void MatrixSymDiagStd::Mp_StM(
DMatrixSlice* gms_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs) const
{
using DenseLinAlgPack::Vp_StV;
// Assert that the dimensions match up.
DenseLinAlgPack::Mp_M_assert_sizes( gms_lhs->rows(), gms_lhs->cols(), BLAS_Cpp::no_trans
, rows(), cols(), trans_rhs );
// Add to the diagonal
Vp_StV( &gms_lhs->diag(), alpha, diag_ );
}
inline
void Vp_MtV(DVectorSlice* vs_lhs, const M& M_rhs1, BLAS_Cpp::Transp trans_rhs1
, const V& V_rhs2, value_type beta)
{
Vp_StMtV(vs_lhs,1.0,M_rhs1,trans_rhs1,V_rhs2,beta);
}
inline
void Mp_MtM(DMatrixSlice* gms_lhs, const M1& M1_rhs1, BLAS_Cpp::Transp trans_rhs1
, const M2& M2_rhs2, BLAS_Cpp::Transp trans_rhs2, value_type beta)
{
Mp_StMtM(gms_lhs,1.0,M1_rhs1,trans_rhs1,M2_rhs2,trans_rhs2,beta);
}
inline
void Vp_V(DVectorSlice* vs_lhs, const V& V_rhs) {
Vp_StV(vs_lhs,1.0,V_rhs);
}
inline
void Mp_M(DMatrixSlice* gms_lhs, const M& M_rhs, BLAS_Cpp::Transp trans_rhs) {
Mp_StM(gms_lhs,1.0,M_rhs,trans_rhs);
}
bool MoochoPack::LineSearchWatchDog_Step::do_step(Algorithm& _algo
, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss)
{
using DenseLinAlgPack::norm_inf;
using DenseLinAlgPack::V_VpV;
using DenseLinAlgPack::Vp_StV;
using DenseLinAlgPack::Vt_S;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::V_MtV;
using ConstrainedOptPack::print_vector_change_stats;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLP &nlp = algo.nlp();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
out << std::boolalpha;
// print step header.
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// /////////////////////////////////////////
// Set references to iteration quantities
//
// Set k+1 first then go back to get k to ensure
// we have backward storage.
DVector
&x_kp1 = s.x().set_k(+1).v();
value_type
&f_kp1 = s.f().set_k(+1);
DVector
&c_kp1 = s.c().set_k(+1).v();
const value_type
&f_k = s.f().get_k(0);
const DVector
&c_k = s.c().get_k(0).v();
const DVector
&x_k = s.x().get_k(0).v();
const DVector
&d_k = s.d().get_k(0).v();
value_type
&alpha_k = s.alpha().get_k(0);
// /////////////////////////////////////
// Compute Dphi_k, phi_kp1 and phi_k
// Dphi_k
const value_type
Dphi_k = merit_func().deriv();
if( Dphi_k >= 0 ) {
throw LineSearchFailure( "LineSearch2ndOrderCorrect_Step::do_step(...) : "
"Error, d_k is not a descent direction for the merit function " );
}
// ph_kp1
value_type
&phi_kp1 = s.phi().set_k(+1) = merit_func().value( f_kp1, c_kp1 );
// Must compute phi(x) at the base point x_k since the penalty parameter may have changed.
const value_type
&phi_k = s.phi().set_k(0) = merit_func().value( f_k, c_k );
// //////////////////////////////////////
// Setup the calculation merit function
// Here f_kp1, and c_kp1 are updated at the same time the
// line search is being performed.
nlp.set_f( &f_kp1 );
nlp.set_c( &c_kp1 );
MeritFuncCalcNLP
phi_calc( &merit_func(), &nlp );
// ////////////////////////////////
// Use Watchdog near the solution
if( watch_k_ == NORMAL_LINE_SEARCH ) {
const value_type
opt_kkt_err_k = s.opt_kkt_err().get_k(0),
feas_kkt_err_k = s.feas_kkt_err().get_k(0);
if( opt_kkt_err_k <= opt_kkt_err_threshold() && feas_kkt_err_k <= feas_kkt_err_threshold() ) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nopt_kkt_err_k = " << opt_kkt_err_k << " <= opt_kkt_err_threshold = "
<< opt_kkt_err_threshold() << std::endl
<< "\nfeas_kkt_err_k = " << feas_kkt_err_k << " <= feas_kkt_err_threshold = "
<< feas_kkt_err_threshold() << std::endl
<< "\nSwitching to watchdog linesearch ...\n";
}
watch_k_ = 0;
}
}
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nTrial point:\n"
<< "phi_k = " << phi_k << std::endl
<< "Dphi_k = " << Dphi_k << std::endl
<< "phi_kp1 = " << phi_kp1 << std::endl;
}
bool ls_success = true,
step_return = true;
switch( watch_k_ ) {
case 0:
{
// Take a full step
const value_type phi_cord = phi_k + eta() * Dphi_k;
const bool accept_step = phi_kp1 <= phi_cord;
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\n*** Zeroth watchdog iteration:\n"
<< "\nphi_kp1 = " << phi_kp1 << ( accept_step ? " <= " : " > " )
<< "phi_k + eta * Dphi_k = " << phi_cord << std::endl;
}
if( phi_kp1 > phi_cord ) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nAccept this increase for now but watch out next iteration!\n";
}
// Save this initial point
xo_ = x_k;
fo_ = f_k;
nrm_co_ = norm_inf( c_k );
do_ = d_k;
phio_ = phi_k;
Dphio_ = Dphi_k;
phiop1_ = phi_kp1;
// Slip the update of the penalty parameter
const value_type mu_k = s.mu().get_k(0);
s.mu().set_k(+1) = mu_k;
// Move on to the next step in the watchdog procedure
watch_k_ = 1;
}
else {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nAll is good!\n";
}
// watch_k_ stays 0
}
step_return = true;
break;
}
case 1:
{
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\n*** First watchdog iteration:\n"
<< "\nDo a line search to determine x_kp1 = x_k + alpha_k * d_k ...\n";
}
// Now do a line search but and we require some type of reduction
const DVectorSlice xd[2] = { x_k(), d_k() };
MeritFuncCalc1DQuadratic phi_calc_1d( phi_calc, 1, xd, &x_kp1() );
ls_success = direct_line_search().do_line_search( phi_calc_1d, phi_k
, &alpha_k, &phi_kp1
, (int)olevel >= (int)PRINT_ALGORITHM_STEPS ?
&out : static_cast<std::ostream*>(0) );
// If the linesearch failed then the rest of the tests will catch this.
value_type phi_cord = 0;
bool test1, test2;
if( ( test1 = ( phi_k <= phio_ ) )
|| ( test2 = phi_kp1 <= ( phi_cord = phio_ + eta() * Dphio_ ) ) )
{
// We will accept this step and and move on.
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out
<< "\nphi_k = " << phi_k << ( test1 ? " <= " : " > " )
<< "phi_km1 = " << phio_ << std::endl
<< "phi_kp1 = " << phi_kp1 << ( test2 ? " <= " : " > " )
<< "phi_km1 + eta * Dphi_km1 = " << phi_cord << std::endl
<< "This is a sufficent reduction so reset watchdog.\n";
}
watch_k_ = 0;
step_return = true;
}
else if ( ! ( test1 = ( phi_kp1 <= phio_ ) ) ) {
// Even this reduction is no good!
// Go back to original point and do a linesearch from there.
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out
<< "\nphi_kp1 = " << phi_kp1 << " > phi_km1 = " << phio_ << std::endl
<< "This is not good reduction in phi so do linesearch from x_km1\n"
<< "\n* Go back to x_km1: x_kp1 = x_k - alpha_k * d_k ...\n";
}
// Go back from x_k to x_km1 for iteration k:
//
// x_kp1 = x_km1
// x_kp1 = x_k - alpha_km1 * d_km1
//
// A negative sign for alpha is an indication that we are backtracking.
//
s.alpha().set_k(0) = -1.0;
s.d().set_k(0).v() = do_;
s.f().set_k(+1) = fo_;
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "Output iteration k ...\n"
<< "k = k+1\n";
}
// Output these iteration quantities
algo.track().output_iteration( algo ); // k
// Transition to iteration k+1
s.next_iteration();
// Take the step from x_k = x_km2 to x_kp1 for iteration k (k+1):
//
// x_kp1 = x_km2 + alpha_n * d_km2
// x_kp1 = x_k + alpha_n * d_km1
// x_kp1 = x_n
//
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\n* Take the step from x_k = x_km2 to x_kp1 for iteration k (k+1)\n"
<< "Find: x_kp1 = x_k + alpha_k * d_k = x_km2 + alpha_k * d_km2\n ...\n";
}
// alpha_k = 1.0
value_type &alpha_k = s.alpha().set_k(0) = 1.0;
// /////////////////////////////////////
// Compute Dphi_k and phi_k
// x_k
const DVector &x_k = xo_;
// d_k
const DVector &d_k = s.d().set_k(0).v() = do_;
// Dphi_k
const value_type &Dphi_k = Dphio_;
// phi_k
const value_type &phi_k = s.phi().set_k(0) = phio_;
// Here f_kp1, and c_kp1 are updated at the same time the
// line search is being performed.
algo.nlp().set_f( &s.f().set_k(+1) );
algo.nlp().set_c( &s.c().set_k(+1).v() );
phi_calc.set_nlp( algo.get_nlp() );
// ////////////////////////////////////////
// Compute x_xp1 and ph_kp1 for full step
// x_kp1 = x_k + alpha_k * d_k
DVector &x_kp1 = s.x().set_k(+1).v();
V_VpV( &x_kp1, x_k, d_k );
// phi_kp1
value_type &phi_kp1 = s.phi().set_k(+1) = phiop1_;
const DVectorSlice xd[2] = { x_k(), d_k() };
MeritFuncCalc1DQuadratic phi_calc_1d( phi_calc, 1, xd, &x_kp1() );
ls_success = direct_line_search().do_line_search(
phi_calc_1d, phi_k
, &alpha_k, &phi_kp1
, (int)olevel >= (int)PRINT_ALGORITHM_STEPS ?
&out : static_cast<std::ostream*>(0) );
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nOutput iteration k (k+1) ...\n"
<< "k = k+1 (k+2)\n"
<< "Reinitialize watchdog algorithm\n";
}
// Output these iteration quantities
algo.track().output_iteration( algo ); // (k+1)
// Transition to iteration k+1 (k+2)
s.next_iteration();
watch_k_ = 0; // Reinitialize the watchdog
// Any update for k (k+2) should use the last updated value
// which was for k-2 (k) since there is not much info for k-1 (k+1).
// Be careful here and make sure this is square with other steps.
algo.do_step_next( EvalNewPoint_name );
step_return = false; // Redirect control
}
else {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out
<< "phi_kp1 = " << phi_kp1 << " <= phi_km1 = " << phio_ << std::endl
<< "\nAccept this step but do a linesearch next iteration!\n";
}
// Slip the update of the penalty parameter
const value_type mu_k = s.mu().get_k(0);
s.mu().set_k(+1) = mu_k;
// Do the last stage of the watchdog procedure next iteration.
watch_k_ = 2;
step_return = true;
}
break;
}
case NORMAL_LINE_SEARCH:
case 2:
{
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
if( watch_k_ == 2 ) {
out << "\n*** Second watchdog iteration:\n"
<< "Do a line search to determine x_kp1 = x_k + alpha_k * d_k ...\n";
}
else {
out << "\n*** Normal linesearch:\n"
<< "Do a line search to determine x_kp1 = x_k + alpha_k * d_k ...\n";
}
}
const DVectorSlice xd[2] = { x_k(), d_k() };
MeritFuncCalc1DQuadratic phi_calc_1d( phi_calc, 1, xd, &x_kp1() );
ls_success = direct_line_search().do_line_search( phi_calc_1d, phi_k
, &alpha_k, &phi_kp1
, (int)olevel >= (int)PRINT_ALGORITHM_STEPS ?
&out : static_cast<std::ostream*>(0) );
if( watch_k_ == 2 )
watch_k_ = 0;
step_return = true;
break;
}
default:
TEST_FOR_EXCEPT(true); // Only local programming error
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nalpha = " << s.alpha().get_k(0) << "\n";
out << "\nphi_kp1 = " << s.phi().get_k(+1) << "\n";
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nd_k = \n" << s.d().get_k(0)();
out << "\nx_kp1 = \n" << s.x().get_k(+1)();
}
if( !ls_success )
throw LineSearchFailure("LineSearchWatchDog_Step::do_step(): Line search failure");
return step_return;
}
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 MeritFunc_PenaltyParamsUpdateWithMult_AddedStep::do_step(Algorithm& _algo
, poss_type step_poss, IterationPack::EDoStepType type
, poss_type assoc_step_poss)
{
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 );
}
MeritFuncPenaltyParams
*params = dynamic_cast<MeritFuncPenaltyParams*>(&merit_func());
if( !params ) {
std::ostringstream omsg;
omsg
<< "MeritFunc_PenaltyParamsUpdateWithMult_AddedStep::do_step(...), Error "
<< "The class " << typeName(&merit_func()) << " does not support the "
<< "MeritFuncPenaltyParams iterface\n";
out << omsg.str();
throw std::logic_error( omsg.str() );
}
MeritFuncNLPDirecDeriv
*direc_deriv = dynamic_cast<MeritFuncNLPDirecDeriv*>(&merit_func());
if( !direc_deriv ) {
std::ostringstream omsg;
omsg
<< "MeritFunc_PenaltyParamsUpdateWithMult_AddedStep::do_step(...), Error "
<< "The class " << typeName(&merit_func()) << " does not support the "
<< "MeritFuncNLPDirecDeriv iterface\n";
out << omsg.str();
throw std::logic_error( omsg.str() );
}
bool perform_update = true;
if( s.mu().updated_k(0) ) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nmu_k is already updated by someone else?\n";
}
const value_type mu_k = s.mu().get_k(0);
if( mu_k == norm_inf_mu_last_ ) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nmu_k " << mu_k << " == norm_inf_mu_last = " << norm_inf_mu_last_
<< "\nso we will take this as a signal to skip the update.\n";
}
perform_update = false;
}
else {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nmu_k " << mu_k << " != norm_inf_mu_last = " << norm_inf_mu_last_
<< "\nso we will ignore this and perform the update anyway.\n";
}
}
}
if(perform_update) {
if ( s.lambda().updated_k(0) ) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nUpdate the penalty parameter...\n";
}
const DVector
&lambda_k = s.lambda().get_k(0).cv();
if( params->mu().size() != lambda_k.size() )
params->resize( lambda_k.size() );
DVectorSlice
mu = params->mu();
const value_type
max_lambda = norm_inf( lambda_k() ),
mult_fact = (1.0 + mult_factor_);
if(near_solution_) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nNear solution, forcing mu(j) >= mu_old(j)...\n";
}
DVector::const_iterator lb_itr = lambda_k.begin();
DVectorSlice::iterator mu_itr = mu.begin();
for( ; lb_itr != lambda_k.end(); ++mu_itr, ++ lb_itr )
*mu_itr = max( max( *mu_itr, mult_fact * ::fabs(*lb_itr) ), small_mu_ );
}
else {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nNot near solution, allowing reduction in mu(j) ...\n";
}
DVector::const_iterator lb_itr = lambda_k.begin();
DVectorSlice::iterator mu_itr = mu.begin();
for( ; lb_itr != lambda_k.end(); ++mu_itr, ++ lb_itr ) {
const value_type lb_j = ::fabs(*lb_itr);
*mu_itr = max(
(3.0 * (*mu_itr) + lb_j) / 4.0
, max( mult_fact * lb_j, small_mu_ )
);
}
value_type kkt_error = s.opt_kkt_err().get_k(0) + s.feas_kkt_err().get_k(0);
if(kkt_error <= kkt_near_sol_) {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nkkt_error = " << kkt_error << " <= kkt_near_sol = "
<< kkt_near_sol_ << std::endl
<< "Switching to forcing mu_k >= mu_km1 in the future\n";
}
near_solution_ = true;
}
}
// Force the ratio
const value_type
max_mu = norm_inf( mu() ),
min_mu = min_mu_ratio_ * max_mu;
for(DVectorSlice::iterator mu_itr = mu.begin(); mu_itr != mu.end(); ++mu_itr)
*mu_itr = max( (*mu_itr), min_mu );
s.mu().set_k(0) = norm_inf_mu_last_ = max_mu;
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nmax(|mu(j)|) = " << (*std::max_element( mu.begin(), mu.end() ))
<< "\nmin(|mu(j)|) = " << (*std::min_element( mu.begin(), mu.end() ))
<< std::endl;
}
if( (int)olevel >= (int)PRINT_VECTORS ) {
out << "\nmu = \n" << mu;
}
}
else {
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nDon't have the info to update penalty parameter so just use the last updated...\n";
}
}
}
// In addition also compute the directional derivative
direc_deriv->calc_deriv( s.Gf().get_k(0)(), s.c().get_k(0)(), s.d().get_k(0)() );
if( (int)olevel >= (int)PRINT_ALGORITHM_STEPS ) {
out << "\nmu_k = " << s.mu().get_k(0) << "\n";
}
return true;
}
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);
}
void MatrixSymPosDefLBFGS::update_Q() const
{
using DenseLinAlgPack::tri;
using DenseLinAlgPack::tri_ele;
using DenseLinAlgPack::Mp_StM;
//
// We need update the factorizations to solve for:
//
// x = inv(Q) * y
//
// [ y1 ] = [ (1/gk)*S'S L ] * [ x1 ]
// [ y2 ] [ L' -D ] [ x2 ]
//
// We will solve the above system using the schur complement:
//
// C = (1/gk)*S'S + L*inv(D)*L'
//
// According to the referenced paper, C is p.d. so:
//
// C = J*J'
//
// We then compute the solution as:
//
// x1 = inv(C) * ( y1 + L*inv(D)*y2 )
// x2 = - inv(D) * ( y2 - L'*x1 )
//
// Therefore we will just update the factorization C = J*J'
//
// Form the upper triangular part of C which will become J
// which we are using storage of QJ
if( QJ_.rows() < m_ )
QJ_.resize( m_, m_ );
const size_type
mb = m_bar_;
DMatrixSlice
C = QJ_(1,mb,1,mb);
// C = L * inv(D) * L'
//
// Here L is a strictly lower triangular (zero diagonal) matrix where:
//
// L = [ 0 0 ]
// [ Lb 0 ]
//
// Lb is lower triangular (nonzero diagonal)
//
// Therefore we compute L*inv(D)*L' as:
//
// C = [ 0 0 ] * [ Db 0 ] * [ 0 Lb' ]
// [ Lb 0 ] [ 0 db ] [ 0 0 ]
//
// = [ 0 0 ] = [ 0 0 ]
// [ 0 Cb ] [ 0 Lb*Db*Lb' ]
//
// We need to compute the upper triangular part of Cb.
C.row(1) = 0.0;
if( mb > 1 )
comp_Cb( STY_(2,mb,1,mb-1), STY_.diag(0)(1,mb-1), &C(2,mb,2,mb) );
// C += (1/gk)*S'S
const DMatrixSliceSym &STS = this->STS();
Mp_StM( &C, (1/gamma_k_), tri( STS.gms(), STS.uplo(), BLAS_Cpp::nonunit )
, BLAS_Cpp::trans );
// Now perform a cholesky factorization of C
// After this factorization the upper triangular part of QJ
// (through C) will contain the cholesky factor.
DMatrixSliceTriEle C_upper = tri_ele( C, BLAS_Cpp::upper );
try {
DenseLinAlgLAPack::potrf( &C_upper );
}
catch( const DenseLinAlgLAPack::FactorizationException &fe ) {
TEUCHOS_TEST_FOR_EXCEPTION(
true, UpdateFailedException
,"Error, the factorization of Q which should be s.p.d. failed with"
" the error message: {" << fe.what() << "}";
);
}
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 );
}
