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// ************************************************************************
//
// Belos: Block Linear Solvers Package
// Copyright 2004 Sandia Corporation
//
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//@HEADER
/// \file BelosSimpleOrthoManager.hpp
/// \brief Simple OrthoManager implementation for benchmarks.
///
#ifndef __Belos_SimpleOrthoManager_hpp
#define __Belos_SimpleOrthoManager_hpp
#include <BelosConfigDefs.hpp>
#include <BelosMultiVecTraits.hpp>
#include <BelosOrthoManager.hpp>
#include <BelosOutputManager.hpp>
#include <Teuchos_ParameterList.hpp>
#include <Teuchos_ParameterListAcceptorDefaultBase.hpp>
#include <Teuchos_StandardCatchMacros.hpp>
#include <Teuchos_TimeMonitor.hpp>
namespace Belos {
/// \class SimpleOrthoManager
/// \brief Simple OrthoManager implementation for benchmarks.
/// \author Mark Hoemmen
///
/// This is a very simple orthogonalization method and should only
/// be used for benchmarks. It performs optional unconditional
/// reorthogonalization (no norm tests), but has no rank-revealing
/// features.
template<class Scalar, class MV>
class SimpleOrthoManager :
public OrthoManager<Scalar, MV>,
public Teuchos::ParameterListAcceptorDefaultBase
{
public:
typedef Scalar scalar_type;
typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType magnitude_type;
typedef Teuchos::SerialDenseMatrix<int, Scalar> mat_type;
typedef Teuchos::RCP<Teuchos::SerialDenseMatrix<int, Scalar> > mat_ptr;
private:
typedef MultiVecTraits<Scalar, MV> MVT;
typedef Teuchos::ScalarTraits<Scalar> STS;
typedef Teuchos::ScalarTraits<magnitude_type> STM;
//! Label for Belos timer display.
std::string label_;
//! Output manager (used mainly for debugging).
Teuchos::RCP<OutputManager<Scalar> > outMan_;
//! Whether or not to do (unconditional) reorthogonalization.
bool reorthogonalize_;
//! Whether to use MGS or CGS in the normalize() step.
bool useMgs_;
//! Default parameter list.
mutable Teuchos::RCP<Teuchos::ParameterList> defaultParams_;
#ifdef BELOS_TEUCHOS_TIME_MONITOR
//! Timer for all orthogonalization operations
Teuchos::RCP<Teuchos::Time> timerOrtho_;
//! Timer for projection operations
Teuchos::RCP<Teuchos::Time> timerProject_;
//! Timer for normalization operations
Teuchos::RCP<Teuchos::Time> timerNormalize_;
/// \brief Instantiate and return a timer with an appropriate label.
///
/// \param prefix [in] Prefix for the timer label, e.g., "Belos"
/// \param timerName [in] Name of the timer, or what the timer
/// is timing, e.g., "Projection" or "Normalization"
///
/// \return Smart pointer to a new Teuchos::Time timer object,
/// to be used via Teuchos::TimeMonitor
static Teuchos::RCP<Teuchos::Time>
makeTimer (const std::string& prefix,
const std::string& timerName)
{
const std::string timerLabel =
prefix.empty() ? timerName : (prefix + ": " + timerName);
return Teuchos::TimeMonitor::getNewCounter (timerLabel);
}
#endif // BELOS_TEUCHOS_TIME_MONITOR
public:
/// \brief Get a default list of parameters.
///
/// The "default" parameter list sets reasonably safe options in
/// terms of accuracy of the computed orthogonalization. Call \c
/// getFastParameters() if you prefer to sacrifice some accuracy
/// for speed.
Teuchos::RCP<const Teuchos::ParameterList>
getValidParameters () const
{
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
const std::string defaultNormalizationMethod ("MGS");
const bool defaultReorthogonalization = false;
if (defaultParams_.is_null()) {
RCP<ParameterList> params = parameterList ("Simple");
params->set ("Normalization", defaultNormalizationMethod,
"Which normalization method to use. Valid values are \"MGS\""
" (for Modified Gram-Schmidt) and \"CGS\" (for Classical "
"Gram-Schmidt).");
params->set ("Reorthogonalization", defaultReorthogonalization,
"Whether to perform one (unconditional) reorthogonalization "
"pass.");
defaultParams_ = params;
}
return defaultParams_;
}
/// \brief Get a "fast" list of parameters.
///
/// The "fast" parameter list favors speed of orthogonalization,
/// but sacrifices some safety and accuracy. Call \c
/// getDefaultParameters() for safer and more accurate options.
Teuchos::RCP<const Teuchos::ParameterList>
getFastParameters ()
{
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
using Teuchos::rcp;
const std::string fastNormalizationMethod ("CGS");
const bool fastReorthogonalization = false;
// Start with a clone of the default parameters.
RCP<ParameterList> fastParams = parameterList (*getValidParameters());
fastParams->set ("Normalization", fastNormalizationMethod);
fastParams->set ("Reorthogonalization", fastReorthogonalization);
return fastParams;
}
void
setParameterList (const Teuchos::RCP<Teuchos::ParameterList>& plist)
{
using Teuchos::ParameterList;
using Teuchos::parameterList;
using Teuchos::RCP;
using Teuchos::Exceptions::InvalidParameter;
RCP<const ParameterList> defaultParams = getValidParameters();
RCP<ParameterList> params;
if (plist.is_null ()) {
params = parameterList (*defaultParams);
} else {
params = plist;
params->validateParametersAndSetDefaults (*defaultParams);
}
const std::string normalizeImpl = params->get<std::string>("Normalization");
const bool reorthogonalize = params->get<bool>("Reorthogonalization");
if (normalizeImpl == "MGS" ||
normalizeImpl == "Mgs" ||
normalizeImpl == "mgs") {
useMgs_ = true;
params->set ("Normalization", std::string ("MGS")); // Standardize.
} else {
useMgs_ = false;
params->set ("Normalization", std::string ("CGS")); // Standardize.
}
reorthogonalize_ = reorthogonalize;
setMyParamList (params);
}
/// \brief Constructor
///
/// \param outMan [in/out] Output manager. If not null, use for
/// various kinds of status output (in particular, for debugging).
///
/// \param label [in] Label for Belos timers.
///
/// \param params [in/out] List of configuration parameters. Call
/// getDefaultParameters() or getFastParameters() for valid
/// parameter lists.
SimpleOrthoManager (const Teuchos::RCP<OutputManager<Scalar> >& outMan,
const std::string& label,
const Teuchos::RCP<Teuchos::ParameterList>& params) :
label_ (label),
outMan_ (outMan)
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerOrtho_ = makeTimer (label, "All orthogonalization");
timerProject_ = makeTimer (label, "Projection");
timerNormalize_ = makeTimer (label, "Normalization");
#endif // BELOS_TEUCHOS_TIME_MONITOR
setParameterList (params);
if (! outMan_.is_null ()) {
using std::endl;
std::ostream& dbg = outMan_->stream(Debug);
dbg << "Belos::SimpleOrthoManager constructor:" << endl
<< "-- Normalization method: "
<< (useMgs_ ? "MGS" : "CGS") << endl
<< "-- Reorthogonalize (unconditionally)? "
<< (reorthogonalize_ ? "Yes" : "No") << endl;
}
}
/// \brief Constructor
///
/// \param label [in] Label for Belos timers.
SimpleOrthoManager (const std::string& label) :
label_ (label)
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
timerOrtho_ = makeTimer (label, "All orthogonalization");
timerProject_ = makeTimer (label, "Projection");
timerNormalize_ = makeTimer (label, "Normalization");
#endif // BELOS_TEUCHOS_TIME_MONITOR
setParameterList (Teuchos::null);
}
//! Virtual destructor for memory safety of derived classes.
virtual ~SimpleOrthoManager() {}
void innerProd (const MV &X, const MV &Y, mat_type& Z) const {
MVT::MvTransMv (STS::one (), X, Y, Z);
}
void norm (const MV& X, std::vector<magnitude_type>& normVec) const {
const int numCols = MVT::GetNumberVecs (X);
// std::vector<T>::size_type is unsigned; int is signed. Mixed
// unsigned/signed comparisons trigger compiler warnings.
if (normVec.size () < static_cast<size_t> (numCols)) {
normVec.resize (numCols); // Resize normvec if necessary.
}
MVT::MvNorm (X, normVec);
}
void
project (MV &X,
Teuchos::Array<mat_ptr> C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor timerMonitorOrtho(*timerOrtho_);
Teuchos::TimeMonitor timerMonitorProject(*timerProject_);
#endif // BELOS_TEUCHOS_TIME_MONITOR
allocateProjectionCoefficients (C, Q, X, true);
rawProject (X, Q, C);
if (reorthogonalize_) { // Unconditional reorthogonalization
Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,Scalar> > > C2;
allocateProjectionCoefficients (C2, Q, X, false);
for (int k = 0; k < Q.size(); ++k)
*C[k] += *C2[k];
}
}
int
normalize (MV &X, mat_ptr B) const
{
#ifdef BELOS_TEUCHOS_TIME_MONITOR
Teuchos::TimeMonitor timerMonitorOrtho(*timerOrtho_);
Teuchos::TimeMonitor timerMonitorProject(*timerNormalize_);
#endif // BELOS_TEUCHOS_TIME_MONITOR
if (useMgs_) {
return normalizeMgs (X, B);
} else {
return normalizeCgs (X, B);
}
}
protected:
virtual int
projectAndNormalizeImpl (MV &X,
Teuchos::Array<mat_ptr> C,
mat_ptr B,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q) const
{
// Don't need time monitors here: project() and normalize() have
// their own.
this->project (X, C, Q);
return this->normalize (X, B);
}
public:
magnitude_type
orthonormError(const MV &X) const
{
const Scalar ONE = STS::one();
const int ncols = MVT::GetNumberVecs(X);
mat_type XTX (ncols, ncols);
innerProd (X, X, XTX);
for (int k = 0; k < ncols; ++k) {
XTX(k,k) -= ONE;
}
return XTX.normFrobenius();
}
magnitude_type
orthogError(const MV &X1, const MV &X2) const
{
const int ncols_X1 = MVT::GetNumberVecs (X1);
const int ncols_X2 = MVT::GetNumberVecs (X2);
mat_type X1_T_X2 (ncols_X1, ncols_X2);
innerProd (X1, X2, X1_T_X2);
return X1_T_X2.normFrobenius();
}
void setLabel (const std::string& label) { label_ = label; }
const std::string& getLabel() const { return label_; }
private:
int
normalizeMgs (MV &X,
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,Scalar> > B) const
{
using Teuchos::Range1D;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::View;
const int numCols = MVT::GetNumberVecs (X);
if (numCols == 0) {
return 0;
}
if (B.is_null ()) {
B = rcp (new mat_type (numCols, numCols));
} else if (B->numRows () != numCols || B->numCols () != numCols) {
B->shape (numCols, numCols);
}
// Modified Gram-Schmidt orthogonalization
std::vector<magnitude_type> normVec (1);
for (int j = 0; j < numCols; ++j) {
RCP<MV> X_cur = MVT::CloneViewNonConst (X, Range1D(j, j));
MV& X_j = *X_cur;
for (int i = 0; i < j; ++i) {
RCP<const MV> X_prv = MVT::CloneView (X, Range1D(i, i));
const MV& X_i = *X_prv;
mat_type B_ij (View, *B, 1, 1, i, j);
innerProd (X_i, X_j, B_ij);
MVT::MvTimesMatAddMv (-STS::one(), X_i, B_ij, STS::one(), X_j);
if (reorthogonalize_) { // Unconditional reorthogonalization
// innerProd() overwrites B(i,j), so save the
// first-pass projection coefficient and update
// B(i,j) afterwards.
const Scalar B_ij_first = (*B)(i, j);
innerProd (X_i, X_j, B_ij);
MVT::MvTimesMatAddMv (-STS::one(), X_i, B_ij, STS::one(), X_j);
(*B)(i, j) += B_ij_first;
}
}
// Normalize column j of X
norm (X_j, normVec);
const magnitude_type theNorm = normVec[0];
(*B)(j, j) = theNorm;
if (normVec[0] != STM::zero()) {
MVT::MvScale (X_j, STS::one() / theNorm);
} else {
return j; // break out early
}
}
return numCols; // full rank, as far as we know
}
int
normalizeCgs (MV &X, mat_ptr B) const
{
using Teuchos::Range1D;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::View;
const int numCols = MVT::GetNumberVecs (X);
if (numCols == 0) {
return 0;
}
if (B.is_null ()) {
B = rcp (new mat_type (numCols, numCols));
} else if (B->numRows() != numCols || B->numCols() != numCols) {
B->shape (numCols, numCols);
}
mat_type& B_ref = *B;
// Classical Gram-Schmidt orthogonalization
std::vector<magnitude_type> normVec (1);
// Space for reorthogonalization
mat_type B2 (numCols, numCols);
// Do the first column first.
{
RCP<MV> X_cur = MVT::CloneViewNonConst (X, Range1D(0, 0));
// Normalize column 0 of X
norm (*X_cur, normVec);
const magnitude_type theNorm = normVec[0];
B_ref(0,0) = theNorm;
if (theNorm != STM::zero ()) {
const Scalar invNorm = STS::one () / theNorm;
MVT::MvScale (*X_cur, invNorm);
}
else {
return 0; // break out early
}
}
// Orthogonalize the remaining columns of X
for (int j = 1; j < numCols; ++j) {
RCP<MV> X_cur = MVT::CloneViewNonConst (X, Range1D(j, j));
RCP<const MV> X_prv = MVT::CloneView (X, Range1D(0, j-1));
mat_type B_prvcur (View, B_ref, j, 1, 0, j);
// Project X_cur against X_prv (first pass)
innerProd (*X_prv, *X_cur, B_prvcur);
MVT::MvTimesMatAddMv (-STS::one(), *X_prv, B_prvcur, STS::one(), *X_cur);
// Unconditional reorthogonalization:
// project X_cur against X_prv (second pass)
if (reorthogonalize_) {
mat_type B2_prvcur (View, B2, j, 1, 0, j);
innerProd (*X_prv, *X_cur, B2_prvcur);
MVT::MvTimesMatAddMv (-STS::one(), *X_prv, B2_prvcur, STS::one(), *X_cur);
B_prvcur += B2_prvcur;
}
// Normalize column j of X
norm (*X_cur, normVec);
const magnitude_type theNorm = normVec[0];
B_ref(j,j) = theNorm;
if (theNorm != STM::zero ()) {
const Scalar invNorm = STS::one () / theNorm;
MVT::MvScale (*X_cur, invNorm);
}
else {
return j; // break out early
}
}
return numCols; // full rank, as far as we know
}
void
allocateProjectionCoefficients (Teuchos::Array<mat_ptr>& C,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q,
const MV& X,
const bool attemptToRecycle = true) const
{
using Teuchos::rcp;
const int num_Q_blocks = Q.size();
const int ncols_X = MVT::GetNumberVecs (X);
C.resize (num_Q_blocks);
// # of block(s) that had to be (re)allocated (either allocated
// freshly, or resized).
int numAllocated = 0;
if (attemptToRecycle) {
for (int i = 0; i < num_Q_blocks; ++i) {
const int ncols_Qi = MVT::GetNumberVecs (*Q[i]);
// Create a new C[i] if necessary, otherwise resize if
// necessary, otherwise fill with zeros.
if (C[i].is_null ()) {
C[i] = rcp (new mat_type (ncols_Qi, ncols_X));
numAllocated++;
}
else {
mat_type& Ci = *C[i];
if (Ci.numRows() != ncols_Qi || Ci.numCols() != ncols_X) {
Ci.shape (ncols_Qi, ncols_X);
numAllocated++;
}
else {
Ci.putScalar (STS::zero());
}
}
}
}
else { // Just allocate; don't try to check if we can recycle
for (int i = 0; i < num_Q_blocks; ++i) {
const int ncols_Qi = MVT::GetNumberVecs (*Q[i]);
C[i] = rcp (new mat_type (ncols_Qi, ncols_X));
numAllocated++;
}
}
if (! outMan_.is_null()) {
using std::endl;
std::ostream& dbg = outMan_->stream(Debug);
dbg << "SimpleOrthoManager::allocateProjectionCoefficients: "
<< "Allocated " << numAllocated << " blocks out of "
<< num_Q_blocks << endl;
}
}
void
rawProject (MV& X,
Teuchos::ArrayView<Teuchos::RCP<const MV> > Q,
Teuchos::ArrayView<mat_ptr> C) const
{
// "Modified Gram-Schmidt" version of Block Gram-Schmidt.
const int num_Q_blocks = Q.size();
for (int i = 0; i < num_Q_blocks; ++i) {
mat_type& Ci = *C[i];
const MV& Qi = *Q[i];
innerProd (Qi, X, Ci);
MVT::MvTimesMatAddMv (-STS::one(), Qi, Ci, STS::one(), X);
}
}
};
} // namespace Belos
#endif // __Belos_SimpleOrthoManager_hpp
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