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)();
}
const MatrixOp::MatNorm
MatrixOpNonsing::calc_cond_num(
EMatNormType requested_norm_type
,bool allow_replacement
) const
{
using BLAS_Cpp::no_trans;
using BLAS_Cpp::trans;
using LinAlgOpPack::V_InvMtV;
const VectorSpace
&space_cols = this->space_cols(),
&space_rows = this->space_rows();
const index_type
num_cols = space_rows.dim();
TEST_FOR_EXCEPTION(
!(requested_norm_type == MAT_NORM_1 || requested_norm_type == MAT_NORM_INF), MethodNotImplemented
,"MatrixOp::calc_norm(...): Error, This default implemenation can only "
"compute the one norm or the infinity norm!"
);
//
// Here we implement Algorithm 2.5 in "Applied Numerical Linear Algebra", Demmel (1997)
// using the momenclature in the text. This is applied to the inverse matrix.
//
const MatrixOpNonsing
&B = *this;
bool
do_trans = requested_norm_type == MAT_NORM_INF;
VectorSpace::vec_mut_ptr_t
x = (do_trans ? space_rows : space_cols).create_member(1.0/num_cols),
w = (do_trans ? space_cols : space_rows).create_member(),
zeta = (do_trans ? space_cols : space_rows).create_member(),
z = (do_trans ? space_rows : space_cols).create_member();
const index_type max_iter = 5; // Recommended by Highman 1988, (see Demmel's reference)
value_type w_nrm = 0.0;
for( index_type k = 0; k <= max_iter; ++k ) {
V_InvMtV( w.get(), B, !do_trans ? no_trans : trans, *x ); // w = B*x
sign( *w, zeta.get() ); // zeta = sign(w)
V_InvMtV( z.get(), B, !do_trans ? trans : no_trans, *zeta ); // z = B'*zeta
value_type z_j = 0.0; // max |z(j)| = ||z||inf
index_type j = 0;
max_abs_ele( *z, &z_j, &j );
const value_type zTx = dot(*z,*x); // z'*x
w_nrm = w->norm_1(); // ||w||1
if( ::fabs(z_j) <= zTx ) { // Update
break;
}
else {
*x = 0.0;
x->set_ele(j,1.0);
}
}
const MatNorm M_nrm = this->calc_norm(requested_norm_type);
return MatNorm( w_nrm * M_nrm.value ,requested_norm_type );
}
void AbstractLinAlgPack::Vp_StV(
VectorMutable* y, const value_type& a, const SpVectorSlice& sx )
{
Vp_V_assert_compatibility(y,sx);
if( sx.nz() ) {
VectorSpace::vec_mut_ptr_t
x = y->space().create_member();
x->set_sub_vector(sub_vec_view(sx));
Vp_StV( y, a, *x );
}
}
void LinAlgOpPack::V_InvMtV(
DVectorSlice* y, const MatrixOpNonsing& M
,BLAS_Cpp::Transp M_trans, const SpVectorSlice& 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();
AbstractLinAlgPack::V_InvMtV( ay.get(), M, M_trans, x );
*y = VectorDenseMutableEncap(*ay)();
}
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 MatrixOpSubView::Vp_StMtV(
VectorMutable* y, value_type a, BLAS_Cpp::Transp M_trans_in
, const Vector& x, value_type b
) const
{
using BLAS_Cpp::no_trans;
using BLAS_Cpp::trans;
assert_initialized();
BLAS_Cpp::Transp
M_trans_trans = ( M_trans_==no_trans ? M_trans_in : BLAS_Cpp::trans_not(M_trans_in) );
// ToDo: Assert compatibility!
if( rng_rows_.full_range() && rng_cols_.full_range() ) {
AbstractLinAlgPack::Vp_StMtV( // The matrix is just transposed
y, a
,*M_full_, M_trans_trans
,x, b );
return;
}
// y = b*y
Vt_S( y, b );
//
// xt1 = 0.0
// xt3 = xt(op_op_rng_cols) = x
// xt3 = 0.0
//
// [ yt1 ] [ xt1 ]
// [ yt2 ] = a * op(op(M_full)) * [ xt3 ]
// [ yt3 ] [ xt3 ]
//
// =>
//
// y += yt2 = yt(op_op_rng_rows)
//
const Range1D
op_op_rng_rows = ( M_trans_trans == no_trans ? rng_rows_ : rng_cols_ ),
op_op_rng_cols = ( M_trans_trans == no_trans ? rng_cols_ : rng_rows_ );
VectorSpace::vec_mut_ptr_t
xt = ( M_trans_trans == no_trans ? M_full_->space_rows() : M_full_->space_cols() ).create_member(),
yt = ( M_trans_trans == no_trans ? M_full_->space_cols() : M_full_->space_rows() ).create_member();
*xt = 0.0;
*xt->sub_view(op_op_rng_cols) = x;
LinAlgOpPack::V_StMtV( yt.get(), a, *M_full_, M_trans_trans, *xt );
LinAlgOpPack::Vp_V( y, *yt->sub_view(op_op_rng_rows) );
}
bool CheckDescentQuasiNormalStep_Step::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using BLAS_Cpp::no_trans;
using AbstractLinAlgPack::dot;
using LinAlgOpPack::V_MtV;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
NLP &nlp = algo.nlp();
const Range1D equ_decomp = s.equ_decomp();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
const size_type
nb = nlp.num_bounded_x();
// Get iteration quantities
IterQuantityAccess<VectorMutable>
&c_iq = s.c(),
&Ypy_iq = s.Ypy();
const Vector::vec_ptr_t
cd_k = c_iq.get_k(0).sub_view(equ_decomp);
const Vector
&Ypy_k = Ypy_iq.get_k(0);
value_type descent_c = -1.0;
if( s.get_iter_quant_id( Gc_name ) != AlgorithmState::DOES_NOT_EXIST ) {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nGc_k exists; compute descent_c = c_k(equ_decomp)'*Gc_k(:,equ_decomp)'*Ypy_k ...\n";
}
const MatrixOp::mat_ptr_t
Gcd_k = s.Gc().get_k(0).sub_view(Range1D(),equ_decomp);
VectorSpace::vec_mut_ptr_t
t = cd_k->space().create_member();
V_MtV( t.get(), *Gcd_k, BLAS_Cpp::trans, Ypy_k );
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nGc_k(:,equ_decomp)'*Ypy_k =\n" << *t;
}
descent_c = dot( *cd_k, *t );
}
else {
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nGc_k does not exist; compute descent_c = c_k(equ_decomp)'*FDGc_k(:,equ_decomp)'*Ypy_k "
<< "using finite differences ...\n";
}
VectorSpace::vec_mut_ptr_t
t = nlp.space_c()->create_member();
calc_fd_prod().calc_deriv_product(
s.x().get_k(0),nb?&nlp.xl():NULL,nb?&nlp.xu():NULL
,Ypy_k,NULL,&c_iq.get_k(0),true,&nlp
,NULL,t.get()
,static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ? &out : NULL
);
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nFDGc_k(:,equ_decomp)'*Ypy_k =\n" << *t->sub_view(equ_decomp);
}
descent_c = dot( *cd_k, *t->sub_view(equ_decomp) );
}
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\ndescent_c = " << descent_c << std::endl;
}
if( descent_c > 0.0 ) { // ToDo: add some allowance for > 0.0 for finite difference errors!
if( static_cast<int>(olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\nError, descent_c > 0.0; this is not a descent direction\n"
<< "Throw TestFailed and terminate the algorithm ...\n";
}
TEST_FOR_EXCEPTION(
true, TestFailed
,"CheckDescentQuasiNormalStep_Step::do_step(...) : Error, descent for the decomposed constraints "
"with respect to the quasi-normal step c_k(equ_decomp)'*FDGc_k(:,equ_decomp)'*Ypy_k = "
<< descent_c << " > 0.0; This is not a descent direction!\n" );
}
return true;
}
bool 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;
}
bool NLPInterfacePack::test_nlp_direct(
NLPDirect *nlp
,OptionsFromStreamPack::OptionsFromStream *options
,std::ostream *out
)
{
using TestingHelperPack::update_success;
bool result;
bool success = true;
Teuchos::VerboseObjectTempState<NLP>
nlpOutputTempState(Teuchos::rcp(nlp,false),Teuchos::getFancyOStream(Teuchos::rcp(out,false)),Teuchos::VERB_LOW);
if(out)
*out
<< "\n****************************"
<< "\n*** test_nlp_direct(...) ***"
<< "\n*****************************\n";
nlp->initialize(true);
// Test the DVector spaces
if(out)
*out << "\nTesting the vector spaces ...\n";
VectorSpaceTester vec_space_tester;
if(options) {
VectorSpaceTesterSetOptions
opt_setter(&vec_space_tester);
opt_setter.set_options(*options);
}
if(out)
*out << "\nTesting nlp->space_x() ...\n";
result = vec_space_tester.check_vector_space(*nlp->space_x(),out);
if(out) {
if(result)
*out << "nlp->space_x() checks out!\n";
else
*out << "nlp->space_x() check failed!\n";
}
update_success( result, &success );
if(out)
*out << "\nTesting nlp->space_x()->sub_space(nlp->var_dep()) ...\n";
result = vec_space_tester.check_vector_space(
*nlp->space_x()->sub_space(nlp->var_dep()),out);
if(out) {
if(result)
*out << "nlp->space_x()->sub_space(nlp->var_dep()) checks out!\n";
else
*out << "nlp->space_x()->sub_space(nlp->var_dep()) check failed!\n";
}
update_success( result, &success );
if(out)
*out << "\nTesting nlp->space_x()->sub_space(nlp->var_indep()) ...\n";
result = vec_space_tester.check_vector_space(
*nlp->space_x()->sub_space(nlp->var_indep()),out);
if(out) {
if(result)
*out << "nlp->space_x()->sub_space(nlp->var_indep()) checks out!\n";
else
*out << "nlp->space_x()->sub_space(nlp->var_indep()) check failed!\n";
}
update_success( result, &success );
if(out)
*out << "\nTesting nlp->space_c() ...\n";
result = vec_space_tester.check_vector_space(*nlp->space_c(),out);
if(out) {
if(result)
*out << "nlp->space_c() checks out!\n";
else
*out << "nlp->space_c() check failed!\n";
}
update_success( result, &success );
if(out)
*out << "\nTesting nlp->space_c()->sub_space(nlp->con_decomp()) ...\n";
result = vec_space_tester.check_vector_space(
*nlp->space_c()->sub_space(nlp->con_decomp()),out);
if(out) {
if(result)
*out << "nlp->space_c()->sub_space(nlp->con_decomp()) checks out!\n";
else
*out << "nlp->space_c()->sub_space(nlp->con_decomp()) check failed!\n";
}
update_success( result, &success );
if( nlp->con_decomp().size() < nlp->m() ) {
if(out)
*out << "\nTesting nlp->space_c()->sub_space(nlp->con_undecomp()) ...\n";
result = vec_space_tester.check_vector_space(
*nlp->space_c()->sub_space(nlp->con_undecomp()),out);
if(out) {
if(result)
*out << "nlp->space_c()->sub_space(nlp->con_undecomp()) checks out!\n";
else
*out << "nlp->space_c()->sub_space(nlp->con_undecomp()) check failed!\n";
}
update_success( result, &success );
}
// Test the NLP interface first!
NLPTester nlp_tester;
if(options) {
NLPTesterSetOptions
nlp_tester_opt_setter(&nlp_tester);
nlp_tester_opt_setter.set_options(*options);
}
const bool print_all_warnings = nlp_tester.print_all();
result = nlp_tester.test_interface(
nlp, nlp->xinit(), print_all_warnings, out );
update_success( result, &success );
// Test the NLPDirect interface now!
const bool supports_Gf = nlp->supports_Gf();
if(out)
*out << "\nCalling nlp->calc_point(...) at nlp->xinit() ...\n";
const size_type
n = nlp->n(),
m = nlp->m();
const Range1D
var_dep = nlp->var_dep(),
var_indep = nlp->var_indep(),
con_decomp = nlp->con_decomp(),
con_undecomp = nlp->con_undecomp();
VectorSpace::vec_mut_ptr_t
c = nlp->space_c()->create_member(),
Gf = nlp->space_x()->create_member(),
py = nlp->space_x()->sub_space(var_dep)->create_member(),
rGf = nlp->space_x()->sub_space(var_indep)->create_member();
NLPDirect::mat_fcty_ptr_t::element_type::obj_ptr_t
GcU = con_decomp.size() < m ? nlp->factory_GcU()->create() : Teuchos::null,
D = nlp->factory_D()->create(),
Uz = con_decomp.size() < m ? nlp->factory_Uz()->create() : Teuchos::null;
nlp->calc_point(
nlp->xinit(), NULL, c.get(), true, supports_Gf?Gf.get():NULL, py.get(), rGf.get()
,GcU.get(), D.get(), Uz.get() );
if(out) {
if(supports_Gf) {
*out << "\n||Gf||inf = " << Gf->norm_inf();
if(nlp_tester.print_all())
*out << "\nGf =\n" << *Gf;
}
*out << "\n||py||inf = " << py->norm_inf();
if(nlp_tester.print_all())
*out << "\npy =\n" << *py;
*out << "\n||rGf||inf = " << rGf->norm_inf();
if(nlp_tester.print_all())
*out << "\nrGf =\n" << *rGf;
if(nlp_tester.print_all())
*out << "\nD =\n" << *D;
if( con_decomp.size() < m ) {
TEST_FOR_EXCEPT(true); // ToDo: Print GcU and Uz
}
*out << "\n";
}
CalcFiniteDiffProd
calc_fd_prod;
if(options) {
CalcFiniteDiffProdSetOptions
options_setter( &calc_fd_prod );
options_setter.set_options(*options);
}
NLPDirectTester
nlp_first_order_direct_tester(Teuchos::rcp(&calc_fd_prod,false));
if(options) {
NLPDirectTesterSetOptions
nlp_tester_opt_setter(&nlp_first_order_direct_tester);
nlp_tester_opt_setter.set_options(*options);
}
result = nlp_first_order_direct_tester.finite_diff_check(
nlp, nlp->xinit()
,nlp->num_bounded_x() ? &nlp->xl() : NULL
,nlp->num_bounded_x() ? &nlp->xu() : NULL
,c.get()
,supports_Gf?Gf.get():NULL,py.get(),rGf.get(),GcU.get(),D.get(),Uz.get()
,print_all_warnings, out
);
update_success( result, &success );
return success;
}
bool CalcReducedGradLagrangianStd_AddedStep::do_step(
Algorithm& _algo, poss_type step_poss, IterationPack::EDoStepType type
,poss_type assoc_step_poss
)
{
using BLAS_Cpp::trans;
using LinAlgOpPack::V_VpV;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::Vp_MtV;
NLPAlgo &algo = rsqp_algo(_algo);
NLPAlgoState &s = algo.rsqp_state();
EJournalOutputLevel olevel = algo.algo_cntr().journal_output_level();
EJournalOutputLevel ns_olevel = algo.algo_cntr().null_space_journal_output_level();
std::ostream& out = algo.track().journal_out();
// print step header.
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
using IterationPack::print_algorithm_step;
print_algorithm_step( algo, step_poss, type, assoc_step_poss, out );
}
// Calculate: rGL = rGf + Z' * nu + Uz' * lambda(equ_undecomp)
IterQuantityAccess<VectorMutable>
&rGL_iq = s.rGL(),
&nu_iq = s.nu(),
&Gf_iq = s.Gf();
VectorMutable &rGL_k = rGL_iq.set_k(0);
if( nu_iq.updated_k(0) && nu_iq.get_k(0).nz() > 0 ) {
// Compute rGL = Z'*(Gf + nu) to reduce the effect of roundoff in this
// catastropic cancelation
const Vector &nu_k = nu_iq.get_k(0);
VectorSpace::vec_mut_ptr_t
tmp = nu_k.space().create_member();
if( (int)olevel >= (int)PRINT_VECTORS )
out << "\nnu_k = \n" << nu_k;
V_VpV( tmp.get(), Gf_iq.get_k(0), nu_k );
if( (int)olevel >= (int)PRINT_VECTORS )
out << "\nGf_k+nu_k = \n" << *tmp;
V_MtV( &rGL_k, s.Z().get_k(0), trans, *tmp );
if( (int)ns_olevel >= (int)PRINT_VECTORS )
out << "\nrGL_k = \n" << rGL_k;
}
else {
rGL_k = s.rGf().get_k(0);
}
// ToDo: Add terms for undecomposed equalities and inequalities!
// + Uz' * lambda(equ_undecomp)
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_ALGORITHM_STEPS) ) {
out << "\n||rGL_k||inf = " << rGL_k.norm_inf() << "\n";
}
if( static_cast<int>(ns_olevel) >= static_cast<int>(PRINT_VECTORS) ) {
out << "\nrGL_k = \n" << rGL_k;
}
return true;
}
void MatrixSymPosDefLBFGS::secant_update(
VectorMutable* s, VectorMutable* y, VectorMutable* Bs
)
{
using AbstractLinAlgPack::BFGS_sTy_suff_p_d;
using AbstractLinAlgPack::dot;
using LinAlgOpPack::V_MtV;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
// Check skipping the BFGS update
const value_type
sTy = dot(*s,*y);
std::ostringstream omsg;
if( !BFGS_sTy_suff_p_d(*s,*y,&sTy,&omsg,"MatrixSymPosDefLBFGS::secant_update(...)" ) ) {
throw UpdateSkippedException( omsg.str() );
}
try {
// Update counters
if( m_bar_ == m_ ) {
// We are at the end of the storage so remove the oldest stored update
// and move updates to make room for the new update. This has to be done for the
// the matrix to behave properly
{for( size_type k = 1; k <= m_-1; ++k ) {
S_->col(k) = S_->col(k+1); // Shift S.col() to the left
Y_->col(k) = Y_->col(k+1); // Shift Y.col() to the left
STY_.col(k)(1,m_-1) = STY_.col(k+1)(2,m_); // Move submatrix STY(2,m-1,2,m-1) up and left
STSYTY_.col(k)(k+1,m_) = STSYTY_.col(k+1)(k+2,m_+1); // Move triangular submatrix STS(2,m-1,2,m-1) up and left
STSYTY_.col(k+1)(1,k) = STSYTY_.col(k+2)(2,k+1); // Move triangular submatrix YTY(2,m-1,2,m-1) up and left
}}
// ToDo: Create an abstract interface, call it MultiVectorShiftVecs, to rearrange S and Y all at once.
// This will be important for parallel performance.
}
else {
m_bar_++;
}
// Set the update vectors
*S_->col(m_bar_) = *s;
*Y_->col(m_bar_) = *y;
// /////////////////////////////////////////////////////////////////////////////////////
// Update S'Y
//
// Update the row and column m_bar
//
// S'Y =
//
// [ s(1)'*y(1) ... s(1)'*y(m_bar) ... s(1)'*y(m_bar) ]
// [ . . . ] row
// [ s(m_bar)'*y(1) ... s(m_bar)'*y(m_bar) ... s(m_bar)'*y(m_bar) ] m_bar
// [ . . . ]
// [ s(m_bar)'*y(1) ... s(m_bar)'*y(m_bar) ... s(m_bar)'*y(m_bar) ]
//
// col m_bar
//
// Therefore we set:
// (S'Y)(:,m_bar) = S'*y(m_bar)
// (S'Y)(m_bar,:) = s(m_bar)'*Y
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member(); // temporary workspace
// (S'Y)(:,m_bar) = S'*y(m_bar)
V_MtV( t.get(), *S, BLAS_Cpp::trans, *y );
STY_.col(m_bar_)(1,m_bar_) = VectorDenseEncap(*t)();
// (S'Y)(m_bar,:)' = Y'*s(m_bar)
V_MtV( t.get(), *Y, BLAS_Cpp::trans, *s );
STY_.row(m_bar_)(1,m_bar_) = VectorDenseEncap(*t)();
// /////////////////////////////////////////////////////////////////
// Update S'S
//
// S'S =
//
// [ s(1)'*s(1) ... symmetric symmetric ]
// [ . . . ] row
// [ s(m_bar)'*s(1) ... s(m_bar)'*s(m_bar) ... symmetric ] m_bar
// [ . . . ]
// [ s(m_bar)'*s(1) ... s(m_bar)'*s(m_bar) ... s(m_bar)'*s(m_bar) ]
//
// col m_bar
//
// Here we will update the lower triangular part of S'S. To do this we
// only need to compute:
// t = S'*s(m_bar) = { s(m_bar)' * [ s(1),..,s(m_bar),..,s(m_bar) ] }'
// then set the appropriate rows and columns of S'S.
Workspace<value_type> work_ws(wss,m_bar_);
DVectorSlice work(&work_ws[0],work_ws.size());
// work = S'*s(m_bar)
V_MtV( t.get(), *S, BLAS_Cpp::trans, *s );
work = VectorDenseEncap(*t)();
// Set row elements
STSYTY_.row(m_bar_+1)(1,m_bar_) = work;
// Set column elements
STSYTY_.col(m_bar_)(m_bar_+1,m_bar_+1) = work(m_bar_,m_bar_);
// /////////////////////////////////////////////////////////////////////////////////////
// Update Y'Y
//
// Update the row and column m_bar
//
// Y'Y =
//
// [ y(1)'*y(1) ... y(1)'*y(m_bar) ... y(1)'*y(m_bar) ]
// [ . . . ] row
// [ symmetric ... y(m_bar)'*y(m_bar) ... y(m_bar)'*y(m_bar) ] m_bar
// [ . . . ]
// [ symmetric ... symmetric ... y(m_bar)'*y(m_bar) ]
//
// col m_bar
//
// Here we will update the upper triangular part of Y'Y. To do this we
// only need to compute:
// t = Y'*y(m_bar) = { y(m_bar)' * [ y(1),..,y(m_bar),..,y(m_bar) ] }'
// then set the appropriate rows and columns of Y'Y.
// work = Y'*y(m_bar)
V_MtV( t.get(), *Y, BLAS_Cpp::trans, *y );
work = VectorDenseEncap(*t)();
// Set row elements
STSYTY_.col(m_bar_+1)(1,m_bar_) = work;
// Set column elements
STSYTY_.row(m_bar_)(m_bar_+1,m_bar_+1) = work(m_bar_,m_bar_);
// /////////////////////////////
// Update gamma_k
// gamma_k = s'*y / y'*y
if(auto_rescaling_)
gamma_k_ = STY_(m_bar_,m_bar_) / STSYTY_(m_bar_,m_bar_+1);
// We do not initially update Q unless we have to form a matrix-vector
// product later.
Q_updated_ = false;
num_secant_updates_++;
} // end try
catch(...) {
// If we throw any exception the we should make the matrix uninitialized
// so that we do not leave this object in an inconsistant state.
n_ = 0;
throw;
}
}
void MatrixSymPosDefLBFGS::V_InvMtV(
VectorMutable* y, BLAS_Cpp::Transp trans_rhs1
, const Vector& x
) const
{
using AbstractLinAlgPack::Vp_StMtV;
using DenseLinAlgPack::V_InvMtV;
using LinAlgOpPack::V_mV;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::Vp_V;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::Vp_MtV;
using DenseLinAlgPack::Vp_StMtV;
typedef VectorDenseEncap vde;
typedef VectorDenseMutableEncap vdme;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
TEUCHOS_TEST_FOR_EXCEPT( !( inverse_is_updated_ ) ); // For now just always update
// y = inv(Bk) * x = Hk * x
//
// = gk*x + [S gk*Y] * [ inv(R')*(D+gk*Y'Y)*inv(R) -inv(R') ] * [ S' ] * x
// [ -inv(R) 0 ] [ gk*Y' ]
//
// Perform in the following (in order):
//
// y = gk*x
//
// t1 = [ S'*x ] <: R^(2*m)
// [ gk*Y'*x ]
//
// t2 = inv(R) * t1(1:m) <: R^(m)
//
// t3 = - inv(R') * t1(m+1,2*m) <: R^(m)
//
// t4 = gk * Y'Y * t2 <: R^(m)
//
// t4 += D*t2
//
// t5 = inv(R') * t4 <: R^(m)
//
// t5 += t3
//
// y += S*t5
//
// y += -gk*Y*t2
// y = gk*x
V_StV( y, gamma_k_, x );
const size_type
mb = m_bar_;
if( !mb )
return; // No updates have been performed.
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
// Get workspace
Workspace<value_type> t1_ws(wss,2*mb);
DVectorSlice t1(&t1_ws[0],t1_ws.size());
Workspace<value_type> t2_ws(wss,mb);
DVectorSlice t2(&t2_ws[0],t2_ws.size());
Workspace<value_type> t3_ws(wss,mb);
DVectorSlice t3(&t3_ws[0],t3_ws.size());
Workspace<value_type> t4_ws(wss,mb);
DVectorSlice t4(&t4_ws[0],t4_ws.size());
Workspace<value_type> t5_ws(wss,mb);
DVectorSlice t5(&t5_ws[0],t5_ws.size());
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member();
const DMatrixSliceTri
&R = this->R();
const DMatrixSliceSym
&YTY = this->YTY();
// t1 = [ S'*x ]
// [ gk*Y'*x ]
V_MtV( t.get(), *S, BLAS_Cpp::trans, x );
t1(1,mb) = vde(*t)();
V_StMtV( t.get(), gamma_k_, *Y, BLAS_Cpp::trans, x );
t1(mb+1,2*mb) = vde(*t)();
// t2 = inv(R) * t1(1:m)
V_InvMtV( &t2, R, BLAS_Cpp::no_trans, t1(1,mb) );
// t3 = - inv(R') * t1(m+1,2*m)
V_mV( &t3, t1(mb+1,2*mb) );
V_InvMtV( &t3, R, BLAS_Cpp::trans, t3 );
// t4 = gk * Y'Y * t2
V_StMtV( &t4, gamma_k_, YTY, BLAS_Cpp::no_trans, t2 );
// t4 += D*t2
Vp_DtV( &t4, t2 );
// t5 = inv(R') * t4
V_InvMtV( &t5, R, BLAS_Cpp::trans, t4 );
// t5 += t3
Vp_V( &t5, t3 );
// y += S*t5
(vdme(*t)() = t5);
Vp_MtV( y, *S, BLAS_Cpp::no_trans, *t );
// y += -gk*Y*t2
(vdme(*t)() = t2);
Vp_StMtV( y, -gamma_k_, *Y, BLAS_Cpp::no_trans, *t );
}
void MatrixSymPosDefLBFGS::Vp_StMtV(
VectorMutable* y, value_type alpha, BLAS_Cpp::Transp trans_rhs1
, const Vector& x, value_type beta
) const
{
using AbstractLinAlgPack::Vt_S;
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::Vp_StMtV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::V_MtV;
typedef VectorDenseEncap vde;
typedef VectorDenseMutableEncap vdme;
using Teuchos::Workspace;
Teuchos::WorkspaceStore* wss = Teuchos::get_default_workspace_store().get();
assert_initialized();
TEUCHOS_TEST_FOR_EXCEPT( !( original_is_updated_ ) ); // For now just always update
// y = b*y + Bk * x
//
// y = b*y + (1/gk)*x - [ (1/gk)*S Y ] * inv(Q) * [ (1/gk)*S' ] * x
// [ Y' ]
// Perform the following operations (in order):
//
// y = b*y
//
// y += (1/gk)*x
//
// t1 = [ (1/gk)*S'*x ] <: R^(2*m)
// [ Y'*x ]
//
// t2 = inv(Q) * t1 <: R^(2*m)
//
// y += -(1/gk) * S * t2(1:m)
//
// y += -1.0 * Y * t2(m+1,2m)
const value_type
invgk = 1.0 / gamma_k_;
// y = b*y
Vt_S( y, beta );
// y += (1/gk)*x
Vp_StV( y, invgk, x );
if( !m_bar_ )
return; // No updates have been added yet.
const multi_vec_ptr_t
S = this->S(),
Y = this->Y();
// Get workspace
const size_type
mb = m_bar_;
Workspace<value_type> t1_ws(wss,2*mb);
DVectorSlice t1(&t1_ws[0],t1_ws.size());
Workspace<value_type> t2_ws(wss,2*mb);
DVectorSlice t2(&t2_ws[0],t2_ws.size());
VectorSpace::vec_mut_ptr_t
t = S->space_rows().create_member();
// t1 = [ (1/gk)*S'*x ]
// [ Y'*x ]
V_StMtV( t.get(), invgk, *S, BLAS_Cpp::trans, x );
t1(1,mb) = vde(*t)();
V_MtV( t.get(), *Y, BLAS_Cpp::trans, x );
t1(mb+1,2*mb) = vde(*t)();
// t2 = inv(Q) * t1
V_invQtV( &t2, t1 );
// y += -(1/gk) * S * t2(1:m)
(vdme(*t)() = t2(1,mb));
Vp_StMtV( y, -invgk, *S, BLAS_Cpp::no_trans, *t );
// y += -1.0 * Y * t2(m+1,2m
(vdme(*t)() = t2(mb+1,2*mb));
Vp_StMtV( y, -1.0, *Y, BLAS_Cpp::no_trans, *t );
}