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PEP
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Basis PEP basis type for the representation of the polynomial |
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CISSExtraction PEP CISS extraction technique |
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Conv PEP convergence test |
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ConvergedReason PEP convergence reasons |
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ErrorType PEP error type to assess accuracy of computed solutions |
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Extract PEP extraction strategy used to obtain eigenvectors of the PEP from the eigenvectors of the linearization |
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JDProjection PEP type of projection to be used in the Jacobi-Davidson solver |
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ProblemType PEP problem type |
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Refine PEP refinement strategy |
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RefineScheme PEP scheme for solving linear systems during iterative refinement |
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Scale PEP scaling strategy |
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Stop PEP stopping test |
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Type PEP type |
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Which PEP desired part of spectrum |
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a new object with type S, a subtype of T |
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Inherited from Inherited from |
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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.
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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.
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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.
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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.
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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.
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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.
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