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/*! \file BelosICGSOrthoManager.hpp
\brief Iterated Classical Gram-Schmidt (ICGS) implementation of the Belos::OrthoManager class
*/
#ifndef BELOS_ICGS_ORTHOMANAGER_HPP
#define BELOS_ICGS_ORTHOMANAGER_HPP
/*! \class Belos::ICGSOrthoManager
\brief An implementation of the Belos::MatOrthoManager that performs orthogonalization
using multiple steps of classical Gram-Schmidt.
\author Chris Baker, Ulrich Hetmaniuk, Rich Lehoucq, and Heidi Thornquist
*/
// #define ORTHO_DEBUG
#include "BelosConfigDefs.hpp"
#include "BelosMultiVecTraits.hpp"
#include "BelosOperatorTraits.hpp"
#include "BelosMatOrthoManager.hpp"
#include "Teuchos_as.hpp"
#include "Teuchos_ParameterListAcceptorDefaultBase.hpp"
#ifdef BELOS_TEUCHOS_TIME_MONITOR
#include "Teuchos_TimeMonitor.hpp"
#endif // BELOS_TEUCHOS_TIME_MONITOR
namespace Belos {
template<class ScalarType, class MV, class OP>
class ICGSOrthoManager :
public MatOrthoManager<ScalarType,MV,OP>,
public Teuchos::ParameterListAcceptorDefaultBase
{
private:
typedef typename Teuchos::ScalarTraits<ScalarType>::magnitudeType MagnitudeType;
typedef typename Teuchos::ScalarTraits<MagnitudeType> MGT;
typedef Teuchos::ScalarTraits<ScalarType> SCT;
typedef MultiVecTraits<ScalarType,MV> MVT;
typedef OperatorTraits<ScalarType,MV,OP> OPT;
public:
//! @name Constructor/Destructor
//@{
//! Constructor specifying re-orthogonalization tolerance.
ICGSOrthoManager( const std::string& label = "Belos",
Teuchos::RCP<const OP> Op = Teuchos::null,
const int max_ortho_steps = 2,
const MagnitudeType blk_tol = 10*MGT::squareroot( MGT::eps() ),
const MagnitudeType sing_tol = 10*MGT::eps() )
: MatOrthoManager<ScalarType,MV,OP>(Op),
max_ortho_steps_( max_ortho_steps ),
blk_tol_( blk_tol ),
sing_tol_( sing_tol ),
label_( label )
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
std::string orthoLabel = label_ + ": Orthogonalization";
timerOrtho_ = Teuchos::TimeMonitor::getNewCounter(orthoLabel);
std::string updateLabel = label_ + ": Ortho (Update)";
timerUpdate_ = Teuchos::TimeMonitor::getNewCounter(updateLabel);
std::string normLabel = label_ + ": Ortho (Norm)";
timerNorm_ = Teuchos::TimeMonitor::getNewCounter(normLabel);
std::string ipLabel = label_ + ": Ortho (Inner Product)";
timerInnerProd_ = Teuchos::TimeMonitor::getNewCounter(ipLabel);
#endif
}
//! Constructor that takes a list of parameters.
ICGSOrthoManager (const Teuchos::RCP<Teuchos::ParameterList>& plist,
const std::string& label = "Belos",
Teuchos::RCP<const OP> Op = Teuchos::null) :
MatOrthoManager<ScalarType,MV,OP>(Op),
max_ortho_steps_ (2),
blk_tol_ (10 * MGT::squareroot (MGT::eps())),
sing_tol_ (10 * MGT::eps()),
label_ (label)
{
setParameterList (plist);
#ifdef BELOS_TEUCHOS_TIME_MONITOR
std::string orthoLabel = label_ + ": Orthogonalization";
timerOrtho_ = Teuchos::TimeMonitor::getNewCounter(orthoLabel);
std::string updateLabel = label_ + ": Ortho (Update)";
timerUpdate_ = Teuchos::TimeMonitor::getNewCounter(updateLabel);
std::string normLabel = label_ + ": Ortho (Norm)";
timerNorm_ = Teuchos::TimeMonitor::getNewCounter(normLabel);
std::string ipLabel = label_ + ": Ortho (Inner Product)";
timerInnerProd_ = Teuchos::TimeMonitor::getNewCounter(ipLabel);
#endif
}
//! Destructor
~ICGSOrthoManager() {}
//@}
//! @name Implementation of Teuchos::ParameterListAcceptorDefaultBase interface
//@{
void
setParameterList (const Teuchos::RCP<Teuchos::ParameterList>& plist)
{
using Teuchos::Exceptions::InvalidParameterName;
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
RCP<const ParameterList> defaultParams = getValidParameters();
RCP<ParameterList> params;
if (plist.is_null()) {
params = parameterList (*defaultParams);
} else {
params = plist;
// Some users might want to specify "blkTol" as "depTol". Due
// to this case, we don't invoke
// validateParametersAndSetDefaults on params. Instead, we go
// through the parameter list one parameter at a time and look
// for alternatives.
}
// Using temporary variables and fetching all values before
// setting the output arguments ensures the strong exception
// guarantee for this function: if an exception is thrown, no
// externally visible side effects (in this case, setting the
// output arguments) have taken place.
int maxNumOrthogPasses;
MagnitudeType blkTol;
MagnitudeType singTol;
try {
maxNumOrthogPasses = params->get<int> ("maxNumOrthogPasses");
} catch (InvalidParameterName&) {
maxNumOrthogPasses = defaultParams->get<int> ("maxNumOrthogPasses");
params->set ("maxNumOrthogPasses", maxNumOrthogPasses);
}
// Handling of the "blkTol" parameter is a special case. This
// is because some users may prefer to call this parameter
// "depTol" for consistency with DGKS. However, our default
// parameter list calls this "blkTol", and we don't want the
// default list's value to override the user's value. Thus, we
// first check the user's parameter list for both names, and
// only then access the default parameter list.
try {
blkTol = params->get<MagnitudeType> ("blkTol");
} catch (InvalidParameterName&) {
try {
blkTol = params->get<MagnitudeType> ("depTol");
// "depTol" is the wrong name, so remove it and replace with
// "blkTol". We'll set "blkTol" below.
params->remove ("depTol");
} catch (InvalidParameterName&) {
blkTol = defaultParams->get<MagnitudeType> ("blkTol");
}
params->set ("blkTol", blkTol);
}
try {
singTol = params->get<MagnitudeType> ("singTol");
} catch (InvalidParameterName&) {
singTol = defaultParams->get<MagnitudeType> ("singTol");
params->set ("singTol", singTol);
}
max_ortho_steps_ = maxNumOrthogPasses;
blk_tol_ = blkTol;
sing_tol_ = singTol;
setMyParamList (params);
}
Teuchos::RCP<const Teuchos::ParameterList>
getValidParameters () const
{
using Teuchos::as;
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
if (defaultParams_.is_null()) {
RCP<ParameterList> params = parameterList ("ICGS");
// Default parameter values for ICGS orthogonalization.
// Documentation will be embedded in the parameter list.
const int defaultMaxNumOrthogPasses = 2;
const MagnitudeType eps = MGT::eps();
const MagnitudeType defaultBlkTol =
as<MagnitudeType> (10) * MGT::squareroot (eps);
const MagnitudeType defaultSingTol = as<MagnitudeType> (10) * eps;
params->set ("maxNumOrthogPasses", defaultMaxNumOrthogPasses,
"Maximum number of orthogonalization passes (includes the "
"first). Default is 2, since \"twice is enough\" for Krylov "
"methods.");
params->set ("blkTol", defaultBlkTol, "Block reorthogonalization "
"threshhold.");
params->set ("singTol", defaultSingTol, "Singular block detection "
"threshold.");
defaultParams_ = params;
}
return defaultParams_;
}
//@}
/// \brief "Fast" but possibly unsafe or less accurate parameters.
///
/// Use this parameter list when you care more about speed than
/// accuracy of the orthogonalization.
Teuchos::RCP<const Teuchos::ParameterList>
getFastParameters () const
{
using Teuchos::as;
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
RCP<const ParameterList> defaultParams = getValidParameters ();
// Start with a clone of the default parameters.
RCP<ParameterList> params = parameterList (*defaultParams);
const int maxBlkOrtho = 1; // No block reorthogonalization
const MagnitudeType blkTol = MGT::zero();
const MagnitudeType singTol = MGT::zero();
params->set ("maxNumOrthogPasses", maxBlkOrtho);
params->set ("blkTol", blkTol);
params->set ("singTol", singTol);
return params;
}
//! @name Accessor routines
//@{
//! Set parameter for block re-orthogonalization threshhold.
void setBlkTol( const MagnitudeType blk_tol ) {
// Update the parameter list as well.
Teuchos::RCP<Teuchos::ParameterList> params = getNonconstParameterList();
if (! params.is_null()) {
// If it's null, then we haven't called setParameterList()
// yet. It's entirely possible to construct the parameter
// list on demand, so we don't try to create the parameter
// list here.
params->set ("blkTol", blk_tol);
}
blk_tol_ = blk_tol;
}
//! Set parameter for singular block detection.
void setSingTol( const MagnitudeType sing_tol ) {
// Update the parameter list as well.
Teuchos::RCP<Teuchos::ParameterList> params = getNonconstParameterList();
if (! params.is_null()) {
// If it's null, then we haven't called setParameterList()
// yet. It's entirely possible to construct the parameter
// list on demand, so we don't try to create the parameter
// list here.
params->set ("singTol", sing_tol);
}
sing_tol_ = sing_tol;
}
//! Return parameter for block re-orthogonalization threshhold.
MagnitudeType getBlkTol() const { return blk_tol_; }
//! Return parameter for singular block detection.
MagnitudeType getSingTol() const { return sing_tol_; }
//@}
//! @name Orthogonalization methods
//@{
/*! \brief Given a list of (mutually and internally) orthonormal bases \c Q, this method
* takes a multivector \c X and projects it onto the space orthogonal to the individual <tt>Q[i]</tt>,
* optionally returning the coefficients of \c X for the individual <tt>Q[i]</tt>. All of this is done with respect
* to the inner product innerProd().
*
* After calling this routine, \c X will be orthogonal to each of the \c <tt>Q[i]</tt>.
*
* The method uses either one or two steps of classical Gram-Schmidt. The algebraically
* equivalent projection matrix is \f$P_Q = I - Q Q^H Op\f$, if \c Op is the matrix specified for
* use in the inner product. Note, this is not an orthogonal projector.
*
@param X [in/out] The multivector to be modified.
On output, \c X will be orthogonal to <tt>Q[i]</tt> with respect to innerProd().
@param MX [in/out] The image of \c X under the operator \c Op.
If \f$ MX != 0\f$: On input, this is expected to be consistent with \c X. On output, this is updated consistent with updates to \c X.
If \f$ MX == 0\f$ or \f$ Op == 0\f$: \c MX is not referenced.
@param C [out] The coefficients of \c X in the \c *Q[i], with respect to innerProd(). If <tt>C[i]</tt> is a non-null pointer
and \c *C[i] matches the dimensions of \c X and \c *Q[i], then the coefficients computed during the orthogonalization
routine will be stored in the matrix \c *C[i]. If <tt>C[i]</tt> is a non-null pointer whose size does not match the dimensions of
\c X and \c *Q[i], then a std::invalid_argument std::exception will be thrown. Otherwise, if <tt>C.size() < i</tt> or <tt>C[i]</tt> is a null
pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.
@param Q [in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each <tt>Q[i]</tt> is assumed to have
orthonormal columns, and the <tt>Q[i]</tt> are assumed to be mutually orthogonal.
*/
void project ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const;
/*! \brief This method calls project(X,Teuchos::null,C,Q); see documentation for that function.
*/
void project ( MV &X,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const {
project(X,Teuchos::null,C,Q);
}
/*! \brief This method takes a multivector \c X and attempts to compute an orthonormal basis for \f$colspan(X)\f$, with respect to innerProd().
*
* The method uses classical Gram-Schmidt, so that the coefficient matrix \c B is upper triangular.
*
* This routine returns an integer \c rank stating the rank of the computed basis. If \c X does not have full rank and the normalize() routine does
* not attempt to augment the subspace, then \c rank may be smaller than the number of columns in \c X. In this case, only the first \c rank columns of
* output \c X and first \c rank rows of \c B will be valid.
*
* The method attempts to find a basis with dimension the same as the number of columns in \c X. It does this by augmenting linearly dependant
* vectors in \c X with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the
* computed basis is less than the number of vectors in \c X.
*
@param X [in/out] The multivector to the modified.
On output, \c X will have some number of orthonormal columns (with respect to innerProd()).
@param MX [in/out] The image of \c X under the operator \c Op.
If \f$ MX != 0\f$: On input, this is expected to be consistent with \c X. On output, this is updated consistent with updates to \c X.
If \f$ MX == 0\f$ or \f$ Op == 0\f$: \c MX is not referenced.
@param B [out] The coefficients of the original \c X with respect to the computed basis. The first rows in \c B
corresponding to the valid columns in \c X will be upper triangular.
@return Rank of the basis computed by this method.
*/
int normalize ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B) const;
/*! \brief This method calls normalize(X,Teuchos::null,B); see documentation for that function.
*/
int normalize ( MV &X, Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B ) const {
return normalize(X,Teuchos::null,B);
}
protected:
/*! \brief Given a set of bases <tt>Q[i]</tt> and a multivector \c X, this method computes an orthonormal basis for \f$colspan(X) - \sum_i colspan(Q[i])\f$.
*
* This routine returns an integer \c rank stating the rank of the computed basis. If the subspace \f$colspan(X) - \sum_i colspan(Q[i])\f$ does not
* have dimension as large as the number of columns of \c X and the orthogonalization manager doe not attempt to augment the subspace, then \c rank
* may be smaller than the number of columns of \c X. In this case, only the first \c rank columns of output \c X and first \c rank rows of \c B will
* be valid.
*
* The method attempts to find a basis with dimension the same as the number of columns in \c 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 \c X.
*
@param X [in/out] The multivector to the modified.
On output, the relevant rows of \c X will be orthogonal to the <tt>Q[i]</tt> and will have orthonormal columns (with respect to innerProd()).
@param MX [in/out] The image of \c X under the operator \c Op.
If \f$ MX != 0\f$: On input, this is expected to be consistent with \c X. On output, this is updated consistent with updates to \c X.
If \f$ MX == 0\f$ or \f$ Op == 0\f$: \c MX is not referenced.
@param C [out] The coefficients of the original \c X in the \c
*Q[i], with respect to innerProd(). If <tt>C[i]</tt> is a
non-null pointer and \c *C[i] matches the dimensions of \c X and
\c *Q[i], then the coefficients computed during the
orthogonalization routine will be stored in the matrix \c
*C[i]. If <tt>C[i]</tt> is a non-null pointer whose size does not
match the dimensions of \c X and \c *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 <tt>C.size() <
i<\tt> or <tt>C[i]</tt> is a null pointer, then the
orthogonalization manager will declare storage for the
coefficients and the user will not have access to them.
@param B [out] The coefficients of the original \c X with respect to the computed basis. The first rows in \c B
corresponding to the valid columns in \c X will be upper triangular.
@param Q [in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each <tt>Q[i]</tt> is assumed to have
orthonormal columns, and the <tt>Q[i]</tt> are assumed to be mutually orthogonal.
@return Rank of the basis computed by this method.
*/
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;
public:
//@}
//! @name Error methods
//@{
/*! \brief This method computes the error in orthonormality of a multivector, measured
* as the Frobenius norm of the difference <tt>innerProd(X,Y) - I</tt>.
*/
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
orthonormError(const MV &X) const {
return orthonormError(X,Teuchos::null);
}
/*! \brief This method computes the error in orthonormality of a multivector, measured
* as the Frobenius norm of the difference <tt>innerProd(X,Y) - I</tt>.
* The method has the option of exploiting a caller-provided \c MX.
*/
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
orthonormError(const MV &X, Teuchos::RCP<const MV> MX) const;
/*! \brief This method computes the error in orthogonality of two multivectors, measured
* as the Frobenius norm of <tt>innerProd(X,Y)</tt>.
*/
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
orthogError(const MV &X1, const MV &X2) const {
return orthogError(X1,Teuchos::null,X2);
}
/*! \brief This method computes the error in orthogonality of two multivectors, measured
* as the Frobenius norm of <tt>innerProd(X,Y)</tt>.
* The method has the option of exploiting a caller-provided \c MX.
*/
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
orthogError(const MV &X1, Teuchos::RCP<const MV> MX1, const MV &X2) const;
//@}
//! @name Label methods
//@{
/*! \brief This method sets the label used by the timers in the orthogonalization manager.
*/
void setLabel(const std::string& label);
/*! \brief This method returns the label being used by the timers in the orthogonalization manager.
*/
const std::string& getLabel() const { return label_; }
//@}
private:
//! Max number of (re)orthogonalization steps, including the first.
int max_ortho_steps_;
//! Block reorthogonalization threshold.
MagnitudeType blk_tol_;
//! Singular block detection threshold.
MagnitudeType sing_tol_;
//! Label for timers.
std::string label_;
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::RCP<Teuchos::Time> timerOrtho_, timerUpdate_,
timerNorm_, timerScale_, timerInnerProd_;
#endif // BELOS_TEUCHOS_TIME_MONITOR
//! Default parameter list.
mutable Teuchos::RCP<Teuchos::ParameterList> defaultParams_;
//! Routine to find an orthonormal basis for X
int findBasis(MV &X, Teuchos::RCP<MV> MX,
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > C,
bool completeBasis, int howMany = -1 ) const;
//! Routine to compute the block orthogonalization
bool blkOrtho1 ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const;
//! Routine to compute the block orthogonalization
bool blkOrtho ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const;
/// Project X against QQ and normalize X, one vector at a time
///
/// \note QQ is called QQ, rather than Q, because we convert it
/// internally from an ArrayView to an Array (named Q inside).
/// This is because the C++ compiler doesn't know how to do type
/// inference (Array has a constructor that takes an ArrayView
/// input). This routine wants an Array rather than an
/// ArrayView internally, because it likes to add (via
/// push_back()) and remove (via resize()) elements to the Q
/// array. Remember that Arrays can be passed by value, just
/// like std::vector objects, so this routine can add whatever
/// it likes to the Q array without changing it from the
/// caller's perspective.
int blkOrthoSing ( 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> > QQ) const;
};
//////////////////////////////////////////////////////////////////////////////////////////////////
// Set the label for this orthogonalization manager and create new timers if it's changed
template<class ScalarType, class MV, class OP>
void ICGSOrthoManager<ScalarType,MV,OP>::setLabel(const std::string& label)
{
if (label != label_) {
label_ = label;
std::string orthoLabel = label_ + ": Orthogonalization";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerOrtho_ = Teuchos::TimeMonitor::getNewCounter(orthoLabel);
#endif
std::string updateLabel = label_ + ": Ortho (Update)";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerUpdate_ = Teuchos::TimeMonitor::getNewCounter(updateLabel);
#endif
std::string normLabel = label_ + ": Ortho (Norm)";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerNorm_ = Teuchos::TimeMonitor::getNewCounter(normLabel);
#endif
std::string ipLabel = label_ + ": Ortho (Inner Product)";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerInnerProd_ = Teuchos::TimeMonitor::getNewCounter(ipLabel);
#endif
}
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Compute the distance from orthonormality
template<class ScalarType, class MV, class OP>
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
ICGSOrthoManager<ScalarType,MV,OP>::orthonormError(const MV &X, Teuchos::RCP<const MV> MX) const {
const ScalarType ONE = SCT::one();
int rank = MVT::GetNumberVecs(X);
Teuchos::SerialDenseMatrix<int,ScalarType> xTx(rank,rank);
MatOrthoManager<ScalarType,MV,OP>::innerProd(X,X,MX,xTx);
for (int i=0; i<rank; i++) {
xTx(i,i) -= ONE;
}
return xTx.normFrobenius();
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Compute the distance from orthogonality
template<class ScalarType, class MV, class OP>
typename Teuchos::ScalarTraits<ScalarType>::magnitudeType
ICGSOrthoManager<ScalarType,MV,OP>::orthogError(const MV &X1, Teuchos::RCP<const MV> MX1, const MV &X2) const {
int r1 = MVT::GetNumberVecs(X1);
int r2 = MVT::GetNumberVecs(X2);
Teuchos::SerialDenseMatrix<int,ScalarType> xTx(r2,r1);
MatOrthoManager<ScalarType,MV,OP>::innerProd(X2,X1,MX1,xTx);
return xTx.normFrobenius();
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Find an Op-orthonormal basis for span(X) - span(W)
template<class ScalarType, class MV, class OP>
int
ICGSOrthoManager<ScalarType, 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
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::is_null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::SerialDenseMatrix;
typedef SerialDenseMatrix< int, ScalarType > serial_dense_matrix_type;
typedef typename Array< RCP< const MV > >::size_type size_type;
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor orthotimer(*timerOrtho_);
#endif
ScalarType ONE = SCT::one();
//ScalarType ZERO = SCT::zero();
int nq = Q.size();
int xc = MVT::GetNumberVecs( X );
ptrdiff_t xr = MVT::GetGlobalLength( X );
int rank = xc;
// If the user doesn't want to store the normalization
// coefficients, allocate some local memory for them. This will
// go away at the end of this method.
if (is_null (B)) {
B = rcp (new serial_dense_matrix_type (xc, xc));
}
// Likewise, if the user doesn't want to store the projection
// coefficients, allocate some local memory for them. Also make
// sure that all the entries of C are the right size. We're going
// to overwrite them anyway, so we don't have to worry about the
// contents (other than to resize them if they are the wrong
// size).
if (C.size() < nq)
C.resize (nq);
for (size_type k = 0; k < nq; ++k)
{
const int numRows = MVT::GetNumberVecs (*Q[k]);
const int numCols = xc; // Number of vectors in X
if (is_null (C[k]))
C[k] = rcp (new serial_dense_matrix_type (numRows, numCols));
else if (C[k]->numRows() != numRows || C[k]->numCols() != numCols)
{
int err = C[k]->reshape (numRows, numCols);
TEUCHOS_TEST_FOR_EXCEPTION(err != 0, std::runtime_error,
"IMGS orthogonalization: failed to reshape "
"C[" << k << "] (the array of block "
"coefficients resulting from projecting X "
"against Q[1:" << nq << "]).");
}
}
/****** DO NOT MODIFY *MX IF _hasOp == false ******/
if (this->_hasOp) {
if (MX == Teuchos::null) {
// we need to allocate space for MX
MX = MVT::Clone(X,MVT::GetNumberVecs(X));
OPT::Apply(*(this->_Op),X,*MX);
}
}
else {
// Op == I --> MX = X (ignore it if the user passed it in)
MX = Teuchos::rcp( &X, false );
}
int mxc = MVT::GetNumberVecs( *MX );
ptrdiff_t mxr = MVT::GetGlobalLength( *MX );
// short-circuit
TEUCHOS_TEST_FOR_EXCEPTION( xc == 0 || xr == 0, std::invalid_argument, "Belos::ICGSOrthoManager::projectAndNormalize(): X must be non-empty" );
int numbas = 0;
for (int i=0; i<nq; i++) {
numbas += MVT::GetNumberVecs( *Q[i] );
}
// check size of B
TEUCHOS_TEST_FOR_EXCEPTION( B->numRows() != xc || B->numCols() != xc, std::invalid_argument,
"Belos::ICGSOrthoManager::projectAndNormalize(): Size of X must be consistant with size of B" );
// check size of X and MX
TEUCHOS_TEST_FOR_EXCEPTION( xc<0 || xr<0 || mxc<0 || mxr<0, std::invalid_argument,
"Belos::ICGSOrthoManager::projectAndNormalize(): MVT returned negative dimensions for X,MX" );
// check size of X w.r.t. MX
TEUCHOS_TEST_FOR_EXCEPTION( xc!=mxc || xr!=mxr, std::invalid_argument,
"Belos::ICGSOrthoManager::projectAndNormalize(): Size of X must be consistant with size of MX" );
// check feasibility
//TEUCHOS_TEST_FOR_EXCEPTION( numbas+xc > xr, std::invalid_argument,
// "Belos::ICGSOrthoManager::projectAndNormalize(): Orthogonality constraints not feasible" );
// Some flags for checking dependency returns from the internal orthogonalization methods
bool dep_flg = false;
// Make a temporary copy of X and MX, just in case a block dependency is detected.
Teuchos::RCP<MV> tmpX, tmpMX;
tmpX = MVT::CloneCopy(X);
if (this->_hasOp) {
tmpMX = MVT::CloneCopy(*MX);
}
if (xc == 1) {
// Use the cheaper block orthogonalization.
// NOTE: Don't check for dependencies because the update has one vector.
dep_flg = blkOrtho1( X, MX, C, Q );
// Normalize the new block X
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor normTimer( *timerNorm_ );
#endif
if ( B == Teuchos::null ) {
B = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>(xc,xc) );
}
std::vector<ScalarType> diag(xc);
MVT::MvDot( X, *MX, diag );
(*B)(0,0) = SCT::squareroot(SCT::magnitude(diag[0]));
rank = 1;
MVT::MvScale( X, ONE/(*B)(0,0) );
if (this->_hasOp) {
// Update MXj.
MVT::MvScale( *MX, ONE/(*B)(0,0) );
}
}
}
else {
// Use the cheaper block orthogonalization.
dep_flg = blkOrtho( X, MX, C, Q );
// If a dependency has been detected in this block, then perform
// the more expensive nonblock (single vector at a time)
// orthogonalization.
if (dep_flg) {
rank = blkOrthoSing( *tmpX, tmpMX, C, B, Q );
// Copy tmpX back into X.
MVT::Assign( *tmpX, X );
if (this->_hasOp) {
MVT::Assign( *tmpMX, *MX );
}
}
else {
// There is no dependency, so orthonormalize new block X
rank = findBasis( X, MX, B, false );
if (rank < xc) {
// A dependency was found during orthonormalization of X,
// rerun orthogonalization using more expensive nonblock
// orthogonalization.
rank = blkOrthoSing( *tmpX, tmpMX, C, B, Q );
// Copy tmpX back into X.
MVT::Assign( *tmpX, X );
if (this->_hasOp) {
MVT::Assign( *tmpMX, *MX );
}
}
}
} // if (xc == 1) {
// this should not raise an std::exception; but our post-conditions oblige us to check
TEUCHOS_TEST_FOR_EXCEPTION( rank > xc || rank < 0, std::logic_error,
"Belos::ICGSOrthoManager::projectAndNormalize(): Debug error in rank variable." );
// Return the rank of X.
return rank;
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Find an Op-orthonormal basis for span(X), with rank numvectors(X)
template<class ScalarType, class MV, class OP>
int ICGSOrthoManager<ScalarType, MV, OP>::normalize(
MV &X, Teuchos::RCP<MV> MX,
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B ) const {
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor orthotimer(*timerOrtho_);
#endif
// call findBasis, with the instruction to try to generate a basis of rank numvecs(X)
return findBasis(X, MX, B, true);
}
//////////////////////////////////////////////////////////////////////////////////////////////////
template<class ScalarType, class MV, class OP>
void ICGSOrthoManager<ScalarType, 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 {
// For the inner product defined by the operator Op or the identity (Op == 0)
// -> Orthogonalize X against each Q[i]
// Modify MX accordingly
//
// Note that when Op is 0, MX is not referenced
//
// Parameter variables
//
// X : Vectors to be transformed
//
// MX : Image of the block of vectors X by the mass matrix
//
// Q : Bases to orthogonalize against. These are assumed orthonormal, mutually and independently.
//
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor orthotimer(*timerOrtho_);
#endif
int xc = MVT::GetNumberVecs( X );
ptrdiff_t xr = MVT::GetGlobalLength( X );
int nq = Q.size();
std::vector<int> qcs(nq);
// short-circuit
if (nq == 0 || xc == 0 || xr == 0) {
return;
}
ptrdiff_t qr = MVT::GetGlobalLength ( *Q[0] );
// if we don't have enough C, expand it with null references
// if we have too many, resize to throw away the latter ones
// if we have exactly as many as we have Q, this call has no effect
C.resize(nq);
/****** DO NOT MODIFY *MX IF _hasOp == false ******/
if (this->_hasOp) {
if (MX == Teuchos::null) {
// we need to allocate space for MX
MX = MVT::Clone(X,MVT::GetNumberVecs(X));
OPT::Apply(*(this->_Op),X,*MX);
}
}
else {
// Op == I --> MX = X (ignore it if the user passed it in)
MX = Teuchos::rcp( &X, false );
}
int mxc = MVT::GetNumberVecs( *MX );
ptrdiff_t mxr = MVT::GetGlobalLength( *MX );
// check size of X and Q w.r.t. common sense
TEUCHOS_TEST_FOR_EXCEPTION( xc<0 || xr<0 || mxc<0 || mxr<0, std::invalid_argument,
"Belos::ICGSOrthoManager::project(): MVT returned negative dimensions for X,MX" );
// check size of X w.r.t. MX and Q
TEUCHOS_TEST_FOR_EXCEPTION( xc!=mxc || xr!=mxr || xr!=qr, std::invalid_argument,
"Belos::ICGSOrthoManager::project(): Size of X not consistant with MX,Q" );
// tally up size of all Q and check/allocate C
int baslen = 0;
for (int i=0; i<nq; i++) {
TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength( *Q[i] ) != qr, std::invalid_argument,
"Belos::ICGSOrthoManager::project(): Q lengths not mutually consistant" );
qcs[i] = MVT::GetNumberVecs( *Q[i] );
TEUCHOS_TEST_FOR_EXCEPTION( qr < qcs[i], std::invalid_argument,
"Belos::ICGSOrthoManager::project(): Q has less rows than columns" );
baslen += qcs[i];
// check size of C[i]
if ( C[i] == Teuchos::null ) {
C[i] = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>(qcs[i],xc) );
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( C[i]->numRows() != qcs[i] || C[i]->numCols() != xc , std::invalid_argument,
"Belos::ICGSOrthoManager::project(): Size of Q not consistant with size of C" );
}
}
// Use the cheaper block orthogonalization, don't check for rank deficiency.
blkOrtho( X, MX, C, Q );
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Find an Op-orthonormal basis for span(X), with the option of extending the subspace so that
// the rank is numvectors(X)
template<class ScalarType, class MV, class OP>
int
ICGSOrthoManager<ScalarType, MV, OP>::
findBasis (MV &X,
Teuchos::RCP<MV> MX,
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B,
bool completeBasis,
int howMany) const
{
// For the inner product defined by the operator Op or the identity (Op == 0)
// -> Orthonormalize X
// Modify MX accordingly
//
// Note that when Op is 0, MX is not referenced
//
// Parameter variables
//
// X : Vectors to be orthonormalized
// MX : Image of the multivector X under the operator Op
// Op : Pointer to the operator for the inner product
//
using Teuchos::as;
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor normTimer (*timerNorm_);
#endif // BELOS_TEUCHOS_TIME_MONITOR
const ScalarType ONE = SCT::one ();
const MagnitudeType ZERO = SCT::magnitude (SCT::zero ());
const int xc = MVT::GetNumberVecs (X);
const ptrdiff_t xr = MVT::GetGlobalLength (X);
if (howMany == -1) {
howMany = xc;
}
/*******************************************************
* If _hasOp == false, we will not reference MX below *
*******************************************************/
// if Op==null, MX == X (via pointer)
// Otherwise, either the user passed in MX or we will allocated and compute it
if (this->_hasOp) {
if (MX == Teuchos::null) {
// we need to allocate space for MX
MX = MVT::Clone(X,xc);
OPT::Apply(*(this->_Op),X,*MX);
}
}
/* if the user doesn't want to store the coefficienets,
* allocate some local memory for them
*/
if ( B == Teuchos::null ) {
B = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>(xc,xc) );
}
const int mxc = (this->_hasOp) ? MVT::GetNumberVecs( *MX ) : xc;
const ptrdiff_t mxr = (this->_hasOp) ? MVT::GetGlobalLength( *MX ) : xr;
// check size of C, B
TEUCHOS_TEST_FOR_EXCEPTION( xc == 0 || xr == 0, std::invalid_argument,
"Belos::ICGSOrthoManager::findBasis(): X must be non-empty" );
TEUCHOS_TEST_FOR_EXCEPTION( B->numRows() != xc || B->numCols() != xc, std::invalid_argument,
"Belos::ICGSOrthoManager::findBasis(): Size of X not consistant with size of B" );
TEUCHOS_TEST_FOR_EXCEPTION( xc != mxc || xr != mxr, std::invalid_argument,
"Belos::ICGSOrthoManager::findBasis(): Size of X not consistant with size of MX" );
TEUCHOS_TEST_FOR_EXCEPTION( as<ptrdiff_t> (xc) > xr, std::invalid_argument,
"Belos::ICGSOrthoManager::findBasis(): Size of X not feasible for normalization" );
TEUCHOS_TEST_FOR_EXCEPTION( howMany < 0 || howMany > xc, std::invalid_argument,
"Belos::ICGSOrthoManager::findBasis(): Invalid howMany parameter" );
/* xstart is which column we are starting the process with, based on howMany
* columns before xstart are assumed to be Op-orthonormal already
*/
int xstart = xc - howMany;
for (int j = xstart; j < xc; j++) {
// numX is
// * number of currently orthonormal columns of X
// * the index of the current column of X
int numX = j;
bool addVec = false;
// Get a view of the vector currently being worked on.
std::vector<int> index(1);
index[0] = numX;
Teuchos::RCP<MV> Xj = MVT::CloneViewNonConst( X, index );
Teuchos::RCP<MV> MXj;
if (this->_hasOp) {
// MXj is a view of the current vector in MX
MXj = MVT::CloneViewNonConst( *MX, index );
}
else {
// MXj is a pointer to Xj, and MUST NOT be modified
MXj = Xj;
}
// Get a view of the previous vectors.
std::vector<int> prev_idx( numX );
Teuchos::RCP<const MV> prevX, prevMX;
if (numX > 0) {
for (int i=0; i<numX; i++) {
prev_idx[i] = i;
}
prevX = MVT::CloneView( X, prev_idx );
if (this->_hasOp) {
prevMX = MVT::CloneView( *MX, prev_idx );
}
}
// Make storage for these Gram-Schmidt iterations.
Teuchos::SerialDenseMatrix<int,ScalarType> product(numX, 1);
std::vector<ScalarType> oldDot( 1 ), newDot( 1 );
//
// Save old MXj vector and compute Op-norm
//
Teuchos::RCP<MV> oldMXj = MVT::CloneCopy( *MXj );
MVT::MvDot( *Xj, *MXj, oldDot );
// Xj^H Op Xj should be real and positive, by the hermitian positive definiteness of Op
TEUCHOS_TEST_FOR_EXCEPTION( SCT::real(oldDot[0]) < ZERO, OrthoError,
"Belos::ICGSOrthoManager::findBasis(): Negative definiteness discovered in inner product" );
if (numX > 0) {
Teuchos::SerialDenseMatrix<int,ScalarType> P2(numX,1);
for (int i=0; i<max_ortho_steps_; ++i) {
// product <- prevX^T MXj
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*prevX,*Xj,MXj,P2);
}
// Xj <- Xj - prevX prevX^T MXj
// = Xj - prevX product
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *prevX, P2, ONE, *Xj );
}
// Update MXj
if (this->_hasOp) {
// MXj <- Op*Xj_new
// = Op*(Xj_old - prevX prevX^T MXj)
// = MXj - prevMX product
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *prevMX, P2, ONE, *MXj );
}
// Set coefficients
if ( i==0 )
product = P2;
else
product += P2;
}
} // if (numX > 0)
// Compute Op-norm with old MXj
MVT::MvDot( *Xj, *oldMXj, newDot );
// Check to see if the new vector is dependent.
if (completeBasis) {
//
// We need a complete basis, so add random vectors if necessary
//
if ( SCT::magnitude(newDot[0]) < SCT::magnitude(sing_tol_*oldDot[0]) ) {
// Add a random vector and orthogonalize it against previous vectors in block.
addVec = true;
#ifdef ORTHO_DEBUG
std::cout << "Belos::ICGSOrthoManager::findBasis() --> Random for column " << numX << std::endl;
#endif
//
Teuchos::RCP<MV> tempXj = MVT::Clone( X, 1 );
Teuchos::RCP<MV> tempMXj;
MVT::MvRandom( *tempXj );
if (this->_hasOp) {
tempMXj = MVT::Clone( X, 1 );
OPT::Apply( *(this->_Op), *tempXj, *tempMXj );
}
else {
tempMXj = tempXj;
}
MVT::MvDot( *tempXj, *tempMXj, oldDot );
//
for (int num_orth=0; num_orth<max_ortho_steps_; num_orth++){
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*prevX,*tempXj,tempMXj,product);
}
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *prevX, product, ONE, *tempXj );
}
if (this->_hasOp) {
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *prevMX, product, ONE, *tempMXj );
}
}
// Compute new Op-norm
MVT::MvDot( *tempXj, *tempMXj, newDot );
//
if ( SCT::magnitude(newDot[0]) >= SCT::magnitude(oldDot[0]*sing_tol_) ) {
// Copy vector into current column of _basisvecs
MVT::Assign( *tempXj, *Xj );
if (this->_hasOp) {
MVT::Assign( *tempMXj, *MXj );
}
}
else {
return numX;
}
}
}
else {
//
// We only need to detect dependencies.
//
if ( SCT::magnitude(newDot[0]) < SCT::magnitude(oldDot[0]*blk_tol_) ) {
return numX;
}
}
// If we haven't left this method yet, then we can normalize the new vector Xj.
// Normalize Xj.
// Xj <- Xj / std::sqrt(newDot)
ScalarType diag = SCT::squareroot(SCT::magnitude(newDot[0]));
{
MVT::MvScale( *Xj, ONE/diag );
if (this->_hasOp) {
// Update MXj.
MVT::MvScale( *MXj, ONE/diag );
}
}
// If we've added a random vector, enter a zero in the j'th diagonal element.
if (addVec) {
(*B)(j,j) = ZERO;
}
else {
(*B)(j,j) = diag;
}
// Save the coefficients, if we are working on the original vector and not a randomly generated one
if (!addVec) {
for (int i=0; i<numX; i++) {
(*B)(i,j) = product(i,0);
}
}
} // for (j = 0; j < xc; ++j)
return xc;
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Routine to compute the block orthogonalization
template<class ScalarType, class MV, class OP>
bool
ICGSOrthoManager<ScalarType, MV, OP>::blkOrtho1 ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const
{
int nq = Q.size();
int xc = MVT::GetNumberVecs( X );
const ScalarType ONE = SCT::one();
std::vector<int> qcs( nq );
for (int i=0; i<nq; i++) {
qcs[i] = MVT::GetNumberVecs( *Q[i] );
}
// Perform the Gram-Schmidt transformation for a block of vectors
Teuchos::Array<Teuchos::RCP<MV> > MQ(nq);
// Define the product Q^T * (Op*X)
for (int i=0; i<nq; i++) {
// Multiply Q' with MX
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],X,MX,*C[i]);
}
// Multiply by Q and subtract the result in X
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *Q[i], *C[i], ONE, X );
}
// Update MX, with the least number of applications of Op as possible
if (this->_hasOp) {
if (xc <= qcs[i]) {
OPT::Apply( *(this->_Op), X, *MX);
}
else {
// this will possibly be used again below; don't delete it
MQ[i] = MVT::Clone( *Q[i], qcs[i] );
OPT::Apply( *(this->_Op), *Q[i], *MQ[i] );
MVT::MvTimesMatAddMv( -ONE, *MQ[i], *C[i], ONE, *MX );
}
}
}
// Do as many steps of classical Gram-Schmidt as required by max_ortho_steps_
for (int j = 1; j < max_ortho_steps_; ++j) {
for (int i=0; i<nq; i++) {
Teuchos::SerialDenseMatrix<int,ScalarType> C2(C[i]->numRows(),C[i]->numCols());
// Apply another step of classical Gram-Schmidt
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],X,MX,C2);
}
*C[i] += C2;
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *Q[i], C2, ONE, X );
}
// Update MX, with the least number of applications of Op as possible
if (this->_hasOp) {
if (MQ[i].get()) {
// MQ was allocated and computed above; use it
MVT::MvTimesMatAddMv( -ONE, *MQ[i], C2, ONE, *MX );
}
else if (xc <= qcs[i]) {
// MQ was not allocated and computed above; it was cheaper to use X before and it still is
OPT::Apply( *(this->_Op), X, *MX);
}
}
} // for (int i=0; i<nq; i++)
} // for (int j = 0; j < max_ortho_steps; ++j)
return false;
}
//////////////////////////////////////////////////////////////////////////////////////////////////
// Routine to compute the block orthogonalization
template<class ScalarType, class MV, class OP>
bool
ICGSOrthoManager<ScalarType, MV, OP>::blkOrtho ( MV &X, Teuchos::RCP<MV> MX,
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const
{
int nq = Q.size();
int xc = MVT::GetNumberVecs( X );
bool dep_flg = false;
const ScalarType ONE = SCT::one();
std::vector<int> qcs( nq );
for (int i=0; i<nq; i++) {
qcs[i] = MVT::GetNumberVecs( *Q[i] );
}
// Perform the Gram-Schmidt transformation for a block of vectors
// Compute the initial Op-norms
std::vector<ScalarType> oldDot( xc );
MVT::MvDot( X, *MX, oldDot );
Teuchos::Array<Teuchos::RCP<MV> > MQ(nq);
// Define the product Q^T * (Op*X)
for (int i=0; i<nq; i++) {
// Multiply Q' with MX
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],X,MX,*C[i]);
}
// Multiply by Q and subtract the result in X
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *Q[i], *C[i], ONE, X );
}
// Update MX, with the least number of applications of Op as possible
if (this->_hasOp) {
if (xc <= qcs[i]) {
OPT::Apply( *(this->_Op), X, *MX);
}
else {
// this will possibly be used again below; don't delete it
MQ[i] = MVT::Clone( *Q[i], qcs[i] );
OPT::Apply( *(this->_Op), *Q[i], *MQ[i] );
MVT::MvTimesMatAddMv( -ONE, *MQ[i], *C[i], ONE, *MX );
}
}
}
// Do as many steps of classical Gram-Schmidt as required by max_ortho_steps_
for (int j = 1; j < max_ortho_steps_; ++j) {
for (int i=0; i<nq; i++) {
Teuchos::SerialDenseMatrix<int,ScalarType> C2(C[i]->numRows(),C[i]->numCols());
// Apply another step of classical Gram-Schmidt
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor innerProdTimer( *timerInnerProd_ );
#endif
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],X,MX,C2);
}
*C[i] += C2;
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor updateTimer( *timerUpdate_ );
#endif
MVT::MvTimesMatAddMv( -ONE, *Q[i], C2, ONE, X );
}
// Update MX, with the least number of applications of Op as possible
if (this->_hasOp) {
if (MQ[i].get()) {
// MQ was allocated and computed above; use it
MVT::MvTimesMatAddMv( -ONE, *MQ[i], C2, ONE, *MX );
}
else if (xc <= qcs[i]) {
// MQ was not allocated and computed above; it was cheaper to use X before and it still is
OPT::Apply( *(this->_Op), X, *MX);
}
}
} // for (int i=0; i<nq; i++)
} // for (int j = 0; j < max_ortho_steps; ++j)
// Compute new Op-norms
std::vector<ScalarType> newDot(xc);
MVT::MvDot( X, *MX, newDot );
// Check to make sure the new block of vectors are not dependent on previous vectors
for (int i=0; i<xc; i++){
if (SCT::magnitude(newDot[i]) < SCT::magnitude(oldDot[i] * blk_tol_)) {
dep_flg = true;
break;
}
} // end for (i=0;...)
return dep_flg;
}
template<class ScalarType, class MV, class OP>
int
ICGSOrthoManager<ScalarType, MV, OP>::blkOrthoSing ( 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> > QQ) const
{
Teuchos::Array<Teuchos::RCP<const MV> > Q (QQ);
const ScalarType ONE = SCT::one();
const ScalarType ZERO = SCT::zero();
int nq = Q.size();
int xc = MVT::GetNumberVecs( X );
std::vector<int> indX( 1 );
std::vector<ScalarType> oldDot( 1 ), newDot( 1 );
std::vector<int> qcs( nq );
for (int i=0; i<nq; i++) {
qcs[i] = MVT::GetNumberVecs( *Q[i] );
}
// Create pointers for the previous vectors of X that have already been orthonormalized.
Teuchos::RCP<const MV> lastQ;
Teuchos::RCP<MV> Xj, MXj;
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > lastC;
// Perform the Gram-Schmidt transformation for each vector in the block of vectors.
for (int j=0; j<xc; j++) {
bool dep_flg = false;
// Get a view of the previously orthogonalized vectors and B, add it to the arrays.
if (j > 0) {
std::vector<int> index( j );
for (int ind=0; ind<j; ind++) {
index[ind] = ind;
}
lastQ = MVT::CloneView( X, index );
// Add these views to the Q and C arrays.
Q.push_back( lastQ );
C.push_back( B );
qcs.push_back( MVT::GetNumberVecs( *lastQ ) );
}
// Get a view of the current vector in X to orthogonalize.
indX[0] = j;
Xj = MVT::CloneViewNonConst( X, indX );
if (this->_hasOp) {
MXj = MVT::CloneViewNonConst( *MX, indX );
}
else {
MXj = Xj;
}
// Compute the initial Op-norms
MVT::MvDot( *Xj, *MXj, oldDot );
Teuchos::Array<Teuchos::RCP<MV> > MQ(Q.size());
// Define the product Q^T * (Op*X)
for (int i=0; i<Q.size(); i++) {
// Get a view of the current serial dense matrix
Teuchos::SerialDenseMatrix<int,ScalarType> tempC( Teuchos::View, *C[i], qcs[i], 1, 0, j );
// Multiply Q' with MX
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],*Xj,MXj,tempC);
// Multiply by Q and subtract the result in Xj
MVT::MvTimesMatAddMv( -ONE, *Q[i], tempC, ONE, *Xj );
// Update MXj, with the least number of applications of Op as possible
if (this->_hasOp) {
if (xc <= qcs[i]) {
OPT::Apply( *(this->_Op), *Xj, *MXj);
}
else {
// this will possibly be used again below; don't delete it
MQ[i] = MVT::Clone( *Q[i], qcs[i] );
OPT::Apply( *(this->_Op), *Q[i], *MQ[i] );
MVT::MvTimesMatAddMv( -ONE, *MQ[i], tempC, ONE, *MXj );
}
}
}
// Do any additional steps of classical Gram-Schmidt orthogonalization
for (int num_ortho_steps=1; num_ortho_steps < max_ortho_steps_; ++num_ortho_steps) {
for (int i=0; i<Q.size(); i++) {
Teuchos::SerialDenseMatrix<int,ScalarType> tempC( Teuchos::View, *C[i], qcs[i], 1, 0, j );
Teuchos::SerialDenseMatrix<int,ScalarType> C2( qcs[i], 1 );
// Apply another step of classical Gram-Schmidt
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],*Xj,MXj,C2);
tempC += C2;
MVT::MvTimesMatAddMv( -ONE, *Q[i], C2, ONE, *Xj );
// Update MXj, with the least number of applications of Op as possible
if (this->_hasOp) {
if (MQ[i].get()) {
// MQ was allocated and computed above; use it
MVT::MvTimesMatAddMv( -ONE, *MQ[i], C2, ONE, *MXj );
}
else if (xc <= qcs[i]) {
// MQ was not allocated and computed above; it was cheaper to use X before and it still is
OPT::Apply( *(this->_Op), *Xj, *MXj);
}
}
} // for (int i=0; i<Q.size(); i++)
} // for (int num_ortho_steps=1; num_ortho_steps < max_ortho_steps_; ++num_ortho_steps)
// Check for linear dependence.
if (SCT::magnitude(newDot[0]) < SCT::magnitude(oldDot[0]*sing_tol_)) {
dep_flg = true;
}
// Normalize the new vector if it's not dependent
if (!dep_flg) {
ScalarType diag = SCT::squareroot(SCT::magnitude(newDot[0]));
MVT::MvScale( *Xj, ONE/diag );
if (this->_hasOp) {
// Update MXj.
MVT::MvScale( *MXj, ONE/diag );
}
// Enter value on diagonal of B.
(*B)(j,j) = diag;
}
else {
// Create a random vector and orthogonalize it against all previous columns of Q.
Teuchos::RCP<MV> tempXj = MVT::Clone( X, 1 );
Teuchos::RCP<MV> tempMXj;
MVT::MvRandom( *tempXj );
if (this->_hasOp) {
tempMXj = MVT::Clone( X, 1 );
OPT::Apply( *(this->_Op), *tempXj, *tempMXj );
}
else {
tempMXj = tempXj;
}
MVT::MvDot( *tempXj, *tempMXj, oldDot );
//
for (int num_orth=0; num_orth<max_ortho_steps_; num_orth++) {
for (int i=0; i<Q.size(); i++) {
Teuchos::SerialDenseMatrix<int,ScalarType> product( qcs[i], 1 );
// Apply another step of classical Gram-Schmidt
MatOrthoManager<ScalarType,MV,OP>::innerProd(*Q[i],*tempXj,tempMXj,product);
MVT::MvTimesMatAddMv( -ONE, *Q[i], product, ONE, *tempXj );
// Update MXj, with the least number of applications of Op as possible
if (this->_hasOp) {
if (MQ[i].get()) {
// MQ was allocated and computed above; use it
MVT::MvTimesMatAddMv( -ONE, *MQ[i], product, ONE, *tempMXj );
}
else if (xc <= qcs[i]) {
// MQ was not allocated and computed above; it was cheaper to use X before and it still is
OPT::Apply( *(this->_Op), *tempXj, *tempMXj);
}
}
} // for (int i=0; i<nq; i++)
}
// Compute the Op-norms after the correction step.
MVT::MvDot( *tempXj, *tempMXj, newDot );
// Copy vector into current column of Xj
if ( SCT::magnitude(newDot[0]) >= SCT::magnitude(oldDot[0]*sing_tol_) ) {
ScalarType diag = SCT::squareroot(SCT::magnitude(newDot[0]));
// Enter value on diagonal of B.
(*B)(j,j) = ZERO;
// Copy vector into current column of _basisvecs
MVT::MvAddMv( ONE/diag, *tempXj, ZERO, *tempXj, *Xj );
if (this->_hasOp) {
MVT::MvAddMv( ONE/diag, *tempMXj, ZERO, *tempMXj, *MXj );
}
}
else {
return j;
}
} // if (!dep_flg)
// Remove the vectors from array
if (j > 0) {
Q.resize( nq );
C.resize( nq );
qcs.resize( nq );
}
} // for (int j=0; j<xc; j++)
return xc;
}
} // namespace Belos
#endif // BELOS_ICGS_ORTHOMANAGER_HPP
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