slepc4py.SLEPc.EPS#

class slepc4py.SLEPc.EPS#

Bases: Object

Eigenvalue Problem Solver.

The Eigenvalue Problem Solver (EPS) is the object provided by slepc4py for specifying a linear eigenvalue problem, either in standard or generalized form. It provides uniform and efficient access to all of the linear eigensolvers included in the package.

Enumerations

`Balance`	EPS type of balancing used for non-Hermitian problems.
`CISSExtraction`	EPS CISS extraction technique.
`CISSQuadRule`	EPS CISS quadrature rule.
`Conv`	EPS convergence test.
`ConvergedReason`	EPS convergence reasons.
`ErrorType`	EPS error type to assess accuracy of computed solutions.
`Extraction`	EPS extraction technique.
`KrylovSchurBSEType`	EPS Krylov-Schur method for BSE problems.
`LanczosReorthogType`	EPS Lanczos reorthogonalization type.
`PowerShiftType`	EPS Power shift type.
`ProblemType`	EPS problem type.
`Stop`	EPS stopping test.
`Type`	EPS type.
`Which`	EPS desired part of spectrum.

Methods Summary

`appendOptionsPrefix`([prefix])	Append to the prefix used for searching for all EPS options in the database.
`cancelMonitor`()	Clear all monitors for an `EPS` object.
`computeError`(i[, etype])	Compute the error associated with the i-th computed eigenpair.
`create`([comm])	Create the EPS object.
`destroy`()	Destroy the EPS object.
`errorView`([etype, viewer])	Display the errors associated with the computed solution.
`getArbitrarySelection`()	Get the arbitrary selection function.
`getArnoldiDelayed`()	Get the type of reorthogonalization used during the Arnoldi iteration.
`getBV`()	Get the basis vectors object associated to the eigensolver.
`getBalance`()	Get the balancing type used by the EPS, and the associated parameters.
`getCISSExtraction`()	Get the extraction technique used in the CISS solver.
`getCISSKSPs`()	Get the array of linear solver objects associated with the CISS solver.
`getCISSQuadRule`()	Get the quadrature rule used in the CISS solver.
`getCISSRefinement`()	Get the values of various refinement parameters in the CISS solver.
`getCISSSizes`()	Get the values of various size parameters in the CISS solver.
`getCISSThreshold`()	Get the values of various threshold parameters in the CISS solver.
`getCISSUseST`()	Get the flag indicating the use of the `ST` object in the CISS solver.
`getConverged`()	Get the number of converged eigenpairs.
`getConvergedReason`()	Get the reason why the `solve()` iteration was stopped.
`getConvergenceTest`()	Get how to compute the error estimate used in the convergence test.
`getDS`()	Get the direct solver associated to the eigensolver.
`getDimensions`()	Get number of eigenvalues to compute and the dimension of the subspace.
`getEigenpair`(i[, Vr, Vi])	Get the i-th solution of the eigenproblem as computed by `solve()`.
`getEigenvalue`(i)	Get the i-th eigenvalue as computed by `solve()`.
`getEigenvalueComparison`()	Get the eigenvalue comparison function.
`getEigenvector`(i[, Vr, Vi])	Get the i-th right eigenvector as computed by `solve()`.
`getErrorEstimate`(i)	Get the error estimate associated to the i-th computed eigenpair.
`getExtraction`()	Get the extraction type used by the EPS object.
`getGDBOrth`()	Get the orthogonalization used in the search subspace.
`getGDBlockSize`()	Get the number of vectors to be added to the searching space.
`getGDDoubleExpansion`()	Get a flag indicating whether the double expansion variant is active.
`getGDInitialSize`()	Get the initial size of the searching space.
`getGDKrylovStart`()	Get a flag indicating if the search subspace is started with a Krylov basis.
`getGDRestart`()	Get the number of vectors of the search space after restart.
`getInterval`()	Get the computational interval for spectrum slicing.
`getInvariantSubspace`()	Get an orthonormal basis of the computed invariant subspace.
`getIterationNumber`()	Get the current iteration number.
`getJDBOrth`()	Get the orthogonalization used in the search subspace.
`getJDBlockSize`()	Get the number of vectors to be added to the searching space.
`getJDConstCorrectionTol`()	Get the flag indicating if the dynamic stopping is being used.
`getJDFix`()	Get the threshold for changing the target in the correction equation.
`getJDInitialSize`()	Get the initial size of the searching space.
`getJDKrylovStart`()	Get a flag indicating if the search subspace is started with a Krylov basis.
`getJDRestart`()	Get the number of vectors of the search space after restart.
`getKrylovSchurBSEType`()	Get the method used for BSE structured eigenproblems (Krylov-Schur).
`getKrylovSchurDetectZeros`()	Get the flag that enforces zero detection in spectrum slicing.
`getKrylovSchurDimensions`()	Get the dimensions used for each subsolve step (spectrum slicing).
`getKrylovSchurInertias`()	Get the values of the shifts and their corresponding inertias.
`getKrylovSchurKSP`()	Get the linear solver object associated with the internal `EPS` object.
`getKrylovSchurLocking`()	Get the locking flag used in the Krylov-Schur method.
`getKrylovSchurPartitions`()	Get the number of partitions of the communicator (spectrum slicing).
`getKrylovSchurRestart`()	Get the restart parameter used in the Krylov-Schur method.
`getKrylovSchurSubcommInfo`()	Get information related to the case of doing spectrum slicing.
`getKrylovSchurSubcommMats`()	Get the eigenproblem matrices stored in the subcommunicator.
`getKrylovSchurSubcommPairs`(i[, v])	Get the i-th eigenpair stored in the multi-communicator of the process.
`getKrylovSchurSubintervals`()	Get the points that delimit the subintervals.
`getLOBPCGBlockSize`()	Get the block size used in the LOBPCG method.
`getLOBPCGLocking`()	Get the locking flag used in the LOBPCG method.
`getLOBPCGRestart`()	Get the restart parameter used in the LOBPCG method.
`getLanczosReorthogType`()	Get the type of reorthogonalization used during the Lanczos iteration.
`getLeftEigenvector`(i[, Wr, Wi])	Get the i-th left eigenvector as computed by `solve()`.
`getLyapIIRanks`()	Get the rank values used for the Lyapunov step.
`getMonitor`()	Get the list of monitor functions.
`getOperators`()	Get the matrices associated with the eigenvalue problem.
`getOptionsPrefix`()	Get the prefix used for searching for all EPS options in the database.
`getPowerShiftType`()	Get the type of shifts used during the power iteration.
`getProblemType`()	Get the problem type from the EPS object.
`getPurify`()	Get the flag indicating whether purification is activated or not.
`getRG`()	Get the region object associated to the eigensolver.
`getRQCGReset`()	Get the reset parameter used in the RQCG method.
`getST`()	Get the spectral transformation object associated to the eigensolver.
`getStoppingTest`()	Get the stopping test function.
`getTarget`()	Get the value of the target.
`getThreshold`()	Get the threshold used in the threshold stopping test.
`getTolerances`()	Get the tolerance and max.
`getTrackAll`()	Get the flag indicating if all residual norms must be computed or not.
`getTrueResidual`()	Get the flag indicating if true residual must be computed explicitly.
`getTwoSided`()	Get the flag indicating if a two-sided variant of the algorithm is being used.
`getType`()	Get the EPS type of this object.
`getWhichEigenpairs`()	Get which portion of the spectrum is to be sought.
`isGeneralized`()	Tell if the EPS object corresponds to a generalized eigenproblem.
`isHermitian`()	Tell if the EPS object corresponds to a Hermitian eigenproblem.
`isPositive`()	Eigenproblem requiring a positive (semi-) definite matrix \(B\).
`isStructured`()	Tell if the EPS object corresponds to a structured eigenvalue problem.
`reset`()	Reset the EPS object.
`setArbitrarySelection`(arbitrary[, args, kargs])	Set an arbitrary selection criterion function.
`setArnoldiDelayed`(delayed)	Set (toggle) delayed reorthogonalization in the Arnoldi iteration.
`setBV`(bv)	Set a basis vectors object associated to the eigensolver.
`setBalance`([balance, iterations, cutoff])	Set the balancing technique to be used by the eigensolver.
`setCISSExtraction`(extraction)	Set the extraction technique used in the CISS solver.
`setCISSQuadRule`(quad)	Set the quadrature rule used in the CISS solver.
`setCISSRefinement`([inner, blsize])	Set the values of various refinement parameters in the CISS solver.
`setCISSSizes`([ip, bs, ms, npart, bsmax, ...])	Set the values of various size parameters in the CISS solver.
`setCISSThreshold`([delta, spur])	Set the values of various threshold parameters in the CISS solver.
`setCISSUseST`(usest)	Set a flag indicating that the CISS solver will use the `ST` object.
`setConvergenceTest`(conv)	Set how to compute the error estimate used in the convergence test.
`setDS`(ds)	Set a direct solver object associated to the eigensolver.
`setDeflationSpace`(space)	Set vectors to form a basis of the deflation space.
`setDimensions`([nev, ncv, mpd])	Set number of eigenvalues to compute and the dimension of the subspace.
`setEigenvalueComparison`(comparison[, args, ...])	Set an eigenvalue comparison function.
`setExtraction`(extraction)	Set the extraction type used by the eigensolver.
`setFromOptions`()	Set EPS options from the options database.
`setGDBOrth`(borth)	Set the orthogonalization that will be used in the search subspace.
`setGDBlockSize`(bs)	Set the number of vectors to be added to the searching space.
`setGDDoubleExpansion`(doubleexp)	Set that the search subspace is expanded with double expansion.
`setGDInitialSize`(initialsize)	Set the initial size of the searching space.
`setGDKrylovStart`([krylovstart])	Set (toggle) starting the search subspace with a Krylov basis.
`setGDRestart`([minv, plusk])	Set the number of vectors of the search space after restart.
`setInitialSpace`(space)	Set the initial space from which the eigensolver starts to iterate.
`setInterval`(inta, intb)	Set the computational interval for spectrum slicing.
`setJDBOrth`(borth)	Set the orthogonalization that will be used in the search subspace.
`setJDBlockSize`(bs)	Set the number of vectors to be added to the searching space.
`setJDConstCorrectionTol`(constant)	Deactivate the dynamic stopping criterion.
`setJDFix`(fix)	Set the threshold for changing the target in the correction equation.
`setJDInitialSize`(initialsize)	Set the initial size of the searching space.
`setJDKrylovStart`([krylovstart])	Set (toggle) starting the search subspace with a Krylov basis.
`setJDRestart`([minv, plusk])	Set the number of vectors of the search space after restart.
`setKrylovSchurBSEType`(bse)	Set the Krylov-Schur variant used for BSE structured eigenproblems.
`setKrylovSchurDetectZeros`(detect)	Set the flag that enforces zero detection in spectrum slicing.
`setKrylovSchurDimensions`([nev, ncv, mpd])	Set the dimensions used for each subsolve step (spectrum slicing).
`setKrylovSchurLocking`(lock)	Set (toggle) locking/non-locking variants of the Krylov-Schur method.
`setKrylovSchurPartitions`(npart)	Set the number of partitions of the communicator (spectrum slicing).
`setKrylovSchurRestart`(keep)	Set the restart parameter for the Krylov-Schur method.
`setKrylovSchurSubintervals`(subint)	Set the subinterval boundaries.
`setLOBPCGBlockSize`(bs)	Set the block size of the LOBPCG method.
`setLOBPCGLocking`(lock)	Toggle between locking and non-locking (LOBPCG method).
`setLOBPCGRestart`(restart)	Set the restart parameter for the LOBPCG method.
`setLanczosReorthogType`(reorthog)	Set the type of reorthogonalization used during the Lanczos iteration.
`setLeftInitialSpace`(space)	Set a left initial space from which the eigensolver starts to iterate.
`setLyapIIRanks`([rkc, rkl])	Set the ranks used in the solution of the Lyapunov equation.
`setMonitor`(monitor[, args, kargs])	Append a monitor function to the list of monitors.
`setOperators`(A[, B])	Set the matrices associated with the eigenvalue problem.
`setOptionsPrefix`([prefix])	Set the prefix used for searching for all EPS options in the database.
`setPowerShiftType`(shift)	Set the type of shifts used during the power iteration.
`setProblemType`(problem_type)	Set the type of the eigenvalue problem.
`setPurify`([purify])	Set (toggle) eigenvector purification.
`setRG`(rg)	Set a region object associated to the eigensolver.
`setRQCGReset`(nrest)	Set the reset parameter of the RQCG iteration.
`setST`(st)	Set a spectral transformation object associated to the eigensolver.
`setStoppingTest`(stopping[, args, kargs])	Set a function to decide when to stop the outer iteration of the eigensolver.
`setTarget`(target)	Set the value of the target.
`setThreshold`(thres[, rel])	Set the threshold used in the threshold stopping test.
`setTolerances`([tol, max_it])	Set the tolerance and max.
`setTrackAll`(trackall)	Set if the solver must compute the residual of all approximate eigenpairs.
`setTrueResidual`(trueres)	Set if the solver must compute the true residual explicitly or not.
`setTwoSided`(twosided)	Set to use a two-sided variant that also computes left eigenvectors.
`setType`(eps_type)	Set the particular solver to be used in the EPS object.
`setUp`()	Set up all the internal data structures.
`setWhichEigenpairs`(which)	Set which portion of the spectrum is to be sought.
`solve`()	Solve the eigensystem.
`updateKrylovSchurSubcommMats`([s, a, Au, t, ...])	Update the eigenproblem matrices stored internally in the communicator.
`valuesView`([viewer])	Display the computed eigenvalues in a viewer.
`vectorsView`([viewer])	Output computed eigenvectors to a viewer.
`view`([viewer])	Print the EPS data structure.

Attributes Summary

`bv`	The basis vectors (`BV`) object associated.
`ds`	The direct solver (`DS`) object associated.
`extraction`	The type of extraction technique to be employed.
`max_it`	The maximum iteration count.
`problem_type`	The type of the eigenvalue problem.
`purify`	Eigenvector purification.
`rg`	The region (`RG`) object associated.
`st`	The spectral transformation (`ST`) object associated.
`target`	The value of the target.
`tol`	The tolerance.
`track_all`	Compute the residual norm of all approximate eigenpairs.
`true_residual`	Compute the true residual explicitly.
`two_sided`	Two-sided that also computes left eigenvectors.
`which`	The portion of the spectrum to be sought.

Methods Documentation

appendOptionsPrefix(prefix=None)#

Append to the prefix used for searching for all EPS options in the database.

Logically collective.

Parameters:: prefix (str | None) – The prefix string to prepend to all EPS option requests.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:513

cancelMonitor()#

Clear all monitors for an EPS object.

Logically collective.

See also

EPSMonitorCancel

Source code at slepc4py/SLEPc/EPS.pyx:1860

Return type:: None

computeError(i, etype=None)#

Compute the error associated with the i-th computed eigenpair.

Collective.

Compute 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 (ErrorType | None) – The error type to compute.

Returns:

The error bound, computed in various ways from the residual norm \(\|Ax-\lambda Bx\|_2\) where \(\lambda\) is the eigenvalue and \(x\) is the eigenvector.

Return type:

float

Notes

The index i should be a value between 0 and nconv-1 (see getConverged()).

If the computation of left eigenvectors was enabled with setTwoSided(), then the error will be computed using the maximum of the value above and the left residual norm \(\|y^*A-\lambda y^*B\|_2\), where \(y\) is the approximate left eigenvector.

Source code at slepc4py/SLEPc/EPS.pyx:2213

create(comm=None)#

Create the EPS object.

Collective.

Parameters:: comm (Comm | None) – MPI communicator; if not provided, it defaults to all processes.
Return type:: Self

See also

EPSCreate

Source code at slepc4py/SLEPc/EPS.pyx:396

destroy()#

Destroy the EPS object.

Collective.

See also

EPSDestroy

Source code at slepc4py/SLEPc/EPS.pyx:370

Return type:: Self

errorView(etype=None, viewer=None)#

Display the errors associated with the computed solution.

Collective.

Display the errors and the eigenvalues.

Parameters:

etype (ErrorType | None) – The error type to compute.
viewer (petsc4py.PETSc.Viewer | None) – Visualization context; if not provided, the standard output is used.

Return type:

None

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.

Source code at slepc4py/SLEPc/EPS.pyx:2256

getArbitrarySelection()#

Get the arbitrary selection function.

Not collective.

Returns:: The arbitrary selection function.
Return type:: EPSArbitraryFunction

See also

setArbitrarySelection

Source code at slepc4py/SLEPc/EPS.pyx:1754

getArnoldiDelayed()#

Get the type of reorthogonalization used during the Arnoldi iteration.

Not collective.

Returns:: True if delayed reorthogonalization is to be used.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:2411

getBV()#

Get the basis vectors object associated to the eigensolver.

Not collective.

Returns:: The basis vectors context.
Return type:: BV

See also

setBV, EPSGetBV

Source code at slepc4py/SLEPc/EPS.pyx:1407

getBalance()#

Get the balancing type used by the EPS, and the associated parameters.

Not collective.

Returns:

balance (Balance) – The balancing method.
iterations (int) – Number of iterations of the balancing algorithm.
cutoff (float) – Cutoff value.

Return type:

tuple[Balance, int, float]

See also

setBalance, EPSGetBalance

Source code at slepc4py/SLEPc/EPS.pyx:693

getCISSExtraction()#

Get the extraction technique used in the CISS solver.

Not collective.

Returns:: The extraction technique.
Return type:: CISSExtraction

Source code at slepc4py/SLEPc/EPS.pyx:3957

getCISSKSPs()#

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

Not collective.

Returns:: The linear solver objects.
Return type:: list of petsc4py.PETSc.KSP

Notes

The number of petsc4py.PETSc.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.

See also

setCISSSizes, EPSCISSGetKSPs

Source code at slepc4py/SLEPc/EPS.pyx:4238

getCISSQuadRule()#

Get the quadrature rule used in the CISS solver.

Not collective.

Returns:: The quadrature rule.
Return type:: CISSQuadRule

See also

setCISSQuadRule, EPSCISSGetQuadRule

Source code at slepc4py/SLEPc/EPS.pyx:3994

getCISSRefinement()#

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

Not collective.

Returns:

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

Return type:

tuple[int, int]

Source code at slepc4py/SLEPc/EPS.pyx:4169

getCISSSizes()#

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

Not collective.

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.

Return type:

tuple[int, int, int, int, int, bool]

See also

setCISSSizes, EPSCISSGetSizes

Source code at slepc4py/SLEPc/EPS.pyx:4067

getCISSThreshold()#

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

Not collective.

Returns:

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

Return type:

tuple[float, float]

Source code at slepc4py/SLEPc/EPS.pyx:4124

getCISSUseST()#

Get the flag indicating the use of the ST object in the CISS solver.

Not collective.

Returns:: Whether to use the ST object or not.
Return type:: bool

See also

setCISSUseST, EPSCISSGetUseST

Source code at slepc4py/SLEPc/EPS.pyx:4219

getConverged()#

Get the number of converged eigenpairs.

Not collective.

Returns:: nconv – Number of converged eigenpairs.
Return type:: int

Notes

This function should be called after solve() has finished.

The value nconv may be different from the number of requested solutions nev, but not larger than ncv, see setDimensions().

Source code at slepc4py/SLEPc/EPS.pyx:1960

getConvergedReason()#

Get the reason why the solve() iteration was stopped.

Not collective.

Returns:: Negative value indicates diverged, positive value converged.
Return type:: ConvergedReason

Source code at slepc4py/SLEPc/EPS.pyx:1941

getConvergenceTest()#

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

Not collective.

Returns:: The method used to compute the error estimate used in the convergence test.
Return type:: Conv

Source code at slepc4py/SLEPc/EPS.pyx:1177

getDS()#

Get the direct solver associated to the eigensolver.

Not collective.

Returns:: The direct solver context.
Return type:: DS

See also

setDS, EPSGetDS

Source code at slepc4py/SLEPc/EPS.pyx:1444

getDimensions()#

Get number of eigenvalues to compute and the dimension of the subspace.

Not collective.

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.

Return type:

tuple[int, int, int]

See also

setDimensions, EPSGetDimensions

Source code at slepc4py/SLEPc/EPS.pyx:1290

getEigenpair(i, Vr=None, Vi=None)#

Get the i-th solution of the eigenproblem as computed by solve().

Collective.

The solution consists of both the eigenvalue and the eigenvector.

Parameters:

i (int) – Index of the solution to be obtained.
Vr (Vec | None) – Placeholder for the returned eigenvector (real part).
Vi (Vec | None) – Placeholder for the returned eigenvector (imaginary part).

Returns:

e – The computed eigenvalue. It will be a real variable in case of a Hermitian or generalized Hermitian eigenproblem. Otherwise it will be a complex variable (possibly with zero imaginary part).

Return type:

Scalar

Notes

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

The 2-norm of the eigenvector is one unless the problem is generalized Hermitian. In this case the eigenvector is normalized with respect to the norm defined by the B matrix.

Source code at slepc4py/SLEPc/EPS.pyx:2090

getEigenvalue(i)#

Get the i-th eigenvalue as computed by solve().

Not collective.

Parameters:: i (int) – Index of the solution to be obtained.
Returns:: The computed eigenvalue. It will be a real variable in case of a Hermitian or generalized Hermitian eigenproblem. Otherwise it will be a complex variable (possibly with zero imaginary part).
Return type:: Scalar

Notes

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

Source code at slepc4py/SLEPc/EPS.pyx:1986

getEigenvalueComparison()#

Get the eigenvalue comparison function.

Not collective.

Returns:: The eigenvalue comparison function.
Return type:: EPSEigenvalueComparison

See also

setEigenvalueComparison

Source code at slepc4py/SLEPc/EPS.pyx:1801

getEigenvector(i, Vr=None, Vi=None)#

Get the i-th right eigenvector as computed by solve().

Collective.

Parameters:

i (int) – Index of the solution to be obtained.
Vr (Vec | None) – Placeholder for the returned eigenvector (real part).
Vi (Vec | None) – Placeholder for the returned eigenvector (imaginary part).

Return type:

None

Notes

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

The 2-norm of the eigenvector is one unless the problem is generalized Hermitian. In this case the eigenvector is normalized with respect to the norm defined by the B matrix.

Source code at slepc4py/SLEPc/EPS.pyx:2024

getErrorEstimate(i)#

Get the error estimate associated to the i-th computed eigenpair.

Not collective.

Parameters:: i (int) – Index of the solution to be considered.
Returns:: Error estimate.
Return type:: float

Notes

This is the error estimate used internally by the eigensolver. The actual error bound can be computed with computeError().

See also

computeError, EPSGetErrorEstimate

Source code at slepc4py/SLEPc/EPS.pyx:2184

getExtraction()#

Get the extraction type used by the EPS object.

Not collective.

Returns:: The method of extraction.
Return type:: Extraction

See also

setExtraction, EPSGetExtraction

Source code at slepc4py/SLEPc/EPS.pyx:768

getGDBOrth()#

Get the orthogonalization used in the search subspace.

Not collective.

Get the orthogonalization used in the search subspace in case of generalized Hermitian problems.

Returns:: Whether to B-orthogonalize the search subspace.
Return type:: bool

See also

setGDBOrth, EPSGDGetBOrth

Source code at slepc4py/SLEPc/EPS.pyx:3334

getGDBlockSize()#

Get the number of vectors to be added to the searching space.

Not collective.

Get the number of vectors to be added to the searching space in every iteration.

Returns:: The number of vectors added to the search space in every iteration.
Return type:: int

See also

setGDBlockSize, EPSGDGetBlockSize

Source code at slepc4py/SLEPc/EPS.pyx:3193

getGDDoubleExpansion()#

Get a flag indicating whether the double expansion variant is active.

Not collective.

Get a flag indicating whether the double expansion variant has been activated or not.

Returns:: True if using double expansion.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:3382

getGDInitialSize()#

Get the initial size of the searching space.

Not collective.

Returns:: The number of vectors of the initial searching subspace.
Return type:: int

Source code at slepc4py/SLEPc/EPS.pyx:3294

getGDKrylovStart()#

Get a flag indicating if the search subspace is started with a Krylov basis.

Not collective.

Returns:: True if starting the search subspace with a Krylov basis.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:3153

getGDRestart()#

Get the number of vectors of the search space after restart.

Not collective.

Get the number of vectors of the search space after restart and the number of vectors saved from the previous iteration.

Returns:

minv (int) – The number of vectors of the search subspace after restart.
plusk (int) – The number of vectors saved from the previous iteration.

Return type:

tuple[int, int]

See also

setGDRestart, EPSGDGetRestart

Source code at slepc4py/SLEPc/EPS.pyx:3241

getInterval()#

Get the computational interval for spectrum slicing.

Not collective.

Returns:

inta (float) – The left end of the interval.
intb (float) – The right end of the interval.

Return type:

tuple[float, float]

Notes

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

See also

setInterval, EPSGetInterval

Source code at slepc4py/SLEPc/EPS.pyx:972

getInvariantSubspace()#

Get an orthonormal basis of the computed invariant subspace.

Collective.

Returns:: Basis of the invariant subspace.
Return type:: list of petsc4py.PETSc.Vec

Notes

This 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).

Source code at slepc4py/SLEPc/EPS.pyx:2140

getIterationNumber()#

Get the current iteration number.

Not collective.

If the call to solve() is complete, then it returns the number of iterations carried out by the solution method.

Returns:: Iteration number.
Return type:: int

Source code at slepc4py/SLEPc/EPS.pyx:1919

getJDBOrth()#

Get the orthogonalization used in the search subspace.

Not collective.

Get the orthogonalization used in the search subspace in case of generalized Hermitian problems.

Returns:: Whether to B-orthogonalize the search subspace.
Return type:: bool

See also

setJDBOrth, EPSJDGetBOrth

Source code at slepc4py/SLEPc/EPS.pyx:3693

getJDBlockSize()#

Get the number of vectors to be added to the searching space.

Not collective.

Get the number of vectors to be added to the searching space in every iteration.

Returns:: The number of vectors added to the search space in every iteration.
Return type:: int

See also

setJDBlockSize, EPSJDGetBlockSize

Source code at slepc4py/SLEPc/EPS.pyx:3464

getJDConstCorrectionTol()#

Get the flag indicating if the dynamic stopping is being used.

Not collective.

Returns:: True if the dynamic stopping criterion is not being used.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:3653

getJDFix()#

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

Not collective.

Returns:: The threshold for changing the target.
Return type:: float

See also

setJDFix, EPSJDGetFix

Source code at slepc4py/SLEPc/EPS.pyx:3608

getJDInitialSize()#

Get the initial size of the searching space.

Not collective.

Returns:: The number of vectors of the initial searching subspace.
Return type:: int

Source code at slepc4py/SLEPc/EPS.pyx:3565

getJDKrylovStart()#

Get a flag indicating if the search subspace is started with a Krylov basis.

Not collective.

Returns:: True if starting the search subspace with a Krylov basis.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:3424

getJDRestart()#

Get the number of vectors of the search space after restart.

Not collective.

Get the number of vectors of the search space after restart and the number of vectors saved from the previous iteration.

Returns:

minv (int) – The number of vectors of the search subspace after restart.
plusk (int) – The number of vectors saved from the previous iteration.

Return type:

tuple[int, int]

See also

setJDRestart, EPSJDGetRestart

Source code at slepc4py/SLEPc/EPS.pyx:3512

getKrylovSchurBSEType()#

Get the method used for BSE structured eigenproblems (Krylov-Schur).

Not collective.

Returns:: The BSE method.
Return type:: KrylovSchurBSEType

Source code at slepc4py/SLEPc/EPS.pyx:2499

getKrylovSchurDetectZeros()#

Get the flag that enforces zero detection in spectrum slicing.

Not collective.

Returns:: The zero detection flag.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:2693

getKrylovSchurDimensions()#

Get the dimensions used for each subsolve step (spectrum slicing).

Not collective.

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.

Return type:

tuple[int, int, int]

Source code at slepc4py/SLEPc/EPS.pyx:2752

getKrylovSchurInertias()#

Get the values of the shifts and their corresponding inertias.

Not collective.

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

Returns:

shifts (ArrayReal) – The values of the shifts used internally in the solver.
inertias (ArrayInt) – The values of the inertia in each shift.

Return type:

tuple[ArrayReal, ArrayInt]

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

If called after solve(), all shifts used internally by the solver are returned (including both endpoints and any intermediate ones). If called before solve() and after setUp() then only the information of the endpoints of subintervals is available.

Source code at slepc4py/SLEPc/EPS.pyx:3050

getKrylovSchurKSP()#

Get the linear solver object associated with the internal EPS object.

Collective.

Get the linear solver object associated with the internal EPS object in case of doing spectrum slicing for a computational interval.

Returns:: The linear solver object.
Return type:: petsc4py.PETSc.KSP

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

When invoked to compute all eigenvalues in an interval with spectrum slicing, KRYLOVSCHUR creates another EPS object internally that is used to compute eigenvalues by chunks near selected shifts. This function allows access to the KSP object associated to this internal EPS object.

In case of having more than one partition, the returned KSP will be different in MPI processes belonging to different partitions. Hence, if required, setKrylovSchurPartitions() must be called BEFORE this function.

Source code at slepc4py/SLEPc/EPS.pyx:3094

getKrylovSchurLocking()#

Get the locking flag used in the Krylov-Schur method.

Not collective.

Returns:: The locking flag.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:2586

getKrylovSchurPartitions()#

Get the number of partitions of the communicator (spectrum slicing).

Not collective.

Returns:: The number of partitions.
Return type:: int

Source code at slepc4py/SLEPc/EPS.pyx:2640

getKrylovSchurRestart()#

Get the restart parameter used in the Krylov-Schur method.

Not collective.

Returns:: The number of vectors to be kept at restart.
Return type:: float

Source code at slepc4py/SLEPc/EPS.pyx:2542

getKrylovSchurSubcommInfo()#

Get information related to the case of doing spectrum slicing.

Collective on the subcommunicator.

Get information related to the case of doing spectrum slicing for a computational interval with multiple communicators.

Returns:

k (int) – Index of the subinterval for the calling process.
n (int) – Number of eigenvalues found in the k-th subinterval.
v (petsc4py.PETSc.Vec) – A vector owned by processes in the subcommunicator with dimensions compatible for locally computed eigenvectors.

Return type:

tuple[int, int, Vec]

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

Source code at slepc4py/SLEPc/EPS.pyx:2777

getKrylovSchurSubcommMats()#

Get the eigenproblem matrices stored in the subcommunicator.

Collective on the subcommunicator.

Get the eigenproblem matrices stored internally in the subcommunicator to which the calling process belongs.

Returns:

A (petsc4py.PETSc.Mat) – The matrix associated with the eigensystem.
B (petsc4py.PETSc.Mat) – The second matrix in the case of generalized eigenproblems.

Return type:

tuple[Mat, Mat] | tuple[Mat, None]

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set. And is relevant only when the number of partitions (setKrylovSchurPartitions()) is larger than one.

This is the analog of getOperators(), but returns the matrices distributed differently (in the subcommunicator rather than in the parent communicator).

These matrices should not be modified by the user.

Source code at slepc4py/SLEPc/EPS.pyx:2855

getKrylovSchurSubcommPairs(i, v=None)#

Get the i-th eigenpair stored in the multi-communicator of the process.

Collective on the subcommunicator (if v is given).

Get the i-th eigenpair stored internally in the multi-communicator to which the calling process belongs.

Parameters:

i (int) – Index of the solution to be obtained.
v (Vec | None) – Placeholder for the returned eigenvector.

Returns:

The computed eigenvalue.

Return type:

Scalar

Notes

Argument v must be a valid Vec object, created by calling getKrylovSchurSubcommInfo().

The index i should be a value between 0 and n-1, where n is the number of vectors in the local subinterval, see getKrylovSchurSubcommInfo().

Source code at slepc4py/SLEPc/EPS.pyx:2811

getKrylovSchurSubintervals()#

Get the points that delimit the subintervals.

Not collective.

Get the points that delimit the subintervals used in spectrum slicing with several partitions.

Returns:: Real values specifying subintervals.
Return type:: ArrayReal

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

If the user passed values with setKrylovSchurSubintervals(), then the same values are returned here. Otherwise, the values computed internally are obtained.

Source code at slepc4py/SLEPc/EPS.pyx:3012

getLOBPCGBlockSize()#

Get the block size used in the LOBPCG method.

Not collective.

Returns:: The block size.
Return type:: int

Source code at slepc4py/SLEPc/EPS.pyx:3777

getLOBPCGLocking()#

Get the locking flag used in the LOBPCG method.

Not collective.

Returns:: The locking flag.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:3864

getLOBPCGRestart()#

Get the restart parameter used in the LOBPCG method.

Not collective.

Returns:: The restart parameter.
Return type:: float

Source code at slepc4py/SLEPc/EPS.pyx:3821

getLanczosReorthogType()#

Get the type of reorthogonalization used during the Lanczos iteration.

Not collective.

Returns:: The type of reorthogonalization.
Return type:: LanczosReorthogType

Source code at slepc4py/SLEPc/EPS.pyx:2453

getLeftEigenvector(i, Wr=None, Wi=None)#

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

Collective.

Parameters:

i (int) – Index of the solution to be obtained.
Wr (Vec | None) – Placeholder for the returned left eigenvector (real part).
Wi (Vec | None) – Placeholder for the returned left eigenvector (imaginary part).

Return type:

None

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().

Source code at slepc4py/SLEPc/EPS.pyx:2058

getLyapIIRanks()#

Get the rank values used for the Lyapunov step.

Not collective.

Returns:

rkc (int) – The compressed rank.
rkl (int) – The Lyapunov rank.

Return type:

tuple[int, int]

See also

setLyapIIRanks, EPSLyapIIGetRanks

Source code at slepc4py/SLEPc/EPS.pyx:3915

getMonitor()#

Get the list of monitor functions.

Not collective.

Returns:: The list of monitor functions.
Return type:: EPSMonitorFunction

See also

setMonitor

Source code at slepc4py/SLEPc/EPS.pyx:1843

getOperators()#

Get the matrices associated with the eigenvalue problem.

Collective.

Returns:

A (petsc4py.PETSc.Mat) – The matrix associated with the eigensystem.
B (petsc4py.PETSc.Mat) – The second matrix in the case of generalized eigenproblems.

Return type:

tuple[Mat, Mat] | tuple[Mat, None]

See also

setOperators, EPSGetOperators

Source code at slepc4py/SLEPc/EPS.pyx:1518

getOptionsPrefix()#

Get the prefix used for searching for all EPS options in the database.

Not collective.

Returns:: The prefix string set for this EPS object.
Return type:: str

Source code at slepc4py/SLEPc/EPS.pyx:463

getPowerShiftType()#

Get the type of shifts used during the power iteration.

Not collective.

Returns:: The type of shift.
Return type:: PowerShiftType

Source code at slepc4py/SLEPc/EPS.pyx:2364

getProblemType()#

Get the problem type from the EPS object.

Not collective.

Returns:: The problem type that was previously set.
Return type:: ProblemType

See also

setProblemType, EPSGetProblemType

Source code at slepc4py/SLEPc/EPS.pyx:553

getPurify()#

Get the flag indicating whether purification is activated or not.

Not collective.

Returns:: Whether purification is activated or not.
Return type:: bool

See also

setPurify, EPSGetPurify

Source code at slepc4py/SLEPc/EPS.pyx:1132

getRG()#

Get the region object associated to the eigensolver.

Not collective.

Returns:: The region context.
Return type:: RG

See also

setRG, EPSGetRG

Source code at slepc4py/SLEPc/EPS.pyx:1481

getRQCGReset()#

Get the reset parameter used in the RQCG method.

Not collective.

Returns:: The number of iterations between resets.
Return type:: int

See also

setRQCGReset, EPSRQCGGetReset

Source code at slepc4py/SLEPc/EPS.pyx:3740

getST()#

Get the spectral transformation object associated to the eigensolver.

Not collective.

Returns:: The spectral transformation.
Return type:: ST

See also

setST, EPSGetST

Source code at slepc4py/SLEPc/EPS.pyx:1370

getStoppingTest()#

Get the stopping test function.

Not collective.

Returns:: The stopping test function.
Return type:: EPSStoppingFunction

See also

setStoppingTest

Source code at slepc4py/SLEPc/EPS.pyx:1708

getTarget()#

Get the value of the target.

Not collective.

Returns:: The value of the target.
Return type:: Scalar

Notes

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

See also

setTarget, EPSGetTarget

Source code at slepc4py/SLEPc/EPS.pyx:922

getThreshold()#

Get the threshold used in the threshold stopping test.

Not collective.

Returns:

thres (float) – The threshold.
rel (bool) – Whether the threshold is relative or not.

Return type:

tuple[float, bool]

See also

setThreshold, EPSGetThreshold

Source code at slepc4py/SLEPc/EPS.pyx:871

getTolerances()#

Get the tolerance and max. iter. count used for convergence tests.

Not collective.

Get the tolerance and iteration limit used by the default EPS convergence tests.

Returns:

tol (float) – The convergence tolerance.
max_it (int) – The maximum number of iterations.

Return type:

tuple[float, int]

See also

setTolerances, EPSGetTolerances

Source code at slepc4py/SLEPc/EPS.pyx:1032

getTrackAll()#

Get the flag indicating if all residual norms must be computed or not.

Not collective.

Returns:: Whether the solver computes all residuals or not.
Return type:: bool

See also

setTrackAll, EPSGetTrackAll

Source code at slepc4py/SLEPc/EPS.pyx:1253

getTrueResidual()#

Get the flag indicating if true residual must be computed explicitly.

Not collective.

Returns:: Whether the solver computes true residuals or not.
Return type:: bool

See also

setTrueResidual, EPSGetTrueResidual

Source code at slepc4py/SLEPc/EPS.pyx:1216

getTwoSided()#

Get the flag indicating if a two-sided variant of the algorithm is being used.

Not collective.

Returns:: Whether the two-sided variant is to be used or not.
Return type:: bool

See also

setTwoSided, EPSGetTwoSided

Source code at slepc4py/SLEPc/EPS.pyx:1085

getType()#

Get the EPS type of this object.

Not collective.

Returns:: The solver currently being used.
Return type:: str

See also

setType, EPSGetType

Source code at slepc4py/SLEPc/EPS.pyx:444

getWhichEigenpairs()#

Get which portion of the spectrum is to be sought.

Not collective.

Returns:: The portion of the spectrum to be sought by the solver.
Return type:: Which

Source code at slepc4py/SLEPc/EPS.pyx:815

isGeneralized()#

Tell if the EPS object corresponds to a generalized eigenproblem.

Not collective.

Returns:: True if the problem is generalized.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:608

isHermitian()#

Tell if the EPS object corresponds to a Hermitian eigenproblem.

Not collective.

Returns:: True if the problem is Hermitian.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:627

isPositive()#

Eigenproblem requiring a positive (semi-) definite matrix \(B\).

Not collective.

Tell if the EPS corresponds to an eigenproblem requiring a positive (semi-) definite matrix \(B\).

Returns:: True if the problem is positive (semi-) definite.
Return type:: bool

Source code at slepc4py/SLEPc/EPS.pyx:646

isStructured()#

Tell if the EPS object corresponds to a structured eigenvalue problem.

Not collective.

Returns:: True if the problem is structured.
Return type:: bool

Notes

The result will be True if the problem type has been set to some structured type such as BSE. This is independent of whether the input matrix has been built with a certain structure with a helper function.

Source code at slepc4py/SLEPc/EPS.pyx:668

reset()#

Reset the EPS object.

Collective.

See also

EPSReset

Source code at slepc4py/SLEPc/EPS.pyx:384

Return type:: None

setArbitrarySelection(arbitrary, args=None, kargs=None)#

Set an arbitrary selection criterion function.

Logically collective.

Set a function to look for eigenvalues according to an arbitrary selection criterion. This criterion can be based on a computation involving the current eigenvector approximation.

Source code at slepc4py/SLEPc/EPS.pyx:1725

Parameters:

arbitrary (EPSArbitraryFunction | None)
args (tuple[Any, ...] | None)
kargs (dict[str, Any] | None)

Return type:

None

setArnoldiDelayed(delayed)#

Set (toggle) delayed reorthogonalization in the Arnoldi iteration.

Logically collective.

Parameters:: delayed (bool) – True if delayed reorthogonalization is to be used.
Return type:: None

Notes

This 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 more slowly compared to the default algorithm.

Source code at slepc4py/SLEPc/EPS.pyx:2383

setBV(bv)#

Set a basis vectors object associated to the eigensolver.

Collective.

Parameters:: bv (BV) – The basis vectors context.
Return type:: None

See also

getBV, EPSSetBV

Source code at slepc4py/SLEPc/EPS.pyx:1427

setBalance(balance=None, iterations=None, cutoff=None)#

Set the balancing technique to be used by the eigensolver.

Logically collective.

Parameters:

balance (Balance | None) – The balancing method.
iterations (int | None) – Number of iterations of the balancing algorithm.
cutoff (float | None) – Cutoff value.

Return type:

None

Notes

When balancing is enabled, the solver works implicitly with matrix \(DAD^{-1}\), where \(D\) is an appropriate diagonal matrix. This improves the accuracy of the computed results in some cases.

Balancing makes sense only for non-Hermitian problems when the required precision is high (i.e., with a small tolerance).

By default, balancing is disabled. The two-sided method is much more effective than the one-sided counterpart, but it requires the system matrices to have the Mat.multTranspose() operation defined.

The parameter iterations is the number of iterations performed by the method. The cutoff value is used only in the two-side variant.

See also

setBalance, EPSGetBalance

Source code at slepc4py/SLEPc/EPS.pyx:718

setCISSExtraction(extraction)#

Set the extraction technique used in the CISS solver.

Logically collective.

Parameters:: extraction (CISSExtraction) – The extraction technique.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:3939

setCISSQuadRule(quad)#

Set the quadrature rule used in the CISS solver.

Logically collective.

Parameters:: quad (CISSQuadRule) – The quadrature rule.
Return type:: None

See also

getCISSQuadRule, EPSCISSSetQuadRule

Source code at slepc4py/SLEPc/EPS.pyx:3976

setCISSRefinement(inner=None, blsize=None)#

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

Logically collective.

Parameters:

inner (int | None) – Number of iterative refinement iterations (inner loop).
blsize (int | None) – Number of iterative refinement iterations (blocksize loop).

Return type:

None

Source code at slepc4py/SLEPc/EPS.pyx:4146

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

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

Logically collective.

Parameters:

ip (int | None) – Number of integration points.
bs (int | None) – Block size.
ms (int | None) – Moment size.
npart (int | None) – Number of partitions when splitting the communicator.
bsmax (int | None) – Maximum block size.
realmats (bool) – True if A and B are real.

Return type:

None

Notes

The default number of partitions is 1. This means the internal petsc4py.PETSc.KSP object is shared among all processes of the EPS communicator. Otherwise, the communicator is split into npart communicators, so that npart petsc4py.PETSc.KSP solves proceed simultaneously.

Source code at slepc4py/SLEPc/EPS.pyx:4013

setCISSThreshold(delta=None, spur=None)#

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

Logically collective.

Parameters:

delta (float | None) – Threshold for numerical rank.
spur (float | None) – Spurious threshold (to discard spurious eigenpairs).

Return type:

None

Source code at slepc4py/SLEPc/EPS.pyx:4101

setCISSUseST(usest)#

Set a flag indicating that the CISS solver will use the ST object.

Logically collective.

Parameters:: usest (bool) – Whether to use the ST object or not.
Return type:: None

Notes

When this option is set, the linear solves can be configured by setting options for the petsc4py.PETSc.KSP object obtained with ST.getKSP(). Otherwise, several petsc4py.PETSc.KSP objects are created, which can be accessed with getCISSKSPs().

The default is to use the ST, unless several partitions have been specified, see setCISSSizes().

Source code at slepc4py/SLEPc/EPS.pyx:4191

setConvergenceTest(conv)#

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

Logically collective.

Parameters:: conv (Conv) – The method used to compute the error estimate used in the convergence test.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:1197

setDS(ds)#

Set a direct solver object associated to the eigensolver.

Collective.

Parameters:: ds (DS) – The direct solver context.
Return type:: None

See also

getDS, EPSSetDS

Source code at slepc4py/SLEPc/EPS.pyx:1464

setDeflationSpace(space)#

Set vectors to form a basis of the deflation space.

Collective.

Parameters:: space (Vec | list[Vec]) – Set of basis vectors of the deflation space.
Return type:: None

Notes

When 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).

These vectors do not persist from one solve() call to the other, so the deflation space should be set every time.

The vectors do not need to be mutually orthonormal, since they are explicitly orthonormalized internally.

Source code at slepc4py/SLEPc/EPS.pyx:1576

setDimensions(nev=None, ncv=None, mpd=None)#

Set number of eigenvalues to compute and the dimension of the subspace.

Logically collective.

Parameters:

nev (int | None) – Number of eigenvalues to compute.
ncv (int | None) – Maximum dimension of the subspace to be used by the solver.
mpd (int | None) – Maximum dimension allowed for the projected problem.

Return type:

None

Notes

Use DETERMINE for ncv and mpd to assign a reasonably good value, which is dependent on the solution method.

The parameters ncv and mpd are intimately related, so that the user is advised to set one of them at most. Normal usage is the following:

In cases where nev is small, the user sets ncv (a reasonable default is 2 * nev).
In cases where nev is large, the user sets mpd.

The value of ncv should always be between nev and (nev + mpd), typically ncv = nev + mpd. If nev is not too large, mpd = nev is a reasonable choice, otherwise a smaller value should be used.

When computing all eigenvalues in an interval, see setInterval(), these parameters lose relevance, and tuning must be done with setKrylovSchurDimensions().

Source code at slepc4py/SLEPc/EPS.pyx:1315

setEigenvalueComparison(comparison, args=None, kargs=None)#

Set an eigenvalue comparison function.

Logically collective.

Notes

This eigenvalue comparison function is used when setWhichEigenpairs() is set to EPS.Which.USER.

Source code at slepc4py/SLEPc/EPS.pyx:1771

Parameters:

comparison (EPSEigenvalueComparison | None)
args (tuple[Any, ...] | None)
kargs (dict[str, Any] | None)

Return type:

None

setExtraction(extraction)#

Set the extraction type used by the eigensolver.

Logically collective.

Parameters:: extraction (Extraction) – The extraction method to be used by the solver.
Return type:: None

Notes

Not all eigensolvers support all types of extraction.

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().

Source code at slepc4py/SLEPc/EPS.pyx:787

setFromOptions()#

Set EPS options from the options database.

Collective.

Notes

To see all options, run your program with the -help option.

This routine must be called before setUp() if the user is to be allowed to set the solver type.

See also

setOptionsPrefix, EPSSetFromOptions

Source code at slepc4py/SLEPc/EPS.pyx:532

Return type:: None

setGDBOrth(borth)#

Set the orthogonalization that will be used in the search subspace.

Logically collective.

Set the orthogonalization that will be used in the search subspace in case of generalized Hermitian problems.

Parameters:: borth (bool) – Whether to B-orthogonalize the search subspace.
Return type:: None

See also

getGDBOrth, EPSGDSetBOrth

Source code at slepc4py/SLEPc/EPS.pyx:3313

setGDBlockSize(bs)#

Set the number of vectors to be added to the searching space.

Logically collective.

Set the number of vectors to be added to the searching space in every iteration.

Parameters:: bs (int) – The number of vectors added to the search space in every iteration.
Return type:: None

See also

getGDBlockSize, EPSGDSetBlockSize

Source code at slepc4py/SLEPc/EPS.pyx:3172

setGDDoubleExpansion(doubleexp)#

Set that the search subspace is expanded with double expansion.

Logically collective.

Parameters:: doubleexp (bool) – True if using double expansion.
Return type:: None

Notes

In the double expansion variant the search subspace is expanded with \(K [A x, B x]\) (double expansion) instead of the classic \(K r\), where \(K\) is the preconditioner, \(x\) the selected approximate eigenvector and \(r\) its associated residual vector.

Source code at slepc4py/SLEPc/EPS.pyx:3356

setGDInitialSize(initialsize)#

Set the initial size of the searching space.

Logically collective.

Parameters:: initialsize (int) – The number of vectors of the initial searching subspace.
Return type:: None

Notes

If the flag in setGDKrylovStart() is set to False and the user provides vectors with setInitialSpace(), up to initialsize vectors will be used; and if the provided vectors are not enough, the solver completes the subspace with random vectors. In case the setGDKrylovStart() flag is True, the solver gets the first vector provided by the user or, if not available, a random vector, and expands the Krylov basis up to initialsize vectors.

Source code at slepc4py/SLEPc/EPS.pyx:3266

setGDKrylovStart(krylovstart=True)#

Set (toggle) starting the search subspace with a Krylov basis.

Logically collective.

Parameters:: krylovstart (bool) – True if starting the search subspace with a Krylov basis.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:3135

setGDRestart(minv=None, plusk=None)#

Set the number of vectors of the search space after restart.

Logically collective.

Set the number of vectors of the search space after restart and the number of vectors saved from the previous iteration.

Parameters:

minv (int) – The number of vectors of the search subspace after restart.
plusk (int) – The number of vectors saved from the previous iteration.

Return type:

None

See also

getGDRestart, EPSGDSetRestart

Source code at slepc4py/SLEPc/EPS.pyx:3215

setInitialSpace(space)#

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

Collective.

Parameters:: space (Vec | list[Vec]) – Set of basis vectors of the initial space.
Return type:: None

Notes

Some solvers start to iterate on a single vector (initial vector). In that case, only the first vector is taken into account and the other vectors are ignored. But other solvers such as SUBSPACE are able to make use of the whole initial subspace as an initial guess.

These vectors do not persist from one solve() call to the other, so the initial space should be set every time.

The vectors do not need to be mutually orthonormal, since they are explicitly orthonormalized internally.

Common usage of this function is when the user can provide a rough approximation of the wanted eigenspace. Then, convergence may be faster.

Source code at slepc4py/SLEPc/EPS.pyx:1614

setInterval(inta, intb)#

Set the computational interval for spectrum slicing.

Logically collective.

Parameters:

inta (float) – The left end of the interval.
intb (float) – The right end of the interval.

Return type:

None

Notes

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

A computational interval is also needed when using polynomial filters, see STFILTER.

Source code at slepc4py/SLEPc/EPS.pyx:998

setJDBOrth(borth)#

Set the orthogonalization that will be used in the search subspace.

Logically collective.

Set the orthogonalization that will be used in the search subspace in case of generalized Hermitian problems.

Parameters:: borth (bool) – Whether to B-orthogonalize the search subspace.
Return type:: None

See also

getJDBOrth, EPSJDSetBOrth

Source code at slepc4py/SLEPc/EPS.pyx:3672

setJDBlockSize(bs)#

Set the number of vectors to be added to the searching space.

Logically collective.

Set the number of vectors to be added to the searching space in every iteration.

Parameters:: bs (int) – The number of vectors added to the search space in every iteration.
Return type:: None

See also

getJDBlockSize, EPSJDSetBlockSize

Source code at slepc4py/SLEPc/EPS.pyx:3443

setJDConstCorrectionTol(constant)#

Deactivate the dynamic stopping criterion.

Logically collective.

Parameters:: constant (bool) – If False, the petsc4py.PETSc.KSP relative tolerance is set to 0.5**i.
Return type:: None

Notes

If this flag is set to False, then the petsc4py.PETSc.KSP relative tolerance is dynamically set to 0.5**i, where i is the number of EPS iterations since the last converged value. By the default, a constant tolerance is used.

Source code at slepc4py/SLEPc/EPS.pyx:3627

setJDFix(fix)#

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

Logically collective.

Parameters:: fix (float) – The threshold for changing the target.
Return type:: None

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.

See also

getJDFix, EPSJDSetFix

Source code at slepc4py/SLEPc/EPS.pyx:3584

setJDInitialSize(initialsize)#

Set the initial size of the searching space.

Logically collective.

Parameters:: initialsize (int) – The number of vectors of the initial searching subspace.
Return type:: None

Notes

If the flag in setJDKrylovStart() is set to False and the user provides vectors with setInitialSpace(), up to initialsize vectors will be used; and if the provided vectors are not enough, the solver completes the subspace with random vectors. In case the setJDKrylovStart() flag is True, the solver gets the first vector provided by the user or, if not available, a random vector, and expands the Krylov basis up to initialsize vectors.

Source code at slepc4py/SLEPc/EPS.pyx:3537

setJDKrylovStart(krylovstart=True)#

Set (toggle) starting the search subspace with a Krylov basis.

Logically collective.

Parameters:: krylovstart (bool) – True if starting the search subspace with a Krylov basis.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:3406

setJDRestart(minv=None, plusk=None)#

Set the number of vectors of the search space after restart.

Logically collective.

Set the number of vectors of the search space after restart and the number of vectors saved from the previous iteration.

Parameters:

minv (int | None) – The number of vectors of the search subspace after restart.
plusk (int | None) – The number of vectors saved from the previous iteration.

Return type:

None

See also

getJDRestart, EPSJDSetRestart

Source code at slepc4py/SLEPc/EPS.pyx:3486

setKrylovSchurBSEType(bse)#

Set the Krylov-Schur variant used for BSE structured eigenproblems.

Logically collective.

Parameters:: bse (KrylovSchurBSEType) – The BSE method.
Return type:: None

Notes

This call is only relevant if the type was set to EPS.Type.KRYLOVSCHUR with setType() and the problem type to EPS.ProblemType.BSE with setProblemType().

Source code at slepc4py/SLEPc/EPS.pyx:2475

setKrylovSchurDetectZeros(detect)#

Set the flag that enforces zero detection in spectrum slicing.

Logically collective.

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

Parameters:: detect (bool) – True if zeros must checked for.
Return type:: None

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

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, especially when several partitions are being used. This feature currently requires an external package for factorizations with support for zero detection, e.g., MUMPS.

Source code at slepc4py/SLEPc/EPS.pyx:2659

setKrylovSchurDimensions(nev=None, ncv=None, mpd=None)#

Set the dimensions used for each subsolve step (spectrum slicing).

Logically collective.

Parameters:

nev (int | None) – Number of eigenvalues to compute.
ncv (int | None) – Maximum dimension of the subspace to be used by the solver.
mpd (int | None) – Maximum dimension allowed for the projected problem.

Return type:

None

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

The meaning of the parameters is the same as in setDimensions(), but the ones here apply to every subsolve done by the child EPS object.

Source code at slepc4py/SLEPc/EPS.pyx:2712

setKrylovSchurLocking(lock)#

Set (toggle) locking/non-locking variants of the Krylov-Schur method.

Logically collective.

Parameters:: lock (bool) – True if the locking variant must be selected.
Return type:: None

Notes

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

Source code at slepc4py/SLEPc/EPS.pyx:2561

setKrylovSchurPartitions(npart)#

Set the number of partitions of the communicator (spectrum slicing).

Logically collective.

Set the number of partitions for the case of doing spectrum slicing for a computational interval with the communicator split in several sub-communicators.

Parameters:: npart (int) – The number of partitions.
Return type:: None

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

By default, npart=1 so all processes in the communicator participate in the processing of the whole interval. If npart>1 then the interval is divided into npart subintervals, each of them being processed by a subset of processes.

The interval is split proportionally unless the separation points are specified with setKrylovSchurSubintervals().

Source code at slepc4py/SLEPc/EPS.pyx:2605

setKrylovSchurRestart(keep)#

Set the restart parameter for the Krylov-Schur method.

Logically collective.

It is the proportion of basis vectors that must be kept after restart.

Parameters:: keep (float) – The number of vectors to be kept at restart.
Return type:: None

Notes

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

Source code at slepc4py/SLEPc/EPS.pyx:2518

setKrylovSchurSubintervals(subint)#

Set the subinterval boundaries.

Logically collective.

Set the subinterval boundaries for spectrum slicing with a computational interval with several partitions.

Parameters:: subint (Sequence[float]) – Real values specifying subintervals.
Return type:: None

Notes

This call makes sense only for spectrum slicing runs, that is, when an interval has been given with setInterval() and SINVERT is set.

This function must be called after setKrylovSchurPartitions(). For npart partitions, the argument subint must contain npart+1 real values sorted in ascending order: subint_0, subint_1, …, subint_npart, where the first and last values must coincide with the interval endpoints set with setInterval(). The subintervals are then defined by two consecutive points: [subint_0,subint_1], [subint_1,subint_2], and so on.

Source code at slepc4py/SLEPc/EPS.pyx:2968

setLOBPCGBlockSize(bs)#

Set the block size of the LOBPCG method.

Logically collective.

Parameters:: bs (int) – The block size.
Return type:: None

Source code at slepc4py/SLEPc/EPS.pyx:3759

setLOBPCGLocking(lock)#

Toggle between locking and non-locking (LOBPCG method).

Logically collective.

Parameters:: lock (bool) – True if the locking variant must be selected.
Return type:: None

Notes

This flag refers to soft locking (converged vectors within the current block iterate), since hard locking is always used (when nev is larger than the block size).

Source code at slepc4py/SLEPc/EPS.pyx:3840

setLOBPCGRestart(restart)#

Set the restart parameter for the LOBPCG method.

Logically collective.

Parameters:: restart (float) – The percentage of the block of vectors to force a restart.
Return type:: None

Notes

The meaning of this parameter is the proportion of vectors within the current block iterate that must have converged in order to force a restart with hard locking. Allowed values are in the range [0.1,1.0]. The default is 0.9.

Source code at slepc4py/SLEPc/EPS.pyx:3796

setLanczosReorthogType(reorthog)#

Set the type of reorthogonalization used during the Lanczos iteration.

Logically collective.

Parameters:: reorthog (LanczosReorthogType) – The type of reorthogonalization.
Return type:: None

Notes

This call is only relevant if the type was set to EPS.Type.LANCZOS with setType().

Source code at slepc4py/SLEPc/EPS.pyx:2430

setLeftInitialSpace(space)#

Set a left initial space from which the eigensolver starts to iterate.

Collective.

Parameters:: space (Vec | list[Vec]) – Set of basis vectors of the left initial space.
Return type:: None

Notes

Left initial vectors are used to initiate the left search space in two-sided eigensolvers. Users should pass here an approximation of the left eigenspace, if available.

The same comments in setInitialSpace() are applicable here.

Source code at slepc4py/SLEPc/EPS.pyx:1652

setLyapIIRanks(rkc=None, rkl=None)#

Set the ranks used in the solution of the Lyapunov equation.

Logically collective.

Parameters:

rkc (int | None) – The compressed rank.
rkl (int | None) – The Lyapunov rank.

Return type:

None

Notes

Lyapunov inverse iteration needs to solve a large-scale Lyapunov equation at each iteration of the eigensolver. For this, an iterative solver (LME) is used, which requires to prescribe the rank of the solution matrix \(X\). This is the meaning of parameter rkl. Later, this matrix is compressed into another matrix of rank rkc. If not provided, rkl is a small multiple of rkc.

See also

getLyapIIRanks, EPSLyapIISetRanks

Source code at slepc4py/SLEPc/EPS.pyx:3883

setMonitor(monitor, args=None, kargs=None)#

Append a monitor function to the list of monitors.

Logically collective.

Source code at slepc4py/SLEPc/EPS.pyx:1818

Parameters:

monitor (EPSMonitorFunction | None)
args (tuple[Any, ...] | None)
kargs (dict[str, Any] | None)

Return type:

None

setOperators(A, B=None)#

Set the matrices associated with the eigenvalue problem.

Collective.

Parameters:

A (Mat) – The matrix associated with the eigensystem.
B (Mat | None) – The second matrix in the case of generalized eigenproblems; if not provided, a standard eigenproblem is assumed.

Return type:

None

Notes

It must be called before setUp(). If it is called again after setUp() and the matrix sizes have changed then the EPS object is reset.

For structured eigenproblem types such as BSE, see setProblemType(), the provided matrices must have been created with the corresponding helper function, i.e., createMatBSE().

Source code at slepc4py/SLEPc/EPS.pyx:1545

setOptionsPrefix(prefix=None)#

Set the prefix used for searching for all EPS options in the database.

Logically collective.

Parameters:: prefix (str | None) – The prefix string to prepend to all EPS option requests.
Return type:: None

Notes

A 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_")

Source code at slepc4py/SLEPc/EPS.pyx:482

setPowerShiftType(shift)#

Set the type of shifts used during the power iteration.

Logically collective.

This can be used to emulate the Rayleigh Quotient Iteration (RQI) method.

Parameters:: shift (PowerShiftType) – The type of shift.
Return type:: None

Notes

This 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.

Source code at slepc4py/SLEPc/EPS.pyx:2328

setProblemType(problem_type)#

Set the type of the eigenvalue problem.

Logically collective.

Parameters:: problem_type (ProblemType) – The problem type to be set.
Return type:: None

Notes

This function must be used to instruct SLEPc to exploit symmetry or other kind of structure. 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., \(A=A^*\)) or generalized Hermitian (i.e., \(A=A^*\), \(B=B^*\), and \(B\) positive definite) then it is recommended to set the problem type so that eigensolver can exploit these properties.

If the user does not call this function, the solver will use a reasonable guess.

For structured problem types such as BSE, the matrices passed in via setOperators() must have been created with the corresponding helper function, i.e., createMatBSE().

Source code at slepc4py/SLEPc/EPS.pyx:572

setPurify(purify=True)#

Set (toggle) eigenvector purification.

Logically collective.

Parameters:: purify (bool) – True to activate purification (default).
Return type:: None

Notes

By default, eigenvectors of generalized symmetric eigenproblems are purified in order to purge directions in the nullspace of matrix \(B\). If the user knows that \(B\) is non-singular, then purification can be safely deactivated and some computational cost is avoided (this is particularly important in interval computations).

Source code at slepc4py/SLEPc/EPS.pyx:1151

setRG(rg)#

Set a region object associated to the eigensolver.

Collective.

Parameters:: rg (RG) – The region context.
Return type:: None

See also

getRG, EPSSetRG

Source code at slepc4py/SLEPc/EPS.pyx:1501

setRQCGReset(nrest)#

Set the reset parameter of the RQCG iteration.

Logically collective.

Parameters:: nrest (int) – The number of iterations between resets.
Return type:: None

Notes

Every nrest iterations the solver performs a Rayleigh-Ritz projection step.

See also

getRQCGReset, EPSRQCGSetReset

Source code at slepc4py/SLEPc/EPS.pyx:3717

setST(st)#

Set a spectral transformation object associated to the eigensolver.

Collective.

Parameters:: st (ST) – The spectral transformation.
Return type:: None

See also

getST, EPSSetST

Source code at slepc4py/SLEPc/EPS.pyx:1390

setStoppingTest(stopping, args=None, kargs=None)#

Set a function to decide when to stop the outer iteration of the eigensolver.

Logically collective.

Source code at slepc4py/SLEPc/EPS.pyx:1684

Parameters:

stopping (EPSStoppingFunction | None)
args (tuple[Any, ...] | None)
kargs (dict[str, Any] | None)

Return type:

None

setTarget(target)#

Set the value of the target.

Logically collective.

Parameters:: target (Scalar) – The value of the target.
Return type:: None

Notes

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

When PETSc is built with real scalars, it is not possible to specify a complex target.

See also

getTarget, EPSSetTarget

Source code at slepc4py/SLEPc/EPS.pyx:945

setThreshold(thres, rel=False)#

Set the threshold used in the threshold stopping test.

Logically collective.

Parameters:

thres (float) – The threshold.
rel (bool) – Whether the threshold is relative or not.

Return type:

None

Notes

This function internally sets a special stopping test based on the threshold, where eigenvalues are computed in sequence until one of the computed eigenvalues is below/above the threshold (depending on whether largest or smallest eigenvalues are computed). The details are given in EPSSetThreshold.

Source code at slepc4py/SLEPc/EPS.pyx:893

setTolerances(tol=None, max_it=None)#

Set the tolerance and max. iter. used by the default EPS convergence tests.

Logically collective.

Parameters:

tol (float | None) – The convergence tolerance.
max_it (int | None) – The maximum number of iterations.

Return type:

None

Notes

Use DETERMINE for max_it to assign a reasonably good value, which is dependent on the solution method.

See also

getTolerances, EPSSetTolerances

Source code at slepc4py/SLEPc/EPS.pyx:1057

setTrackAll(trackall)#

Set if the solver must compute the residual of all approximate eigenpairs.

Logically collective.

Parameters:: trackall (bool) – Whether to compute all residuals or not.
Return type:: None

See also

getTrackAll, EPSSetTrackAll

Source code at slepc4py/SLEPc/EPS.pyx:1272

setTrueResidual(trueres)#

Set if the solver must compute the true residual explicitly or not.

Logically collective.

Parameters:: trueres (bool) – Whether the solver computes true residuals or not.
Return type:: None

See also

getTrueResidual, EPSSetTrueResidual

Source code at slepc4py/SLEPc/EPS.pyx:1235

setTwoSided(twosided)#

Set to use a two-sided variant that also computes left eigenvectors.

Logically collective.

Parameters:: twosided (bool) – Whether the two-sided variant is to be used or not.
Return type:: None

Notes

If the user sets twosided to True then the solver uses a variant of the algorithm that computes both right and left eigenvectors. This is usually much more costly. This option is not available in all solvers.

When using two-sided solvers, the problem matrices must have both the Mat.mult and Mat.multTranspose operations defined.

Source code at slepc4py/SLEPc/EPS.pyx:1104

setType(eps_type)#

Set the particular solver to be used in the EPS object.

Logically collective.

Parameters:: eps_type (Type | str) – The solver to be used.
Return type:: None

Notes

The default is 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.

See also

getType, EPSSetType

Source code at slepc4py/SLEPc/EPS.pyx:417

setUp()#

Set up all the internal data structures.

Collective.

Notes

Sets up all the internal data structures necessary for the execution of the eigensolver. This includes the setup of the internal ST object.

This 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.

Source code at slepc4py/SLEPc/EPS.pyx:1875

Return type:: None

setWhichEigenpairs(which)#

Set which portion of the spectrum is to be sought.

Logically collective.

Parameters:: which (Which) – The portion of the spectrum to be sought by the solver.
Return type:: None

Notes

Not 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.

The target is a scalar value provided with setTarget().

The criterion EPS.Which.TARGET_IMAGINARY is available only in case PETSc and SLEPc have been built with complex scalars.

EPS.Which.ALL is intended for use in combination with an interval (see setInterval()), when all eigenvalues within the interval are requested, or in the context of the EPS.Type.CISS solver for computing all eigenvalues in a region.

Source code at slepc4py/SLEPc/EPS.pyx:834

solve()#

Solve the eigensystem.

Collective.

Notes

The problem matrices are specified with setOperators().

solve() will return without generating an error regardless of whether all requested solutions were computed or not. Call getConverged() to get the actual number of computed solutions, and getConvergedReason() to determine if the solver converged or failed and why.

Source code at slepc4py/SLEPc/EPS.pyx:1897

Return type:: None

updateKrylovSchurSubcommMats(s=1.0, a=1.0, Au=None, t=1.0, b=1.0, Bu=None, structure=None, globalup=False)#

Update the eigenproblem matrices stored internally in the communicator.

Collective.

Update the eigenproblem matrices stored internally in the subcommunicator to which the calling process belongs.

Parameters:

s (Scalar) – Scalar that multiplies the existing A matrix.
a (Scalar) – Scalar used in the axpy operation on A.
Au (petsc4py.PETSc.Mat | None) – The matrix used in the axpy operation on A.
t (Scalar) – Scalar that multiplies the existing B matrix.
b (Scalar) – Scalar used in the axpy operation on B.
Bu (petsc4py.PETSc.Mat | None) – The matrix used in the axpy operation on B.
structure (petsc4py.PETSc.Mat.Structure | None) – Either same, different, or a subset of the non-zero sparsity pattern.
globalup (bool) – Whether global matrices must be updated or not.

Return type:

None

Notes

This function modifies the eigenproblem matrices at subcommunicator level, and optionally updates the global matrices in the parent communicator. The updates are expressed as \(A \leftarrow s A + a Au\), \(B \leftarrow t B + b Bu\).

It is possible to update one of the matrices, or both.

The matrices Au and Bu must be equal in all subcommunicators.

The structure flag is passed to the petsc4py.PETSc.Mat.axpy operations to perform the updates.

If globalup is True, communication is carried out to reconstruct the updated matrices in the parent communicator.

Source code at slepc4py/SLEPc/EPS.pyx:2897

valuesView(viewer=None)#

Display the computed eigenvalues in a viewer.

Collective.