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NEP
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CISSExtraction NEP CISS extraction technique |
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Conv NEP convergence test |
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ConvergedReason NEP convergence reasons |
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ErrorType NEP error type to assess accuracy of computed solutions |
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ProblemType NEP problem type |
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Refine NEP refinement strategy |
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RefineScheme NEP scheme for solving linear systems during iterative refinement |
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Stop NEP stopping test |
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Type NEP type |
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Which NEP 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 NEP options in the database. Parameters ---------- prefix: string The prefix string to prepend to all NEP option requests. |
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. |
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. |
Creates the NEP object. Parameters ---------- comm: Comm, optional. MPI communicator. If not provided, it defaults to all processes. |
Destroys the NEP object.
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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. |
Obtain the basis vectors object associated to the eigensolver. Returns ------- bv: BV The basis vectors context. |
Gets the extraction technique used in the CISS solver. Returns ------- extraction: `NEP.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: `NEP.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: NEP.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. |
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 |
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. |
Retrieve the polynomial eigensolver object associated with the nonlinear eigensolver. Returns ------- pep: `PEP` The polynomial eigensolver. |
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. |
Returns the function to compute the Jacobian T'(lambda) and the matrix. Parameters ---------- J: Mat Jacobian matrix jacobian: Jacobian evaluation routine |
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()`. |
Retrieve the linear solver object associated with the nonlinear eigensolver. Returns ------- ksp: `KSP` The linear solver object. |
Indicates how often the preconditioner is rebuilt. Returns ------- lag: int The lag parameter. |
Retrieve the linear eigensolver object associated with the nonlinear eigensolver. Returns ------- eps: `EPS` The linear eigensolver. |
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. |
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. |
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. |
Gets the locking flag used in the NLEIGS method. Returns ------- lock: bool The locking flag. |
Gets the list of shifts used in the Rational Krylov method. Returns ------- shifts: array of scalars The shift values. |
Gets the restart parameter used in the NLEIGS method. Returns ------- keep: float The number of vectors to be kept at restart. |
Gets the prefix used for searching for all NEP options in the database. Returns ------- prefix: string The prefix string set for this NEP object.
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Gets the problem type from the `NEP` object. Returns ------- problem_type: `NEP.ProblemType` enumerate The problem type that was previously set. |
Obtain the region object associated to the eigensolver. Returns ------- rg: RG The region context. |
Returns the constant tolerance flag. Returns ------- cct: bool If True, the `KSP` relative tolerance is constant. |
Returns the threshold value that controls deflation. Returns ------- deftol: float The threshold value. |
Returns the flag about using the Hermitian version of the scalar nonlinear equation. Returns ------- herm: bool If True, the Hermitian version is used. |
Retrieve the linear solver object associated with the nonlinear eigensolver. Returns ------- ksp: `KSP` The linear solver object. |
Indicates how often the preconditioner is rebuilt. Returns ------- lag: int The lag parameter. |
Gets the maximum number of inner iterations of RII. Returns ------- its: int Maximum inner iterations. |
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 |
Obtain the `KSP` object used by the eigensolver in the refinement phase. Returns ------- ksp: `KSP` The linear solver object. |
Returns the threshold value that controls deflation. Returns ------- deftol: float The threshold value. |
Retrieve the linear eigensolver object associated with the nonlinear eigensolver. Returns ------- eps: `EPS` The linear eigensolver. |
Retrieve the left eigensolver. Returns ------- eps: `EPS` The linear eigensolver. |
Retrieve the linear solver object associated with the nonlinear eigensolver. Returns ------- ksp: `KSP` The linear solver object. |
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. |
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 NEP convergence tests. Returns ------- tol: float The convergence tolerance. maxit: 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. |
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. |
Gets the NEP type of this object. Returns ------- type: `NEP.Type` enumerate The solver currently being used.
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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. |
Associates a basis vectors object to the eigensolver. Parameters ---------- bv: BV The basis vectors context. |
Sets the extraction technique used in the CISS solver. Parameters ---------- extraction: `NEP.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 `NEP` 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: NEP.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. |
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.
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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) |
Sets the initial space from which the eigensolver starts to iterate. Parameters ---------- space: Vec or sequence of Vec The initial space |
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. |
Associate a polynomial eigensolver object to the nonlinear eigensolver. Parameters ---------- pep: `PEP` The polynomial eigensolver. |
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 |
Associate a linear solver object to the nonlinear eigensolver. Parameters ---------- ksp: `KSP` The linear solver object. |
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. |
Associate a linear eigensolver object to the nonlinear eigensolver. Parameters ---------- eps: `EPS` The linear eigensolver. |
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. |
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. |
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). |
Sets a list of shifts to be used in the Rational Krylov method. Parameters ---------- shifts: array of scalars Values specifying the shifts. |
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. |
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.
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Specifies the type of the eigenvalue problem. Parameters ---------- problem_type: `NEP.ProblemType` enumerate The problem type to be set. |
Associates a region object to the eigensolver. Parameters ---------- rg: RG The region context. |
Sets a flag to keep the tolerance used in the linear solver constant. Parameters ---------- cct: bool If True, the `KSP` relative tolerance is constant. |
Sets the threshold value used to switch between deflated and non-deflated iteration. Parameters ---------- deftol: float The threshold value. |
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. |
Associate a linear solver object to the nonlinear eigensolver. Parameters ---------- ksp: `KSP` The linear solver object. |
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. |
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. |
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 |
Sets the threshold value used to switch between deflated and non-deflated iteration. Parameters ---------- deftol: float The threshold value. |
Associate a linear eigensolver object to the nonlinear eigensolver. Parameters ---------- eps: `EPS` The linear eigensolver. |
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. |
Associate a linear solver object to the nonlinear eigensolver. Parameters ---------- ksp: `KSP` The linear solver object. |
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. |
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 in convergence tests. Parameters ---------- tol: float, optional The convergence tolerance. maxit: 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. |
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. |
Selects the particular solver to be used in the NEP object. Parameters ---------- nep_type: `NEP.Type` enumerate The solver to be used. |
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. |
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 NEP data structure. Parameters ---------- viewer: Viewer, optional. Visualization context; if not provided, the standard output is used.
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