Package slepc4py :: Module SLEPc :: Class SVD
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Class SVD


SVD
Nested Classes [hide private]
  Conv
SVD convergence test
  ConvergedReason
SVD convergence reasons
  ErrorType
SVD error type to assess accuracy of computed solutions
  ProblemType
SVD problem type
  Stop
SVD stopping test
  TRLanczosGBidiag
SVD TRLanczos bidiagonalization choices for the GSVD case
  Type
SVD types
  Which
SVD desired part of spectrum
Instance Methods [hide private]
a new object with type S, a subtype of T
__new__(S, ...)
 
appendOptionsPrefix(self, prefix)
Appends to the prefix used for searching for all SVD options in the database.
 
cancelMonitor(self)
Clears all monitors for an SVD object.
 
computeError(self, int i, etype=None)
Computes the error (based on the residual norm) associated with the i-th singular triplet.
 
create(self, comm=None)
Creates the SVD object.
 
destroy(self)
Destroys the SVD object.
 
errorView(self, etype=None, Viewer viewer=None)
Displays the errors associated with the computed solution (as well as the eigenvalues).
 
getBV(self)
Obtain the basis vectors objects associated to the SVD object.
 
getConverged(self)
Gets the number of converged singular triplets.
 
getConvergedReason(self)
Gets the reason why the solve() iteration was stopped.
 
getConvergenceTest(self)
Return the method used to compute the error estimate used in the convergence test.
 
getCrossEPS(self)
Retrieve the eigensolver object (EPS) associated to the singular value solver.
 
getCrossExplicitMatrix(self)
Returns the flag indicating if A^T*A is built explicitly.
 
getCyclicEPS(self)
Retrieve the eigensolver object (EPS) associated to the singular value solver.
 
getCyclicExplicitMatrix(self)
Returns the flag indicating if H(A) = [ 0 A ; A^T 0 ] is built explicitly.
 
getDS(self)
Obtain the direct solver associated to the singular value solver.
 
getDimensions(self)
Gets the number of singular values to compute and the dimension of the subspace.
 
getImplicitTranspose(self)
Gets the mode used to handle the transpose of the matrix associated with the singular value problem.
 
getIterationNumber(self)
Gets the current iteration number.
 
getLanczosOneSide(self)
Gets if the variant of the Lanczos method to be used is one-sided or two-sided.
 
getMonitor(self)
Gets the list of monitor functions.
 
getOperators(self)
Gets the matrices associated with the singular value problem.
 
getOptionsPrefix(self)
Gets the prefix used for searching for all SVD options in the database.
 
getProblemType(self)
Gets the problem type from the SVD object.
 
getSignature(self)
Gets the signature matrix defining a hyperbolic singular value problem.
 
getSingularTriplet(self, int i, Vec U=None, Vec V=None)
Gets the i-th triplet of the singular value decomposition as computed by solve().
 
getStoppingTest(self)
Gets the stopping function.
 
getTRLanczosExplicitMatrix(self)
Returns the flag indicating if Z=[A;B] is built explicitly.
 
getTRLanczosGBidiag(self)
Returns bidiagonalization choice used in the GSVD TRLanczos solver.
 
getTRLanczosKSP(self)
Retrieve the linear solver object associated with the SVD solver.
 
getTRLanczosLocking(self)
Gets the locking flag used in the thick-restart Lanczos method.
 
getTRLanczosOneSide(self)
Gets if the variant of the thick-restart Lanczos method to be used is one-sided or two-sided.
 
getTRLanczosRestart(self)
Gets the restart parameter used in the thick-restart Lanczos method.
 
getTolerances(self)
Gets the tolerance and maximum iteration count used by the default SVD convergence tests.
 
getTrackAll(self)
Returns the flag indicating whether all residual norms must be computed or not.
 
getType(self)
Gets the SVD type of this object.
 
getValue(self, int i)
Gets the i-th singular value as computed by solve().
 
getVectors(self, int i, Vec U, Vec V)
Gets the i-th left and right singular vectors as computed by solve().
 
getWhichSingularTriplets(self)
Returns which singular triplets are to be sought.
 
isGeneralized(self)
Tells whether the SVD object corresponds to a generalized singular value problem.
 
isHyperbolic(self)
Tells whether the SVD object corresponds to a hyperbolic singular value problem.
 
reset(self)
Resets the SVD object.
 
setBV(self, BV V, BV U=None)
Associates basis vectors objects to the SVD solver.
 
setConvergenceTest(self, conv)
Specifies how to compute the error estimate used in the convergence test.
 
setCrossEPS(self, EPS eps)
Associate an eigensolver object (EPS) to the singular value solver.
 
setCrossExplicitMatrix(self, flag=True)
Indicate if the eigensolver operator A^T*A must be computed explicitly.
 
setCyclicEPS(self, EPS eps)
Associate an eigensolver object (EPS) to the singular value solver.
 
setCyclicExplicitMatrix(self, flag=True)
Indicate if the eigensolver operator H(A) = [ 0 A ; A^T 0 ] must be computed explicitly.
 
setDS(self, DS ds)
Associates a direct solver object to the singular value solver.
 
setDimensions(self, nsv=None, ncv=None, mpd=None)
Sets the number of singular values to compute and the dimension of the subspace.
 
setFromOptions(self)
Sets SVD options from the options database.
 
setImplicitTranspose(self, mode)
Indicates how to handle the transpose of the matrix associated with the singular value problem.
 
setInitialSpaces(self, spaceright=None, spaceleft=None)
Sets the initial spaces from which the SVD solver starts to iterate.
 
setLanczosOneSide(self, flag=True)
Indicate if the variant of the Lanczos method to be used is one-sided or two-sided.
 
setMonitor(self, monitor, args=None, kargs=None)
Appends a monitor function to the list of monitors.
 
setOperator(self, Mat A, Mat B=None)
Sets the matrices associated with the singular value problem.
 
setOperators(self, Mat A, Mat B=None)
Sets the matrices associated with the singular value problem.
 
setOptionsPrefix(self, prefix)
Sets the prefix used for searching for all SVD options in the database.
 
setProblemType(self, problem_type)
Specifies the type of the singular value problem.
 
setSignature(self, Vec omega=None)
Sets the signature matrix defining a hyperbolic singular value problem.
 
setStoppingTest(self, stopping, args=None, kargs=None)
Sets a function to decide when to stop the outer iteration of the eigensolver.
 
setTRLanczosExplicitMatrix(self, flag=True)
Indicate if the matrix Z=[A;B] must be built explicitly.
 
setTRLanczosGBidiag(self, bidiag)
Sets the bidiagonalization choice to use in the GSVD TRLanczos solver.
 
setTRLanczosKSP(self, KSP ksp)
Associate a linear solver object to the SVD solver.
 
setTRLanczosLocking(self, lock)
Choose between locking and non-locking variants of the thick-restart Lanczos method.
 
setTRLanczosOneSide(self, flag=True)
Indicate if the variant of the thick-restart Lanczos method to be used is one-sided or two-sided.
 
setTRLanczosRestart(self, keep)
Sets the restart parameter for the thick-restart Lanczos method, in particular the proportion of basis vectors that must be kept after restart.
 
setTolerances(self, tol=None, max_it=None)
Sets the tolerance and maximum iteration count used by the default SVD convergence tests.
 
setTrackAll(self, trackall)
Specifies if the solver must compute the residual of all approximate singular triplets or not.
 
setType(self, svd_type)
Selects the particular solver to be used in the SVD object.
 
setUp(self)
Sets up all the internal data structures necessary for the execution of the singular value solver.
 
setWhichSingularTriplets(self, which)
Specifies which singular triplets are to be sought.
 
solve(self)
Solves the singular value problem.
 
valuesView(self, Viewer viewer=None)
Displays the computed singular values in a viewer.
 
vectorsView(self, Viewer viewer=None)
Outputs computed singular vectors to a viewer.
 
view(self, Viewer viewer=None)
Prints the SVD data structure.

Inherited from petsc4py.PETSc.Object: __copy__, __deepcopy__, __eq__, __ge__, __gt__, __le__, __lt__, __ne__, __nonzero__, compose, decRef, getAttr, getClassId, getClassName, getComm, getDict, getName, getRefCount, getTabLevel, incRef, incrementTabLevel, query, setAttr, setName, setTabLevel, stateGet, stateIncrease, stateSet, viewFromOptions

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __init__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties [hide private]
  ds
  max_it
  problem_type
  tol
  track_all
  transpose_mode
  which

Inherited from petsc4py.PETSc.Object: classid, comm, fortran, handle, klass, name, prefix, refcount, type

Inherited from object: __class__

Method Details [hide private]

__new__(S, ...)

 
Returns: a new object with type S, a subtype of T
Overrides: object.__new__

appendOptionsPrefix(self, prefix)

 

Appends to the prefix used for searching for all SVD options in the database.

Parameters

prefix: string
The prefix string to prepend to all SVD option requests.
Overrides: petsc4py.PETSc.Object.appendOptionsPrefix

computeError(self, int i, etype=None)

 

Computes the error (based on the residual norm) associated with the i-th singular triplet.

Parameters

i: int
Index of the solution to be considered.
etype: SVD.ErrorType enumerate
The error type to compute.

Returns

e: real
The relative error bound, computed in various ways from the residual norm sqrt(n1^2+n2^2) where n1 = ||A*v-sigma*u||_2, n2 = ||A^T*u-sigma*v||_2, sigma is the singular value, u and v are the left and right singular vectors.

Notes

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

create(self, comm=None)

 

Creates the SVD object.

Parameters

comm: Comm, optional
MPI communicator; if not provided, it defaults to all processes.

destroy(self)

 
Destroys the SVD object.
Overrides: petsc4py.PETSc.Object.destroy

errorView(self, etype=None, Viewer viewer=None)

 

Displays the errors associated with the computed solution (as well as the eigenvalues).

Parameters

etype: SVD.ErrorType enumerate, optional
The error type to compute.
viewer: Viewer, optional.
Visualization context; if not provided, the standard output is used.

Notes

By default, this function checks the error of all eigenpairs and prints the eigenvalues if all of them are below the requested tolerance. If the viewer has format ASCII_INFO_DETAIL then a table with eigenvalues and corresponding errors is printed.

getBV(self)

 

Obtain the basis vectors objects associated to the SVD object.

Returns

V: BV
The basis vectors context for right singular vectors.
U: BV
The basis vectors context for left singular vectors.

getConverged(self)

 

Gets the number of converged singular triplets.

Returns

nconv: int
Number of converged singular triplets.

Notes

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

getConvergedReason(self)

 

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

Returns

reason: SVD.ConvergedReason enumerate
Negative value indicates diverged, positive value converged.

getConvergenceTest(self)

 

Return the method used to compute the error estimate used in the convergence test.

Returns

conv: SVD.Conv
The method used to compute the error estimate used in the convergence test.

getCrossEPS(self)

 

Retrieve the eigensolver object (EPS) associated to the singular value solver.

Returns

eps: EPS
The eigensolver object.

getCrossExplicitMatrix(self)

 

Returns the flag indicating if A^T*A is built explicitly.

Returns

flag: bool
True if A^T*A is built explicitly.

getCyclicEPS(self)

 

Retrieve the eigensolver object (EPS) associated to the singular value solver.

Returns

eps: EPS
The eigensolver object.

getCyclicExplicitMatrix(self)

 

Returns the flag indicating if H(A) = [ 0 A ; A^T 0 ] is built explicitly.

Returns

flag: bool
True if H(A) is built explicitly.

getDS(self)

 

Obtain the direct solver associated to the singular value solver.

Returns

ds: DS
The direct solver context.

getDimensions(self)

 

Gets the number of singular values to compute and the dimension of the subspace.

Returns

nsv: int
Number of singular values to compute.
ncv: int
Maximum dimension of the subspace to be used by the solver.
mpd: int
Maximum dimension allowed for the projected problem.

getImplicitTranspose(self)

 

Gets the mode used to handle the transpose of the matrix associated with the singular value problem.

Returns

impl: bool
How to handle the transpose (implicitly or not).

getIterationNumber(self)

 

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

Returns

its: int
Iteration number.

getLanczosOneSide(self)

 

Gets if the variant of the Lanczos method to be used is one-sided or two-sided.

Returns

delayed: bool
True if the method is one-sided.

getOperators(self)

 

Gets the matrices associated with the singular value problem.

Returns

A: Mat
The matrix associated with the singular value problem.
B: Mat
The second matrix in the case of GSVD.

getOptionsPrefix(self)

 

Gets the prefix used for searching for all SVD options in the database.

Returns

prefix: string
The prefix string set for this SVD object.
Overrides: petsc4py.PETSc.Object.getOptionsPrefix

getProblemType(self)

 

Gets the problem type from the SVD object.

Returns

problem_type: SVD.ProblemType enumerate
The problem type that was previously set.

getSignature(self)

 

Gets the signature matrix defining a hyperbolic singular value problem.

Returns

omega: Vec
A vector containing the diagonal elements of the signature matrix.

getSingularTriplet(self, int i, Vec U=None, Vec V=None)

 

Gets the i-th triplet of the singular value decomposition as computed by solve(). The solution consists of the singular value and its left and right singular vectors.

Parameters

i: int
Index of the solution to be obtained.
U: Vec
Placeholder for the returned left singular vector.
V: Vec
Placeholder for the returned right singular vector.

Returns

s: float
The computed singular value.

Notes

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

getTRLanczosExplicitMatrix(self)

 

Returns the flag indicating if Z=[A;B] is built explicitly.

Returns

flag: bool
True if Z=[A;B] is built explicitly.

getTRLanczosGBidiag(self)

 

Returns bidiagonalization choice used in the GSVD TRLanczos solver.

Returns

bidiag: SVD.TRLanczosGBidiag enumerate
The bidiagonalization choice.

getTRLanczosKSP(self)

 

Retrieve the linear solver object associated with the SVD solver.

Returns

ksp: KSP
The linear solver object.

getTRLanczosLocking(self)

 

Gets the locking flag used in the thick-restart Lanczos method.

Returns

lock: bool
The locking flag.

getTRLanczosOneSide(self)

 

Gets if the variant of the thick-restart Lanczos method to be used is one-sided or two-sided.

Returns

delayed: bool
True if the method is one-sided.

getTRLanczosRestart(self)

 

Gets the restart parameter used in the thick-restart Lanczos method.

Returns

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

getTolerances(self)

 

Gets the tolerance and maximum iteration count used by the default SVD convergence tests.

Returns

tol: float
The convergence tolerance.
max_it: int
The maximum number of iterations

getTrackAll(self)

 

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

Returns

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

getType(self)

 

Gets the SVD type of this object.

Returns

type: SVD.Type enumerate
The solver currently being used.
Overrides: petsc4py.PETSc.Object.getType

getValue(self, int i)

 

Gets the i-th singular value as computed by solve().

Parameters

i: int
Index of the solution to be obtained.

Returns

s: float
The computed singular value.

Notes

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

getVectors(self, int i, Vec U, Vec V)

 

Gets the i-th left and right singular vectors as computed by solve().

Parameters

i: int
Index of the solution to be obtained.
U: Vec
Placeholder for the returned left singular vector.
V: Vec
Placeholder for the returned right singular vector.

Notes

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

getWhichSingularTriplets(self)

 

Returns which singular triplets are to be sought.

Returns

which: SVD.Which enumerate
The singular values to be sought (either largest or smallest).

isGeneralized(self)

 

Tells whether the SVD object corresponds to a generalized singular value problem.

Returns

flag: bool
True if two matrices were set with setOperators().

isHyperbolic(self)

 

Tells whether the SVD object corresponds to a hyperbolic singular value problem.

Returns

flag: bool
True if the problem was specified as hyperbolic.

setBV(self, BV V, BV U=None)

 

Associates basis vectors objects to the SVD solver.

Parameters

V: BV
The basis vectors context for right singular vectors.
U: BV
The basis vectors context for left singular vectors.

setConvergenceTest(self, conv)

 

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

Parameters

conv: SVD.Conv
The method used to compute the error estimate used in the convergence test.

setCrossEPS(self, EPS eps)

 

Associate an eigensolver object (EPS) to the singular value solver.

Parameters

eps: EPS
The eigensolver object.

setCrossExplicitMatrix(self, flag=True)

 

Indicate if the eigensolver operator A^T*A must be computed explicitly.

Parameters

flag: bool
True if A^T*A is built explicitly.

setCyclicEPS(self, EPS eps)

 

Associate an eigensolver object (EPS) to the singular value solver.

Parameters

eps: EPS
The eigensolver object.

setCyclicExplicitMatrix(self, flag=True)

 

Indicate if the eigensolver operator H(A) = [ 0 A ; A^T 0 ] must be computed explicitly.

Parameters

flag: bool
True if H(A) is built explicitly.

setDS(self, DS ds)

 

Associates a direct solver object to the singular value solver.

Parameters

ds: DS
The direct solver context.

setDimensions(self, nsv=None, ncv=None, mpd=None)

 

Sets the number of singular values to compute and the dimension of the subspace.

Parameters

nsv: int, optional
Number of singular values to compute.
ncv: int, optional
Maximum dimension of the subspace to be used by the solver.
mpd: int, optional
Maximum dimension allowed for the projected problem.

Notes

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

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

setFromOptions(self)

 

Sets SVD options from the options database. This routine must be called before setUp() if the user is to be allowed to set the solver type.

Notes

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

Overrides: petsc4py.PETSc.Object.setFromOptions

setImplicitTranspose(self, mode)

 

Indicates how to handle the transpose of the matrix associated with the singular value problem.

Parameters

impl: bool
How to handle the transpose (implicitly or not).

Notes

By default, the transpose of the matrix is explicitly built (if the matrix has defined the MatTranspose operation).

If this flag is set to true, the solver does not build the transpose, but handles it implicitly via MatMultTranspose().

setInitialSpaces(self, spaceright=None, spaceleft=None)

 

Sets the initial spaces from which the SVD solver starts to iterate.

Parameters

spaceright: sequence of Vec
The right initial space.
spaceleft: sequence of Vec
The left initial space.

setLanczosOneSide(self, flag=True)

 

Indicate if the variant of the Lanczos method to be used is one-sided or two-sided.

Parameters

flag: bool
True if the method is one-sided.

Notes

By default, a two-sided variant is selected, which is sometimes slightly more robust. However, the one-sided variant is faster because it avoids the orthogonalization associated to left singular vectors. It also saves the memory required for storing such vectors.

setOperator(self, Mat A, Mat B=None)

 

Sets the matrices associated with the singular value problem.

Parameters

A: Mat
The matrix associated with the singular value problem.
B: Mat, optional
The second matrix in the case of GSVD; if not provided, a usual SVD is assumed.

setOperators(self, Mat A, Mat B=None)

 

Sets the matrices associated with the singular value problem.

Parameters

A: Mat

The matrix associated with the singular value problem.

B: Mat, optional

The second matrix in the case of GSVD; if not provided, a usual SVD is assumed.

setOptionsPrefix(self, prefix)

 

Sets the prefix used for searching for all SVD options in the database.

Parameters

prefix: string
The prefix string to prepend to all SVD option requests.

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 SVD contexts, one could call:

S1.setOptionsPrefix("svd1_")
S2.setOptionsPrefix("svd2_")
Overrides: petsc4py.PETSc.Object.setOptionsPrefix

setProblemType(self, problem_type)

 

Specifies the type of the singular value problem.

Parameters

problem_type: SVD.ProblemType enumerate
The problem type to be set.

setSignature(self, Vec omega=None)

 

Sets the signature matrix defining a hyperbolic singular value problem.

Parameters

omega: Vec, optional
A vector containing the diagonal elements of the signature matrix.

setTRLanczosExplicitMatrix(self, flag=True)

 

Indicate if the matrix Z=[A;B] must be built explicitly.

Parameters

flag: bool
True if Z=[A;B] is built explicitly.

setTRLanczosGBidiag(self, bidiag)

 

Sets the bidiagonalization choice to use in the GSVD TRLanczos solver.

Parameters

bidiag: SVD.TRLanczosGBidiag enumerate
The bidiagonalization choice.

setTRLanczosKSP(self, KSP ksp)

 

Associate a linear solver object to the SVD solver.

Parameters

ksp: KSP
The linear solver object.

setTRLanczosLocking(self, lock)

 

Choose between locking and non-locking variants of the thick-restart Lanczos method.

Parameters

lock: bool
True if the locking variant must be selected.

Notes

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

setTRLanczosOneSide(self, flag=True)

 

Indicate if the variant of the thick-restart Lanczos method to be used is one-sided or two-sided.

Parameters

flag: bool
True if the method is one-sided.

Notes

By default, a two-sided variant is selected, which is sometimes slightly more robust. However, the one-sided variant is faster because it avoids the orthogonalization associated to left singular vectors.

setTRLanczosRestart(self, keep)

 

Sets the restart parameter for the thick-restart Lanczos method, in particular the proportion of basis vectors that must be kept after restart.

Parameters

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

Notes

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

setTolerances(self, tol=None, max_it=None)

 

Sets the tolerance and maximum iteration count used by the default SVD convergence tests.

Parameters

tol: float, optional
The convergence tolerance.
max_it: int, optional
The maximum number of iterations

Notes

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

setTrackAll(self, trackall)

 

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

Parameters

trackall: bool
Whether compute all residuals or not.

setType(self, svd_type)

 

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

Parameters

svd_type: SVD.Type enumerate
The solver to be used.

Notes

See SVD.Type for available methods. The default is CROSS. Normally, it is best to use setFromOptions() and then set the SVD 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.

setUp(self)

 

Sets up all the internal data structures necessary for the execution of the singular value solver.

Notes

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.

setWhichSingularTriplets(self, which)

 

Specifies which singular triplets are to be sought.

Parameters

which: SVD.Which enumerate
The singular values to be sought (either largest or smallest).

valuesView(self, Viewer viewer=None)

 

Displays the computed singular values in a viewer.

Parameters

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

vectorsView(self, Viewer viewer=None)

 

Outputs computed singular vectors to a viewer.

Parameters

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

view(self, Viewer viewer=None)

 

Prints the SVD data structure.

Parameters

viewer: Viewer, optional
Visualization context; if not provided, the standard output is used.
Overrides: petsc4py.PETSc.Object.view