PEP convergence test
  ConvergedReason
PEP convergence reasons
  ErrorType
PEP error type to assess accuracy of computed solutions
  Extract
Extraction strategy used to obtain eigenvectors of the PEP from the eigenvectors of the linearization
  ProblemType
PEP problem type
  Refine
PEP refinement strategy
  RefineScheme
Scheme for solving linear systems during iterative refinement
  Scale
PEP scaling strategy
  Type
PEP type
  Which
PEP desired part of spectrum
Instance Methods [hide private]
a new object with type S, a subtype of T
__new__(S, ...)
 
appendOptionsPrefix(self, prefix)
Appends to the prefix used for searching for all PEP options in the database.
 
cancelMonitor(self)
Clears all monitors for a PEP object.
 
computeError(self, int i, etype=None)
Computes the error (based on the residual norm) associated with the i-th computed eigenpair.
 
create(self, comm=None)
Creates the PEP object.
 
destroy(self)
Destroys the PEP object.
 
errorView(self, etype=None, Viewer viewer=None)
Displays the errors associated with the computed solution (as well as the eigenvalues).
 
getBV(self)
Obtain the basis vectors object associated to the eigensolver.
 
getBasis(self)
Gets the type of polynomial basis used to describe the polynomial eigenvalue problem.
 
getConverged(self)
Gets the number of converged eigenpairs.
 
getConvergedReason(self)
Gets the reason why the solve() iteration was stopped.
 
getConvergenceTest(self)
Return the method used to compute the error estimate used in the convergence test.
 
getDimensions(self)
Gets the number of eigenvalues to compute and the dimension of the subspace.
 
getEigenpair(self, int i, Vec Vr=None, Vec Vi=None)
Gets the i-th solution of the eigenproblem as computed by solve().
 
getErrorEstimate(self, int i)
Returns the error estimate associated to the i-th computed eigenpair.
 
getIterationNumber(self)
Gets the current iteration number.
 
getLinearCompanionForm(self)
Returns the number of the companion form that will be used for the linearization of a quadratic eigenproblem.
 
getLinearEPS(self)
Retrieve the eigensolver object (EPS) associated to the polynomial eigenvalue solver.
 
getLinearExplicitMatrix(self)
Returns the flag indicating if the matrices A and B for the linearization are built explicitly.
 
getOperators(self)
Gets the matrices associated with the eigenvalue problem.
 
getOptionsPrefix(self)
Gets the prefix used for searching for all PEP options in the database.
 
getProblemType(self)
Gets the problem type from the PEP object.
 
getRG(self)
Obtain the region object associated to the eigensolver.
 
getRefine(self)
Gets the refinement strategy used by the PEP object, and the associated parameters.
 
getST(self)
Obtain the spectral transformation (ST) object associated to the eigensolver object.
 
getScale(self, Vec Dl=None, Vec Dr=None)
Gets the strategy used for scaling the polynomial eigenproblem.
 
getTolerances(self)
Gets the tolerance and maximum iteration count used by the default PEP convergence tests.
 
getTrackAll(self)
Returns the flag indicating whether all residual norms must be computed or not.
 
getType(self)
Gets the PEP type of this object.
 
getWhichEigenpairs(self)
Returns which portion of the spectrum is to be sought.
 
reset(self)
Resets the PEP object.
 
setBV(self, BV bv)
Associates a basis vectors object to the eigensolver.
 
setBasis(self, basis)
Specifies the type of polynomial basis used to describe the polynomial eigenvalue problem.
 
setConvergenceTest(self, conv)
Specifies how to compute the error estimate used in the convergence test.
 
setDimensions(self, nev=None, ncv=None, mpd=None)
Sets the number of eigenvalues to compute and the dimension of the subspace.
 
setFromOptions(self)
Sets PEP options from the options database.
 
setInitialSpace(self, space)
Sets the initial space from which the eigensolver starts to iterate.
 
setLinearCompanionForm(self, cform)
Choose between the two companion forms available for the linearization of a quadratic eigenproblem.
 
setLinearEPS(self, EPS eps)
Associate an eigensolver object (EPS) to the polynomial eigenvalue solver.
 
setLinearExplicitMatrix(self, flag)
Indicate if the matrices A and B for the linearization of the problem must be built explicitly.
 
setOperators(self, operators)
Sets the matrices associated with the eigenvalue problem.
 
setOptionsPrefix(self, prefix)
Sets the prefix used for searching for all PEP options in the database.
 
setProblemType(self, problem_type)
Specifies the type of the eigenvalue problem.
 
setRG(self, RG rg)
Associates a region object to the eigensolver.
 
setRefine(self, ref, npart=None, tol=None, its=None, scheme=None)
Sets the refinement strategy used by the PEP object, and the associated parameters.
 
setST(self, ST st)
Associates a spectral transformation object to the eigensolver.
 
setScale(self, scale, alpha=None, Vec Dl=None, Vec Dr=None, its=None, lbda=None)
Sets the scaling strategy to be used for scaling the polynomial problem before attempting to solve.
 
setTolerances(self, tol=None, max_it=None)
Sets the tolerance and maximum iteration count used by the default PEP convergence tests.
 
setTrackAll(self, trackall)
Specifies if the solver must compute the residual of all approximate eigenpairs or not.
 
setType(self, pep_type)
Selects the particular solver to be used in the PEP object.
 
setUp(self)
Sets up all the internal data structures necessary for the execution of the eigensolver.
 
setWhichEigenpairs(self, which)
Specifies which portion of the spectrum is to be sought.
 
solve(self)
Solves the eigensystem.
 
view(self, Viewer viewer=None)
Prints the PEP data structure.

Inherited from petsc4py.PETSc.Object: __copy__, __deepcopy__, __eq__, __ge__, __gt__, __le__, __lt__, __ne__, __nonzero__, compose, decRef, getAttr, getClassId, getClassName, getComm, getDict, getName, getRefCount, getTabLevel, incRef, incrementTabLevel, query, setAttr, setName, setTabLevel, stateIncrease

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __init__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties [hide private]

Inherited from petsc4py.PETSc.Object: classid, comm, fortran, handle, klass, name, prefix, refcount, type

Inherited from object: __class__

Method Details [hide private]

__new__(S, ...)

 
Returns: a new object with type S, a subtype of T
Overrides: object.__new__

appendOptionsPrefix(self, prefix)

 

Appends to the prefix used for searching for all PEP options in the database.

Parameters

prefix: string
The prefix string to prepend to all PEP option requests.

computeError(self, int i, etype=None)

 

Computes the error (based on the residual norm) associated with the i-th computed eigenpair.

Parameters

i: int
Index of the solution to be considered.
etype: PEP.ErrorType enumerate
The error type to compute.

Returns

error: real
The error bound, computed in various ways from the residual norm ||P(l)x||_2 where l is the eigenvalue and x is the eigenvector.

Notes

The index i should be a value between 0 and nconv-1 (see getConverged()).

create(self, comm=None)

 

Creates the PEP object.

Parameters

comm: Comm, optional.
MPI communicator. If not provided, it defaults to all processes.

destroy(self)

 
Destroys the PEP object.
Overrides: petsc4py.PETSc.Object.destroy

errorView(self, etype=None, Viewer viewer=None)

 

Displays the errors associated with the computed solution (as well as the eigenvalues).

Parameters

etype: PEP.ErrorType enumerate, optional
The error type to compute.
viewer: Viewer, optional.
Visualization context; if not provided, the standard output is used.

Notes

By default, this function checks the error of all eigenpairs and prints the eigenvalues if all of them are below the requested tolerance. If the viewer has format ASCII_INFO_DETAIL then a table with eigenvalues and corresponding errors is printed.

getBV(self)

 

Obtain the basis vectors object associated to the eigensolver.

Returns

bv: BV
The basis vectors context.

getBasis(self)

 

Gets the type of polynomial basis used to describe the polynomial eigenvalue problem.

Returns

basis: PEP.Basis enumerate
the basis that was previously set.

getConverged(self)

 

Gets the number of converged eigenpairs.

Returns

nconv: int
Number of converged eigenpairs.

getConvergedReason(self)

 

Gets the reason why the solve() iteration was stopped.

Returns

reason: PEP.ConvergedReason enumerate
Negative value indicates diverged, positive value converged.

getConvergenceTest(self)

 

Return the method used to compute the error estimate used in the convergence test.

Returns

conv: PEP.Conv
The method used to compute the error estimate used in the convergence test.

getDimensions(self)

 

Gets the number of eigenvalues to compute and the dimension of the subspace.

Returns

nev: int
Number of eigenvalues to compute.
ncv: int
Maximum dimension of the subspace to be used by the solver.
mpd: int
Maximum dimension allowed for the projected problem.

getEigenpair(self, int i, Vec Vr=None, Vec Vi=None)

 

Gets the i-th solution of the eigenproblem as computed by solve(). The solution consists of both the eigenvalue and the eigenvector.

Parameters

i: int
Index of the solution to be obtained.
Vr: Vec, optional
Placeholder for the returned eigenvector (real part).
Vi: Vec, optional
Placeholder for the returned eigenvector (imaginary part).

Returns

e: scalar (possibly complex)
The computed eigenvalue.

getErrorEstimate(self, int i)

 

Returns the error estimate associated to the i-th computed eigenpair.

Parameters

i: int
Index of the solution to be considered.

Returns

error: real
Error estimate.

getIterationNumber(self)

 

Gets the current iteration number. If the call to solve() is complete, then it returns the number of iterations carried out by the solution method.

Returns

its: int
Iteration number.

getLinearCompanionForm(self)

 

Returns the number of the companion form that will be used for the linearization of a quadratic eigenproblem.

Returns

cform: integer
1 or 2 (first or second companion form).

getLinearEPS(self)

 

Retrieve the eigensolver object (EPS) associated to the polynomial eigenvalue solver.

Returns

eps: EPS
The linear eigensolver.

getLinearExplicitMatrix(self)

 

Returns the flag indicating if the matrices A and B for the linearization are built explicitly.

Returns

flag: boolean

getOperators(self)

 

Gets the matrices associated with the eigenvalue problem.

Returns

operators: tuple of Mat
The matrices associated with the eigensystem.

getOptionsPrefix(self)

 

Gets the prefix used for searching for all PEP options in the database.

Returns

prefix: string
The prefix string set for this PEP object.
Overrides: petsc4py.PETSc.Object.getOptionsPrefix

getProblemType(self)

 

Gets the problem type from the PEP object.

Returns

problem_type: PEP.ProblemType enumerate
The problem type that was previously set.

getRG(self)

 

Obtain the region object associated to the eigensolver.

Returns

rg: RG
The region context.

getRefine(self)

 

Gets the refinement strategy used by the PEP object, and the associated parameters.

Returns

ref: PEP.Refine
The refinement type.
npart: int
The number of partitions of the communicator.
tol: real
The convergence tolerance.
its: int
The maximum number of refinement iterations.
scheme: PEP.RefineScheme
Scheme for solving linear systems

getST(self)

 

Obtain the spectral transformation (ST) object associated to the eigensolver object.

Returns

st: ST
The spectral transformation.

getScale(self, Vec Dl=None, Vec Dr=None)

 

Gets the strategy used for scaling the polynomial eigenproblem.

Parameters

Dl: Vec, optional
Placeholder for the returned left diagonal matrix.
Dr: Vec, optional
Placeholder for the returned right diagonal matrix.

Returns

scale: PEP.Scale enumerate
The scaling strategy.
alpha: real
The scaling factor.
its: integer
The number of iteration of diagonal scaling.
lbda: real
Approximation of the wanted eigenvalues (modulus).

getTolerances(self)

 

Gets the tolerance and maximum iteration count used by the default PEP convergence tests.

Returns

tol: float
The convergence tolerance.
max_it: int
The maximum number of iterations

getTrackAll(self)

 

Returns the flag indicating whether all residual norms must be computed or not.

Returns

trackall: bool
Whether the solver compute all residuals or not.

getType(self)

 

Gets the PEP type of this object.

Returns

type: PEP.Type enumerate
The solver currently being used.
Overrides: petsc4py.PETSc.Object.getType

getWhichEigenpairs(self)

 

Returns which portion of the spectrum is to be sought.

Returns

which: PEP.Which enumerate
The portion of the spectrum to be sought by the solver.

setBV(self, BV bv)

 

Associates a basis vectors object to the eigensolver.

Parameters

bv: BV
The basis vectors context.

setBasis(self, basis)

 

Specifies the type of polynomial basis used to describe the polynomial eigenvalue problem.

Parameters

basis: PEP.Basis enumerate
the basis to be set.

setConvergenceTest(self, conv)

 

Specifies how to compute the error estimate used in the convergence test.

Parameters

conv: PEP.Conv
The method used to compute the error estimate used in the convergence test.

setDimensions(self, nev=None, ncv=None, mpd=None)

 

Sets the number of eigenvalues to compute and the dimension of the subspace.

Parameters

nev: int, optional
Number of eigenvalues to compute.
ncv: int, optional
Maximum dimension of the subspace to be used by the solver.
mpd: int, optional
Maximum dimension allowed for the projected problem.

setFromOptions(self)

 
Sets PEP options from the options database. This routine must be called before setUp() if the user is to be allowed to set the solver type.
Overrides: petsc4py.PETSc.Object.setFromOptions

setInitialSpace(self, space)

 

Sets the initial space from which the eigensolver starts to iterate.

Parameters

space: Vec or sequence of Vec
The initial space

setLinearCompanionForm(self, cform)

 

Choose between the two companion forms available for the linearization of a quadratic eigenproblem.

Parameters

cform: integer
1 or 2 (first or second companion form).

setLinearEPS(self, EPS eps)

 

Associate an eigensolver object (EPS) to the polynomial eigenvalue solver.

Parameters

eps: EPS
The linear eigensolver.

setLinearExplicitMatrix(self, flag)

 

Indicate if the matrices A and B for the linearization of the problem must be built explicitly.

Parameters

flag: boolean
boolean flag indicating if the matrices are built explicitly .

setOperators(self, operators)

 

Sets the matrices associated with the eigenvalue problem.

Parameters

operators: sequence of Mat
The matrices associated with the eigensystem.

setOptionsPrefix(self, prefix)

 

Sets the prefix used for searching for all PEP options in the database.

Parameters

prefix: string
The prefix string to prepend to all PEP option requests.
Overrides: petsc4py.PETSc.Object.setOptionsPrefix

setProblemType(self, problem_type)

 

Specifies the type of the eigenvalue problem.

Parameters

problem_type: PEP.ProblemType enumerate
The problem type to be set.

setRG(self, RG rg)

 

Associates a region object to the eigensolver.

Parameters

rg: RG
The region context.

setRefine(self, ref, npart=None, tol=None, its=None, scheme=None)

 

Sets the refinement strategy used by the PEP object, and the associated parameters.

Parameters

ref: PEP.Refine
The refinement type.
npart: int, optional
The number of partitions of the communicator.
tol: real, optional
The convergence tolerance.
its: int, optional
The maximum number of refinement iterations.
scheme: PEP.RefineScheme, optional
Scheme for linear system solves

setST(self, ST st)

 

Associates a spectral transformation object to the eigensolver.

Parameters

st: ST
The spectral transformation.

setScale(self, scale, alpha=None, Vec Dl=None, Vec Dr=None, its=None, lbda=None)

 

Sets the scaling strategy to be used for scaling the polynomial problem before attempting to solve.

Parameters

scale: PEP.Scale enumerate
The scaling strategy.
alpha: real, optional
The scaling factor.
Dl: Vec, optional
The left diagonal matrix.
Dr: Vec, optional
The right diagonal matrix.
its: integer, optional
The number of iteration of diagonal scaling.
lbda: real, optional
Approximation of the wanted eigenvalues (modulus).

setTolerances(self, tol=None, max_it=None)

 

Sets the tolerance and maximum iteration count used by the default PEP convergence tests.

Parameters

tol: float, optional
The convergence tolerance.
max_it: int, optional
The maximum number of iterations

setTrackAll(self, trackall)

 

Specifies if the solver must compute the residual of all approximate eigenpairs or not.

Parameters

trackall: bool
Whether compute all residuals or not.

setType(self, pep_type)

 

Selects the particular solver to be used in the PEP object.

Parameters

pep_type: PEP.Type enumerate
The solver to be used.

setWhichEigenpairs(self, which)

 

Specifies which portion of the spectrum is to be sought.

Parameters

which: PEP.Which enumerate
The portion of the spectrum to be sought by the solver.

view(self, Viewer viewer=None)

 

Prints the PEP data structure.

Parameters

viewer: Viewer, optional.
Visualization context; if not provided, the standard output is used.
Overrides: petsc4py.PETSc.Object.view