Inheritance diagram for Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >:

Collaboration diagram for Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >:

Public Member Functions
Teuchos::RCP< const Teuchos::ParameterList >	getFastParameters () const
	"Fast" but possibly unsafe or less accurate parameters. More...

Constructor/Destructor
	ICGSOrthoManager (const std::string &label="Belos", Teuchos::RCP< const OP > Op=Teuchos::null, const int max_ortho_steps=max_ortho_steps_default_, const MagnitudeType blk_tol=blk_tol_default_, const MagnitudeType sing_tol=sing_tol_default_)
	Constructor specifying re-orthogonalization tolerance.

	ICGSOrthoManager (const Teuchos::RCP< Teuchos::ParameterList > &plist, const std::string &label="Belos", Teuchos::RCP< const OP > Op=Teuchos::null)
	Constructor that takes a list of parameters.

	~ICGSOrthoManager ()
	Destructor.

Implementation of Teuchos::ParameterListAcceptorDefaultBase interface
void	setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &plist)

Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

Accessor routines
void	setBlkTol (const MagnitudeType blk_tol)
	Set parameter for block re-orthogonalization threshhold.

void	setSingTol (const MagnitudeType sing_tol)
	Set parameter for singular block detection.

MagnitudeType	getBlkTol () const
	Return parameter for block re-orthogonalization threshhold.

MagnitudeType	getSingTol () const
	Return parameter for singular block detection.

Error methods
Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormError (const MV &X) const
	This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference `innerProd(X,Y) - I`.

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormError (const MV &X, Teuchos::RCP< const MV > MX) const
	This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference `innerProd(X,Y) - I`. The method has the option of exploiting a caller-provided `MX`.

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogError (const MV &X1, const MV &X2) const
	This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of `innerProd(X,Y)`.

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogError (const MV &X1, Teuchos::RCP< const MV > MX1, const MV &X2) const
	This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of `innerProd(X,Y)`. The method has the option of exploiting a caller-provided `MX`.

Label methods
void	setLabel (const std::string &label)
	This method sets the label used by the timers in the orthogonalization manager.

const std::string &	getLabel () const
	This method returns the label being used by the timers in the orthogonalization manager.

Static Public Attributes
Default orthogonalization constants
static const int	max_ortho_steps_default_
	Max number of (re)orthogonalization steps, including the first (default).

static const MagnitudeType	blk_tol_default_
	Block reorthogonalization threshold (default).

static const MagnitudeType	sing_tol_default_
	Singular block detection threshold (default).

static const int	max_ortho_steps_fast_
	Max number of (re)orthogonalization steps, including the first (fast).

static const MagnitudeType	blk_tol_fast_
	Block reorthogonalization threshold (fast).

static const MagnitudeType	sing_tol_fast_
	Singular block detection threshold (fast).

Orthogonalization methods
void	project (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Given a list of (mutually and internally) orthonormal bases `Q`, this method takes a multivector `X` and projects it onto the space orthogonal to the individual `Q[i]`, optionally returning the coefficients of `X` for the individual `Q[i]`. All of this is done with respect to the inner product innerProd(). More...

void	project (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	This method calls project(X,Teuchos::null,C,Q); see documentation for that function.

int	normalize (MV &X, Teuchos::RCP< MV > MX, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method takes a multivector `X` and attempts to compute an orthonormal basis for , with respect to innerProd(). More...

int	normalize (MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method calls normalize(X,Teuchos::null,B); see documentation for that function.

virtual int	projectAndNormalizeWithMxImpl (MV &X, Teuchos::RCP< MV > MX, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Given a set of bases `Q[i]` and a multivector `X`, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ . More...

Member Function Documentation

template<class Storage , class MV , class OP >

Teuchos::RCP<const Teuchos::ParameterList> Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >::getFastParameters ( ) const

inline

"Fast" but possibly unsafe or less accurate parameters.

Use this parameter list when you care more about speed than accuracy of the orthogonalization.

template<class Storage , class MV , class OP >

int Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >::normalize	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B
	)		const

This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$ , with respect to innerProd().

The method uses classical Gram-Schmidt, so that the coefficient matrix B is upper triangular.

This routine returns an integer rank stating the rank of the computed basis. If X does not have full rank and the normalize() routine does not attempt to augment the subspace, then rank may be smaller than the number of columns in X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors in X with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters

X	[in/out] The multivector to the modified. On output, `X` will have some number of orthonormal columns (with respect to innerProd()).
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
B	[out] The coefficients of the original `X` with respect to the computed basis. The first rows in `B` corresponding to the valid columns in `X` will be upper triangular.

Returns: Rank of the basis computed by this method.

template<class Storage , class MV , class OP >

void Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >::project	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

Given a list of (mutually and internally) orthonormal bases Q, this method takes a multivector X and projects it onto the space orthogonal to the individual Q[i], optionally returning the coefficients of X for the individual Q[i]. All of this is done with respect to the inner product innerProd().

After calling this routine, X will be orthogonal to each of the Q[i].

The method uses either one or two steps of classical Gram-Schmidt. The algebraically equivalent projection matrix is $P_Q = I - Q Q^H Op$ , if Op is the matrix specified for use in the inner product. Note, this is not an orthogonal projector.

Parameters

X	[in/out] The multivector to be modified. On output, `X` will be orthogonal to `Q[i]` with respect to innerProd().
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
C	[out] The coefficients of `X` in the `Q`[i], with respect to innerProd(). If `C[i]` is a non-null pointer and `C`[i] matches the dimensions of `X` and `Q`[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix `C`[i]. If `C[i]` is a non-null pointer whose size does not match the dimensions of `X` and `*Q`[i], then a std::invalid_argument std::exception will be thrown. Otherwise, if `C.size() < i` or `C[i]` is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.
Q	[in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each `Q[i]` is assumed to have orthonormal columns, and the `Q[i]` are assumed to be mutually orthogonal.

template<class Storage , class MV , class OP >

virtual int Belos::ICGSOrthoManager< Sacado::MP::Vector< Storage >, MV, OP >::projectAndNormalizeWithMxImpl	(	MV &	X,
		Teuchos::RCP< MV >	MX,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

protectedvirtual

Given a set of bases Q[i] and a multivector X, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ .

This routine returns an integer rank stating the rank of the computed basis. If the subspace $colspan(X) - \sum_i colspan(Q[i])$ does not have dimension as large as the number of columns of X and the orthogonalization manager doe not attempt to augment the subspace, then rank may be smaller than the number of columns of X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters

X	[in/out] The multivector to the modified. On output, the relevant rows of `X` will be orthogonal to the `Q[i]` and will have orthonormal columns (with respect to innerProd()).
MX	[in/out] The image of `X` under the operator `Op`. If : On input, this is expected to be consistent with `X`. On output, this is updated consistent with updates to `X`. If or : `MX` is not referenced.
C	[out] The coefficients of the original `X` in the `Q`[i], with respect to innerProd(). If `C[i]` is a non-null pointer and `C`[i] matches the dimensions of `X` and `Q`[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix `C`[i]. If `C[i]` is a non-null pointer whose size does not match the dimensions of `X` and `Q`[i], then C[i] will first be resized to the correct size. This will destroy the original contents of the matrix. (This is a change from previous behavior, in which a std::invalid_argument exception was thrown if *C[i] was of the wrong size.) Otherwise, if `C.size() < i<> or C[i] is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.`
B	`[out] The coefficients of the original X with respect to the computed basis. The first rows in B corresponding to the valid columns in X will be upper triangular.`
Q	`[in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each Q[i] is assumed to have orthonormal columns, and the Q[i] are assumed to be mutually orthogonal.`

Returns: Rank of the basis computed by this method.

The documentation for this class was generated from the following file:

Belos_ICGS_OrthoManager_MP_Vector.hpp

Public Member Functions

Static Public Attributes

Orthogonalization methods

Member Function Documentation