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 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 );
}
}
}
}
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 );
}