void dense_Vp_StPtMtV(
DVectorSlice *y
,value_type a
,const GenPermMatrixSlice &P
,BLAS_Cpp::Transp P_trans
,const M_t &M
,BLAS_Cpp::Transp M_trans
,const V_t &x
,value_type b
)
{
using BLAS_Cpp::no_trans;
using BLAS_Cpp::trans;
using BLAS_Cpp::trans_not;
using BLAS_Cpp::rows;
using BLAS_Cpp::cols;
using DenseLinAlgPack::dot;
using DenseLinAlgPack::DVector;
using DenseLinAlgPack::Vt_S;
using AbstractLinAlgPack::dot;
using AbstractLinAlgPack::Vp_StMtV;
using AbstractLinAlgPack::GenPermMatrixSlice;
typedef AbstractLinAlgPack::EtaVector eta;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
// Validate the sizes
//
// y += op(P)*op(M)*x
//
const DenseLinAlgPack::size_type
ny = y->size(),
nx = x.size(),
opM_rows = rows( M.rows(), M.cols(), M_trans ),
opM_cols = cols( M.rows(), M.cols(), M_trans );
if( ny != rows( P.rows(), P.cols(), P_trans )
|| nx != opM_cols
|| cols( P.rows(), P.cols(), P_trans ) != opM_rows )
throw std::length_error( "MatrixOp::Vp_StPtMtV(...) : Error, "
"sizes of arguments does not match up" );
//
// Compute y = b*y + a*op(P)*op(M)*x in a resonably efficient manner. This
// implementation will assume that M is stored as a dense matrix. Either
// t = op(M)*x is computed first (O(opM_rows*nx) flops) then y = b*y + a*op(P)*t
// (O(ny) + O(P_nz) flops) or each row of t' = e(j)' * op(M) (O(nx) flops)
// is computed one at a time and then y(i) = b*y(i) + a*t'*x (O(nx) flops)
// where op(P)(i,j) = 1.0. In the latter case, there are P_nz rows
// of op(M) that have to be generated so the total cost is O(P_nz*nx).
// Therefore, we will do the former if opM_rows < P_nz and the latter otherwise.
//
if( !P.nz() ) {
// y = b*y
if(b==0.0) *y = 0.0;
else if(b!=1.0) Vt_S(y,b);
}
else if( opM_rows > P.nz() || P.is_identity() ) {
// t = op(M)*x
Workspace<value_type> t_ws(wss,opM_rows);
DVectorSlice t(&t_ws[0],t_ws.size());
LinAlgOpPack::V_MtV( &t, M, M_trans, x );
// y = b*y + a*op(P)*t
Vp_StMtV( y, a, P, P_trans, t(), b );
}
else {
// y = b*y
if(b==0.0) *y = 0.0;
else if(b!=1.0) Vt_S(y,b);
// Compute t' = e(j)' * op(M) then y(i) += a*t'*x where op(P)(i,j) = 1.0
Workspace<value_type> t_ws(wss,opM_cols);
DVectorSlice t(&t_ws[0],t_ws.size());
if( P.is_identity() ) {
for( size_type k = 1; k <= P.nz(); ++k ) {
const size_type
i = k,
j = k;
// t = op(M') * e(j)
LinAlgOpPack::V_MtV( &t, M, trans_not(M_trans), eta(j,opM_rows)() );
// y(i) += a*t'*x
(*y)(i) += a * dot( t(), x );
}
}
else {
for( GenPermMatrixSlice::const_iterator itr = P.begin(); itr != P.end(); ++itr ) {
const DenseLinAlgPack::size_type
i = P_trans == no_trans ? itr->row_i() : itr->col_j(),
j = P_trans == no_trans ? itr->col_j() : itr->row_i();
// t = op(M') * e(j)
LinAlgOpPack::V_MtV( &t, M, trans_not(M_trans), eta(j,opM_rows)() );
// y(i) += a*t'*x
(*y)(i) += a * dot( t(), x );
}
}
}
}
bool ReducedHessianSecantUpdateLPBFGS_Strategy::perform_update(
DVectorSlice* s_bfgs, DVectorSlice* y_bfgs, bool first_update
,std::ostream& out, EJournalOutputLevel olevel, NLPAlgo *algo, NLPAlgoState *s
,MatrixOp *rHL_k
)
{
using std::setw;
using std::endl;
using std::right;
using Teuchos::dyn_cast;
namespace rcp = MemMngPack;
using Teuchos::RCP;
using LinAlgOpPack::V_MtV;
using DenseLinAlgPack::dot;
using AbstractLinAlgPack::norm_inf;
using AbstractLinAlgPack::transVtMtV;
typedef ConstrainedOptPack::MatrixHessianSuperBasic MHSB_t;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n*** (LPBFGS) Full limited memory BFGS to projected BFGS ...\n";
}
#ifdef _WINDOWS
MHSB_t &rHL_super = dynamic_cast<MHSB_t&>(*rHL_k);
#else
MHSB_t &rHL_super = dyn_cast<MHSB_t>(*rHL_k);
#endif
const size_type
n = algo->nlp().n(),
r = algo->nlp().r(),
n_pz = n-r;
bool do_projected_rHL_RR = false;
// See if we still have a limited memory BFGS update matrix
RCP<MatrixSymPosDefLBFGS> // We don't want this to be deleted until we are done with it
lbfgs_rHL_RR = Teuchos::rcp_const_cast<MatrixSymPosDefLBFGS>(
Teuchos::rcp_dynamic_cast<const MatrixSymPosDefLBFGS>(rHL_super.B_RR_ptr()) );
if( lbfgs_rHL_RR.get() && rHL_super.Q_R().is_identity() ) {
//
// We have a limited memory BFGS matrix and have not started projected BFGS updating
// yet so lets determine if it is time to consider switching
//
// Check that the current update is sufficiently p.d. before we do anything
const value_type
sTy = dot(*s_bfgs,*y_bfgs),
yTy = dot(*y_bfgs,*y_bfgs);
if( !ConstrainedOptPack::BFGS_sTy_suff_p_d(
*s_bfgs,*y_bfgs,&sTy
, int(olevel) >= int(PRINT_ALGORITHM_STEPS) ? &out : NULL )
&& !proj_bfgs_updater().bfgs_update().use_dampening()
)
{
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nWarning! use_damening == false so there is no way we can perform any"
" kind of BFGS update (projected or not) so we will skip it!\n";
}
quasi_newton_stats_(*s).set_k(0).set_updated_stats(
QuasiNewtonStats::INDEF_SKIPED );
return true;
}
// Consider if we can even look at the active set yet.
const bool consider_switch = lbfgs_rHL_RR->num_secant_updates() >= min_num_updates_proj_start();
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nnum_previous_updates = " << lbfgs_rHL_RR->num_secant_updates()
<< ( consider_switch ? " >= " : " < " )
<< "min_num_updates_proj_start = " << min_num_updates_proj_start()
<< ( consider_switch
? "\nConsidering if we should switch to projected BFGS updating of superbasics ...\n"
: "\nNot time to consider switching to projected BFGS updating of superbasics yet!" );
}
if( consider_switch ) {
//
// Our job here is to determine if it is time to switch to projected projected
// BFGS updating.
//
if( act_set_stats_(*s).updated_k(-1) ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nDetermining if projected BFGS updating of superbasics should begin ...\n";
}
// Determine if the active set has calmed down enough
const SpVector
&nu_km1 = s->nu().get_k(-1);
const SpVectorSlice
nu_indep = nu_km1(s->var_indep());
const bool
act_set_calmed_down
= PBFGSPack::act_set_calmed_down(
act_set_stats_(*s).get_k(-1)
,proj_bfgs_updater().act_set_frac_proj_start()
,olevel,out
),
max_num_updates_exceeded
= lbfgs_rHL_RR->m_bar() >= max_num_updates_proj_start();
do_projected_rHL_RR = act_set_calmed_down || max_num_updates_exceeded;
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
if( act_set_calmed_down ) {
out << "\nThe active set has calmed down enough so lets further consider switching to\n"
<< "projected BFGS updating of superbasic variables ...\n";
}
else if( max_num_updates_exceeded ) {
out << "\nThe active set has not calmed down enough but num_previous_updates = "
<< lbfgs_rHL_RR->m_bar() << " >= max_num_updates_proj_start = " << max_num_updates_proj_start()
<< "\nso we will further consider switching to projected BFGS updating of superbasic variables ...\n";
}
else {
out << "\nIt is not time to switch to projected BFGS so just keep performing full limited memory BFGS for now ...\n";
}
}
if( do_projected_rHL_RR ) {
//
// Determine the set of initially fixed and free independent variables.
//
typedef Workspace<size_type> i_x_t;
typedef Workspace<ConstrainedOptPack::EBounds> bnd_t;
i_x_t i_x_free(wss,n_pz);
i_x_t i_x_fixed(wss,n_pz);
bnd_t bnd_fixed(wss,n_pz);
i_x_t l_x_fixed_sorted(wss,n_pz);
size_type n_pz_X = 0, n_pz_R = 0;
// rHL = rHL_scale * I
value_type
rHL_scale = sTy > 0.0 ? yTy/sTy : 1.0;
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nScaling for diagonal intitial rHL = rHL_scale*I, rHL_scale = " << rHL_scale << std::endl;
}
value_type sRTBRRsR = 0.0, sRTyR = 0.0, sXTBXXsX = 0.0, sXTyX = 0.0;
// Get the elements in i_x_free[] for variables that are definitely free
// and initialize s_R'*B_RR*s_R and s_R'*y_R
PBFGSPack::init_i_x_free_sRTsR_sRTyR(
nu_indep, *s_bfgs, *y_bfgs
, &n_pz_R, &i_x_free[0], &sRTBRRsR, &sRTyR );
sRTBRRsR *= rHL_scale;
Workspace<value_type> rHL_XX_diag_ws(wss,nu_indep.nz());
DVectorSlice rHL_XX_diag(&rHL_XX_diag_ws[0],rHL_XX_diag_ws.size());
rHL_XX_diag = rHL_scale;
// Sort fixed variables according to |s_X(i)^2*B_XX(i,i)|/|sRTBRRsR| + |s_X(i)*y_X(i)|/|sRTyR|
// and initialize s_X'*B_XX*s_X and s_X*y_X
PBFGSPack::sort_fixed_max_cond_viol(
nu_indep,*s_bfgs,*y_bfgs,rHL_XX_diag,sRTBRRsR,sRTyR
,&sXTBXXsX,&sXTyX,&l_x_fixed_sorted[0]);
// Pick initial set of i_x_free[] and i_x_fixed[] (sorted!)
PBFGSPack::choose_fixed_free(
proj_bfgs_updater().project_error_tol()
,proj_bfgs_updater().super_basic_mult_drop_tol(),nu_indep
,*s_bfgs,*y_bfgs,rHL_XX_diag,&l_x_fixed_sorted[0]
,olevel,out,&sRTBRRsR,&sRTyR,&sXTBXXsX,&sXTyX
,&n_pz_X,&n_pz_R,&i_x_free[0],&i_x_fixed[0],&bnd_fixed[0] );
if( n_pz_R < n_pz ) {
//
// We are ready to transition to projected BFGS updating!
//
// Determine if we are be using dense or limited memory BFGS?
const bool
low_num_super_basics = n_pz_R <= num_superbasics_switch_dense();
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_BASIC_ALGORITHM_INFO) ) {
out << "\nSwitching to projected BFGS updating ..."
<< "\nn_pz_R = " << n_pz_R << ( low_num_super_basics ? " <= " : " > " )
<< " num_superbasics_switch_dense = " << num_superbasics_switch_dense()
<< ( low_num_super_basics
? "\nThere are not too many superbasic variables so use dense projected BFGS ...\n"
: "\nThere are too many superbasic variables so use limited memory projected BFGS ...\n"
);
}
// Create new matrix to use for rHL_RR initialized to rHL_RR = rHL_scale*I
RCP<MatrixSymSecant>
rHL_RR = NULL;
if( low_num_super_basics ) {
rHL_RR = new MatrixSymPosDefCholFactor(
NULL // Let it allocate its own memory
,NULL // ...
,n_pz // maximum size
,lbfgs_rHL_RR->maintain_original()
,lbfgs_rHL_RR->maintain_inverse()
);
}
else {
rHL_RR = new MatrixSymPosDefLBFGS(
n_pz, lbfgs_rHL_RR->m()
,lbfgs_rHL_RR->maintain_original()
,lbfgs_rHL_RR->maintain_inverse()
,lbfgs_rHL_RR->auto_rescaling()
);
}
rHL_RR->init_identity( n_pz_R, rHL_scale );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ITERATION_QUANTITIES) ) {
out << "\nrHL_RR after intialized to rHL_RR = rHL_scale*I but before performing current BFGS update:\nrHL_RR =\n"
<< dynamic_cast<MatrixOp&>(*rHL_RR); // I know this is okay!
}
// Initialize rHL_XX = rHL_scale*I
#ifdef _WINDOWS
MatrixSymInitDiag
&rHL_XX = dynamic_cast<MatrixSymInitDiag&>(
const_cast<MatrixSymOp&>(*rHL_super.B_XX_ptr()));
#else
MatrixSymInitDiag
&rHL_XX = dyn_cast<MatrixSymInitDiag>(
const_cast<MatrixSymOp&>(*rHL_super.B_XX_ptr()));
#endif
rHL_XX.init_identity( n_pz_X, rHL_scale );
// Reinitialize rHL
rHL_super.initialize(
n_pz, n_pz_R, &i_x_free[0], &i_x_fixed[0], &bnd_fixed[0]
,Teuchos::rcp_const_cast<const MatrixSymWithOpFactorized>(
Teuchos::rcp_dynamic_cast<MatrixSymWithOpFactorized>(rHL_RR))
,NULL,BLAS_Cpp::no_trans,rHL_super.B_XX_ptr()
);
//
// Perform the current BFGS update first
//
MatrixSymOp
&rHL_RR_op = dynamic_cast<MatrixSymOp&>(*rHL_RR);
const GenPermMatrixSlice
&Q_R = rHL_super.Q_R(),
&Q_X = rHL_super.Q_X();
// Get projected BFGS update vectors y_bfgs_R, s_bfgs_R
Workspace<value_type>
y_bfgs_R_ws(wss,Q_R.cols()),
s_bfgs_R_ws(wss,Q_R.cols()),
y_bfgs_X_ws(wss,Q_X.cols()),
s_bfgs_X_ws(wss,Q_X.cols());
DVectorSlice y_bfgs_R(&y_bfgs_R_ws[0],y_bfgs_R_ws.size());
DVectorSlice s_bfgs_R(&s_bfgs_R_ws[0],s_bfgs_R_ws.size());
DVectorSlice y_bfgs_X(&y_bfgs_X_ws[0],y_bfgs_X_ws.size());
DVectorSlice s_bfgs_X(&s_bfgs_X_ws[0],s_bfgs_X_ws.size());
V_MtV( &y_bfgs_R, Q_R, BLAS_Cpp::trans, *y_bfgs ); // y_bfgs_R = Q_R'*y_bfgs
V_MtV( &s_bfgs_R, Q_R, BLAS_Cpp::trans, *s_bfgs ); // s_bfgs_R = Q_R'*s_bfgs
V_MtV( &y_bfgs_X, Q_X, BLAS_Cpp::trans, *y_bfgs ); // y_bfgs_X = Q_X'*y_bfgs
V_MtV( &s_bfgs_X, Q_X, BLAS_Cpp::trans, *s_bfgs ); // s_bfgs_X = Q_X'*s_bfgs
// Update rHL_RR
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nPerform current BFGS update on " << n_pz_R << " x " << n_pz_R << " projected "
<< "reduced Hessian for the superbasic variables where B = rHL_RR...\n";
}
QuasiNewtonStats quasi_newton_stats;
proj_bfgs_updater().bfgs_update().perform_update(
&s_bfgs_R(),&y_bfgs_R(),false,out,olevel,algo->algo_cntr().check_results()
,&rHL_RR_op, &quasi_newton_stats );
// Perform previous updates if possible
if( lbfgs_rHL_RR->m_bar() ) {
const size_type num_add_updates = std::_MIN(num_add_recent_updates(),lbfgs_rHL_RR->m_bar());
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nAdd the min(num_previous_updates,num_add_recent_updates) = min(" << lbfgs_rHL_RR->m_bar()
<< "," << num_add_recent_updates() << ") = " << num_add_updates << " most recent BFGS updates if possible ...\n";
}
// Now add previous update vectors
const value_type
project_error_tol = proj_bfgs_updater().project_error_tol();
const DMatrixSlice
S = lbfgs_rHL_RR->S(),
Y = lbfgs_rHL_RR->Y();
size_type k = lbfgs_rHL_RR->k_bar(); // Location in S and Y of most recent update vectors
for( size_type l = 1; l <= num_add_updates; ++l, --k ) {
if(k == 0) k = lbfgs_rHL_RR->m_bar(); // see MatrixSymPosDefLBFGS
// Check to see if this update satisfies the required conditions.
// Start with the condition on s'*y since this are cheap to check.
V_MtV( &s_bfgs_X(), Q_X, BLAS_Cpp::trans, S.col(k) ); // s_bfgs_X = Q_X'*s_bfgs
V_MtV( &y_bfgs_X(), Q_X, BLAS_Cpp::trans, Y.col(k) ); // y_bfgs_X = Q_X'*y_bfgs
sRTyR = dot( s_bfgs_R, y_bfgs_R );
sXTyX = dot( s_bfgs_X, y_bfgs_X );
bool
sXTyX_cond = ::fabs(sXTyX/sRTyR) <= project_error_tol,
do_update = sXTyX_cond,
sXTBXXsX_cond = false;
if( sXTyX_cond ) {
// Check the second more expensive condition
V_MtV( &s_bfgs_R(), Q_R, BLAS_Cpp::trans, S.col(k) ); // s_bfgs_R = Q_R'*s_bfgs
V_MtV( &y_bfgs_R(), Q_R, BLAS_Cpp::trans, Y.col(k) ); // y_bfgs_R = Q_R'*y_bfgs
sRTBRRsR = transVtMtV( s_bfgs_R, rHL_RR_op, BLAS_Cpp::no_trans, s_bfgs_R );
sXTBXXsX = rHL_scale * dot( s_bfgs_X, s_bfgs_X );
sXTBXXsX_cond = sXTBXXsX/sRTBRRsR <= project_error_tol;
do_update = sXTBXXsX_cond && sXTyX_cond;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n---------------------------------------------------------------------"
<< "\nprevious update " << l
<< "\n\nChecking projection error:\n"
<< "\n|s_X'*y_X|/|s_R'*y_R| = |" << sXTyX << "|/|" << sRTyR
<< "| = " << ::fabs(sXTyX/sRTyR)
<< ( sXTyX_cond ? " <= " : " > " ) << " project_error_tol = "
<< project_error_tol;
if( sXTyX_cond ) {
out << "\n(s_X'*rHL_XX*s_X/s_R'*rHL_RR*s_R) = (" << sXTBXXsX
<< ") = " << (sXTBXXsX/sRTBRRsR)
<< ( sXTBXXsX_cond ? " <= " : " > " ) << " project_error_tol = "
<< project_error_tol;
}
out << ( do_update
? "\n\nAttemping to add this previous update where B = rHL_RR ...\n"
: "\n\nCan not add this previous update ...\n" );
}
if( do_update ) {
// ( rHL_RR, s_bfgs_R, y_bfgs_R ) -> rHL_RR (this should not throw an exception!)
try {
proj_bfgs_updater().bfgs_update().perform_update(
&s_bfgs_R(),&y_bfgs_R(),false,out,olevel,algo->algo_cntr().check_results()
,&rHL_RR_op, &quasi_newton_stats );
}
catch( const MatrixSymSecant::UpdateSkippedException& excpt ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nOops! The " << l << "th most recent BFGS update was rejected?:\n"
<< excpt.what() << std::endl;
}
}
}
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n---------------------------------------------------------------------\n";
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ITERATION_QUANTITIES) ) {
out << "\nrHL_RR after adding previous BFGS updates:\nrHL_BRR =\n"
<< dynamic_cast<MatrixOp&>(*rHL_RR);
}
}
else {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nThere were no previous update vectors to add!\n";
}
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ITERATION_QUANTITIES) ) {
out << "\nFull rHL after complete reinitialization:\nrHL =\n" << *rHL_k;
}
quasi_newton_stats_(*s).set_k(0).set_updated_stats(
QuasiNewtonStats::REINITIALIZED );
return true;
}
else {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nn_pz_R == n_pz = " << n_pz_R << ", No variables would be removed from "
<< "the superbasis so just keep on performing limited memory BFGS for now ...\n";
}
do_projected_rHL_RR = false;
}
}
}
}
// If we have not switched to PBFGS then just update the full limited memory BFGS matrix
if(!do_projected_rHL_RR) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nPerform current BFGS update on " << n_pz << " x " << n_pz << " full "
<< "limited memory reduced Hessian B = rHL ...\n";
}
proj_bfgs_updater().bfgs_update().perform_update(
s_bfgs,y_bfgs,first_update,out,olevel,algo->algo_cntr().check_results()
,lbfgs_rHL_RR.get()
,&quasi_newton_stats_(*s).set_k(0)
);
return true;
}
}
else {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nWe have already switched to projected BFGS updating ...\n";
}
}
//
// If we get here then we must have switched to
// projected updating so lets just pass it on!
//
return proj_bfgs_updater().perform_update(
s_bfgs,y_bfgs,first_update,out,olevel,algo,s,rHL_k);
}
