Class PEP

Returns:

a new object with type S, a subtype of T

Overrides: object.__new__

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.

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()`).

Creates the PEP object.

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

Destroys the PEP object.

Overrides: petsc4py.PETSc.Object.destroy

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.

Obtain the basis vectors object associated to the eigensolver.

Returns
-------
bv: BV
    The basis vectors context.

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

Returns
-------
basis: `PEP.Basis` enumerate
    the basis that was previously set.

Gets the extraction technique used in the CISS solver.

Returns
-------
extraction: `PEP.CISSExtraction` enumerate
       The extraction technique.

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.

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).

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.

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.

Gets the number of converged eigenpairs.

Returns
-------
nconv: int
    Number of converged eigenpairs.

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

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

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.

Obtain the direct solver associated to the eigensolver.

Returns
-------
ds: DS
    The direct solver context.

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.

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.

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.

Gets the extraction technique used by the `PEP` object.

Returns
-------
extract: `PEP.Extract` enumerate
       The extraction strategy.

Gets the computational interval for spectrum slicing.

Returns
-------
inta: float
        The left end of the interval.
intb: float
        The right end of the interval.

Notes
-----
If the interval was not set by the user, then zeros are returned.

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.

Gets threshold for changing the target in the correction equation.

Returns
-------
fix: float
      The threshold for changing the target.

Returns the maximum allowed value of the minimality index.

Returns
-------
flag: int
    The maximum minimality index.

Gets the type of projection to be used in the Jacobi-Davidson solver.

Returns
-------
proj: `PEP.JDProjection` enumerate
       The type of projection.

Gets the restart parameter used in the Jacobi-Davidson method.

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

Returns the flag for reusing the preconditioner.

Returns
-------
flag: bool
    The reuse flag.

Retrieve the eigensolver object associated to the polynomial
eigenvalue solver.

Returns
-------
eps: `EPS`
    The linear eigensolver.

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

Returns
-------
flag: bool
    Boolean flag indicating if the matrices are built explicitly.

Returns the coefficients that define the linearization of a quadratic eigenproblem.

Returns
-------
alpha: float
    First parameter of the linearization.
beta: float
    Second parameter of the linearization.

Gets the matrices associated with the eigenvalue problem.

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

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

Gets the problem type from the PEP object.

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

Gets the locking flag used in the Q-Arnoldi method.

Returns
-------
lock: bool
      The locking flag.

Gets the restart parameter used in the Q-Arnoldi method.

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

Obtain the region object associated to the eigensolver.

Returns
-------
rg: RG
    The region context.

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

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

Returns
-------
ksp: `KSP`
     The linear solver object.

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

Returns
-------
st: ST
    The spectral transformation.

Gets the flag for the eigenvalue type check in spectrum slicing.

Returns
-------
flag: bool
    Whether the eigenvalue type is checked or not.

Gets the flag that enforces zero detection in spectrum slicing.

Returns
-------
detect: bool
      The zero detection flag.

Gets the dimensions used for each subsolve step in case of doing
spectrum slicing for a computational interval.

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.

Gets the values of the shifts and their corresponding inertias
in case of doing spectrum slicing for a computational interval.

Returns
-------
shifts: list of float
     The values of the shifts used internally in the solver.
inertias: list of int
     The values of the inertia in each shift.

Returns the coefficients that define the linearization of a quadratic eigenproblem.

Returns
-------
alpha: float
    First parameter of the linearization.
beta: float
    Second parameter of the linearization.

Gets the locking flag used in the STOAR method.

Returns
-------
lock: bool
      The locking flag.

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: int
    The number of iteration of diagonal scaling.
lbda: real
    Approximation of the wanted eigenvalues (modulus).

Gets the locking flag used in the TOAR method.

Returns
-------
lock: bool
      The locking flag.

Gets the restart parameter used in the TOAR method.

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

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.

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

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

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

Gets the PEP type of this object.

Returns
-------
type: `PEP.Type` enumerate
    The solver currently being used.

Overrides: petsc4py.PETSc.Object.getType

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.

Associates a basis vectors object to the eigensolver.

Parameters
----------
bv: BV
    The basis vectors context.

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

Parameters
----------
basis: `PEP.Basis` enumerate
    the basis to be set.

Sets the extraction technique used in the CISS solver.

Parameters
----------
extraction: `PEP.CISSExtraction` enumerate
       The extraction technique.

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).

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 `PEP` communicator. Otherwise, the
communicator is split into npart communicators, so that `npart` `KSP` solves
proceed simultaneously.

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).

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.

Associates a direct solver object to the eigensolver.

Parameters
----------
ds: DS
    The direct solver context.

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.

Specifies the extraction strategy to be used.

Parameters
----------
extract: `PEP.Extract` enumerate
       The extraction strategy.

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

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

Parameters
----------
space: Vec or sequence of Vec
   The initial space

Defines the computational interval for spectrum slicing.

Parameters
----------
inta: float
        The left end of the interval.
intb: float
        The right end of the interval.

Notes
-----
Spectrum slicing is a technique employed for computing all
eigenvalues of symmetric quadratic eigenproblems in a given interval.
This function provides the interval to be considered. It must
be used in combination with `PEP.Which.ALL`, see
`setWhichEigenpairs()`.

Sets the threshold for changing the target in the correction
equation.

Parameters
----------
fix: float
      Threshold for changing the target.

Notes
-----
The target in the correction equation is fixed at the first iterations.
When the norm of the residual vector is lower than the fix value,
the target is set to the corresponding eigenvalue.

Sets the maximum allowed value for the minimality index.

Parameters
----------
flag: int
    The maximum minimality index.

Sets the type of projection to be used in the Jacobi-Davidson solver.

Parameters
----------
proj: `PEP.JDProjection` enumerate
       The type of projection.

Sets the restart parameter for the Jacobi-Davidson 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.

Sets a flag indicating whether the preconditioner must be reused or not.

Parameters
----------
flag: bool
    The reuse flag.

Associate an eigensolver object to the polynomial eigenvalue solver.

Parameters
----------
eps: `EPS`
    The linear eigensolver.

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

Parameters
----------
flag: bool
    Boolean flag indicating if the matrices are built explicitly.

Set the coefficients that define the linearization of a quadratic eigenproblem.

Parameters
----------
alpha: float
    First parameter of the linearization.
beta: float
    Second parameter of the linearization.

Sets the matrices associated with the eigenvalue problem.

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

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

Specifies the type of the eigenvalue problem.

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

Choose between locking and non-locking variants of the
Q-Arnoldi 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).

Sets the restart parameter for the Q-Arnoldi 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.

Associates a region object to the eigensolver.

Parameters
----------
rg: RG
    The region context.

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

Associates a spectral transformation object to the
eigensolver.

Parameters
----------
st: ST
    The spectral transformation.

Sets a flag to check that all the eigenvalues obtained throughout
the spectrum slicing computation have the same definite type.

Parameters
----------
flag: bool
    Whether the eigenvalue type is checked or not.

Sets a flag to enforce detection of zeros during the factorizations
throughout the spectrum slicing computation.

Parameters
----------
detect: bool
      True if zeros must checked for.

Notes
-----
A zero in the factorization indicates that a shift coincides with
an eigenvalue.

This flag is turned off by default, and may be necessary in some cases.
This feature currently requires an external package for factorizations
with support for zero detection, e.g. MUMPS.

Sets the dimensions used for each subsolve step in case of doing
spectrum slicing for a computational interval. The meaning of the
parameters is the same as in `setDimensions()`.

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.

Set the coefficients that define the linearization of a quadratic eigenproblem.

Parameters
----------
alpha: float
    First parameter of the linearization.
beta: float
    Second parameter of the linearization.

Choose between locking and non-locking variants of the
STOAR 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).

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: int, optional
    The number of iteration of diagonal scaling.
lbda: real, optional
    Approximation of the wanted eigenvalues (modulus).

Choose between locking and non-locking variants of the
TOAR 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).

Sets the restart parameter for the TOAR 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.

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()`.

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

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

Parameters
----------
trackall: bool
    Whether compute all residuals or not.

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

Parameters
----------
pep_type: `PEP.Type` enumerate
    The solver to be used.

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.

Displays the computed eigenvalues in a viewer.

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

Outputs computed eigenvectors to a viewer.

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

Prints the PEP data structure.

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

Overrides: petsc4py.PETSc.Object.view