Belos
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An implementation of the Belos::MatOrthoManager that performs orthogonalization using multiple steps of modified Gram-Schmidt. More...
#include <BelosIMGSOrthoManager.hpp>
Public Member Functions | |
Constructor/Destructor | |
IMGSOrthoManager (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. More... | |
IMGSOrthoManager (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. More... | |
~IMGSOrthoManager () | |
Destructor. More... | |
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. More... | |
void | setSingTol (const MagnitudeType sing_tol) |
Set parameter for singular block detection. More... | |
MagnitudeType | getBlkTol () const |
Return parameter for block re-orthogonalization threshhold. More... | |
MagnitudeType | getSingTol () const |
Return parameter for singular block detection. More... | |
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 . More... | |
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 . More... | |
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) . More... | |
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 . More... | |
Label methods | |
void | setLabel (const std::string &label) |
This method sets the label used by the timers in the orthogonalization manager. More... | |
const std::string & | getLabel () const |
This method returns the label being used by the timers in the orthogonalization manager. More... | |
Public Member Functions inherited from Belos::MatOrthoManager< ScalarType, MV, OP > | |
MatOrthoManager (Teuchos::RCP< const OP > Op=Teuchos::null) | |
Default constructor. More... | |
virtual | ~MatOrthoManager () |
Destructor. More... | |
void | setOp (Teuchos::RCP< const OP > Op) |
Set operator. More... | |
Teuchos::RCP< const OP > | getOp () const |
Get operator. More... | |
void | innerProd (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const |
Provides the inner product defining the orthogonality concepts, using the provided operator. More... | |
void | innerProd (const MV &X, const MV &Y, Teuchos::RCP< const MV > MY, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const |
Provides the inner product defining the orthogonality concepts, using the provided operator. The method has the options of exploiting a caller-provided MX . More... | |
void | norm (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const |
Provides the norm induced by innerProd(). More... | |
void | norm (const MV &X, Teuchos::RCP< const MV > MX, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const |
Compute norm of each column of X. More... | |
int | projectAndNormalize (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 . More... | |
Public Member Functions inherited from Belos::OrthoManager< ScalarType, MV > | |
OrthoManager () | |
Default constructor. More... | |
virtual | ~OrthoManager () |
Destructor. More... | |
int | projectAndNormalize (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const |
Project X against the Q[i] and normalize X. More... | |
Public Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase | |
RCP< ParameterList > | getNonconstParameterList () |
RCP< ParameterList > | unsetParameterList () |
RCP< const ParameterList > | getParameterList () const |
Static Public Attributes | |
Default orthogonalization constants | |
static const int | max_ortho_steps_default_ = 1 |
Max number of (re)orthogonalization steps, including the first (default). More... | |
static const MagnitudeType | blk_tol_default_ |
Block reorthogonalization threshold (default). More... | |
static const MagnitudeType | sing_tol_default_ = 10*Teuchos::ScalarTraits<typename IMGSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::eps() |
Singular block detection threshold (default). More... | |
static const int | max_ortho_steps_fast_ = 1 |
Max number of (re)orthogonalization steps, including the first (fast). More... | |
static const MagnitudeType | blk_tol_fast_ = Teuchos::ScalarTraits<typename IMGSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero() |
Block reorthogonalization threshold (fast). More... | |
static const MagnitudeType | sing_tol_fast_ = Teuchos::ScalarTraits<typename IMGSOrthoManager<ScalarType,MV,OP>::MagnitudeType>::zero() |
Singular block detection threshold (fast). More... | |
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. More... | |
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. More... | |
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 . More... | |
Additional Inherited Members | |
Protected Member Functions inherited from Belos::MatOrthoManager< ScalarType, MV, OP > | |
virtual int | projectAndNormalizeImpl (MV &X, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const |
Protected Member Functions inherited from Belos::OrthoManager< ScalarType, MV > | |
Protected Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase | |
void | setMyParamList (const RCP< ParameterList > ¶mList) |
RCP< ParameterList > | getMyNonconstParamList () |
RCP< const ParameterList > | getMyParamList () const |
Protected Attributes inherited from Belos::MatOrthoManager< ScalarType, MV, OP > | |
Teuchos::RCP< const OP > | _Op |
bool | _hasOp |
An implementation of the Belos::MatOrthoManager that performs orthogonalization using multiple steps of modified Gram-Schmidt.
Definition at line 83 of file BelosIMGSOrthoManager.hpp.
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Constructor specifying re-orthogonalization tolerance.
Definition at line 99 of file BelosIMGSOrthoManager.hpp.
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Constructor that takes a list of parameters.
Definition at line 129 of file BelosIMGSOrthoManager.hpp.
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Destructor.
Definition at line 159 of file BelosIMGSOrthoManager.hpp.
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Implements Teuchos::ParameterListAcceptor.
Definition at line 165 of file BelosIMGSOrthoManager.hpp.
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Reimplemented from Teuchos::ParameterListAcceptor.
Definition at line 237 of file BelosIMGSOrthoManager.hpp.
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Set parameter for block re-orthogonalization threshhold.
Definition at line 252 of file BelosIMGSOrthoManager.hpp.
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Set parameter for singular block detection.
Definition at line 255 of file BelosIMGSOrthoManager.hpp.
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Return parameter for block re-orthogonalization threshhold.
Definition at line 258 of file BelosIMGSOrthoManager.hpp.
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Return parameter for singular block detection.
Definition at line 261 of file BelosIMGSOrthoManager.hpp.
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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 modified Gram-Schmidt. The algebraically equivalent projection matrix is , if Op
is the matrix specified for use in the inner product. Note, this is not an orthogonal projector.
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. |
Implements Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 799 of file BelosIMGSOrthoManager.hpp.
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This method calls project(X,Teuchos::null,C,Q); see documentation for that function.
Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 303 of file BelosIMGSOrthoManager.hpp.
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This method takes a multivector X
and attempts to compute an orthonormal basis for , with respect to innerProd().
The method uses modified 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
.
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. |
Implements Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 783 of file BelosIMGSOrthoManager.hpp.
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This method calls normalize(X,Teuchos::null,B); see documentation for that function.
Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 341 of file BelosIMGSOrthoManager.hpp.
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Given a set of bases Q[i]
and a multivector X
, this method computes an orthonormal basis for .
This routine returns an integer rank
stating the rank of the computed basis. If the subspace 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
.
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 |
B | [out] The coefficients of the original |
Q | [in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each |
Rank of the basis computed by this method.
Implements Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 601 of file BelosIMGSOrthoManager.hpp.
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This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I
.
Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 403 of file BelosIMGSOrthoManager.hpp.
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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
.
Implements Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 573 of file BelosIMGSOrthoManager.hpp.
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This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y)
.
Reimplemented from Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 418 of file BelosIMGSOrthoManager.hpp.
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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
.
Implements Belos::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 588 of file BelosIMGSOrthoManager.hpp.
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This method sets the label used by the timers in the orthogonalization manager.
Implements Belos::OrthoManager< ScalarType, MV >.
Definition at line 546 of file BelosIMGSOrthoManager.hpp.
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This method returns the label being used by the timers in the orthogonalization manager.
Implements Belos::OrthoManager< ScalarType, MV >.
Definition at line 440 of file BelosIMGSOrthoManager.hpp.
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Max number of (re)orthogonalization steps, including the first (default).
Definition at line 448 of file BelosIMGSOrthoManager.hpp.
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Block reorthogonalization threshold (default).
Definition at line 450 of file BelosIMGSOrthoManager.hpp.
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Singular block detection threshold (default).
Definition at line 452 of file BelosIMGSOrthoManager.hpp.
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Max number of (re)orthogonalization steps, including the first (fast).
Definition at line 455 of file BelosIMGSOrthoManager.hpp.
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Block reorthogonalization threshold (fast).
Definition at line 457 of file BelosIMGSOrthoManager.hpp.
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Singular block detection threshold (fast).
Definition at line 459 of file BelosIMGSOrthoManager.hpp.