Package slepc4py :: Module SLEPc :: Class NEP
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Class NEP


NEP
Nested Classes [hide private]
  CISSExtraction
NEP CISS extraction technique
  Conv
NEP convergence test
  ConvergedReason
NEP convergence reasons
  ErrorType
NEP error type to assess accuracy of computed solutions
  ProblemType
NEP problem type
  Refine
NEP refinement strategy
  RefineScheme
NEP scheme for solving linear systems during iterative refinement
  Stop
NEP stopping test
  Type
NEP type
  Which
NEP 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 NEP options in the database.
 
applyResolvent(self, omega, Vec v, Vec r, RG rg=None)
Applies the resolvent T^{-1}(z) to a given vector.
 
cancelMonitor(self)
Clears all monitors for a NEP 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 NEP object.
 
destroy(self)
Destroys the NEP 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.
 
getCISSExtraction(self)
Gets the extraction technique used in the CISS solver.
 
getCISSKSPs(self)
Retrieve the array of linear solver objects associated with the CISS solver.
 
getCISSRefinement(self)
Gets the values of various refinement parameters in the CISS solver.
 
getCISSSizes(self)
Gets the values of various size parameters in the CISS solver.
 
getCISSThreshold(self)
Gets the values of various threshold parameters in the CISS solver.
 
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.
 
getDS(self)
Obtain the direct solver associated to the eigensolver.
 
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.
 
getFunction(self)
Returns the function to compute the nonlinear Function T(lambda) and the matrix.
 
getInterpolInterpolation(self)
Gets the tolerance and maximum degree when building the interpolation polynomial.
 
getInterpolPEP(self)
Retrieve the polynomial eigensolver object associated with the nonlinear eigensolver.
 
getIterationNumber(self)
Gets the current iteration number.
 
getJacobian(self)
Returns the function to compute the Jacobian T'(lambda) and the matrix.
 
getLeftEigenvector(self, int i, Vec Wr, Vec Wi=None)
Gets the i-th left eigenvector as computed by solve().
 
getMonitor(self)
Gets the list of monitor functions.
 
getNArnoldiKSP(self)
Retrieve the linear solver object associated with the nonlinear eigensolver.
 
getNArnoldiLagPreconditioner(self)
Indicates how often the preconditioner is rebuilt.
 
getNLEIGSEPS(self)
Retrieve the linear eigensolver object associated with the nonlinear eigensolver.
 
getNLEIGSFullBasis(self)
Gets the flag that indicates if NLEIGS is using the full-basis variant.
 
getNLEIGSInterpolation(self)
Gets the tolerance and maximum degree when building the interpolation via divided differences.
 
getNLEIGSKSPs(self)
Retrieve the array of linear solver objects associated with the NLEIGS solver.
 
getNLEIGSLocking(self)
Gets the locking flag used in the NLEIGS method.
 
getNLEIGSRKShifts(self)
Gets the list of shifts used in the Rational Krylov method.
 
getNLEIGSRestart(self)
Gets the restart parameter used in the NLEIGS method.
 
getOptionsPrefix(self)
Gets the prefix used for searching for all NEP options in the database.
 
getProblemType(self)
Gets the problem type from the NEP object.
 
getRG(self)
Obtain the region object associated to the eigensolver.
 
getRIIConstCorrectionTol(self)
Returns the constant tolerance flag.
 
getRIIDeflationThreshold(self)
Returns the threshold value that controls deflation.
 
getRIIHermitian(self)
Returns the flag about using the Hermitian version of the scalar nonlinear equation.
 
getRIIKSP(self)
Retrieve the linear solver object associated with the nonlinear eigensolver.
 
getRIILagPreconditioner(self)
Indicates how often the preconditioner is rebuilt.
 
getRIIMaximumIterations(self)
Gets the maximum number of inner iterations of RII.
 
getRefine(self)
Gets the refinement strategy used by the NEP object, and the associated parameters.
 
getRefineKSP(self)
Obtain the KSP object used by the eigensolver in the refinement phase.
 
getSLPDeflationThreshold(self)
Returns the threshold value that controls deflation.
 
getSLPEPS(self)
Retrieve the linear eigensolver object associated with the nonlinear eigensolver.
 
getSLPEPSLeft(self)
Retrieve the left eigensolver.
 
getSLPKSP(self)
Retrieve the linear solver object associated with the nonlinear eigensolver.
 
getSplitOperator(self)
Returns the operator of the nonlinear eigenvalue problem in split form.
 
getStoppingTest(self)
Gets the stopping function.
 
getTarget(self)
Gets the value of the target.
 
getTolerances(self)
Gets the tolerance and maximum iteration count used by the default NEP convergence tests.
 
getTrackAll(self)
Returns the flag indicating whether all residual norms must be computed or not.
 
getTwoSided(self)
Returns the flag indicating whether a two-sided variant of the algorithm is being used or not.
 
getType(self)
Gets the NEP type of this object.
 
getWhichEigenpairs(self)
Returns which portion of the spectrum is to be sought.
 
reset(self)
Resets the NEP object.
 
setBV(self, BV bv)
Associates a basis vectors object to the eigensolver.
 
setCISSExtraction(self, extraction)
Sets the extraction technique used in the CISS solver.
 
setCISSRefinement(self, inner=None, blsize=None)
Sets the values of various refinement parameters in the CISS solver.
 
setCISSSizes(self, ip=None, bs=None, ms=None, npart=None, bsmax=None, realmats=False)
Sets the values of various size parameters in the CISS solver.
 
setCISSThreshold(self, delta=None, spur=None)
Sets the values of various threshold parameters in the CISS solver.
 
setConvergenceTest(self, conv)
Specifies how to compute the error estimate used in the convergence test.
 
setDS(self, DS ds)
Associates a direct solver object to the eigensolver.
 
setDimensions(self, nev=None, ncv=None, mpd=None)
Sets the number of eigenvalues to compute and the dimension of the subspace.
 
setFromOptions(self)
Sets NEP options from the options database.
 
setFunction(self, function, Mat F=None, Mat P=None, args=None, kargs=None)
Sets the function to compute the nonlinear Function T(lambda) as well as the location to store the matrix.
 
setInitialSpace(self, space)
Sets the initial space from which the eigensolver starts to iterate.
 
setInterpolInterpolation(self, tol=None, deg=None)
Sets the tolerance and maximum degree when building the interpolation polynomial.
 
setInterpolPEP(self, PEP pep)
Associate a polynomial eigensolver object to the nonlinear eigensolver.
 
setJacobian(self, jacobian, Mat J=None, args=None, kargs=None)
Sets the function to compute the Jacobian T'(lambda) as well as the location to store the matrix.
 
setMonitor(self, monitor, args=None, kargs=None)
Appends a monitor function to the list of monitors.
 
setNArnoldiKSP(self, KSP ksp)
Associate a linear solver object to the nonlinear eigensolver.
 
setNArnoldiLagPreconditioner(self, lag)
Determines when the preconditioner is rebuilt in the nonlinear solve.
 
setNLEIGSEPS(self, EPS eps)
Associate a linear eigensolver object to the nonlinear eigensolver.
 
setNLEIGSFullBasis(self, fullbasis=True)
Choose between TOAR-basis (default) and full-basis variants of the NLEIGS method.
 
setNLEIGSInterpolation(self, tol=None, deg=None)
Sets the tolerance and maximum degree when building the interpolation via divided differences.
 
setNLEIGSLocking(self, lock)
Choose between locking and non-locking variants of the NLEIGS method.
 
setNLEIGSRKShifts(self, shifts)
Sets a list of shifts to be used in the Rational Krylov method.
 
setNLEIGSRestart(self, keep)
Sets the restart parameter for the NLEIGS method, in particular the proportion of basis vectors that must be kept after restart.
 
setOptionsPrefix(self, prefix)
Sets the prefix used for searching for all NEP 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.
 
setRIIConstCorrectionTol(self, cct)
Sets a flag to keep the tolerance used in the linear solver constant.
 
setRIIDeflationThreshold(self, deftol)
Sets the threshold value used to switch between deflated and non-deflated iteration.
 
setRIIHermitian(self, herm)
Sets a flag to indicate if the Hermitian version of the scalar nonlinear equation must be used by the solver.
 
setRIIKSP(self, KSP ksp)
Associate a linear solver object to the nonlinear eigensolver.
 
setRIILagPreconditioner(self, lag)
Determines when the preconditioner is rebuilt in the nonlinear solve.
 
setRIIMaximumIterations(self, its)
Sets the maximum number of inner iterations to be used in the RII solver.
 
setRefine(self, ref, npart=None, tol=None, its=None, scheme=None)
Sets the refinement strategy used by the NEP object, and the associated parameters.
 
setSLPDeflationThreshold(self, deftol)
Sets the threshold value used to switch between deflated and non-deflated iteration.
 
setSLPEPS(self, EPS eps)
Associate a linear eigensolver object to the nonlinear eigensolver.
 
setSLPEPSLeft(self, EPS eps)
Associate a linear eigensolver object to the nonlinear eigensolver, used to compute left eigenvectors in the two-sided variant of SLP.
 
setSLPKSP(self, KSP ksp)
Associate a linear solver object to the nonlinear eigensolver.
 
setSplitOperator(self, A, f, structure=None)
Sets the operator of the nonlinear eigenvalue problem in split form.
 
setStoppingTest(self, stopping, args=None, kargs=None)
Sets a function to decide when to stop the outer iteration of the eigensolver.
 
setTarget(self, target)
Sets the value of the target.
 
setTolerances(self, tol=None, maxit=None)
Sets the tolerance and maximum iteration count used in convergence tests.
 
setTrackAll(self, trackall)
Specifies if the solver must compute the residual of all approximate eigenpairs or not.
 
setTwoSided(self, twosided)
Sets the solver to use a two-sided variant so that left eigenvectors are also computed.
 
setType(self, nep_type)
Selects the particular solver to be used in the NEP 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.
 
valuesView(self, Viewer viewer=None)
Displays the computed eigenvalues in a viewer.
 
vectorsView(self, Viewer viewer=None)
Outputs computed eigenvectors to a viewer.
 
view(self, Viewer viewer=None)
Prints the NEP 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, viewFromOptions

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

Properties [hide private]
  bv
  ds
  max_it
  problem_type
  rg
  target
  tol
  track_all
  which

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 NEP options in the database.

Parameters

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

applyResolvent(self, omega, Vec v, Vec r, RG rg=None)

 

Applies the resolvent T^{-1}(z) to a given vector.

Parameters

omega: scalar
Value where the resolvent must be evaluated.
v: Vec
Input vector.
r: Vec
Placeholder for the result vector.
rg: RG object, optional
Region.

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: NEP.ErrorType enumerate
The error type to compute.

Returns

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

create(self, comm=None)

 

Creates the NEP object.

Parameters

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

destroy(self)

 
Destroys the NEP 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: NEP.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.

getCISSExtraction(self)

 

Gets the extraction technique used in the CISS solver.

Returns

extraction: NEP.CISSExtraction enumerate
The extraction technique.

getCISSKSPs(self)

 

Retrieve the array of linear solver objects associated with the CISS solver.

Returns

ksp: list of KSP
The linear solver objects.

Notes

The number of KSP solvers is equal to the number of integration points divided by the number of partitions. This value is halved in the case of real matrices with a region centered at the real axis.

getCISSRefinement(self)

 

Gets the values of various refinement parameters in the CISS solver.

Returns

inner: int
Number of iterative refinement iterations (inner loop).
blsize: int
Number of iterative refinement iterations (blocksize loop).

getCISSSizes(self)

 

Gets the values of various size parameters in the CISS solver.

Returns

ip: int
Number of integration points.
bs: int
Block size.
ms: int
Moment size.
npart: int
Number of partitions when splitting the communicator.
bsmax: int
Maximum block size.
realmats: bool
True if A and B are real.

getCISSThreshold(self)

 

Gets the values of various threshold parameters in the CISS solver.

Returns

delta: float
Threshold for numerical rank.
spur: float
Spurious threshold (to discard spurious eigenpairs.

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

getDS(self)

 

Obtain the direct solver associated to the eigensolver.

Returns

ds: DS
The direct solver context.

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.

getFunction(self)

 

Returns the function to compute the nonlinear Function T(lambda) and the matrix.

Parameters

F: Mat
Function matrix
P: Mat
preconditioner matrix (usually the same as the F)
function:
Function evaluation routine

getInterpolInterpolation(self)

 

Gets the tolerance and maximum degree when building the interpolation polynomial.

Returns

tol: float
The tolerance to stop computing polynomial coefficients.
deg: int
The maximum degree of interpolation.

getInterpolPEP(self)

 

Retrieve the polynomial eigensolver object associated with the nonlinear eigensolver.

Returns

pep: PEP
The polynomial eigensolver.

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.

getJacobian(self)

 

Returns the function to compute the Jacobian T'(lambda) and the matrix.

Parameters

J: Mat
Jacobian matrix
jacobian:
Jacobian evaluation routine

getLeftEigenvector(self, int i, Vec Wr, Vec Wi=None)

 

Gets the i-th left eigenvector as computed by solve().

Parameters

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

Notes

The index i should be a value between 0 and nconv-1 (see getConverged()). Eigensolutions are indexed according to the ordering criterion established with setWhichEigenpairs().

Left eigenvectors are available only if the twosided flag was set with setTwoSided().

getNArnoldiKSP(self)

 

Retrieve the linear solver object associated with the nonlinear eigensolver.

Returns

ksp: KSP
The linear solver object.

getNArnoldiLagPreconditioner(self)

 

Indicates how often the preconditioner is rebuilt.

Returns

lag: int
The lag parameter.

getNLEIGSEPS(self)

 

Retrieve the linear eigensolver object associated with the nonlinear eigensolver.

Returns

eps: EPS
The linear eigensolver.

getNLEIGSFullBasis(self)

 

Gets the flag that indicates if NLEIGS is using the full-basis variant.

Returns

fullbasis: bool
True if the full-basis variant must be selected.

getNLEIGSInterpolation(self)

 

Gets the tolerance and maximum degree when building the interpolation via divided differences.

Returns

tol: float
The tolerance to stop computing divided differences.
deg: int
The maximum degree of interpolation.

getNLEIGSKSPs(self)

 

Retrieve the array of linear solver objects associated with the NLEIGS solver.

Returns

ksp: list of KSP
The linear solver objects.

Notes

The number of KSP solvers is equal to the number of shifts provided by the user, or 1 if the user did not provide shifts.

getNLEIGSLocking(self)

 

Gets the locking flag used in the NLEIGS method.

Returns

lock: bool
The locking flag.

getNLEIGSRKShifts(self)

 

Gets the list of shifts used in the Rational Krylov method.

Returns

shifts: array of scalars
The shift values.

getNLEIGSRestart(self)

 

Gets the restart parameter used in the NLEIGS method.

Returns

keep: float
The number of vectors to be kept at restart.

getOptionsPrefix(self)

 

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

Returns

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

getProblemType(self)

 

Gets the problem type from the NEP object.

Returns

problem_type: NEP.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.

getRIIConstCorrectionTol(self)

 

Returns the constant tolerance flag.

Returns

cct: bool
If True, the KSP relative tolerance is constant.

getRIIDeflationThreshold(self)

 

Returns the threshold value that controls deflation.

Returns

deftol: float
The threshold value.

getRIIHermitian(self)

 

Returns the flag about using the Hermitian version of the scalar nonlinear equation.

Returns

herm: bool
If True, the Hermitian version is used.

getRIIKSP(self)

 

Retrieve the linear solver object associated with the nonlinear eigensolver.

Returns

ksp: KSP
The linear solver object.

getRIILagPreconditioner(self)

 

Indicates how often the preconditioner is rebuilt.

Returns

lag: int
The lag parameter.

getRIIMaximumIterations(self)

 

Gets the maximum number of inner iterations of RII.

Returns

its: int
Maximum inner iterations.

getRefine(self)

 

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

Returns

ref: NEP.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: NEP.RefineScheme
Scheme for solving linear systems

getRefineKSP(self)

 

Obtain the KSP object used by the eigensolver in the refinement phase.

Returns

ksp: KSP
The linear solver object.

getSLPDeflationThreshold(self)

 

Returns the threshold value that controls deflation.

Returns

deftol: float
The threshold value.

getSLPEPS(self)

 

Retrieve the linear eigensolver object associated with the nonlinear eigensolver.

Returns

eps: EPS
The linear eigensolver.

getSLPEPSLeft(self)

 

Retrieve the left eigensolver.

Returns

eps: EPS
The linear eigensolver.

getSLPKSP(self)

 

Retrieve the linear solver object associated with the nonlinear eigensolver.

Returns

ksp: KSP
The linear solver object.

getSplitOperator(self)

 

Returns the operator of the nonlinear eigenvalue problem in split form.

Returns

A: sequence of Mat
Coefficient matrices of the split form.
f: sequence of FN
Scalar functions of the split form.
structure: PETSc.Mat.Structure enumerate
Structure flag for matrices.

getTarget(self)

 

Gets the value of the target.

Returns

target: float (real or complex)
The value of the target.

Notes

If the target was not set by the user, then zero is returned.

getTolerances(self)

 

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

Returns

tol: float
The convergence tolerance.
maxit: 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.

getTwoSided(self)

 

Returns the flag indicating whether a two-sided variant of the algorithm is being used or not.

Returns

twosided: bool
Whether the two-sided variant is to be used or not.

getType(self)

 

Gets the NEP type of this object.

Returns

type: NEP.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: NEP.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.

setCISSExtraction(self, extraction)

 

Sets the extraction technique used in the CISS solver.

Parameters

extraction: NEP.CISSExtraction enumerate
The extraction technique.

setCISSRefinement(self, inner=None, blsize=None)

 

Sets the values of various refinement parameters in the CISS solver.

Parameters

inner: int, optional
Number of iterative refinement iterations (inner loop).
blsize: int, optional
Number of iterative refinement iterations (blocksize loop).

setCISSSizes(self, ip=None, bs=None, ms=None, npart=None, bsmax=None, realmats=False)

 

Sets the values of various size parameters in the CISS solver.

Parameters

ip: int, optional
Number of integration points.
bs: int, optional
Block size.
ms: int, optional
Moment size.
npart: int, optional
Number of partitions when splitting the communicator.
bsmax: int, optional
Maximum block size.
realmats: bool, optional
True if A and B are real.

Notes

The default number of partitions is 1. This means the internal KSP object is shared among all processes of the NEP communicator. Otherwise, the communicator is split into npart communicators, so that npart KSP solves proceed simultaneously.

setCISSThreshold(self, delta=None, spur=None)

 

Sets the values of various threshold parameters in the CISS solver.

Parameters

delta: float
Threshold for numerical rank.
spur: float
Spurious threshold (to discard spurious eigenpairs).

setConvergenceTest(self, conv)

 

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

Parameters

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

setDS(self, DS ds)

 

Associates a direct solver object to the eigensolver.

Parameters

ds: DS
The direct solver context.

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 NEP 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

setFunction(self, function, Mat F=None, Mat P=None, args=None, kargs=None)

 

Sets the function to compute the nonlinear Function T(lambda) as well as the location to store the matrix.

Parameters

function:
Function evaluation routine
F: Mat
Function matrix
P: Mat
preconditioner matrix (usually the same as F)

setInitialSpace(self, space)

 

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

Parameters

space: Vec or sequence of Vec
The initial space

setInterpolInterpolation(self, tol=None, deg=None)

 

Sets the tolerance and maximum degree when building the interpolation polynomial.

Parameters

tol: float, optional
The tolerance to stop computing polynomial coefficients.
deg: int, optional
The maximum degree of interpolation.

setInterpolPEP(self, PEP pep)

 

Associate a polynomial eigensolver object to the nonlinear eigensolver.

Parameters

pep: PEP
The polynomial eigensolver.

setJacobian(self, jacobian, Mat J=None, args=None, kargs=None)

 

Sets the function to compute the Jacobian T'(lambda) as well as the location to store the matrix.

Parameters

jacobian:
Jacobian evaluation routine
J: Mat
Jacobian matrix

setNArnoldiKSP(self, KSP ksp)

 

Associate a linear solver object to the nonlinear eigensolver.

Parameters

ksp: KSP
The linear solver object.

setNArnoldiLagPreconditioner(self, lag)

 

Determines when the preconditioner is rebuilt in the nonlinear solve.

Parameters

lag: int
0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is computed within the nonlinear iteration, 2 means every second time the Jacobian is built, etc.

Notes

The default is 1. The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

setNLEIGSEPS(self, EPS eps)

 

Associate a linear eigensolver object to the nonlinear eigensolver.

Parameters

eps: EPS
The linear eigensolver.

setNLEIGSFullBasis(self, fullbasis=True)

 

Choose between TOAR-basis (default) and full-basis variants of the NLEIGS method.

Parameters

fullbasis: bool
True if the full-basis variant must be selected.

setNLEIGSInterpolation(self, tol=None, deg=None)

 

Sets the tolerance and maximum degree when building the interpolation via divided differences.

Parameters

tol: float, optional
The tolerance to stop computing divided differences.
deg: int, optional
The maximum degree of interpolation.

setNLEIGSLocking(self, lock)

 

Choose between locking and non-locking variants of the NLEIGS method.

Parameters

lock: bool
True if the locking variant must be selected.

Notes

The default is to lock converged eigenpairs when the method restarts. This behaviour can be changed so that all directions are kept in the working subspace even if already converged to working accuracy (the non-locking variant).

setNLEIGSRKShifts(self, shifts)

 

Sets a list of shifts to be used in the Rational Krylov method.

Parameters

shifts: array of scalars
Values specifying the shifts.

setNLEIGSRestart(self, keep)

 

Sets the restart parameter for the NLEIGS method, in particular the proportion of basis vectors that must be kept after restart.

Parameters

keep: float
The number of vectors to be kept at restart.

Notes

Allowed values are in the range [0.1,0.9]. The default is 0.5.

setOptionsPrefix(self, prefix)

 

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

Parameters

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

setProblemType(self, problem_type)

 

Specifies the type of the eigenvalue problem.

Parameters

problem_type: NEP.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.

setRIIConstCorrectionTol(self, cct)

 

Sets a flag to keep the tolerance used in the linear solver constant.

Parameters

cct: bool
If True, the KSP relative tolerance is constant.

setRIIDeflationThreshold(self, deftol)

 

Sets the threshold value used to switch between deflated and non-deflated iteration.

Parameters

deftol: float
The threshold value.

setRIIHermitian(self, herm)

 

Sets a flag to indicate if the Hermitian version of the scalar nonlinear equation must be used by the solver.

Parameters

herm: bool
If True, the Hermitian version is used.

setRIIKSP(self, KSP ksp)

 

Associate a linear solver object to the nonlinear eigensolver.

Parameters

ksp: KSP
The linear solver object.

setRIILagPreconditioner(self, lag)

 

Determines when the preconditioner is rebuilt in the nonlinear solve.

Parameters

lag: int
0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is computed within the nonlinear iteration, 2 means every second time the Jacobian is built, etc.

setRIIMaximumIterations(self, its)

 

Sets the maximum number of inner iterations to be used in the RII solver. These are the Newton iterations related to the computation of the nonlinear Rayleigh functional.

Parameters

its: int
Maximum inner iterations.

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

 

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

Parameters

ref: NEP.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: NEP.RefineScheme, optional
Scheme for linear system solves

setSLPDeflationThreshold(self, deftol)

 

Sets the threshold value used to switch between deflated and non-deflated iteration.

Parameters

deftol: float
The threshold value.

setSLPEPS(self, EPS eps)

 

Associate a linear eigensolver object to the nonlinear eigensolver.

Parameters

eps: EPS
The linear eigensolver.

setSLPEPSLeft(self, EPS eps)

 

Associate a linear eigensolver object to the nonlinear eigensolver, used to compute left eigenvectors in the two-sided variant of SLP.

Parameters

eps: EPS
The linear eigensolver.

setSLPKSP(self, KSP ksp)

 

Associate a linear solver object to the nonlinear eigensolver.

Parameters

ksp: KSP
The linear solver object.

setSplitOperator(self, A, f, structure=None)

 

Sets the operator of the nonlinear eigenvalue problem in split form.

Parameters

A: Mat or sequence of Mat
Coefficient matrices of the split form.
f: sequence of FN
Scalar functions of the split form.
structure: PETSc.Mat.Structure enumerate, optional
Structure flag for matrices.

setTarget(self, target)

 

Sets the value of the target.

Parameters

target: float (real or complex)
The value of the target.

Notes

The target is a scalar value used to determine the portion of the spectrum of interest. It is used in combination with setWhichEigenpairs().

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

 

Sets the tolerance and maximum iteration count used in convergence tests.

Parameters

tol: float, optional
The convergence tolerance.
maxit: 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.

setTwoSided(self, twosided)

 

Sets the solver to use a two-sided variant so that left eigenvectors are also computed.

Parameters

twosided: bool
Whether the two-sided variant is to be used or not.

setType(self, nep_type)

 

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

Parameters

nep_type: NEP.Type enumerate
The solver to be used.

setWhichEigenpairs(self, which)

 

Specifies which portion of the spectrum is to be sought.

Parameters

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

valuesView(self, Viewer viewer=None)

 

Displays the computed eigenvalues in a viewer.

Parameters

viewer: Viewer, optional.
Visualization context; if not provided, the standard output is used.

vectorsView(self, Viewer viewer=None)

 

Outputs computed eigenvectors to a viewer.

Parameters

viewer: Viewer, optional.
Visualization context; if not provided, the standard output is used.

view(self, Viewer viewer=None)

 

Prints the NEP data structure.

Parameters

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