void LinAlgOpPack::Mp_StM(
DMatrixSlice* C, value_type a
,const MatrixOp& B, BLAS_Cpp::Transp B_trans
)
{
using AbstractLinAlgPack::VectorSpace;
using AbstractLinAlgPack::VectorDenseEncap;
using AbstractLinAlgPack::MatrixOpGetGMS;
using AbstractLinAlgPack::MatrixDenseEncap;
const MatrixOpGetGMS
*B_get_gms = dynamic_cast<const MatrixOpGetGMS*>(&B);
if(B_get_gms) {
DenseLinAlgPack::Mp_StM( C, a, MatrixDenseEncap(*B_get_gms)(), B_trans );
}
else {
const size_type num_cols = C->cols();
VectorSpace::multi_vec_mut_ptr_t
B_mv = ( B_trans == BLAS_Cpp::no_trans
? B.space_cols() : B.space_rows()
).create_members(num_cols);
assign(B_mv.get(),B,B_trans);
for( size_type j = 1; j <= num_cols; ++j ) {
DenseLinAlgPack::Vp_StV(&C->col(j),a,VectorDenseEncap(*B_mv->col(j))());
}
}
}
bool VariableBoundsTester::check_in_bounds(
std::ostream* out, bool print_all_warnings, bool print_vectors
,const Vector& xL, const char xL_name[]
,const Vector& xU, const char xU_name[]
,const Vector& x, const char x_name[]
)
{
using AbstractLinAlgPack::max_near_feas_step;
if(out)
*out
<< "\n*** Checking that variables are in bounds\n";
VectorSpace::vec_mut_ptr_t zero = x.space().create_member(0.0);
std::pair<value_type,value_type>
u = max_near_feas_step( x, *zero, xL, xU, warning_tol() );
if(u.first < 0.0) {
if(out)
*out << "\nWarning! the variables " << xL_name << " <= " << x_name << " <= " << xU_name
<< " are out of bounds by more than warning_tol = " << warning_tol() << "\n";
u = max_near_feas_step( x, *zero, xL, xU, error_tol() );
if(u.first < 0.0) {
if(out)
*out << "\nError! the variables " << xL_name << " <= " << x_name << " <= " << xU_name
<< " are out of bounds by more than error_tol = " << error_tol() << "\n";
return false;
}
}
return true;
}
void LinAlgOpPack::Vp_StPtMtV(
DVectorSlice* y, value_type a
,const GenPermMatrixSlice& P, BLAS_Cpp::Transp P_trans
,const MatrixOp& M, BLAS_Cpp::Transp M_trans
,const DVectorSlice& x, value_type b
)
{
namespace mmp = MemMngPack;
using BLAS_Cpp::no_trans;
using AbstractLinAlgPack::VectorMutableDense;
using AbstractLinAlgPack::VectorDenseMutableEncap;
using AbstractLinAlgPack::Vp_StPtMtV;
VectorSpace::space_ptr_t
ay_space = ( M_trans == no_trans ? M.space_cols() : M.space_rows() ).space(P,P_trans);
VectorSpace::vec_mut_ptr_t
ay = ( ay_space.get()
? ay_space->create_member()
: Teuchos::rcp_implicit_cast<VectorMutable>(
Teuchos::rcp(new VectorMutableDense(BLAS_Cpp::rows(P.rows(),P.cols(),P_trans)))
) ),
ax = ( M_trans == no_trans ? M.space_rows() : M.space_cols() ).create_member();
(VectorDenseMutableEncap(*ay))() = *y;
(VectorDenseMutableEncap(*ax))() = x;
Vp_StPtMtV( ay.get(), a, P, P_trans, M, M_trans, *ax, b );
*y = VectorDenseMutableEncap(*ay)();
}
bool MultiVectorMutableCols::syrk(
BLAS_Cpp::Transp M_trans, value_type alpha
, value_type beta, MatrixSymOp* sym_lhs ) const
{
using LinAlgOpPack::dot;
MatrixSymOpGetGMSSymMutable
*symwo_gms_lhs = dynamic_cast<MatrixSymOpGetGMSSymMutable*>(sym_lhs);
if(!symwo_gms_lhs) {
return MatrixOp::syrk(M_trans,alpha,beta,sym_lhs); // Boot it
}
MatrixDenseSymMutableEncap DMatrixSliceSym(symwo_gms_lhs);
const int num_vecs = this->col_vecs_.size();
TEST_FOR_EXCEPTION(
num_vecs != DMatrixSliceSym().rows(), std::logic_error
,"MultiVectorMutableCols::syrk(...) : Error, sizes do not match up!" );
// Fill the upper or lower triangular region.
if( DMatrixSliceSym().uplo() == BLAS_Cpp::upper ) {
for( int i = 1; i <= num_vecs; ++i ) {
for( int j = i; j <= num_vecs; ++j ) { // Upper triangle!
DMatrixSliceSym().gms()(i,j) = beta * DMatrixSliceSym().gms()(i,j) + alpha * dot(*col_vecs_[i-1],*col_vecs_[j-1]);
}
}
}
else {
for( int i = 1; i <= num_vecs; ++i ) {
for( int j = 1; j <= i; ++j ) { // Lower triangle!
DMatrixSliceSym().gms()(i,j) = beta * DMatrixSliceSym().gms()(i,j) + alpha * dot(*col_vecs_[i-1],*col_vecs_[j-1]);
}
}
}
return true;
}
void LinAlgOpPack::Vp_StMtV(
DVectorSlice* y, value_type a, const MatrixOp& M
,BLAS_Cpp::Transp M_trans, const SpVectorSlice& x, value_type b
)
{
using BLAS_Cpp::no_trans;
using AbstractLinAlgPack::VectorDenseMutableEncap;
VectorSpace::vec_mut_ptr_t
ay = ( M_trans == no_trans ? M.space_cols() : M.space_rows() ).create_member();
(VectorDenseMutableEncap(*ay))() = *y;
AbstractLinAlgPack::Vp_StMtV( ay.get(), a, M, M_trans, x, b );
*y = VectorDenseMutableEncap(*ay)();
}
void LinAlgOpPack::V_InvMtV(
DVector* y, const MatrixOpNonsing& M
,BLAS_Cpp::Transp M_trans, const DVectorSlice& x
)
{
using BLAS_Cpp::trans;
using AbstractLinAlgPack::VectorDenseMutableEncap;
VectorSpace::vec_mut_ptr_t
ay = ( M_trans == trans ? M.space_cols() : M.space_rows() ).create_member(),
ax = ( M_trans == trans ? M.space_rows() : M.space_cols() ).create_member();
(VectorDenseMutableEncap(*ax))() = x;
AbstractLinAlgPack::V_InvMtV( ay.get(), M, M_trans, *ax );
*y = VectorDenseMutableEncap(*ay)();
}
value_type MeritFuncCalc1DQuadratic::operator()(value_type alpha) const
{
using AbstractLinAlgPack::Vp_StV;
*x_ = *d_[0];
value_type alpha_i = alpha;
for( size_type i = 1; i <= p_; ++i, alpha_i *= alpha ) {
Vp_StV( x_, alpha_i, *d_[i] );
}
return phi_( *x_ );
}
void ExampleNLPObjGrad::imp_calc_f(const Vector& x, bool newx
, const ZeroOrderInfo& zero_order_info) const
{
using AbstractLinAlgPack::dot;
assert_is_initialized();
f(); // assert f is set
TEUCHOS_TEST_FOR_EXCEPTION( n() != x.dim(), std::length_error, "ExampleNLPObjGrad::imp_calc_f(...)" );
// f(x) = (obj_scale/2) * sum( x(i)^2, for i = 1..n )
*zero_order_info.f = obj_scale_ / 2.0 * dot(x,x);
}
void MatrixHessianRelaxed::Vp_StMtV(
DVectorSlice* y, value_type a, BLAS_Cpp::Transp M_trans
, const SpVectorSlice& x, value_type b ) const
{
using BLAS_Cpp::no_trans;
using BLAS_Cpp::trans;
using AbstractLinAlgPack::Vp_StMtV;
//
// y = b*y + a * M * x
//
// = b*y + a * [ H 0 ] * [ x1 ]
// [ 0 bigM ] [ x2 ]
//
// =>
//
// y1 = b*y1 + a*H*x1
//
// y2 = b*y2 + bigM * x2
//
LinAlgOpPack::Vp_MtV_assert_sizes(y->size(),rows(),cols(),M_trans,x.size());
DVectorSlice
y1 = (*y)(1,n_);
value_type
&y2 = (*y)(n_+1);
const SpVectorSlice
x1 = x(1,n_);
const SpVectorSlice::element_type
*x2_ele = x.lookup_element(n_+1);
const value_type
x2 = x2_ele ? x2_ele->value() : 0.0;
// y1 = b*y1 + a*H*x1
Vp_StMtV( &y1, a, *H_, no_trans, x1, b );
// y2 = b*y2 + bigM * x2
if( b == 0.0 )
y2 = bigM_ * x2;
else
y2 = b*y2 + bigM_ * x2;
}
void MultiVectorMutableCols::Vp_StMtV(
VectorMutable* y, value_type a, BLAS_Cpp::Transp M_trans
,const SpVectorSlice& x, value_type b
) const
{
using AbstractLinAlgPack::dot;
// y = b*y
LinAlgOpPack::Vt_S(y,b);
if( M_trans == BLAS_Cpp::no_trans ) {
//
// y += a*M*x
//
// =>
//
// y += a * x(1) * M(:,1) + a * x(2) * M(:,2) + ...
//
SpVectorSlice::difference_type o = x.offset();
for( SpVectorSlice::const_iterator itr = x.begin(); itr != x.end(); ++itr ) {
const size_type j = itr->index() + o;
LinAlgOpPack::Vp_StV( y, a * itr->value(), *col_vecs_[j-1] );
}
}
else {
//
// y += a*M'*x
//
// =>
//
// y(1) += a M(:,1)*x
// y(2) += a M(:,2)*x
// ...
//
for( size_type j = 1; j <= col_vecs_.size(); ++j )
y->set_ele(
j
,y->get_ele(j) + a * dot(*col_vecs_[j-1],x)
);
}
}
void MultiVectorMutableCols::Vp_StMtV(
VectorMutable* y, value_type a, BLAS_Cpp::Transp M_trans
,const Vector& x, value_type b
) const
{
using AbstractLinAlgPack::dot;
// y = b*y
LinAlgOpPack::Vt_S(y,b);
if( M_trans == BLAS_Cpp::no_trans ) {
//
// y += a*M*x
//
// =>
//
// y += a * x(1) * M(:,1) + a * x(2) * M(:,2) + ...
//
for( size_type j = 1; j <= col_vecs_.size(); ++j )
LinAlgOpPack::Vp_StV( y, a * x.get_ele(j), *col_vecs_[j-1] );
}
else {
//
// y += a*M'*x
//
// =>
//
// y(1) += a M(:,1)*x
// y(2) += a M(:,2)*x
// ...
//
for( size_type j = 1; j <= col_vecs_.size(); ++j )
y->set_ele(
j
,y->get_ele(j) + a * dot(*col_vecs_[j-1],x)
);
}
}
bool ReducedHessianExactStd_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
, poss_type assoc_step_poss)
{
using Teuchos::dyn_cast;
using DenseLinAlgPack::nonconst_sym;
using AbstractLinAlgPack::Mp_StMtMtM;
typedef AbstractLinAlgPack::MatrixSymDenseInitialize MatrixSymDenseInitialize;
typedef AbstractLinAlgPack::MatrixSymOp MatrixSymOp;
using ConstrainedOptPack::NLPSecondOrder;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLPSecondOrder
#ifdef _WINDOWS
&nlp = dynamic_cast<NLPSecondOrder&>(algo.nlp());
#else
&nlp = dyn_cast<NLPSecondOrder>(algo.nlp());
#endif
MatrixSymOp
*HL_sym_op = dynamic_cast<MatrixSymOp*>(&s.HL().get_k(0));
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 );
}
// problem size
size_type n = nlp.n(),
r = nlp.r(),
nind = n - r;
// Compute HL first (You may want to move this into its own step later?)
if( !s.lambda().updated_k(-1) ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "Initializing lambda_km1 = nlp.get_lambda_init ... \n";
}
nlp.get_init_lagrange_mult( &s.lambda().set_k(-1).v(), NULL );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "||lambda_km1||inf = " << s.lambda().get_k(-1).norm_inf() << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "lambda_km1 = \n" << s.lambda().get_k(-1)();
}
}
nlp.set_HL( HL_sym_op );
nlp.calc_HL( s.x().get_k(0)(), s.lambda().get_k(-1)(), false );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ITERATION_QUANTITIES) ) {
s.HL().get_k(0).output( out << "\nHL_k = \n" );
}
// If rHL has already been updated for this iteration then just leave it.
if( !s.rHL().updated_k(0) ) {
if( !HL_sym_op ) {
std::ostringstream omsg;
omsg
<< "ReducedHessianExactStd_Step::do_step(...) : Error, "
<< "The matrix HL with the concrete type "
<< typeName(s.HL().get_k(0)) << " does not support the "
<< "MatrixSymOp iterface";
throw std::logic_error( omsg.str() );
}
MatrixSymDenseInitialize
*rHL_sym_init = dynamic_cast<MatrixSymDenseInitialize*>(&s.rHL().set_k(0));
if( !rHL_sym_init ) {
std::ostringstream omsg;
omsg
<< "ReducedHessianExactStd_Step::do_step(...) : Error, "
<< "The matrix rHL with the concrete type "
<< typeName(s.rHL().get_k(0)) << " does not support the "
<< "MatrixSymDenseInitialize iterface";
throw std::logic_error( omsg.str() );
}
// Compute the dense reduced Hessian
DMatrix rHL_sym_store(nind,nind);
DMatrixSliceSym rHL_sym(rHL_sym_store(),BLAS_Cpp::lower);
Mp_StMtMtM( &rHL_sym, 1.0, MatrixSymOp::DUMMY_ARG, *HL_sym_op
, s.Z().get_k(0), BLAS_Cpp::no_trans, 0.0 );
if( (int)olevel >= (int)PRINT_ITERATION_QUANTITIES ) {
out << "\nLower triangular partion of dense reduced Hessian (ignore nonzeros above diagonal):\nrHL_dense = \n" << rHL_sym_store();
}
// Set the reduced Hessain
rHL_sym_init->initialize( rHL_sym );
if( (int)olevel >= (int)PRINT_ITERATION_QUANTITIES ) {
s.rHL().get_k(0).output( out << "\nrHL_k = \n" );
}
}
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;
}
bool NLPDirectTester::finite_diff_check(
NLPDirect *nlp
,const Vector &xo
,const Vector *xl
,const Vector *xu
,const Vector *c
,const Vector *Gf
,const Vector *py
,const Vector *rGf
,const MatrixOp *GcU
,const MatrixOp *D
,const MatrixOp *Uz
,bool print_all_warnings
,std::ostream *out
) const
{
using std::setw;
using std::endl;
using std::right;
using AbstractLinAlgPack::sum;
using AbstractLinAlgPack::dot;
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::random_vector;
using AbstractLinAlgPack::assert_print_nan_inf;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::Vp_MtV;
using LinAlgOpPack::M_StM;
using LinAlgOpPack::M_StMtM;
typedef VectorSpace::vec_mut_ptr_t vec_mut_ptr_t;
// using AbstractLinAlgPack::TestingPack::CompareDenseVectors;
// using AbstractLinAlgPack::TestingPack::CompareDenseSparseMatrices;
using TestingHelperPack::update_success;
bool success = true, preformed_fd;
if(out) {
*out << std::boolalpha
<< std::endl
<< "*********************************************************\n"
<< "*** NLPDirectTester::finite_diff_check(...) ***\n"
<< "*********************************************************\n";
}
const Range1D
var_dep = nlp->var_dep(),
var_indep = nlp->var_indep(),
con_decomp = nlp->con_decomp(),
con_undecomp = nlp->con_undecomp();
NLP::vec_space_ptr_t
space_x = nlp->space_x(),
space_c = nlp->space_c();
// //////////////////////////////////////////////
// Validate the input
TEST_FOR_EXCEPTION(
py && !c, std::invalid_argument
,"NLPDirectTester::finite_diff_check(...) : "
"Error, if py!=NULL then c!=NULL must also be true!" );
const CalcFiniteDiffProd
&fd_deriv_prod = this->calc_fd_prod();
const value_type
rand_y_l = -1.0, rand_y_u = 1.0,
small_num = ::sqrt(std::numeric_limits<value_type>::epsilon());
try {
// ///////////////////////////////////////////////
// (1) Check Gf
if(Gf) {
switch( Gf_testing_method() ) {
case FD_COMPUTE_ALL: {
// Compute FDGf outright
TEST_FOR_EXCEPT(true); // ToDo: update above!
break;
}
case FD_DIRECTIONAL: {
// Compute FDGF'*y using random y's
if(out)
*out
<< "\nComparing products Gf'*y with finite difference values FDGf'*y for "
<< "random y's ...\n";
vec_mut_ptr_t y = space_x->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
value_type
Gf_y = dot( *Gf, *y ),
FDGf_y;
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*y,NULL,NULL,true,nlp,&FDGf_y,NULL,out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
assert_print_nan_inf(FDGf_y, "FDGf'*y",true,out);
const value_type
calc_err = ::fabs( ( Gf_y - FDGf_y )/( ::fabs(Gf_y) + ::fabs(FDGf_y) + small_num ) );
if( calc_err >= Gf_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if(out)
*out
<< "\nrel_err(Gf'*y,FDGf'*y) = "
<< "rel_err(" << Gf_y << "," << FDGf_y << ") = "
<< calc_err << endl;
if( calc_err >= Gf_error_tol() ) {
if(out) {
*out
<< "Error, above relative error exceeded Gf_error_tol = " << Gf_error_tol() << endl;
if(dump_all()) {
*out << "\ny =\n" << *y;
}
}
}
}
if(out && num_warning_viol)
*out
<< "\nThere were " << num_warning_viol << " warning tolerance "
<< "violations out of num_fd_directions = " << num_fd_directions()
<< " computations of FDGf'*y\n"
<< "and the maximum violation was " << max_warning_viol
<< " > Gf_waring_tol = " << Gf_warning_tol() << endl;
break;
}
default:
TEST_FOR_EXCEPT(true); // Invalid value
}
}
// /////////////////////////////////////////////
// (2) Check py = -inv(C)*c
//
// We want to check;
//
// FDC * (inv(C)*c) \approx c
// \_________/
// -py
//
// We can compute this as:
//
// FDC * py = [ FDC, FDN ] * [ -py ; 0 ]
// \__________/
// FDA'
//
// t1 = [ -py ; 0 ]
//
// t2 = FDA'*t1
//
// Compare t2 \approx c
//
if(py) {
if(out)
*out
<< "\nComparing c with finite difference product FDA'*[ -py; 0 ] = -FDC*py ...\n";
// t1 = [ -py ; 0 ]
VectorSpace::vec_mut_ptr_t
t1 = space_x->create_member();
V_StV( t1->sub_view(var_dep).get(), -1.0, *py );
*t1->sub_view(var_indep) = 0.0;
// t2 = FDA'*t1
VectorSpace::vec_mut_ptr_t
t2 = nlp->space_c()->create_member();
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t2.get(),out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
const value_type
sum_c = sum(*c),
sum_t2 = sum(*t2);
assert_print_nan_inf(sum_t2, "sum(-FDC*py)",true,out);
const value_type
calc_err = ::fabs( ( sum_c - sum_t2 )/( ::fabs(sum_c) + ::fabs(sum_t2) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(c),sum(-FDC*py)) = "
<< "rel_err(" << sum_c << "," << sum_t2 << ") = "
<< calc_err << endl;
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\nt1 = [ -py; 0 ] =\n" << *t1
<< "\nt2 = FDA'*t1 = -FDC*py =\n" << *t2;
update_success( false, &success );
}
if( calc_err >= Gc_warning_tol() ) {
if(out)
*out
<< "\nWarning, above relative error exceeded Gc_warning_tol = " << Gc_warning_tol() << endl;
}
}
// /////////////////////////////////////////////
// (3) Check D = -inv(C)*N
if(D) {
switch( Gc_testing_method() ) {
case FD_COMPUTE_ALL: {
//
// Compute FDN outright and check
// -FDC * D \aprox FDN
//
// We want to compute:
//
// FDC * -D = [ FDC, FDN ] * [ -D; 0 ]
// \__________/
// FDA'
//
// To compute the above we perform:
//
// T = FDA' * [ -D; 0 ] (one column at a time)
//
// Compare T \approx FDN
//
/*
// FDN
DMatrix FDN(m,n-m);
fd_deriv_computer.calc_deriv( xo, xl, xu
, Range1D(m+1,n), nlp, NULL
, &FDN() ,BLAS_Cpp::trans, out );
// T = FDA' * [ -D; 0 ] (one column at a time)
DMatrix T(m,n-m);
DVector t(n);
t(m+1,n) = 0.0;
for( int s = 1; s <= n-m; ++s ) {
// t = [ -D(:,s); 0 ]
V_StV( &t(1,m), -1.0, D->col(s) );
// T(:,s) = FDA' * t
fd_deriv_prod.calc_deriv_product(
xo,xl,xu,t(),NULL,NULL,nlp,NULL,&T.col(s),out);
}
// Compare T \approx FDN
if(out)
*out
<< "\nChecking the computed D = -inv(C)*N\n"
<< "where D(i,j) = (-FDC*D)(i,j), dM(i,j) = FDN(i,j) ...\n";
result = comp_M.comp(
T(), FDN, BLAS_Cpp::no_trans
, CompareDenseSparseMatrices::FULL_MATRIX
, CompareDenseSparseMatrices::REL_ERR_BY_COL
, Gc_warning_tol(), Gc_error_tol()
, print_all_warnings, out );
update_success( result, &success );
if(!result) return false;
*/
TEST_FOR_EXCEPT(true); // Todo: Implement above!
break;
}
case FD_DIRECTIONAL: {
//
// Compute -FDC * D * v \aprox FDN * v
// for random v's
//
// We will compute this as:
//
// t1 = [ 0; y ] <: R^(n)
//
// t2 = FDA' * t1 ( FDN * y ) <: R^(m)
//
// t1 = [ -D * y ; 0 ] <: R^(n)
//
// t3 = FDA' * t1 ( -FDC * D * y ) <: R^(m)
//
// Compare t2 \approx t3
//
if(out)
*out
<< "\nComparing finite difference products -FDC*D*y with FDN*y for "
"random vectors y ...\n";
VectorSpace::vec_mut_ptr_t
y = space_x->sub_space(var_indep)->create_member(),
t1 = space_x->create_member(),
t2 = space_c->create_member(),
t3 = space_c->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
// t1 = [ 0; y ] <: R^(n)
*t1->sub_view(var_dep) = 0.0;
*t1->sub_view(var_indep) = *y;
// t2 = FDA' * t1 ( FDN * y ) <: R^(m)
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t2.get(),out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
// t1 = [ -D * y ; 0 ] <: R^(n)
V_StMtV( t1->sub_view(var_dep).get(), -1.0, *D, BLAS_Cpp::no_trans, *y );
*t1->sub_view(var_indep) = 0.0;
// t3 = FDA' * t1 ( -FDC * D * y ) <: R^(m)
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t3.get(),out,dump_all(),dump_all()
);
// Compare t2 \approx t3
const value_type
sum_t2 = sum(*t2),
sum_t3 = sum(*t3);
const value_type
calc_err = ::fabs( ( sum_t2 - sum_t3 )/( ::fabs(sum_t2) + ::fabs(sum_t3) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(-FDC*D*y),sum(FDN*y)) = "
<< "rel_err(" << sum_t3 << "," << sum_t2 << ") = "
<< calc_err << endl;
if( calc_err >= Gc_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl
<< "Stoping the tests!\n";
if(print_all_warnings)
*out << "\ny =\n" << *y
<< "\nt1 = [ -D*y; 0 ] =\n" << *t1
<< "\nt2 = FDA' * [ 0; y ] = FDN * y =\n" << *t2
<< "\nt3 = FDA' * t1 = -FDC * D * y =\n" << *t3;
update_success( false, &success );
}
}
if(out && num_warning_viol)
*out
<< "\nThere were " << num_warning_viol << " warning tolerance "
<< "violations out of num_fd_directions = " << num_fd_directions()
<< " computations of sum(FDC*D*y) and sum(FDN*y)\n"
<< "and the maximum relative iolation was " << max_warning_viol
<< " > Gc_waring_tol = " << Gc_warning_tol() << endl;
break;
}
default:
TEST_FOR_EXCEPT(true);
}
}
// ///////////////////////////////////////////////
// (4) Check rGf = Gf(var_indep) + D'*Gf(var_dep)
if(rGf) {
if( Gf && D ) {
if(out)
*out
<< "\nComparing rGf_tmp = Gf(var_indep) - D'*Gf(var_dep) with rGf ...\n";
VectorSpace::vec_mut_ptr_t
rGf_tmp = space_x->sub_space(var_indep)->create_member();
*rGf_tmp = *Gf->sub_view(var_indep);
Vp_MtV( rGf_tmp.get(), *D, BLAS_Cpp::trans, *Gf->sub_view(var_dep) );
const value_type
sum_rGf_tmp = sum(*rGf_tmp),
sum_rGf = sum(*rGf);
const value_type
calc_err = ::fabs( ( sum_rGf_tmp - sum_rGf )/( ::fabs(sum_rGf_tmp) + ::fabs(sum_rGf) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(rGf_tmp),sum(rGf)) = "
<< "rel_err(" << sum_rGf_tmp << "," << sum_rGf << ") = "
<< calc_err << endl;
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\nrGf_tmp =\n" << *rGf_tmp
<< "\nrGf =\n" << *rGf;
update_success( false, &success );
}
if( calc_err >= Gc_warning_tol() ) {
if(out)
*out
<< "\nWarning, above relative error exceeded Gc_warning_tol = "
<< Gc_warning_tol() << endl;
}
}
else if( D ) {
if(out)
*out
<< "\nComparing rGf'*y with the finite difference product"
<< " fd_prod(f,[D*y;y]) for random vectors y ...\n";
VectorSpace::vec_mut_ptr_t
y = space_x->sub_space(var_indep)->create_member(),
t = space_x->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
// t = [ D*y; y ]
LinAlgOpPack::V_MtV(&*t->sub_view(var_dep),*D,BLAS_Cpp::no_trans,*y);
*t->sub_view(var_indep) = *y;
value_type fd_rGf_y = 0.0;
// fd_Gf_y
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t,NULL,NULL,true,nlp,&fd_rGf_y,NULL,out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
if(out) *out << "fd_prod(f,[D*y;y]) = " << fd_rGf_y << "\n";
// rGf_y = rGf'*y
const value_type rGf_y = dot(*rGf,*y);
if(out) *out << "rGf'*y = " << rGf_y << "\n";
// Compare fd_rGf_y and rGf*y
const value_type
calc_err = ::fabs( ( rGf_y - fd_rGf_y )/( ::fabs(rGf_y) + ::fabs(fd_rGf_y) + small_num ) );
if( calc_err >= Gc_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if(out)
*out
<< "\nrel_err(rGf'*y,fd_prod(f,[D*y;y])) = "
<< "rel_err(" << fd_rGf_y << "," << rGf_y << ") = "
<< calc_err << endl;
if( calc_err >= Gf_error_tol() ) {
if(out)
*out << "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\ny =\n" << *y
<< "\nt = [ D*y; y ] =\n" << *t;
update_success( false, &success );
}
}
}
else {
TEST_FOR_EXCEPT(true); // ToDo: Test rGf without D? (This is not going to be easy!)
}
}
// ///////////////////////////////////////////////////
// (5) Check GcU, and/or Uz (for undecomposed equalities)
if(GcU || Uz) {
TEST_FOR_EXCEPT(true); // ToDo: Implement!
}
FD_NOT_PREFORMED:
if(!preformed_fd) {
if(out)
*out
<< "\nError, the finite difference computation was not preformed due to cramped bounds\n"
<< "Finite difference test failed!\n" << endl;
return false;
}
} // end try
catch( const AbstractLinAlgPack::NaNInfException& except ) {
if(out)
*out
<< "Error, found a NaN or Inf. Stoping tests\n";
success = false;
}
if( out ) {
if( success )
*out
<< "\nCongradulations, all the finite difference errors where within the\n"
"specified error tolerances!\n";
else
*out
<< "\nOh no, at least one of the above finite difference tests failed!\n";
}
return success;
}
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;
}
}
bool LineSearchFullStep_Step::do_step(Algorithm& _algo
, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss)
{
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::assert_print_nan_inf;
using LinAlgOpPack::V_VpV;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLP &nlp = algo.nlp();
const size_type
m = nlp.m();
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 );
}
// alpha_k = 1.0
IterQuantityAccess<value_type>
&alpha_iq = s.alpha();
if( !alpha_iq.updated_k(0) )
alpha_iq.set_k(0) = 1.0;
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nf_k = " << s.f().get_k(0);
if(m)
out << "\n||c_k||inf = " << s.c().get_k(0).norm_inf();
out << "\nalpha_k = " << alpha_iq.get_k(0) << std::endl;
}
// x_kp1 = x_k + d_k
IterQuantityAccess<VectorMutable> &x_iq = s.x();
const Vector &x_k = x_iq.get_k(0);
VectorMutable &x_kp1 = x_iq.set_k(+1);
x_kp1 = x_k;
Vp_StV( &x_kp1, alpha_iq.get_k(0), s.d().get_k(0) );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||x_kp1||inf = " << s.x().get_k(+1).norm_inf() << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nx_kp1 =\n" << s.x().get_k(+1);
}
if(algo.algo_cntr().check_results()) {
assert_print_nan_inf(
x_kp1, "x_kp1",true
,int(olevel) >= int(PRINT_ALGORITHM_STEPS) ? &out : NULL
);
if( nlp.num_bounded_x() ) {
if(!bounds_tester().check_in_bounds(
int(olevel) >= int(PRINT_ALGORITHM_STEPS) ? &out : NULL
, int(olevel) >= int(PRINT_VECTORS) // print_all_warnings
, int(olevel) >= int(PRINT_ITERATION_QUANTITIES) // print_vectors
, nlp.xl(), "xl"
, nlp.xu(), "xu"
, x_kp1, "x_kp1"
))
{
TEST_FOR_EXCEPTION(
true, TestFailed
,"LineSearchFullStep_Step::do_step(...) : Error, "
"the variables bounds xl <= x_k(+1) <= xu where violated!" );
}
}
}
// Calcuate f and c at the new point.
nlp.unset_quantities();
nlp.set_f( &s.f().set_k(+1) );
if(m) nlp.set_c( &s.c().set_k(+1) );
nlp.calc_f(x_kp1);
if(m) nlp.calc_c( x_kp1, false );
nlp.unset_quantities();
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nf_kp1 = " << s.f().get_k(+1);
if(m)
out << "\n||c_kp1||inf = " << s.c().get_k(+1).norm_inf();
out << std::endl;
}
if( m && static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nc_kp1 =\n" << s.c().get_k(+1);
}
if(algo.algo_cntr().check_results()) {
assert_print_nan_inf( s.f().get_k(+1), "f(x_kp1)", true, &out );
if(m)
assert_print_nan_inf( s.c().get_k(+1), "c(x_kp1)", true, &out );
}
return true;
}
void ExampleNLPFirstOrder::imp_calc_Gc(
const Vector& x, bool newx, const FirstOrderInfo& first_order_info) const
{
namespace rcp = MemMngPack;
using Teuchos::dyn_cast;
using AbstractLinAlgPack::Vp_S; // Should not have to do this!
const index_type
n = this->n(),
m = this->m();
const Range1D
var_dep = this->var_dep(),
var_indep = this->var_indep();
// Get references to aggregate C and N matrices (if allocated)
MatrixOpNonsing
*C_aggr = NULL;
MatrixOp
*N_aggr = NULL;
BasisSystemComposite::get_C_N(
first_order_info.Gc, &C_aggr, &N_aggr ); // Will return NULLs if Gc is not initialized
// Allocate C and N matrix objects if not done yet!
Teuchos::RCP<MatrixOpNonsing>
C_ptr = Teuchos::null;
Teuchos::RCP<MatrixOp>
N_ptr = Teuchos::null;
if( C_aggr == NULL ) {
const VectorSpace::space_ptr_t
space_x = this->space_x(),
space_xD = space_x->sub_space(var_dep);
C_ptr = Teuchos::rcp(new MatrixSymDiagStd(space_xD->create_member()));
N_ptr = Teuchos::rcp(new MatrixSymDiagStd(space_xD->create_member()));
C_aggr = C_ptr.get();
N_aggr = N_ptr.get();
}
// Get references to concreate C and N matrices
MatrixSymDiagStd
&C = dyn_cast<MatrixSymDiagStd>(*C_aggr);
MatrixSymDiagStd
&N = dyn_cast<MatrixSymDiagStd>(*N_aggr);
// Get x = [ x_D' x_I ]
Vector::vec_ptr_t
x_D = x.sub_view(var_dep),
x_I = x.sub_view(var_indep);
// Set the diagonals of C and N (this is the only computation going on here)
C.diag() = *x_I; // C.diag = x_I - 1.0
Vp_S( &C.diag(), -1.0 ); // ...
N.diag() = *x_D; // N.diag = x_D - 10.0
Vp_S( &N.diag(), -10.0 ); // ...
// Initialize the matrix object Gc if not done so yet
if( C_ptr.get() != NULL ) {
BasisSystemComposite::initialize_Gc(
this->space_x(), var_dep, var_indep
,this->space_c()
,C_ptr, N_ptr
,first_order_info.Gc
);
}
}
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();
}
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 PreEvalNewPointBarrier_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using Teuchos::dyn_cast;
using IterationPack::print_algorithm_step;
using AbstractLinAlgPack::force_in_bounds_buffer;
NLPAlgo &algo = dyn_cast<NLPAlgo>(_algo);
IpState &s = dyn_cast<IpState>(_algo.state());
NLP &nlp = algo.nlp();
NLPFirstOrder *nlp_foi = dynamic_cast<NLPFirstOrder*>(&nlp);
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
if(!nlp.is_initialized())
nlp.initialize(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 );
}
IterQuantityAccess<value_type> &barrier_parameter_iq = s.barrier_parameter();
IterQuantityAccess<VectorMutable> &x_iq = s.x();
if( x_iq.last_updated() == IterQuantity::NONE_UPDATED )
{
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) )
{
out << "\nInitialize x with x_k = nlp.xinit() ...\n"
<< " and push x_k within bounds.\n";
}
VectorMutable& x_k = x_iq.set_k(0) = nlp.xinit();
// apply transformation operator to push x sufficiently within bounds
force_in_bounds_buffer(relative_bound_push_,
absolute_bound_push_,
nlp.xl(),
nlp.xu(),
&x_k);
// evaluate the func and constraints
IterQuantityAccess<value_type>
&f_iq = s.f();
IterQuantityAccess<VectorMutable>
&Gf_iq = s.Gf(),
*c_iq = nlp.m() > 0 ? &s.c() : NULL;
IterQuantityAccess<MatrixOp>
*Gc_iq = nlp_foi ? &s.Gc() : NULL;
using AbstractLinAlgPack::assert_print_nan_inf;
assert_print_nan_inf(x_k, "x", true, NULL); // With throw exception if Inf or NaN!
// Wipe out storage for computed iteration quantities (just in case?) : RAB: 7/29/2002
if(f_iq.updated_k(0))
f_iq.set_not_updated_k(0);
if(Gf_iq.updated_k(0))
Gf_iq.set_not_updated_k(0);
if (c_iq)
{
if(c_iq->updated_k(0))
c_iq->set_not_updated_k(0);
}
if (nlp_foi)
{
if(Gc_iq->updated_k(0))
Gc_iq->set_not_updated_k(0);
}
}
if (barrier_parameter_iq.last_updated() == IterQuantity::NONE_UPDATED)
{
barrier_parameter_iq.set_k(-1) = 0.1; // RAB: 7/29/2002: This should be parameterized! (allow user to set this!)
}
// Print vector information
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) )
{
out << "x_k =\n" << x_iq.get_k(0);
}
return true;
}
bool CheckConvergenceStd_Strategy::Converged(
Algorithm& _algo
)
{
using AbstractLinAlgPack::assert_print_nan_inf;
using AbstractLinAlgPack::combined_nu_comp_err;
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();
const size_type
n = nlp.n(),
m = nlp.m(),
nb = nlp.num_bounded_x();
// Get the iteration quantities
IterQuantityAccess<value_type>
&opt_kkt_err_iq = s.opt_kkt_err(),
&feas_kkt_err_iq = s.feas_kkt_err(),
&comp_kkt_err_iq = s.comp_kkt_err();
IterQuantityAccess<VectorMutable>
&x_iq = s.x(),
&d_iq = s.d(),
&Gf_iq = s.Gf(),
*c_iq = m ? &s.c() : NULL,
*rGL_iq = n > m ? &s.rGL() : NULL,
*GL_iq = n > m ? &s.GL() : NULL,
*nu_iq = n > m ? &s.nu() : NULL;
// opt_err = (||rGL||inf or ||GL||) / (||Gf|| + scale_kkt_factor)
value_type
norm_inf_Gf_k = 0.0,
norm_inf_GLrGL_k = 0.0;
if( n > m && scale_opt_error_by_Gf() && Gf_iq.updated_k(0) ) {
assert_print_nan_inf(
norm_inf_Gf_k = Gf_iq.get_k(0).norm_inf(),
"||Gf_k||inf",true,&out
);
}
// NOTE:
// The strategy object CheckConvergenceIP_Strategy assumes
// that this will always be the gradient of the lagrangian
// of the original problem, not the gradient of the lagrangian
// for psi. (don't use augmented nlp info here)
if( n > m ) {
if( opt_error_check() == OPT_ERROR_REDUCED_GRADIENT_LAGR ) {
assert_print_nan_inf( norm_inf_GLrGL_k = rGL_iq->get_k(0).norm_inf(),
"||rGL_k||inf",true,&out);
}
else {
assert_print_nan_inf( norm_inf_GLrGL_k = GL_iq->get_k(0).norm_inf(),
"||GL_k||inf",true,&out);
}
}
const value_type
opt_scale_factor = 1.0 + norm_inf_Gf_k,
opt_err = norm_inf_GLrGL_k / opt_scale_factor;
// feas_err
const value_type feas_err = ( ( m ? c_iq->get_k(0).norm_inf() : 0.0 ) );
// comp_err
value_type comp_err = 0.0;
if ( n > m ) {
if (nb > 0) {
comp_err = combined_nu_comp_err(nu_iq->get_k(0), x_iq.get_k(0), nlp.xl(), nlp.xu());
}
if(m) {
assert_print_nan_inf( feas_err,"||c_k||inf",true,&out);
}
}
// scaling factors
const value_type
scale_opt_factor = CalculateScalingFactor(s, scale_opt_error_by()),
scale_feas_factor = CalculateScalingFactor(s, scale_feas_error_by()),
scale_comp_factor = CalculateScalingFactor(s, scale_comp_error_by());
// kkt_err
const value_type
opt_kkt_err_k = opt_err/scale_opt_factor,
feas_kkt_err_k = feas_err/scale_feas_factor,
comp_kkt_err_k = comp_err/scale_comp_factor;
// update the iteration quantities
if(n > m) opt_kkt_err_iq.set_k(0) = opt_kkt_err_k;
feas_kkt_err_iq.set_k(0) = feas_kkt_err_k;
comp_kkt_err_iq.set_k(0) = comp_kkt_err_k;
// step_err
value_type step_err = 0.0;
if( d_iq.updated_k(0) ) {
step_err = AbstractLinAlgPack::max_rel_step(x_iq.get_k(0),d_iq.get_k(0));
assert_print_nan_inf( step_err,"max(d(i)/max(1,x(i)),i=1...n)",true,&out);
}
const value_type
opt_tol = algo.algo_cntr().opt_tol(),
feas_tol = algo.algo_cntr().feas_tol(),
comp_tol = algo.algo_cntr().comp_tol(),
step_tol = algo.algo_cntr().step_tol();
const bool found_solution =
opt_kkt_err_k < opt_tol
&& feas_kkt_err_k < feas_tol
&& comp_kkt_err_k < comp_tol
&& step_err < step_tol;
if( int(olevel) >= int(PRINT_ALGORITHM_STEPS) || (int(olevel) >= int(PRINT_BASIC_ALGORITHM_INFO) && found_solution) )
{
out
<< "\nscale_opt_factor = " << scale_opt_factor
<< " (scale_opt_error_by = " << (scale_opt_error_by()==SCALE_BY_ONE ? "SCALE_BY_ONE"
: (scale_opt_error_by()==SCALE_BY_NORM_INF_X ? "SCALE_BY_NORM_INF_X"
: "SCALE_BY_NORM_2_X" ) ) << ")"
<< "\nscale_feas_factor = " << scale_feas_factor
<< " (scale_feas_error_by = " << (scale_feas_error_by()==SCALE_BY_ONE ? "SCALE_BY_ONE"
: (scale_feas_error_by()==SCALE_BY_NORM_INF_X ? "SCALE_BY_NORM_INF_X"
: "SCALE_BY_NORM_2_X" ) ) << ")"
<< "\nscale_comp_factor = " << scale_comp_factor
<< " (scale_comp_error_by = " << (scale_comp_error_by()==SCALE_BY_ONE ? "SCALE_BY_ONE"
: (scale_comp_error_by()==SCALE_BY_NORM_INF_X ? "SCALE_BY_NORM_INF_X"
: "SCALE_BY_NORM_2_X" ) ) << ")"
<< "\nopt_scale_factor = " << opt_scale_factor
<< " (scale_opt_error_by_Gf = " << (scale_opt_error_by_Gf()?"true":"false") << ")"
<< "\nopt_kkt_err_k = " << opt_kkt_err_k << ( opt_kkt_err_k < opt_tol ? " < " : " > " )
<< "opt_tol = " << opt_tol
<< "\nfeas_kkt_err_k = " << feas_kkt_err_k << ( feas_kkt_err_k < feas_tol ? " < " : " > " )
<< "feas_tol = " << feas_tol
<< "\ncomp_kkt_err_k = " << comp_kkt_err_k << ( comp_kkt_err_k < comp_tol ? " < " : " > " )
<< "comp_tol = " << comp_tol
<< "\nstep_err = " << step_err << ( step_err < step_tol ? " < " : " > " )
<< "step_tol = " << step_tol
<< std::endl;
}
return found_solution;
}
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 );
}
bool CheckConvergenceIP_Strategy::Converged(
Algorithm& _algo
)
{
using Teuchos::dyn_cast;
using AbstractLinAlgPack::num_bounded;
using AbstractLinAlgPack::IP_comp_err_with_mu;
// Calculate kkt errors and check for overall convergence
//bool found_solution = CheckConvergenceStd_Strategy::Converged(_algo);
bool found_solution = false;
// Recalculate the complementarity error including mu
// Get the iteration quantities
IpState &s = dyn_cast<IpState>(*_algo.get_state());
NLPAlgo& algo = rsqp_algo(_algo);
NLP& nlp = algo.nlp();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
// Get necessary iteration quantities
const value_type &mu_km1 = s.barrier_parameter().get_k(-1);
const Vector& x_k = s.x().get_k(0);
const VectorMutable& Gf_k = s.Gf().get_k(0);
const Vector& rGL_k = s.rGL().get_k(0);
const Vector& c_k = s.c().get_k(0);
const Vector& vl_k = s.Vl().get_k(0).diag();
const Vector& vu_k = s.Vu().get_k(0).diag();
// Calculate the errors with Andreas' scaling
value_type& opt_err = s.opt_kkt_err().set_k(0);
value_type& feas_err = s.feas_kkt_err().set_k(0);
value_type& comp_err = s.comp_kkt_err().set_k(0);
value_type& comp_err_mu = s.comp_err_mu().set_k(0);
// scaling
value_type scale_1 = 1 + x_k.norm_1()/x_k.dim();
Teuchos::RCP<VectorMutable> temp = Gf_k.clone();
temp->axpy(-1.0, vl_k);
temp->axpy(1.0, vu_k);
value_type scale_2 = temp->norm_1();
scale_2 += vl_k.norm_1() + vu_k.norm_1();
*temp = nlp.infinite_bound();
const size_type nlb = num_bounded(nlp.xl(), *temp, nlp.infinite_bound());
*temp = -nlp.infinite_bound();
const size_type nub = num_bounded(*temp, nlp.xu(), nlp.infinite_bound());
scale_2 = 1 + scale_2/(1+nlp.m()+nlb+nub);
// Calculate the opt_err
opt_err = rGL_k.norm_inf() / scale_2;
// Calculate the feas_err
feas_err = c_k.norm_inf() / scale_1;
// Calculate the comp_err
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nx =\n" << s.x().get_k(0);
out << "\nxl =\n" << nlp.xl();
out << "\nvl =\n" << s.Vl().get_k(0).diag();
out << "\nxu =\n" << nlp.xu();
out << "\nvu =\n" << s.Vu().get_k(0).diag();
}
comp_err = IP_comp_err_with_mu(
0.0, nlp.infinite_bound(), s.x().get_k(0), nlp.xl(), nlp.xu()
,s.Vl().get_k(0).diag(), s.Vu().get_k(0).diag());
comp_err_mu = IP_comp_err_with_mu(
mu_km1, nlp.infinite_bound(), s.x().get_k(0), nlp.xl(), nlp.xu()
,s.Vl().get_k(0).diag(), s.Vu().get_k(0).diag());
comp_err = comp_err / scale_2;
comp_err_mu = comp_err_mu / scale_2;
// check for convergence
const value_type opt_tol = algo.algo_cntr().opt_tol();
const value_type feas_tol = algo.algo_cntr().feas_tol();
const value_type comp_tol = algo.algo_cntr().comp_tol();
if (opt_err < opt_tol && feas_err < feas_tol && comp_err < comp_tol)
{
found_solution = true;
}
if( int(olevel) >= int(PRINT_ALGORITHM_STEPS) || (int(olevel) >= int(PRINT_BASIC_ALGORITHM_INFO) && found_solution) )
{
out
<< "\nopt_kkt_err_k = " << opt_err << ( opt_err < opt_tol ? " < " : " > " )
<< "opt_tol = " << opt_tol
<< "\nfeas_kkt_err_k = " << feas_err << ( feas_err < feas_tol ? " < " : " > " )
<< "feas_tol = " << feas_tol
<< "\ncomp_kkt_err_k = " << comp_err << ( comp_err < comp_tol ? " < " : " > " )
<< "comp_tol = " << comp_tol
<< "\ncomp_err_mu = " << comp_err_mu
<< "\nbarrier_parameter_k (mu_km1) = " << mu_km1
<< "comp_tol = " << comp_tol
<< std::endl;
}
return found_solution;
}
bool MoochoPack::CalcDFromYPYZPZ_Step::do_step(Algorithm& _algo
, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss)
{
using Teuchos::implicit_cast;
using AbstractLinAlgPack::dot;
using LinAlgOpPack::V_VpV;
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( implicit_cast<int>(olevel) >= implicit_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// d = Ypy + Zpz
VectorMutable &d_k = s.d().set_k(0);
const Vector &Ypy_k = s.Ypy().get_k(0);
const Vector &Zpz_k = s.Zpz().get_k(0);
V_VpV( &d_k, Ypy_k, Zpz_k );
Range1D
var_dep = s.var_dep(),
var_indep = s.var_indep();
if( implicit_cast<int>(olevel) >= implicit_cast<int>(PRINT_ALGORITHM_STEPS) ) {
const value_type very_small = std::numeric_limits<value_type>::min();
out
<< "\n(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)\n"
<< " = ("<<dot(Ypy_k,Zpz_k)<<")/("<<Ypy_k.norm_2()<<" * "<<Zpz_k.norm_2()<<" + "<<very_small<<")\n"
<< " = " << dot(Ypy_k,Zpz_k) / ( Ypy_k.norm_2() * Zpz_k.norm_2() + very_small ) << "\n";
/*
ConstrainedOptPack::print_vector_change_stats(
s.x().get_k(0), "x", s.d().get_k(0), "d", out );
*/
// ToDo: Replace the above with a reduction operator!
}
if( implicit_cast<int>(olevel) >= implicit_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||d_k||inf = " << d_k.norm_inf();
if( var_dep.size() )
out << "\n||d(var_dep)_k||inf = " << d_k.sub_view(var_dep)->norm_inf();
if( var_indep.size() )
out << "\n||d(var_indep)_k||inf = " << d_k.sub_view(var_indep)->norm_inf();
out << std::endl;
}
if( implicit_cast<int>(olevel) >= implicit_cast<int>(PRINT_VECTORS) ) {
out << "\nd_k = \n" << d_k;
if( var_dep.size() )
out << "\nd(var_dep)_k = \n" << *d_k.sub_view(var_dep);
}
if( implicit_cast<int>(ns_olevel) >= implicit_cast<int>(PRINT_VECTORS) ) {
if( var_indep.size() )
out << "\nd(var_indep)_k = \n" << *d_k.sub_view(var_indep);
}
return true;
}
bool EvalNewPointStd_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 AbstractLinAlgPack::assert_print_nan_inf;
using IterationPack::print_algorithm_step;
using NLPInterfacePack::NLPFirstOrder;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLPFirstOrder &nlp = dyn_cast<NLPFirstOrder>(algo.nlp());
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>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
if(!nlp.is_initialized())
nlp.initialize(algo.algo_cntr().check_results());
Teuchos::VerboseObjectTempState<NLP>
nlpOutputTempState(rcp(&nlp,false),Teuchos::getFancyOStream(rcp(&out,false)),convertToVerbLevel(olevel));
const size_type
n = nlp.n(),
nb = nlp.num_bounded_x(),
m = nlp.m();
size_type
r = 0;
// Get the iteration quantity container objects
IterQuantityAccess<value_type>
&f_iq = s.f();
IterQuantityAccess<VectorMutable>
&x_iq = s.x(),
*c_iq = m > 0 ? &s.c() : NULL,
&Gf_iq = s.Gf();
IterQuantityAccess<MatrixOp>
*Gc_iq = m > 0 ? &s.Gc() : NULL,
*Z_iq = NULL,
*Y_iq = NULL,
*Uz_iq = NULL,
*Uy_iq = NULL;
IterQuantityAccess<MatrixOpNonsing>
*R_iq = NULL;
MatrixOp::EMatNormType mat_nrm_inf = MatrixOp::MAT_NORM_INF;
const bool calc_matrix_norms = algo.algo_cntr().calc_matrix_norms();
const bool calc_matrix_info_null_space_only = algo.algo_cntr().calc_matrix_info_null_space_only();
if( x_iq.last_updated() == IterQuantity::NONE_UPDATED ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nx is not updated for any k so set x_k = nlp.xinit() ...\n";
}
x_iq.set_k(0) = nlp.xinit();
}
// Validate x
if( nb && algo.algo_cntr().check_results() ) {
assert_print_nan_inf(
x_iq.get_k(0), "x_k", true
, int(olevel) >= int(PRINT_ALGORITHM_STEPS) ? &out : NULL
);
if( nlp.num_bounded_x() > 0 ) {
if(!bounds_tester().check_in_bounds(
int(olevel) >= int(PRINT_ALGORITHM_STEPS) ? &out : NULL
,int(olevel) >= int(PRINT_VECTORS) // print_all_warnings
,int(olevel) >= int(PRINT_ITERATION_QUANTITIES) // print_vectors
,nlp.xl(), "xl"
,nlp.xu(), "xu"
,x_iq.get_k(0), "x_k"
))
{
TEUCHOS_TEST_FOR_EXCEPTION(
true, TestFailed
,"EvalNewPointStd_Step::do_step(...) : Error, "
"the variables bounds xl <= x_k <= xu where violated!" );
}
}
}
Vector &x = x_iq.get_k(0);
Range1D var_dep(Range1D::INVALID), var_indep(Range1D::INVALID);
if( s.get_decomp_sys().get() ) {
const ConstrainedOptPack::DecompositionSystemVarReduct
*decomp_sys_vr = dynamic_cast<ConstrainedOptPack::DecompositionSystemVarReduct*>(&s.decomp_sys());
if(decomp_sys_vr) {
var_dep = decomp_sys_vr->var_dep();
var_indep = decomp_sys_vr->var_indep();
}
s.var_dep(var_dep);
s.var_indep(var_indep);
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||x_k||inf = " << x.norm_inf();
if( var_dep.size() )
out << "\n||x(var_dep)_k||inf = " << x.sub_view(var_dep)->norm_inf();
if( var_indep.size() )
out << "\n||x(var_indep)_k||inf = " << x.sub_view(var_indep)->norm_inf();
out << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nx_k = \n" << x;
if( var_dep.size() )
out << "\nx(var_dep)_k = \n" << *x.sub_view(var_dep);
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
if( var_indep.size() )
out << "\nx(var_indep)_k = \n" << *x.sub_view(var_indep);
}
// Set the references to the current point's quantities to be updated
const bool f_k_updated = f_iq.updated_k(0);
const bool Gf_k_updated = Gf_iq.updated_k(0);
const bool c_k_updated = m > 0 ? c_iq->updated_k(0) : false;
const bool Gc_k_updated = m > 0 ? Gc_iq->updated_k(0) : false;
nlp.unset_quantities();
if(!f_k_updated) nlp.set_f( &f_iq.set_k(0) );
if(!Gf_k_updated) nlp.set_Gf( &Gf_iq.set_k(0) );
if( m > 0 ) {
if(!c_k_updated) nlp.set_c( &c_iq->set_k(0) );
if(!Gc_k_updated) nlp.set_Gc( &Gc_iq->set_k(0) );
}
// Calculate Gc at x_k
bool new_point = true;
if(m > 0) {
if(!Gc_k_updated) nlp.calc_Gc( x, new_point );
new_point = false;
}
//
// Update (or select a new) range/null decomposition
//
bool new_decomp_selected = false;
if( m > 0 ) {
// Update the range/null decomposition
decomp_sys_handler().update_decomposition(
algo, s, nlp, decomp_sys_testing(), decomp_sys_testing_print_level()
,&new_decomp_selected
);
r = s.equ_decomp().size();
Z_iq = ( n > m && r > 0 ) ? &s.Z() : NULL;
Y_iq = ( r > 0 ) ? &s.Y() : NULL;
Uz_iq = ( m > 0 && m > r ) ? &s.Uz() : NULL;
Uy_iq = ( m > 0 && m > r ) ? &s.Uy() : NULL;
R_iq = ( m > 0 ) ? &s.R() : NULL;
// Determine if we will test the decomp_sys or not
const DecompositionSystem::ERunTests
ds_test_what = ( ( decomp_sys_testing() == DecompositionSystemHandler_Strategy::DST_TEST
|| ( decomp_sys_testing() == DecompositionSystemHandler_Strategy::DST_DEFAULT
&& algo.algo_cntr().check_results() ) )
? DecompositionSystem::RUN_TESTS
: DecompositionSystem::NO_TESTS );
// Determine the output level for decomp_sys
DecompositionSystem::EOutputLevel ds_olevel;
switch(olevel) {
case PRINT_NOTHING:
case PRINT_BASIC_ALGORITHM_INFO:
ds_olevel = DecompositionSystem::PRINT_NONE;
break;
case PRINT_ALGORITHM_STEPS:
case PRINT_ACTIVE_SET:
ds_olevel = DecompositionSystem::PRINT_BASIC_INFO;
break;
case PRINT_VECTORS:
ds_olevel = DecompositionSystem::PRINT_VECTORS;
break;
case PRINT_ITERATION_QUANTITIES:
ds_olevel = DecompositionSystem::PRINT_EVERY_THING;
break;
default:
TEUCHOS_TEST_FOR_EXCEPT(true); // Should not get here!
};
// Test the decomposition system
if( ds_test_what == DecompositionSystem::RUN_TESTS ) {
// Set the output level
if( decomp_sys_tester().print_tests() == DecompositionSystemTester::PRINT_NOT_SELECTED ) {
DecompositionSystemTester::EPrintTestLevel ds_olevel;
switch(olevel) {
case PRINT_NOTHING:
case PRINT_BASIC_ALGORITHM_INFO:
ds_olevel = DecompositionSystemTester::PRINT_NONE;
break;
case PRINT_ALGORITHM_STEPS:
case PRINT_ACTIVE_SET:
ds_olevel = DecompositionSystemTester::PRINT_BASIC;
break;
case PRINT_VECTORS:
ds_olevel = DecompositionSystemTester::PRINT_MORE;
break;
case PRINT_ITERATION_QUANTITIES:
ds_olevel = DecompositionSystemTester::PRINT_ALL;
break;
default:
TEUCHOS_TEST_FOR_EXCEPT(true); // Should not get here!
}
decomp_sys_tester().print_tests(ds_olevel);
decomp_sys_tester().dump_all( olevel == PRINT_ITERATION_QUANTITIES );
}
// Run the tests
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nTesting the range/null decompostion ...\n";
}
const bool
decomp_sys_passed = decomp_sys_tester().test_decomp_system(
s.decomp_sys()
,Gc_iq->get_k(0) // Gc
,Z_iq ? &Z_iq->get_k(0) : NULL // Z
,&Y_iq->get_k(0) // Y
,&R_iq->get_k(0) // R
,m > r ? &Uz_iq->get_k(0) : NULL // Uz
,m > r ? &Uy_iq->get_k(0) : NULL // Uy
,( olevel >= PRINT_ALGORITHM_STEPS ) ? &out : NULL
);
TEUCHOS_TEST_FOR_EXCEPTION(
!decomp_sys_passed, TestFailed
,"EvalNewPointStd_Step::do_step(...) : Error, "
"the tests of the decomposition system failed!" );
}
}
else {
// Unconstrained problem
Z_iq = &s.Z();
dyn_cast<MatrixSymIdent>(Z_iq->set_k(0)).initialize( nlp.space_x() );
s.equ_decomp(Range1D::Invalid);
s.equ_undecomp(Range1D::Invalid);
}
// Calculate the rest of the quantities. If decomp_sys is a variable
// reduction decomposition system object, then nlp will be hip to the
// basis selection and will permute these quantities to that basis.
// Note that x will already be permuted to the current basis.
if(!Gf_k_updated) { nlp.calc_Gf( x, new_point ); new_point = false; }
if( m && (!c_k_updated || new_decomp_selected ) ) {
if(c_k_updated) nlp.set_c( &c_iq->set_k(0) ); // This was not set earlier!
nlp.calc_c( x, false);
}
if(!f_k_updated) {
nlp.calc_f( x, false);
}
nlp.unset_quantities();
// Check for NaN and Inf
assert_print_nan_inf(f_iq.get_k(0),"f_k",true,&out);
if(m)
assert_print_nan_inf(c_iq->get_k(0),"c_k",true,&out);
assert_print_nan_inf(Gf_iq.get_k(0),"Gf_k",true,&out);
// Print the iteration quantities before we test the derivatives for debugging
// Update the selection of dependent and independent variables
if( s.get_decomp_sys().get() ) {
const ConstrainedOptPack::DecompositionSystemVarReduct
*decomp_sys_vr = dynamic_cast<ConstrainedOptPack::DecompositionSystemVarReduct*>(&s.decomp_sys());
if(decomp_sys_vr) {
var_dep = decomp_sys_vr->var_dep();
var_indep = decomp_sys_vr->var_indep();
}
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nPrinting the updated iteration quantities ...\n";
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nf_k = " << f_iq.get_k(0);
out << "\n||Gf_k||inf = " << Gf_iq.get_k(0).norm_inf();
if( var_dep.size() )
out << "\n||Gf_k(var_dep)_k||inf = " << Gf_iq.get_k(0).sub_view(var_dep)->norm_inf();
if( var_indep.size() )
out << "\n||Gf_k(var_indep)_k||inf = " << Gf_iq.get_k(0).sub_view(var_indep)->norm_inf();
if(m) {
out << "\n||c_k||inf = " << c_iq->get_k(0).norm_inf();
if( calc_matrix_norms && !calc_matrix_info_null_space_only )
out << "\n||Gc_k||inf = " << Gc_iq->get_k(0).calc_norm(mat_nrm_inf).value;
if( n > r && calc_matrix_norms && !calc_matrix_info_null_space_only )
out << "\n||Z||inf = " << Z_iq->get_k(0).calc_norm(mat_nrm_inf).value;
if( r && calc_matrix_norms && !calc_matrix_info_null_space_only )
out << "\n||Y||inf = " << Y_iq->get_k(0).calc_norm(mat_nrm_inf).value;
if( r && calc_matrix_norms && !calc_matrix_info_null_space_only )
out << "\n||R||inf = " << R_iq->get_k(0).calc_norm(mat_nrm_inf).value;
if( algo.algo_cntr().calc_conditioning() && !calc_matrix_info_null_space_only ) {
out << "\ncond_inf(R) = " << R_iq->get_k(0).calc_cond_num(mat_nrm_inf).value;
}
if( m > r && calc_matrix_norms && !calc_matrix_info_null_space_only ) {
out << "\n||Uz_k||inf = " << Uz_iq->get_k(0).calc_norm(mat_nrm_inf).value;
out << "\n||Uy_k||inf = " << Uy_iq->get_k(0).calc_norm(mat_nrm_inf).value;
}
}
out << std::endl;
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ITERATION_QUANTITIES) ) {
if(m)
out << "\nGc_k =\n" << Gc_iq->get_k(0);
if( n > r )
out << "\nZ_k =\n" << Z_iq->get_k(0);
if(r) {
out << "\nY_k =\n" << Y_iq->get_k(0);
out << "\nR_k =\n" << R_iq->get_k(0);
}
if( m > r ) {
out << "\nUz_k =\n" << Uz_iq->get_k(0);
out << "\nUy_k =\n" << Uy_iq->get_k(0);
}
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nGf_k =\n" << Gf_iq.get_k(0);
if( var_dep.size() )
out << "\nGf(var_dep)_k =\n " << *Gf_iq.get_k(0).sub_view(var_dep);
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
if( var_indep.size() )
out << "\nGf(var_indep)_k =\n" << *Gf_iq.get_k(0).sub_view(var_indep);
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
if(m)
out << "\nc_k = \n" << c_iq->get_k(0);
}
// Check the derivatives if we are checking the results
if( fd_deriv_testing() == FD_TEST
|| ( fd_deriv_testing() == FD_DEFAULT && algo.algo_cntr().check_results() ) )
{
if( olevel >= PRINT_ALGORITHM_STEPS ) {
out << "\n*** Checking derivatives by finite differences\n";
}
const bool
nlp_passed = deriv_tester().finite_diff_check(
&nlp
,x
,nb ? &nlp.xl() : NULL
,nb ? &nlp.xu() : NULL
,m ? &Gc_iq->get_k(0) : NULL
,&Gf_iq.get_k(0)
,olevel >= PRINT_VECTORS
,( olevel >= PRINT_ALGORITHM_STEPS ) ? &out : NULL
);
TEUCHOS_TEST_FOR_EXCEPTION(
!nlp_passed, TestFailed
,"EvalNewPointStd_Step::do_step(...) : Error, "
"the tests of the nlp derivatives failed!" );
}
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);
}
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 PostEvalNewPointBarrier_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using Teuchos::dyn_cast;
using IterationPack::print_algorithm_step;
using AbstractLinAlgPack::inv_of_difference;
using AbstractLinAlgPack::correct_upper_bound_multipliers;
using AbstractLinAlgPack::correct_lower_bound_multipliers;
using LinAlgOpPack::Vp_StV;
NLPAlgo &algo = dyn_cast<NLPAlgo>(_algo);
IpState &s = dyn_cast<IpState>(_algo.state());
NLP &nlp = algo.nlp();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
if(!nlp.is_initialized())
nlp.initialize(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 );
}
IterQuantityAccess<VectorMutable> &x_iq = s.x();
IterQuantityAccess<MatrixSymDiagStd> &Vl_iq = s.Vl();
IterQuantityAccess<MatrixSymDiagStd> &Vu_iq = s.Vu();
///***********************************************************
// Calculate invXl = diag(1/(x-xl))
// and invXu = diag(1/(xu-x)) matrices
///***********************************************************
// get references to x, invXl, and invXu
VectorMutable& x = x_iq.get_k(0);
MatrixSymDiagStd& invXu = s.invXu().set_k(0);
MatrixSymDiagStd& invXl = s.invXl().set_k(0);
//std::cout << "xu=\n";
//nlp.xu().output(std::cout);
inv_of_difference(1.0, nlp.xu(), x, &invXu.diag());
inv_of_difference(1.0, x, nlp.xl(), &invXl.diag());
//std::cout << "invXu=\v";
//invXu.output(std::cout);
//std::cout << "\ninvXl=\v";
//invXl.output(std::cout);
// Check for divide by zeros -
using AbstractLinAlgPack::assert_print_nan_inf;
assert_print_nan_inf(invXu.diag(), "invXu", true, &out);
assert_print_nan_inf(invXl.diag(), "invXl", true, &out);
// These should never go negative either - could be a useful check
// Initialize Vu and Vl if necessary
if ( /*!Vu_iq.updated_k(0) */ Vu_iq.last_updated() == IterQuantity::NONE_UPDATED )
{
VectorMutable& vu = Vu_iq.set_k(0).diag();
vu = 0;
Vp_StV(&vu, s.barrier_parameter().get_k(-1), invXu.diag());
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) )
{
out << "\nInitialize Vu with barrier_parameter * invXu ...\n";
}
}
if ( /*!Vl_iq.updated_k(0) */ Vl_iq.last_updated() == IterQuantity::NONE_UPDATED )
{
VectorMutable& vl = Vl_iq.set_k(0).diag();
vl = 0;
Vp_StV(&vl, s.barrier_parameter().get_k(-1), invXl.diag());
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) )
{
out << "\nInitialize Vl with barrier_parameter * invXl ...\n";
}
}
if (s.num_basis().updated_k(0))
{
// Basis changed, reorder Vl and Vu
if (Vu_iq.updated_k(-1))
{ Vu_iq.set_k(0,-1); }
if (Vl_iq.updated_k(-1))
{ Vl_iq.set_k(0,-1); }
VectorMutable& vu = Vu_iq.set_k(0).diag();
VectorMutable& vl = Vl_iq.set_k(0).diag();
s.P_var_last().permute( BLAS_Cpp::trans, &vu ); // Permute back to original order
s.P_var_last().permute( BLAS_Cpp::trans, &vl ); // Permute back to original order
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nx resorted vl and vu to the original order\n" << x;
}
s.P_var_current().permute( BLAS_Cpp::no_trans, &vu ); // Permute to new (current) order
s.P_var_current().permute( BLAS_Cpp::no_trans, &vl ); // Permute to new (current) order
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "\nx resorted to new basis \n" << x;
}
}
correct_upper_bound_multipliers(nlp.xu(), +NLP::infinite_bound(), &Vu_iq.get_k(0).diag());
correct_lower_bound_multipliers(nlp.xl(), -NLP::infinite_bound(), &Vl_iq.get_k(0).diag());
if( (int)olevel >= (int)PRINT_VECTORS )
{
out << "x=\n" << s.x().get_k(0);
out << "xl=\n" << nlp.xl();
out << "vl=\n" << s.Vl().get_k(0).diag();
out << "xu=\n" << nlp.xu();
out << "vu=\n" << s.Vu().get_k(0).diag();
}
// Update general algorithm bound multipliers
VectorMutable& v = s.nu().set_k(0);
v = Vu_iq.get_k(0).diag();
Vp_StV(&v,-1.0,Vl_iq.get_k(0).diag());
// Print vector information
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) )
{
out << "invXu_k.diag()=\n" << invXu.diag();
out << "invXl_k.diag()=\n" << invXl.diag();
out << "Vu_k.diag()=\n" << Vu_iq.get_k(0).diag();
out << "Vl_k.diag()=\n" << Vl_iq.get_k(0).diag();
out << "nu_k=\n" << s.nu().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;
}
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 );
}