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Class EPS class of method |
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ConvergedReason EPS convergence reasons |
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Extraction EPS extraction technique |
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LanczosReorthogType EPS Lanczos reorthogonalization type |
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PowerShiftType EPS Power shift type. |
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ProblemType EPS problem type |
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Type EPS type |
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Which EPS desired piece 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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extraction | |||
ip | |||
max_it | |||
problem_type | |||
st | |||
target | |||
tol | |||
which | |||
Inherited from Inherited from |
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Add vectors to the basis of the deflation space. Parameters
NotesWhen a deflation space is given, the eigensolver seeks the eigensolution in the restriction of the problem to the orthogonal complement of this space. This can be used for instance in the case that an invariant subspace is known beforehand (such as the nullspace of the matrix). The basis vectors can be provided all at once or incrementally with several calls to attachDeflationSpace(). Set |
Computes the relative error bound associated with the i-th computed eigenpair. Parameters
Returns
NotesThe index i should be a value between 0 and nconv-1 (see getConverged(). Eigenpairs are indexed according to the ordering criterion established with setWhichEigenpairs(). |
Computes the left relative error bound associated with the i-th computed eigenpair (only available in two-sided eigensolvers). Parameters
Returns
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Computes the norm of the residual vector associated with the i-th computed eigenpair. Parameters
Returns
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Computes the norm of the residual vector associated with the i-th computed left eigenpair (only available in two-sided eigensolvers). Parameters
Returns
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Creates the EPS object. Parameters
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Gets the type of reorthogonalization used during the Arnoldi iteration. Returns
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Gets the eigensolver class from the EPS object. Returns
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Gets the number of converged eigenpairs. Returns
NotesThis function should be called after solve() has finished. |
Gets the reason why the solve() iteration was stopped. Returns
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Gets the number of eigenvalues to compute and the dimension of the subspace. Returns
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Gets the i-th solution of the eigenproblem as computed by solve(). The solution consists of both the eigenvalue and the eigenvector. Parameters
Returns
NotesThe index i should be a value between 0 and nconv-1 (see getConverged(). Eigenpairs are indexed according to the ordering criterion established with setWhichEigenpairs(). |
Returns the error estimate associated to the i-th computed eigenpair. Parameters
Returns
NotesThis is the error estimate used internally by the eigensolver. The actual error bound can be computed with computeRelativeError(). |
Returns the left error estimate associated to the i-th computed eigenpair (only available in two-sided eigensolvers). Parameters
Returns
NotesThis is the error estimate used internally by the eigensolver. The actual error bound can be computed with computeRelativeError(). |
Gets the extraction type used by the EPS object. Returns
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Obtain the inner product associated to the eigensolver. Returns
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Gets the initial vector associated with the eigensolver; if the vector was not set it will return a NULL vector or a vector randomly generated by setUp(). Returns
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Gets the left initial vector associated with the eigensolver; if the vector was not set it will return a NULL vector or a vector randomly generated by setUp(). Returns
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Gets an orthonormal basis of the computed invariant subspace. Returns
NotesThis function should be called after solve() has finished. The returned vectors span an invariant subspace associated with the computed eigenvalues. An invariant subspace X of A` satisfies ``A x in X for all x in X (a similar definition applies for generalized eigenproblems). |
Gets an orthonormal basis of the computed left invariant subspace (only available in two-sided eigensolvers). Returns
NotesSee getInvariantSubspace() for additional information. |
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
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Gets the type of reorthogonalization used during the Lanczos iteration. Returns
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Gets the total number of operator applications, inner product operations and linear iterations used by the ST object during the last solve() call. Returns
NotesWhen the eigensolver algorithm invokes ST.apply() then a linear system must be solved (except in the case of standard eigenproblems and shift transformation). The number of iterations required in this solve is accumulated into a counter whose value is returned by this function. These counters are reset to zero at each successive call to solve(). |
Gets the matrices associated with the eigenvalue problem. Returns
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Gets the prefix used for searching for all EPS options in the database. Returns
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Gets the type of shifts used during the power iteration. Returns
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Gets the problem type from the EPS object. Returns
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Obtain the spectral transformation (ST) object associated to the eigensolver object. Returns
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Gets the value of the target. Returns
NotesIf the target was not set by the user, then zero is returned. |
Gets the tolerance and maximum iteration count used by the default EPS convergence tests. Returns
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Gets the EPS type of this object. Returns
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Gets the i-th eigenvalue as computed by solve(). Parameters
Returns
NotesThe index i should be a value between 0 and nconv-1 (see getConverged(). Eigenpairs are indexed according to the ordering criterion established with setWhichEigenpairs(). |
Gets the i-th eigenvector as computed by solve(). Parameters
NotesThe index i should be a value between 0 and nconv-1 (see getConverged(). Eigenpairs are indexed according to the ordering criterion established with setWhichEigenpairs(). |
Gets the i-th left eigenvector as computed by solve(), (only available in two-sided eigensolvers). Parameters
NotesThe index i should be a value between 0 and nconv-1 (see getConverged(). Eigenpairs are indexed according to the ordering criterion established with setWhichEigenpairs(). |
Returns which portion of the spectrum is to be sought. Returns
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Tells whether the EPS object corresponds to a generalized eigenvalue problem. Returns
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Tells whether the EPS object corresponds to a Hermitian eigenvalue problem. Returns
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Activates or deactivates delayed reorthogonalization in the Arnoldi iteration. Parameters
NotesThis call is only relevant if the type was set to EPS.Type.ARNOLDI with setType(). Delayed reorthogonalization is an aggressive optimization for the Arnoldi eigensolver than may provide better scalability, but sometimes makes the solver converge less than the default algorithm. |
Specifies the eigensolver class, either one-sided or two-sided. Parameters
NotesAllowed solver classes are: one-sided (EPS.Class.ONE_SIDE) and two-sided (EPS.Class.TWO_SIDE). One-sided eigensolvers are the standard ones, which allow the computation of eigenvalues and (right) eigenvectors, whereas two-sided eigensolvers compute left eigenvectors as well. |
Sets the number of eigenvalues to compute and the dimension of the subspace. Parameters
NotesUse DECIDE for The parameters
The value of |
Sets the extraction type used by the EPS object. Parameters
NotesNot all eigensolvers support all types of extraction. See the SLEPc documentation for details. By default, a standard Rayleigh-Ritz extraction is used. Other extractions may be useful when computing interior eigenvalues. Harmonic-type extractions are used in combination with a target. See setTarget(). |
Sets EPS options from the options database. This routine must be called before setUp() if the user is to be allowed to set the solver type. NotesTo see all options, run your program with the -help option.
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Associates an inner product to the eigensolver. Parameters
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Sets the initial vector from which the eigensolver starts to iterate. Parameters
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Sets the left initial vector from which the eigensolver starts to iterate, corresponding to the left recurrence (two-sided solvers). Parameters
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Sets the type of reorthogonalization used during the Lanczos iteration. Parameters
NotesThis call is only relevant if the type was set to EPS.Type.LANCZOS with setType(). |
Sets the matrices associated with the eigenvalue problem. Parameters
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Sets the prefix used for searching for all EPS options in the database. Parameters
NotesA hyphen (-) must NOT be given at the beginning of the prefix name. The first character of all runtime options is AUTOMATICALLY the hyphen. For example, to distinguish between the runtime options for two different EPS contexts, one could call: E1.setOptionsPrefix("eig1_") E2.setOptionsPrefix("eig2_")
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Sets the type of shifts used during the power iteration. This can be used to emulate the Rayleigh Quotient Iteration (RQI) method. Parameters
NotesThis call is only relevant if the type was set to EPS.Type.POWER with setType(). By default, shifts are constant (EPS.PowerShiftType.CONSTANT) and the iteration is the simple power method (or inverse iteration if a shift-and-invert transformation is being used). A variable shift can be specified (EPS.PowerShiftType.RAYLEIGH or EPS.PowerShiftType.WILKINSON). In this case, the iteration behaves rather like a cubic converging method as RQI. |
Specifies the type of the eigenvalue problem. Parameters
NotesAllowed values are: Hermitian (HEP), non-Hermitian (NHEP), generalized Hermitian (GHEP), generalized non-Hermitian (GNHEP), and generalized non-Hermitian with positive semi-definite B (PGNHEP). This function must be used to instruct SLEPc to exploit symmetry. If no problem type is specified, by default a non-Hermitian problem is assumed (either standard or generalized). If the user knows that the problem is Hermitian (i.e. A=A^H) or generalized Hermitian (i.e. A=A^H, B=B^H, and B positive definite) then it is recommended to set the problem type so that eigensolver can exploit these properties. |
Associates a spectral transformation object to the eigensolver. Parameters
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Sets the value of the target. Parameters
NotesThe target is a scalar value used to determine the portion of the spectrum of interest. If the target is not specified, then eigenvalues are computed according to the which parameter, see setWhichEigenpairs(). If the target is specified, then the sought-after eigenvalues are those closest to the target. |
Sets the tolerance and maximum iteration count used by the default EPS convergence tests. Parameters
NotesUse DECIDE for maxits to assign a reasonably good value, which is dependent on the solution method. |
Selects the particular solver to be used in the EPS object. Parameters
NotesSee EPS.Type for available methods. The default is EPS.Type.KRYLOVSCHUR. Normally, it is best to use setFromOptions() and then set the EPS type from the options database rather than by using this routine. Using the options database provides the user with maximum flexibility in evaluating the different available methods. |
Sets up all the internal data structures necessary for the execution of the eigensolver. NotesThis function need not be called explicitly in most cases, since solve() calls it. It can be useful when one wants to measure the set-up time separately from the solve time. |
Specifies which portion of the spectrum is to be sought. Parameters
NotesNot all eigensolvers implemented in EPS account for all the possible values. Also, some values make sense only for certain types of problems. If SLEPc is compiled for real numbers EPS.Which.LARGEST_IMAGINARY and EPS.Which.SMALLEST_IMAGINARY use the absolute value of the imaginary part for eigenvalue selection. |
Prints the EPS data structure. Parameters
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