bool MoochoPack::CrossTermExactStd_Step::do_step(Algorithm& _algo
, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss)
{
using LinAlgOpPack::V_MtV;
using DenseLinAlgPack::norm_inf;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( _algo, step_poss, type, assoc_step_poss, out );
}
// tmp = HL * Ypy
DVector tmp;
V_MtV( &tmp, s.HL().get_k(0), BLAS_Cpp::no_trans, s.Ypy().get_k(0)() );
// w = Z' * tmp
V_MtV( &s.w().set_k(0).v(), s.Z().get_k(0), BLAS_Cpp::trans, tmp() );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||w||inf = " << s.w().get_k(0).norm_inf() << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nw_k =\n" << s.w().get_k(0)();
}
return true;
}
bool CheckDescentQuasiNormalStep_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using BLAS_Cpp::no_trans;
using AbstractLinAlgPack::dot;
using LinAlgOpPack::V_MtV;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLP &nlp = algo.nlp();
const Range1D equ_decomp = s.equ_decomp();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
const size_type
nb = nlp.num_bounded_x();
// Get iteration quantities
IterQuantityAccess<VectorMutable>
&c_iq = s.c(),
&Ypy_iq = s.Ypy();
const Vector::vec_ptr_t
cd_k = c_iq.get_k(0).sub_view(equ_decomp);
const Vector
&Ypy_k = Ypy_iq.get_k(0);
value_type descent_c = -1.0;
if( s.get_iter_quant_id( Gc_name ) != AlgorithmState::DOES_NOT_EXIST ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nGc_k exists; compute descent_c = c_k(equ_decomp)'*Gc_k(:,equ_decomp)'*Ypy_k ...\n";
}
const MatrixOp::mat_ptr_t
Gcd_k = s.Gc().get_k(0).sub_view(Range1D(),equ_decomp);
VectorSpace::vec_mut_ptr_t
t = cd_k->space().create_member();
V_MtV( t.get(), *Gcd_k, BLAS_Cpp::trans, Ypy_k );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nGc_k(:,equ_decomp)'*Ypy_k =\n" << *t;
}
descent_c = dot( *cd_k, *t );
}
else {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nGc_k does not exist; compute descent_c = c_k(equ_decomp)'*FDGc_k(:,equ_decomp)'*Ypy_k "
<< "using finite differences ...\n";
}
VectorSpace::vec_mut_ptr_t
t = nlp.space_c()->create_member();
calc_fd_prod().calc_deriv_product(
s.x().get_k(0),nb?&nlp.xl():NULL,nb?&nlp.xu():NULL
,Ypy_k,NULL,&c_iq.get_k(0),true,&nlp
,NULL,t.get()
,static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ? &out : NULL
);
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nFDGc_k(:,equ_decomp)'*Ypy_k =\n" << *t->sub_view(equ_decomp);
}
descent_c = dot( *cd_k, *t->sub_view(equ_decomp) );
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\ndescent_c = " << descent_c << std::endl;
}
if( descent_c > 0.0 ) { // ToDo: add some allowance for > 0.0 for finite difference errors!
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nError, descent_c > 0.0; this is not a descent direction\n"
<< "Throw TestFailed and terminate the algorithm ...\n";
}
TEST_FOR_EXCEPTION(
true, TestFailed
,"CheckDescentQuasiNormalStep_Step::do_step(...) : Error, descent for the decomposed constraints "
"with respect to the quasi-normal step c_k(equ_decomp)'*FDGc_k(:,equ_decomp)'*Ypy_k = "
<< descent_c << " > 0.0; This is not a descent direction!\n" );
}
return true;
}
bool TangentialStepIP_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using BLAS_Cpp::no_trans;
using Teuchos::dyn_cast;
using AbstractLinAlgPack::assert_print_nan_inf;
using LinAlgOpPack::Vt_S;
using LinAlgOpPack::Vp_StV;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::V_InvMtV;
using LinAlgOpPack::M_StM;
using LinAlgOpPack::Mp_StM;
using LinAlgOpPack::assign;
NLPAlgo &algo = rsqp_algo(_algo);
IpState &s = dyn_cast<IpState>(_algo.state());
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// Compute qp_grad which is an approximation to rGf + Z'*(mu*(invXu*e-invXl*e) + no_cross_term
// minimize round off error by calc'ing Z'*(Gf + mu*(invXu*e-invXl*e))
// qp_grad_k = Z'*(Gf + mu*(invXu*e-invXl*e))
const MatrixSymDiagStd &invXu = s.invXu().get_k(0);
const MatrixSymDiagStd &invXl = s.invXl().get_k(0);
const value_type &mu = s.barrier_parameter().get_k(0);
const MatrixOp &Z_k = s.Z().get_k(0);
Teuchos::RCP<VectorMutable> rhs = s.Gf().get_k(0).clone();
Vp_StV( rhs.get(), mu, invXu.diag() );
Vp_StV( rhs.get(), -1.0*mu, invXl.diag() );
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
{
out << "\n||Gf_k + mu_k*(invXu_k-invXl_k)||inf = " << rhs->norm_inf() << std::endl;
}
if( (int)olevel >= (int)PRINT_VECTORS)
{
out << "\nGf_k + mu_k*(invXu_k-invXl_k) =\n" << *rhs;
}
VectorMutable &qp_grad_k = s.qp_grad().set_k(0);
V_MtV(&qp_grad_k, Z_k, BLAS_Cpp::trans, *rhs);
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
{
out << "\n||Z_k'*(Gf_k + mu_k*(invXu_k-invXl_k))||inf = " << qp_grad_k.norm_inf() << std::endl;
}
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nZ_k'*(Gf_k + mu_k*(invXu_k-invXl_k)) =\n" << qp_grad_k;
}
// error check for cross term
value_type &zeta = s.zeta().set_k(0);
const Vector &w_sigma = s.w_sigma().get_k(0);
// need code to calculate damping parameter
zeta = 1.0;
Vp_StV(&qp_grad_k, zeta, w_sigma);
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
{
out << "\n||qp_grad_k||inf = " << qp_grad_k.norm_inf() << std::endl;
}
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nqp_grad_k =\n" << qp_grad_k;
}
// build the "Hessian" term B = rHL + rHB
// should this be MatrixSymOpNonsing
const MatrixSymOp &rHL_k = s.rHL().get_k(0);
const MatrixSymOp &rHB_k = s.rHB().get_k(0);
MatrixSymOpNonsing &B_k = dyn_cast<MatrixSymOpNonsing>(s.B().set_k(0));
if (B_k.cols() != Z_k.cols())
{
// Initialize space in rHB
dyn_cast<MatrixSymInitDiag>(B_k).init_identity(Z_k.space_rows(), 0.0);
}
// M_StM(&B_k, 1.0, rHL_k, no_trans);
assign(&B_k, rHL_k, BLAS_Cpp::no_trans);
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nB_k = rHL_k =\n" << B_k;
}
Mp_StM(&B_k, 1.0, rHB_k, BLAS_Cpp::no_trans);
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nB_k = rHL_k + rHB_k =\n" << B_k;
}
// Solve the system pz = - inv(rHL) * qp_grad
VectorMutable &pz_k = s.pz().set_k(0);
V_InvMtV( &pz_k, B_k, no_trans, qp_grad_k );
Vt_S( &pz_k, -1.0 );
// Zpz = Z * pz
V_MtV( &s.Zpz().set_k(0), s.Z().get_k(0), no_trans, pz_k );
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
{
out << "\n||pz||inf = " << s.pz().get_k(0).norm_inf()
<< "\nsum(Zpz) = " << AbstractLinAlgPack::sum(s.Zpz().get_k(0)) << std::endl;
}
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\npz_k = \n" << s.pz().get_k(0);
out << "\nnu_k = \n" << s.nu().get_k(0);
out << "\nZpz_k = \n" << s.Zpz().get_k(0);
out << std::endl;
}
if(algo.algo_cntr().check_results())
{
assert_print_nan_inf(s.pz().get_k(0), "pz_k",true,&out);
assert_print_nan_inf(s.Zpz().get_k(0), "Zpz_k",true,&out);
}
return true;
}
bool TangentialStepWithInequStd_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using Teuchos::RCP;
using Teuchos::dyn_cast;
using ::fabs;
using LinAlgOpPack::Vt_S;
using LinAlgOpPack::V_VpV;
using LinAlgOpPack::V_VmV;
using LinAlgOpPack::Vp_StV;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_MtV;
// using ConstrainedOptPack::min_abs;
using AbstractLinAlgPack::max_near_feas_step;
typedef VectorMutable::vec_mut_ptr_t vec_mut_ptr_t;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
EJournalOutputLevel ns_olevel = algo.algo_cntr().null_space_journal_output_level();
std::ostream &out = algo.track().journal_out();
//const bool check_results = algo.algo_cntr().check_results();
// print step header.
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// problem dimensions
const size_type
//n = algo.nlp().n(),
m = algo.nlp().m(),
r = s.equ_decomp().size();
// Get the iteration quantity container objects
IterQuantityAccess<value_type>
&alpha_iq = s.alpha(),
&zeta_iq = s.zeta(),
&eta_iq = s.eta();
IterQuantityAccess<VectorMutable>
&dl_iq = dl_iq_(s),
&du_iq = du_iq_(s),
&nu_iq = s.nu(),
*c_iq = m > 0 ? &s.c() : NULL,
*lambda_iq = m > 0 ? &s.lambda() : NULL,
&rGf_iq = s.rGf(),
&w_iq = s.w(),
&qp_grad_iq = s.qp_grad(),
&py_iq = s.py(),
&pz_iq = s.pz(),
&Ypy_iq = s.Ypy(),
&Zpz_iq = s.Zpz();
IterQuantityAccess<MatrixOp>
&Z_iq = s.Z(),
//*Uz_iq = (m > r) ? &s.Uz() : NULL,
*Uy_iq = (m > r) ? &s.Uy() : NULL;
IterQuantityAccess<MatrixSymOp>
&rHL_iq = s.rHL();
IterQuantityAccess<ActSetStats>
&act_set_stats_iq = act_set_stats_(s);
// Accessed/modified/updated (just some)
VectorMutable *Ypy_k = (m ? &Ypy_iq.get_k(0) : NULL);
const MatrixOp &Z_k = Z_iq.get_k(0);
VectorMutable &pz_k = pz_iq.set_k(0);
VectorMutable &Zpz_k = Zpz_iq.set_k(0);
// Comupte qp_grad which is an approximation to rGf + Z'*HL*Y*py
// qp_grad = rGf
VectorMutable
&qp_grad_k = ( qp_grad_iq.set_k(0) = rGf_iq.get_k(0) );
// qp_grad += zeta * w
if( w_iq.updated_k(0) ) {
if(zeta_iq.updated_k(0))
Vp_StV( &qp_grad_k, zeta_iq.get_k(0), w_iq.get_k(0) );
else
Vp_V( &qp_grad_k, w_iq.get_k(0) );
}
//
// Set the bounds for:
//
// dl <= Z*pz + Y*py <= du -> dl - Ypy <= Z*pz <= du - Ypz
vec_mut_ptr_t
bl = s.space_x().create_member(),
bu = s.space_x().create_member();
if(m) {
// bl = dl_k - Ypy_k
V_VmV( bl.get(), dl_iq.get_k(0), *Ypy_k );
// bu = du_k - Ypy_k
V_VmV( bu.get(), du_iq.get_k(0), *Ypy_k );
}
else {
*bl = dl_iq.get_k(0);
*bu = du_iq.get_k(0);
}
// Print out the QP bounds for the constraints
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nqp_grad_k = \n" << qp_grad_k;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nbl = \n" << *bl;
out << "\nbu = \n" << *bu;
}
//
// Determine if we should perform a warm start or not.
//
bool do_warm_start = false;
if( act_set_stats_iq.updated_k(-1) ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nDetermining if the QP should use a warm start ...\n";
}
// We need to see if we should preform a warm start for the next iteration
ActSetStats &stats = act_set_stats_iq.get_k(-1);
const size_type
num_active = stats.num_active(),
num_adds = stats.num_adds(),
num_drops = stats.num_drops();
const value_type
frac_same
= ( num_adds == ActSetStats::NOT_KNOWN || num_active == 0
? 0.0
: my_max(((double)(num_active)-num_adds-num_drops) / num_active, 0.0 ) );
do_warm_start = ( num_active > 0 && frac_same >= warm_start_frac() );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nnum_active = " << num_active;
if( num_active ) {
out << "\nmax(num_active-num_adds-num_drops,0)/(num_active) = "
<< "max("<<num_active<<"-"<<num_adds<<"-"<<num_drops<<",0)/("<<num_active<<") = "
<< frac_same;
if( do_warm_start )
out << " >= ";
else
out << " < ";
out << "warm_start_frac = " << warm_start_frac();
}
if( do_warm_start )
out << "\nUse a warm start this time!\n";
else
out << "\nDon't use a warm start this time!\n";
}
}
// Use active set from last iteration as an estimate for current active set
// if we are to use a warm start.
//
// ToDo: If the selection of dependent and independent variables changes
// then you will have to adjust this or not perform a warm start at all!
if( do_warm_start ) {
nu_iq.set_k(0,-1);
}
else {
nu_iq.set_k(0) = 0.0; // No guess of the active set
}
VectorMutable &nu_k = nu_iq.get_k(0);
//
// Setup the reduced QP subproblem
//
// The call to the QP is setup for the more flexible call to the QPSolverRelaxed
// interface to deal with the three independent variabilities: using simple
// bounds for pz or not, general inequalities included or not, and extra equality
// constraints included or not.
// If this method of calling the QP solver were not used then 4 separate
// calls to solve_qp(...) would have to be included to handle the four possible
// QP formulations.
//
// The numeric arguments for the QP solver (in the nomenclatrue of QPSolverRelaxed)
const value_type qp_bnd_inf = NLP::infinite_bound();
const Vector &qp_g = qp_grad_k;
const MatrixSymOp &qp_G = rHL_iq.get_k(0);
const value_type qp_etaL = 0.0;
vec_mut_ptr_t qp_dL = Teuchos::null;
vec_mut_ptr_t qp_dU = Teuchos::null;
Teuchos::RCP<const MatrixOp>
qp_E = Teuchos::null;
BLAS_Cpp::Transp qp_trans_E = BLAS_Cpp::no_trans;
vec_mut_ptr_t qp_b = Teuchos::null;
vec_mut_ptr_t qp_eL = Teuchos::null;
vec_mut_ptr_t qp_eU = Teuchos::null;
Teuchos::RCP<const MatrixOp>
qp_F = Teuchos::null;
BLAS_Cpp::Transp qp_trans_F = BLAS_Cpp::no_trans;
vec_mut_ptr_t qp_f = Teuchos::null;
value_type qp_eta = 0.0;
VectorMutable &qp_d = pz_k; // pz_k will be updated directly!
vec_mut_ptr_t qp_nu = Teuchos::null;
vec_mut_ptr_t qp_mu = Teuchos::null;
vec_mut_ptr_t qp_Ed = Teuchos::null;
vec_mut_ptr_t qp_lambda = Teuchos::null;
//
// Determine if we can use simple bounds on pz.
//
// If we have a variable-reduction null-space matrix
// (with any choice for Y) then:
//
// d = Z*pz + (1-eta) * Y*py
//
// [ d(var_dep) ] = [ D ] * pz + (1-eta) * [ Ypy(var_dep) ]
// [ d(var_indep) ] [ I ] [ Ypy(var_indep) ]
//
// For a cooridinate decomposition (Y = [ I ; 0 ]) then Ypy(var_indep) ==
// 0.0 and in this case the bounds on d(var_indep) become simple bounds on
// pz even with the relaxation. Also, if dl(var_dep) and du(var_dep) are
// unbounded, then we can also use simple bounds since we don't need the
// relaxation and we can set eta=0. In this case we just have to subtract
// from the upper and lower bounds on pz!
//
// Otherwise, we can not use simple variable bounds and implement the
// relaxation properly.
//
const MatrixIdentConcat
*Zvr = dynamic_cast<const MatrixIdentConcat*>( &Z_k );
const Range1D
var_dep = Zvr ? Zvr->D_rng() : Range1D::Invalid,
var_indep = Zvr ? Zvr->I_rng() : Range1D();
RCP<Vector> Ypy_indep;
const value_type
Ypy_indep_norm_inf
= ( m ? (Ypy_indep=Ypy_k->sub_view(var_indep))->norm_inf() : 0.0);
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
out
<< "\nDetermine if we can use simple bounds on pz ...\n"
<< " m = " << m << std::endl
<< " dynamic_cast<const MatrixIdentConcat*>(&Z_k) = " << Zvr << std::endl
<< " ||Ypy_k(var_indep)||inf = " << Ypy_indep_norm_inf << std::endl;
const bool
bounded_var_dep
= (
m > 0
&&
num_bounded( *bl->sub_view(var_dep), *bu->sub_view(var_dep), qp_bnd_inf )
);
const bool
use_simple_pz_bounds
= (
m == 0
||
( Zvr != NULL && ( Ypy_indep_norm_inf == 0.0 || bounded_var_dep == 0 ) )
);
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS )
out
<< (use_simple_pz_bounds
? "\nUsing simple bounds on pz ...\n"
: "\nUsing bounds on full Z*pz ...\n")
<< (bounded_var_dep
? "\nThere are finite bounds on dependent variables. Adding extra inequality constrints for D*pz ...\n"
: "\nThere are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...\n" ) ;
if( use_simple_pz_bounds ) {
// Set simple bound constraints on pz
qp_dL = bl->sub_view(var_indep);
qp_dU = bu->sub_view(var_indep);
qp_nu = nu_k.sub_view(var_indep); // nu_k(var_indep) will be updated directly!
if( m && bounded_var_dep ) {
// Set general inequality constraints for D*pz
qp_E = Teuchos::rcp(&Zvr->D(),false);
qp_b = Ypy_k->sub_view(var_dep);
qp_eL = bl->sub_view(var_dep);
qp_eU = bu->sub_view(var_dep);
qp_mu = nu_k.sub_view(var_dep); // nu_k(var_dep) will be updated directly!
qp_Ed = Zpz_k.sub_view(var_dep); // Zpz_k(var_dep) will be updated directly!
}
else {
// Leave these as NULL since there is no extra general inequality constraints
}
}
else if( !use_simple_pz_bounds ) { // ToDo: Leave out parts for unbounded dependent variables!
// There are no simple bounds! (leave qp_dL, qp_dU and qp_nu as null)
// Set general inequality constraints for Z*pz
qp_E = Teuchos::rcp(&Z_k,false);
qp_b = Teuchos::rcp(Ypy_k,false);
qp_eL = bl;
qp_eU = bu;
qp_mu = Teuchos::rcp(&nu_k,false);
qp_Ed = Teuchos::rcp(&Zpz_k,false); // Zpz_k will be updated directly!
}
else {
TEST_FOR_EXCEPT(true);
}
// Set the general equality constriants (if they exist)
Range1D equ_undecomp = s.equ_undecomp();
if( m > r && m > 0 ) {
// qp_f = Uy_k * py_k + c_k(equ_undecomp)
qp_f = s.space_c().sub_space(equ_undecomp)->create_member();
V_MtV( qp_f.get(), Uy_iq->get_k(0), BLAS_Cpp::no_trans, py_iq.get_k(0) );
Vp_V( qp_f.get(), *c_iq->get_k(0).sub_view(equ_undecomp) );
// Must resize for the undecomposed constriants if it has not already been
qp_F = Teuchos::rcp(&Uy_iq->get_k(0),false);
qp_lambda = lambda_iq->set_k(0).sub_view(equ_undecomp); // lambda_k(equ_undecomp), will be updated directly!
}
// Setup the rest of the arguments
QPSolverRelaxed::EOutputLevel
qp_olevel;
switch( olevel ) {
case PRINT_NOTHING:
qp_olevel = QPSolverRelaxed::PRINT_NONE;
break;
case PRINT_BASIC_ALGORITHM_INFO:
qp_olevel = QPSolverRelaxed::PRINT_NONE;
break;
case PRINT_ALGORITHM_STEPS:
qp_olevel = QPSolverRelaxed::PRINT_BASIC_INFO;
break;
case PRINT_ACTIVE_SET:
qp_olevel = QPSolverRelaxed::PRINT_ITER_SUMMARY;
break;
case PRINT_VECTORS:
qp_olevel = QPSolverRelaxed::PRINT_ITER_VECTORS;
break;
case PRINT_ITERATION_QUANTITIES:
qp_olevel = QPSolverRelaxed::PRINT_EVERY_THING;
break;
default:
TEST_FOR_EXCEPT(true);
}
// ToDo: Set print options so that only vectors matrices etc
// are only printed in the null space
//
// Solve the QP
//
qp_solver().infinite_bound(qp_bnd_inf);
const QPSolverStats::ESolutionType
solution_type =
qp_solver().solve_qp(
int(olevel) == int(PRINT_NOTHING) ? NULL : &out
,qp_olevel
,( algo.algo_cntr().check_results()
? QPSolverRelaxed::RUN_TESTS : QPSolverRelaxed::NO_TESTS )
,qp_g, qp_G, qp_etaL, qp_dL.get(), qp_dU.get()
,qp_E.get(), qp_trans_E, qp_E.get() ? qp_b.get() : NULL
,qp_E.get() ? qp_eL.get() : NULL, qp_E.get() ? qp_eU.get() : NULL
,qp_F.get(), qp_trans_F, qp_F.get() ? qp_f.get() : NULL
,NULL // obj_d
,&qp_eta, &qp_d
,qp_nu.get()
,qp_mu.get(), qp_E.get() ? qp_Ed.get() : NULL
,qp_F.get() ? qp_lambda.get() : NULL
,NULL // qp_Fd
);
//
// Check the optimality conditions for the QP
//
std::ostringstream omsg;
bool throw_qp_failure = false;
if( qp_testing() == QP_TEST
|| ( qp_testing() == QP_TEST_DEFAULT && algo.algo_cntr().check_results() ) )
{
if( int(olevel) >= int(PRINT_ALGORITHM_STEPS) ) {
out << "\nChecking the optimality conditions of the reduced QP subproblem ...\n";
}
if(!qp_tester().check_optimality_conditions(
solution_type,qp_solver().infinite_bound()
,int(olevel) == int(PRINT_NOTHING) ? NULL : &out
,int(olevel) >= int(PRINT_VECTORS) ? true : false
,int(olevel) >= int(PRINT_ITERATION_QUANTITIES) ? true : false
,qp_g, qp_G, qp_etaL, qp_dL.get(), qp_dU.get()
,qp_E.get(), qp_trans_E, qp_E.get() ? qp_b.get() : NULL
,qp_E.get() ? qp_eL.get() : NULL, qp_E.get() ? qp_eU.get() : NULL
,qp_F.get(), qp_trans_F, qp_F.get() ? qp_f.get() : NULL
,NULL // obj_d
,&qp_eta, &qp_d
,qp_nu.get()
,qp_mu.get(), qp_E.get() ? qp_Ed.get() : NULL
,qp_F.get() ? qp_lambda.get() : NULL
,NULL // qp_Fd
))
{
omsg << "\n*** Alert! at least one of the QP optimality conditions did not check out.\n";
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << omsg.str();
}
throw_qp_failure = true;
}
}
//
// Set the solution
//
if( !use_simple_pz_bounds ) {
// Everything is already updated!
}
else if( use_simple_pz_bounds ) {
// Just have to set Zpz_k(var_indep) = pz_k
*Zpz_k.sub_view(var_indep) = pz_k;
if( m && !bounded_var_dep ) {
// Must compute Zpz_k(var_dep) = D*pz
LinAlgOpPack::V_MtV( &*Zpz_k.sub_view(var_dep), Zvr->D(), BLAS_Cpp::no_trans, pz_k );
// ToDo: Remove the compuation of Zpz here unless you must
}
}
else {
TEST_FOR_EXCEPT(true);
}
// Set the solution statistics
qp_solver_stats_(s).set_k(0) = qp_solver().get_qp_stats();
// Cut back Ypy_k = (1-eta) * Ypy_k
const value_type eps = std::numeric_limits<value_type>::epsilon();
if( fabs(qp_eta - 0.0) > eps ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out
<< "\n*** Alert! the QP was infeasible (eta = "<<qp_eta<<"). Cutting back Ypy_k = (1.0 - eta)*Ypy_k ...\n";
}
Vt_S( Ypy_k, 1.0 - qp_eta );
}
// eta_k
eta_iq.set_k(0) = qp_eta;
//
// Modify the solution if we have to!
//
switch(solution_type) {
case QPSolverStats::OPTIMAL_SOLUTION:
break; // we are good!
case QPSolverStats::PRIMAL_FEASIBLE_POINT:
{
omsg
<< "\n*** Alert! the returned QP solution is PRIMAL_FEASIBLE_POINT but not optimal!\n";
if( primal_feasible_point_error() )
omsg
<< "\n*** primal_feasible_point_error == true, this is an error!\n";
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << omsg.str();
}
throw_qp_failure = primal_feasible_point_error();
break;
}
case QPSolverStats::DUAL_FEASIBLE_POINT:
{
omsg
<< "\n*** Alert! the returned QP solution is DUAL_FEASIBLE_POINT"
<< "\n*** but not optimal so we cut back the step ...\n";
if( dual_feasible_point_error() )
omsg
<< "\n*** dual_feasible_point_error == true, this is an error!\n";
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << omsg.str();
}
// Cut back the step to fit in the bounds
//
// dl <= u*(Ypy_k+Zpz_k) <= du
//
vec_mut_ptr_t
zero = s.space_x().create_member(0.0),
d_tmp = s.space_x().create_member();
V_VpV( d_tmp.get(), *Ypy_k, Zpz_k );
const std::pair<value_type,value_type>
u_steps = max_near_feas_step( *zero, *d_tmp, dl_iq.get_k(0), du_iq.get_k(0), 0.0 );
const value_type
u = my_min( u_steps.first, 1.0 ); // largest positive step size
alpha_iq.set_k(0) = u;
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nFinding u s.t. dl <= u*(Ypy_k+Zpz_k) <= du\n"
<< "max step length u = " << u << std::endl
<< "alpha_k = u = " << alpha_iq.get_k(0) << std::endl;
}
throw_qp_failure = dual_feasible_point_error();
break;
}
case QPSolverStats::SUBOPTIMAL_POINT:
{
omsg
<< "\n*** Alert!, the returned QP solution is SUBOPTIMAL_POINT!\n";
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << omsg.str();
}
throw_qp_failure = true;
break;
}
default:
TEST_FOR_EXCEPT(true); // should not happen!
}
//
// Output the final solution!
//
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||pz_k||inf = " << s.pz().get_k(0).norm_inf()
<< "\nnu_k.nz() = " << s.nu().get_k(0).nz()
<< "\nmax(|nu_k(i)|) = " << s.nu().get_k(0).norm_inf()
// << "\nmin(|nu_k(i)|) = " << min_abs( s.nu().get_k(0)() )
;
if( m > r ) out << "\n||lambda_k(undecomp)||inf = " << s.lambda().get_k(0).norm_inf();
out << "\n||Zpz_k||2 = " << s.Zpz().get_k(0).norm_2()
;
if(qp_eta > 0.0) out << "\n||Ypy||2 = " << s.Ypy().get_k(0).norm_2();
out << std::endl;
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\npz_k = \n" << s.pz().get_k(0);
if(var_indep.size())
out << "\nnu_k(var_indep) = \n" << *s.nu().get_k(0).sub_view(var_indep);
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
if(var_indep.size())
out << "\nZpz(var_indep)_k = \n" << *s.Zpz().get_k(0).sub_view(var_indep);
out << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
if(var_dep.size())
out << "\nZpz(var_dep)_k = \n" << *s.Zpz().get_k(0).sub_view(var_dep);
out << "\nZpz_k = \n" << s.Zpz().get_k(0);
out << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nnu_k = \n" << s.nu().get_k(0);
if(var_dep.size())
out << "\nnu_k(var_dep) = \n" << *s.nu().get_k(0).sub_view(var_dep);
if( m > r )
out << "\nlambda_k(equ_undecomp) = \n" << *s.lambda().get_k(0).sub_view(equ_undecomp);
if(qp_eta > 0.0) out << "\nYpy = \n" << s.Ypy().get_k(0);
}
if( qp_eta == 1.0 ) {
omsg
<< "TangentialStepWithInequStd_Step::do_step(...) : Error, a QP relaxation parameter\n"
<< "of eta = " << qp_eta << " was calculated and therefore it must be assumed\n"
<< "that the NLP's constraints are infeasible\n"
<< "Throwing an InfeasibleConstraints exception!\n";
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << omsg.str();
}
throw InfeasibleConstraints(omsg.str());
}
if( throw_qp_failure )
throw QPFailure( omsg.str(), qp_solver().get_qp_stats() );
return true;
}
QPSolverStats::ESolutionType
QPSolverRelaxedQPKWIK::imp_solve_qp(
std::ostream* out, EOutputLevel olevel, ERunTests test_what
,const Vector& g, const MatrixSymOp& G
,value_type etaL
,const Vector* dL, const Vector* dU
,const MatrixOp* E, BLAS_Cpp::Transp trans_E, const Vector* b
,const Vector* eL, const Vector* eU
,const MatrixOp* F, BLAS_Cpp::Transp trans_F, const Vector* f
,value_type* obj_d
,value_type* eta, VectorMutable* d
,VectorMutable* nu
,VectorMutable* mu, VectorMutable* Ed
,VectorMutable* lambda, VectorMutable* Fd
)
{
using Teuchos::dyn_cast;
using DenseLinAlgPack::nonconst_tri_ele;
using LinAlgOpPack::dot;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::assign;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_MtV;
using AbstractLinAlgPack::EtaVector;
using AbstractLinAlgPack::transVtMtV;
using AbstractLinAlgPack::num_bounded;
using ConstrainedOptPack::MatrixExtractInvCholFactor;
// /////////////////////////
// Map to QPKWIK input
// Validate that rHL is of the proper type.
const MatrixExtractInvCholFactor &cG
= dyn_cast<const MatrixExtractInvCholFactor>(G);
// Determine the number of sparse bounds on variables and inequalities.
// By default set for the dense case
const value_type inf = this->infinite_bound();
const size_type
nd = d->dim(),
m_in = E ? b->dim() : 0,
m_eq = F ? f->dim() : 0,
nvarbounds = dL ? num_bounded(*dL,*dU,inf) : 0,
ninequbounds = E ? num_bounded(*eL,*eU,inf) : 0,
nequalities = F ? f->dim() : 0;
// Determine if this is a QP with a structure different from the
// one just solved.
const bool same_qp_struct = ( N_ == nd && M1_ == nvarbounds && M2_ == ninequbounds && M3_ == nequalities );
/////////////////////////////////////////////////////////////////
// Set the input parameters to be sent to QPKWIKNEW
// N
N_ = nd;
// M1
M1_ = nvarbounds;
// M2
M2_ = ninequbounds;
// M3
M3_ = nequalities;
// GRAD
GRAD_ = VectorDenseEncap(g)();
// UINV_AUG
//
// UINV_AUG = [ sqrt(bigM) 0 ]
// [ 0 L' ]
//
UINV_AUG_.resize(N_+1,N_+1);
cG.extract_inv_chol( &nonconst_tri_ele( UINV_AUG_(2,N_+1,2,N_+1), BLAS_Cpp::upper ) );
UINV_AUG_(1,1) = 1.0 / ::sqrt( NUMPARAM_[2] );
UINV_AUG_.col(1)(2,N_+1) = 0.0;
UINV_AUG_.row(1)(2,N_+1) = 0.0;
// LDUINV_AUG
LDUINV_AUG_ = UINV_AUG_.rows();
// IBND, BL , BU, A, LDA, YPY
IBND_INV_.resize( nd + m_in);
std::fill( IBND_INV_.begin(), IBND_INV_.end(), 0 ); // Initialize the zero
IBND_.resize( my_max( 1, M1_ + M2_ ) );
BL_.resize( my_max( 1, M1_ + M2_ ) );
BU_.resize( my_max( 1, M1_ + M2_ + M3_ ) );
LDA_ = my_max( 1, M2_ + M3_ );
A_.resize( LDA_, ( M2_ + M3_ > 0 ? N_ : 1 ) );
YPY_.resize( my_max( 1, M1_ + M2_ ) );
if(M1_)
YPY_(1,M1_) = 0.0; // Must be for this QP interface
// Initialize variable bound constraints
if( dL ) {
VectorDenseEncap dL_de(*dL);
VectorDenseEncap dU_de(*dU);
// read iterators
AbstractLinAlgPack::sparse_bounds_itr
dLU_itr( dL_de().begin(), dL_de().end()
,dU_de().begin(), dU_de().end()
,inf );
// written iterators
IBND_t::iterator
IBND_itr = IBND_.begin(),
IBND_end = IBND_.begin() + M1_;
DVector::iterator
BL_itr = BL_.begin(),
BU_itr = BU_.begin(),
YPY_itr = YPY_.begin();
// Loop
for( size_type ibnd_i = 1; IBND_itr != IBND_end; ++ibnd_i, ++dLU_itr ) {
IBND_INV_[dLU_itr.index()-1] = ibnd_i;
*IBND_itr++ = dLU_itr.index();
*BL_itr++ = dLU_itr.lbound();
*BU_itr++ = dLU_itr.ubound();
*YPY_itr++ = 0.0; // Must be zero with this QP interface
}
}
// Initialize inequality constraints
if(M2_) {
VectorDenseEncap eL_de(*eL);
VectorDenseEncap eU_de(*eU);
VectorDenseEncap b_de(*b);
AbstractLinAlgPack::sparse_bounds_itr
eLU_itr( eL_de().begin(), eL_de().end()
,eU_de().begin(), eU_de().end()
,inf );
if( M2_ < m_in ) {
// Initialize BL, BU, YPY and A for sparse bounds on general inequalities
// written iterators
DVector::iterator
BL_itr = BL_.begin() + M1_,
BU_itr = BU_.begin() + M1_,
YPY_itr = YPY_.begin() + M1_;
IBND_t::iterator
ibnds_itr = IBND_.begin() + M1_;
// loop
for(size_type i = 1; i <= M2_; ++i, ++eLU_itr, ++ibnds_itr ) {
TEST_FOR_EXCEPT( !( !eLU_itr.at_end() ) );
const size_type k = eLU_itr.index();
*BL_itr++ = eLU_itr.lbound();
*BU_itr++ = eLU_itr.ubound();
*YPY_itr++ = b_de()(k);
*ibnds_itr = k; // Only for my record, not used by QPKWIK
IBND_INV_[nd+k-1] = M1_ + i;
// Add the corresponding row of op(E) to A
// y == A.row(i)'
// y' = e_k' * op(E) => y = op(E')*e_k
DVectorSlice y = A_.row(i);
EtaVector e_k(k,eL_de().dim());
V_MtV( &y( 1, N_ ), *E, BLAS_Cpp::trans_not(trans_E), e_k() ); // op(E')*e_k
}
}
else {
//
// Initialize BL, BU, YPY and A for dense bounds on general inequalities
//
// Initialize BL(M1+1:M1+M2), BU(M1+1:M1+M2)
// and IBND(M1+1:M1+M2) = identity (only for my record, not used by QPKWIK)
DVector::iterator
BL_itr = BL_.begin() + M1_,
BU_itr = BU_.begin() + M1_;
IBND_t::iterator
ibnds_itr = IBND_.begin() + M1_;
for(size_type i = 1; i <= m_in; ++i ) {
if( !eLU_itr.at_end() && eLU_itr.index() == i ) {
*BL_itr++ = eLU_itr.lbound();
*BU_itr++ = eLU_itr.ubound();
++eLU_itr;
}
else {
*BL_itr++ = -inf;
*BU_itr++ = +inf;
}
*ibnds_itr++ = i;
IBND_INV_[nd+i-1]= M1_ + i;
}
// A(1:M2,1:N) = op(E)
assign( &A_(1,M2_,1,N_), *E, trans_E );
// YPY
YPY_(M1_+1,M1_+M2_) = b_de();
}
}
// Initialize equalities
if(M3_) {
V_StV( &BU_( M1_ + M2_ + 1, M1_ + M2_ + M3_ ), -1.0, VectorDenseEncap(*f)() );
assign( &A_( M2_ + 1, M2_ + M3_, 1, N_ ), *F, trans_F );
}
// IYPY
IYPY_ = 1; // ???
// WARM
WARM_ = 0; // Cold start by default
// MAX_ITER
MAX_ITER_ = static_cast<f_int>(max_qp_iter_frac() * N_);
// INF
INF_ = ( same_qp_struct ? 1 : 0 );
// Initilize output, internal state and workspace quantities.
if(!same_qp_struct) {
X_.resize(N_);
NACTSTORE_ = 0;
IACTSTORE_.resize(N_+1);
IACT_.resize(N_+1);
UR_.resize(N_+1);
ISTATE_.resize( QPKWIKNEW_CppDecl::qpkwiknew_listate(N_,M1_,M2_,M3_) );
LRW_ = QPKWIKNEW_CppDecl::qpkwiknew_lrw(N_,M1_,M2_,M3_);
RW_.resize(LRW_);
}
// /////////////////////////////////////////////
// Setup a warm start form the input arguments
//
// Interestingly enough, QPKWIK sorts all of the
// constraints according to scaled multiplier values
// and mixes equality with inequality constriants.
// It seems to me that you should start with equality
// constraints first.
WARM_ = 0;
NACTSTORE_ = 0;
if( m_eq ) {
// Add equality constraints first since we know these will
// be part of the active set.
for( size_type j = 1; j <= m_eq; ++j ) {
IACTSTORE_[NACTSTORE_] = 2*M1_ + 2*M2_ + j;
++NACTSTORE_;
}
}
if( ( nu && nu->nz() ) || ( mu && mu->nz() ) ) {
// Add inequality constraints
const size_type
nu_nz = nu ? nu->nz() : 0,
mu_nz = mu ? mu->nz() : 0;
// Combine all the multipliers for the bound and general inequality
// constraints and sort them from the largest to the smallest. Hopefully
// the constraints with the larger multiplier values will not be dropped
// from the active set.
SpVector gamma( nd + 1 + m_in , nu_nz + mu_nz );
typedef SpVector::element_type ele_t;
if(nu && nu_nz) {
VectorDenseEncap nu_de(*nu);
DVectorSlice::const_iterator
nu_itr = nu_de().begin(),
nu_end = nu_de().end();
index_type i = 1;
while( nu_itr != nu_end ) {
for( ; *nu_itr == 0.0; ++nu_itr, ++i );
gamma.add_element(ele_t(i,*nu_itr));
++nu_itr; ++i;
}
}
if(mu && mu_nz) {
VectorDenseEncap mu_de(*mu);
DVectorSlice::const_iterator
mu_itr = mu_de().begin(),
mu_end = mu_de().end();
index_type i = 1;
while( mu_itr != mu_end ) {
for( ; *mu_itr == 0.0; ++mu_itr, ++i );
gamma.add_element(ele_t(i+nd,*mu_itr));
++mu_itr; ++i;
}
}
std::sort( gamma.begin(), gamma.end()
, AbstractLinAlgPack::SortByDescendingAbsValue() );
// Now add the inequality constraints in decreasing order
const SpVector::difference_type o = gamma.offset();
for( SpVector::const_iterator itr = gamma.begin(); itr != gamma.end(); ++itr ) {
const size_type j = itr->index() + o;
const value_type val = itr->value();
if( j <= nd ) { // Variable bound
const size_type ibnd_i = IBND_INV_[j-1];
TEST_FOR_EXCEPT( !( ibnd_i ) );
IACTSTORE_[NACTSTORE_]
= (val < 0.0
? ibnd_i // lower bound (see IACT(*))
: M1_ + M2_ + ibnd_i // upper bound (see IACT(*))
);
++NACTSTORE_;
}
else if( j <= nd + m_in ) { // General inequality constraint
const size_type ibnd_i = IBND_INV_[j-1]; // offset into M1_ + ibnd_j
TEST_FOR_EXCEPT( !( ibnd_i ) );
IACTSTORE_[NACTSTORE_]
= (val < 0.0
? ibnd_i // lower bound (see IACT(*))
: M1_ + M2_ + ibnd_i // upper bound (see IACT(*))
);
++NACTSTORE_;
}
}
}
if( NACTSTORE_ > 0 )
WARM_ = 1;
// /////////////////////////
// Call QPKWIK
if( out && olevel > PRINT_NONE ) {
*out
<< "\nCalling QPKWIK to solve QP problem ...\n";
}
QPKWIKNEW_CppDecl::qpkwiknew(
N_, M1_, M2_, M3_, &GRAD_(1), &UINV_AUG_(1,1), LDUINV_AUG_, &IBND_[0]
,&BL_(1), &BU_(1), &A_(1,1), LDA_, &YPY_(1), IYPY_, WARM_, NUMPARAM_, MAX_ITER_, &X_(1)
,&NACTSTORE_, &IACTSTORE_[0], &INF_, &NACT_, &IACT_[0], &UR_[0], &EXTRA_
,&ITER_, &NUM_ADDS_, &NUM_DROPS_, &ISTATE_[0], LRW_, &RW_[0]
);
// ////////////////////////
// Map from QPKWIK output
// eta
*eta = EXTRA_;
// d
(VectorDenseMutableEncap(*d))() = X_();
// nu (simple variable bounds) and mu (general inequalities)
if(nu) *nu = 0.0;
if(mu) *mu = 0.0;
// ToDo: Create VectorDenseMutableEncap views for faster access!
{for(size_type i = 1; i <= NACT_; ++i) {
size_type j = IACT_[i-1];
EConstraintType type = constraint_type(M1_,M2_,M3_,j);
FortranTypes::f_int idc = constraint_index(M1_,M2_,M3_,&IBND_[0],type,j);
switch(type) {
case NU_L:
nu->set_ele( idc , -UR_(i) );
break;
case GAMA_L:
mu->set_ele( IBND_[ M1_ + idc - 1 ], -UR_(i) );
break;
case NU_U:
nu->set_ele( idc, UR_(i)) ;
break;
case GAMA_U:
mu->set_ele( IBND_[ M1_ + idc - 1 ], UR_(i) );
break;
case LAMBDA:
lambda->set_ele( idc, UR_(i) );
break;
}
}}
// obj_d (This could be updated within QPKWIK in the future)
if(obj_d) {
// obj_d = g'*d + 1/2 * d' * G * g
*obj_d = dot(g,*d) + 0.5 * transVtMtV(*d,G,BLAS_Cpp::no_trans,*d);
}
// Ed (This could be updated within QPKWIK in the future)
if(Ed) {
V_MtV( Ed, *E, trans_E, *d );
}
// Fd (This could be updated within QPKWIK in the future)
if(Fd) {
V_MtV( Fd, *F, trans_F, *d );
}
// Set the QP statistics
QPSolverStats::ESolutionType solution_type;
if( INF_ >= 0 ) {
solution_type = QPSolverStats::OPTIMAL_SOLUTION;
}
else if( INF_ == -1 ) { // Infeasible constraints
TEST_FOR_EXCEPTION(
true, QPSolverRelaxed::Infeasible
,"QPSolverRelaxedQPKWIK::solve_qp(...) : Error, QP is infeasible" );
}
else if( INF_ == -2 ) { // LRW too small
TEST_FOR_EXCEPT( !( INF_ != -2 ) ); // Local programming error?
}
else if( INF_ == -3 ) { // Max iterations exceeded
solution_type = QPSolverStats::DUAL_FEASIBLE_POINT;
}
else {
TEST_FOR_EXCEPT(true); // Unknown return value!
}
qp_stats_.set_stats(
solution_type, QPSolverStats::CONVEX
,ITER_, NUM_ADDS_, NUM_DROPS_
,WARM_==1, *eta > 0.0 );
return qp_stats_.solution_type();
}
bool CalcReducedGradLagrangianStd_AddedStep::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using BLAS_Cpp::trans;
using LinAlgOpPack::V_VpV;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::Vp_MtV;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
EJournalOutputLevel ns_olevel = algo.algo_cntr().null_space_journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// Calculate: rGL = rGf + Z' * nu + Uz' * lambda(equ_undecomp)
IterQuantityAccess<VectorMutable>
&rGL_iq = s.rGL(),
&nu_iq = s.nu(),
&Gf_iq = s.Gf();
VectorMutable &rGL_k = rGL_iq.set_k(0);
if( nu_iq.updated_k(0) && nu_iq.get_k(0).nz() > 0 ) {
// Compute rGL = Z'*(Gf + nu) to reduce the effect of roundoff in this
// catastropic cancelation
const Vector &nu_k = nu_iq.get_k(0);
VectorSpace::vec_mut_ptr_t
tmp = nu_k.space().create_member();
if( (int)olevel >= (int)PRINT_VECTORS )
out << "\nnu_k = \n" << nu_k;
V_VpV( tmp.get(), Gf_iq.get_k(0), nu_k );
if( (int)olevel >= (int)PRINT_VECTORS )
out << "\nGf_k+nu_k = \n" << *tmp;
V_MtV( &rGL_k, s.Z().get_k(0), trans, *tmp );
if( (int)ns_olevel >= (int)PRINT_VECTORS )
out << "\nrGL_k = \n" << rGL_k;
}
else {
rGL_k = s.rGf().get_k(0);
}
// ToDo: Add terms for undecomposed equalities and inequalities!
// + Uz' * lambda(equ_undecomp)
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||rGL_k||inf = " << rGL_k.norm_inf() << "\n";
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nrGL_k = \n" << rGL_k;
}
return true;
}
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);
}
void MatrixSymPosDefLBFGS::secant_update(
VectorMutable* s, VectorMutable* y, VectorMutable* Bs
)
{
using AbstractLinAlgPack::BFGS_sTy_suff_p_d;
using AbstractLinAlgPack::dot;
using LinAlgOpPack::V_MtV;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
// Check skipping the BFGS update
const value_type
sTy = dot(*s,*y);
std::ostringstream omsg;
if( !BFGS_sTy_suff_p_d(*s,*y,&sTy,&omsg,"MatrixSymPosDefLBFGS::secant_update(...)" ) ) {
throw UpdateSkippedException( omsg.str() );
}
try {
// Update counters
if( m_bar_ == m_ ) {
// We are at the end of the storage so remove the oldest stored update
// and move updates to make room for the new update. This has to be done for the
// the matrix to behave properly
{for( size_type k = 1; k <= m_-1; ++k ) {
S_->col(k) = S_->col(k+1); // Shift S.col() to the left
Y_->col(k) = Y_->col(k+1); // Shift Y.col() to the left
STY_.col(k)(1,m_-1) = STY_.col(k+1)(2,m_); // Move submatrix STY(2,m-1,2,m-1) up and left
STSYTY_.col(k)(k+1,m_) = STSYTY_.col(k+1)(k+2,m_+1); // Move triangular submatrix STS(2,m-1,2,m-1) up and left
STSYTY_.col(k+1)(1,k) = STSYTY_.col(k+2)(2,k+1); // Move triangular submatrix YTY(2,m-1,2,m-1) up and left
}}
// ToDo: Create an abstract interface, call it MultiVectorShiftVecs, to rearrange S and Y all at once.
// This will be important for parallel performance.
}
else {
m_bar_++;
}
// Set the update vectors
*S_->col(m_bar_) = *s;
*Y_->col(m_bar_) = *y;
// /////////////////////////////////////////////////////////////////////////////////////
// Update S'Y
//
// Update the row and column m_bar
//
// S'Y =
//
// [ s(1)'*y(1) ... s(1)'*y(m_bar) ... s(1)'*y(m_bar) ]
// [ . . . ] row
// [ s(m_bar)'*y(1) ... s(m_bar)'*y(m_bar) ... s(m_bar)'*y(m_bar) ] m_bar
// [ . . . ]
// [ s(m_bar)'*y(1) ... s(m_bar)'*y(m_bar) ... s(m_bar)'*y(m_bar) ]
//
// col m_bar
//
// Therefore we set:
// (S'Y)(:,m_bar) = S'*y(m_bar)
// (S'Y)(m_bar,:) = s(m_bar)'*Y
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member(); // temporary workspace
// (S'Y)(:,m_bar) = S'*y(m_bar)
V_MtV( t.get(), *S, BLAS_Cpp::trans, *y );
STY_.col(m_bar_)(1,m_bar_) = VectorDenseEncap(*t)();
// (S'Y)(m_bar,:)' = Y'*s(m_bar)
V_MtV( t.get(), *Y, BLAS_Cpp::trans, *s );
STY_.row(m_bar_)(1,m_bar_) = VectorDenseEncap(*t)();
// /////////////////////////////////////////////////////////////////
// Update S'S
//
// S'S =
//
// [ s(1)'*s(1) ... symmetric symmetric ]
// [ . . . ] row
// [ s(m_bar)'*s(1) ... s(m_bar)'*s(m_bar) ... symmetric ] m_bar
// [ . . . ]
// [ s(m_bar)'*s(1) ... s(m_bar)'*s(m_bar) ... s(m_bar)'*s(m_bar) ]
//
// col m_bar
//
// Here we will update the lower triangular part of S'S. To do this we
// only need to compute:
// t = S'*s(m_bar) = { s(m_bar)' * [ s(1),..,s(m_bar),..,s(m_bar) ] }'
// then set the appropriate rows and columns of S'S.
Workspace<value_type> work_ws(wss,m_bar_);
DVectorSlice work(&work_ws[0],work_ws.size());
// work = S'*s(m_bar)
V_MtV( t.get(), *S, BLAS_Cpp::trans, *s );
work = VectorDenseEncap(*t)();
// Set row elements
STSYTY_.row(m_bar_+1)(1,m_bar_) = work;
// Set column elements
STSYTY_.col(m_bar_)(m_bar_+1,m_bar_+1) = work(m_bar_,m_bar_);
// /////////////////////////////////////////////////////////////////////////////////////
// Update Y'Y
//
// Update the row and column m_bar
//
// Y'Y =
//
// [ y(1)'*y(1) ... y(1)'*y(m_bar) ... y(1)'*y(m_bar) ]
// [ . . . ] row
// [ symmetric ... y(m_bar)'*y(m_bar) ... y(m_bar)'*y(m_bar) ] m_bar
// [ . . . ]
// [ symmetric ... symmetric ... y(m_bar)'*y(m_bar) ]
//
// col m_bar
//
// Here we will update the upper triangular part of Y'Y. To do this we
// only need to compute:
// t = Y'*y(m_bar) = { y(m_bar)' * [ y(1),..,y(m_bar),..,y(m_bar) ] }'
// then set the appropriate rows and columns of Y'Y.
// work = Y'*y(m_bar)
V_MtV( t.get(), *Y, BLAS_Cpp::trans, *y );
work = VectorDenseEncap(*t)();
// Set row elements
STSYTY_.col(m_bar_+1)(1,m_bar_) = work;
// Set column elements
STSYTY_.row(m_bar_)(m_bar_+1,m_bar_+1) = work(m_bar_,m_bar_);
// /////////////////////////////
// Update gamma_k
// gamma_k = s'*y / y'*y
if(auto_rescaling_)
gamma_k_ = STY_(m_bar_,m_bar_) / STSYTY_(m_bar_,m_bar_+1);
// We do not initially update Q unless we have to form a matrix-vector
// product later.
Q_updated_ = false;
num_secant_updates_++;
} // end try
catch(...) {
// If we throw any exception the we should make the matrix uninitialized
// so that we do not leave this object in an inconsistant state.
n_ = 0;
throw;
}
}
void MatrixSymPosDefLBFGS::V_InvMtV(
VectorMutable* y, BLAS_Cpp::Transp trans_rhs1
, const Vector& x
) const
{
using AbstractLinAlgPack::Vp_StMtV;
using DenseLinAlgPack::V_InvMtV;
using LinAlgOpPack::V_mV;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::Vp_MtV;
using DenseLinAlgPack::Vp_StMtV;
typedef VectorDenseEncap vde;
typedef VectorDenseMutableEncap vdme;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
TEUCHOS_TEST_FOR_EXCEPT( !( inverse_is_updated_ ) ); // For now just always update
// y = inv(Bk) * x = Hk * x
//
// = gk*x + [S gk*Y] * [ inv(R')*(D+gk*Y'Y)*inv(R) -inv(R') ] * [ S' ] * x
// [ -inv(R) 0 ] [ gk*Y' ]
//
// Perform in the following (in order):
//
// y = gk*x
//
// t1 = [ S'*x ] <: R^(2*m)
// [ gk*Y'*x ]
//
// t2 = inv(R) * t1(1:m) <: R^(m)
//
// t3 = - inv(R') * t1(m+1,2*m) <: R^(m)
//
// t4 = gk * Y'Y * t2 <: R^(m)
//
// t4 += D*t2
//
// t5 = inv(R') * t4 <: R^(m)
//
// t5 += t3
//
// y += S*t5
//
// y += -gk*Y*t2
// y = gk*x
V_StV( y, gamma_k_, x );
const size_type
mb = m_bar_;
if( !mb )
return; // No updates have been performed.
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
// Get workspace
Workspace<value_type> t1_ws(wss,2*mb);
DVectorSlice t1(&t1_ws[0],t1_ws.size());
Workspace<value_type> t2_ws(wss,mb);
DVectorSlice t2(&t2_ws[0],t2_ws.size());
Workspace<value_type> t3_ws(wss,mb);
DVectorSlice t3(&t3_ws[0],t3_ws.size());
Workspace<value_type> t4_ws(wss,mb);
DVectorSlice t4(&t4_ws[0],t4_ws.size());
Workspace<value_type> t5_ws(wss,mb);
DVectorSlice t5(&t5_ws[0],t5_ws.size());
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member();
const DMatrixSliceTri
&R = this->R();
const DMatrixSliceSym
&YTY = this->YTY();
// t1 = [ S'*x ]
// [ gk*Y'*x ]
V_MtV( t.get(), *S, BLAS_Cpp::trans, x );
t1(1,mb) = vde(*t)();
V_StMtV( t.get(), gamma_k_, *Y, BLAS_Cpp::trans, x );
t1(mb+1,2*mb) = vde(*t)();
// t2 = inv(R) * t1(1:m)
V_InvMtV( &t2, R, BLAS_Cpp::no_trans, t1(1,mb) );
// t3 = - inv(R') * t1(m+1,2*m)
V_mV( &t3, t1(mb+1,2*mb) );
V_InvMtV( &t3, R, BLAS_Cpp::trans, t3 );
// t4 = gk * Y'Y * t2
V_StMtV( &t4, gamma_k_, YTY, BLAS_Cpp::no_trans, t2 );
// t4 += D*t2
Vp_DtV( &t4, t2 );
// t5 = inv(R') * t4
V_InvMtV( &t5, R, BLAS_Cpp::trans, t4 );
// t5 += t3
Vp_V( &t5, t3 );
// y += S*t5
(vdme(*t)() = t5);
Vp_MtV( y, *S, BLAS_Cpp::no_trans, *t );
// y += -gk*Y*t2
(vdme(*t)() = t2);
Vp_StMtV( y, -gamma_k_, *Y, BLAS_Cpp::no_trans, *t );
}
void MatrixSymPosDefLBFGS::Vp_StMtV(
VectorMutable* y, value_type alpha, BLAS_Cpp::Transp trans_rhs1
, const Vector& x, value_type beta
) const
{
using AbstractLinAlgPack::Vt_S;
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::Vp_StMtV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::V_MtV;
typedef VectorDenseEncap vde;
typedef VectorDenseMutableEncap vdme;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
TEUCHOS_TEST_FOR_EXCEPT( !( original_is_updated_ ) ); // For now just always update
// y = b*y + Bk * x
//
// y = b*y + (1/gk)*x - [ (1/gk)*S Y ] * inv(Q) * [ (1/gk)*S' ] * x
// [ Y' ]
// Perform the following operations (in order):
//
// y = b*y
//
// y += (1/gk)*x
//
// t1 = [ (1/gk)*S'*x ] <: R^(2*m)
// [ Y'*x ]
//
// t2 = inv(Q) * t1 <: R^(2*m)
//
// y += -(1/gk) * S * t2(1:m)
//
// y += -1.0 * Y * t2(m+1,2m)
const value_type
invgk = 1.0 / gamma_k_;
// y = b*y
Vt_S( y, beta );
// y += (1/gk)*x
Vp_StV( y, invgk, x );
if( !m_bar_ )
return; // No updates have been added yet.
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
// Get workspace
const size_type
mb = m_bar_;
Workspace<value_type> t1_ws(wss,2*mb);
DVectorSlice t1(&t1_ws[0],t1_ws.size());
Workspace<value_type> t2_ws(wss,2*mb);
DVectorSlice t2(&t2_ws[0],t2_ws.size());
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member();
// t1 = [ (1/gk)*S'*x ]
// [ Y'*x ]
V_StMtV( t.get(), invgk, *S, BLAS_Cpp::trans, x );
t1(1,mb) = vde(*t)();
V_MtV( t.get(), *Y, BLAS_Cpp::trans, x );
t1(mb+1,2*mb) = vde(*t)();
// t2 = inv(Q) * t1
V_invQtV( &t2, t1 );
// y += -(1/gk) * S * t2(1:m)
(vdme(*t)() = t2(1,mb));
Vp_StMtV( y, -invgk, *S, BLAS_Cpp::no_trans, *t );
// y += -1.0 * Y * t2(m+1,2m
(vdme(*t)() = t2(mb+1,2*mb));
Vp_StMtV( y, -1.0, *Y, BLAS_Cpp::no_trans, *t );
}