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ConstrainedOptPack::MatrixSymPosDefLBFGS Class Reference

Implementation of limited Memory BFGS matrix for arbitrary vector spaces. More...

#include <ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp>

Inheritance diagram for ConstrainedOptPack::MatrixSymPosDefLBFGS:
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List of all members.

Classes

class  PostMod
 PostMod class to use with MemMngPack::AbstractFactorStd. More...

Public Member Functions

 MatrixSymPosDefLBFGS (size_type max_size=0, size_type m=10, bool maintain_original=true, bool maintain_inverse=true, bool auto_rescaling=false)
 Calls initial_setup(,,,)
 STANDARD_MEMBER_COMPOSITION_MEMBERS (bool, auto_rescaling)
 Set whether automatic rescaling is used or not.
void initial_setup (size_type max_size=0, size_type m=10, bool maintain_original=true, bool maintain_inverse=true, bool auto_rescaling=false)
 Initial setup for the matrix.
size_type m () const
 
size_type m_bar () const
 
size_type k_bar () const
 
value_type gamma_k () const
 
const DMatrixSlice S () const
 
const DMatrixSlice Y () const
 
bool maintain_original () const
 
bool maintain_inverse () const
 
size_type num_secant_updates () const
 Returns the total number of successful secant updates performed.
size_type rows () const
 

Private Types

typedef
VectorSpace::multi_vec_mut_ptr_t 
multi_vec_mut_ptr_t

Private Member Functions

const DMatrixSliceTri R () const
 
const DMatrixSliceTri Lb () const
 Strictly lower triangular part of L.
DMatrixSlice STY ()
 
const DMatrixSlice STY () const
 
DMatrixSliceSym STS ()
 
const DMatrixSliceSym STS () const
 
DMatrixSliceSym YTY ()
 
const DMatrixSliceSym YTY () const
 
void V_invQtV (DVectorSlice *y, const DVectorSlice &x) const
 y = inv(Q) * x
void Vp_DtV (DVectorSlice *y, const DVectorSlice &x) const
 y += D * x
void update_Q () const
 Update Q.
void assert_initialized () const
 
const DMatrixSliceTri R () const
 
const DMatrixSliceTri Lb () const
 Strictly lower triangular part of L.
DMatrixSlice STY ()
 
const DMatrixSlice STY () const
 
DMatrixSliceSym STS ()
 
const DMatrixSliceSym STS () const
 
DMatrixSliceSym YTY ()
 
const DMatrixSliceSym YTY () const
 
void V_invQtV (DVectorSlice *y, const DVectorSlice &x) const
 y = inv(Q) * x
void Vp_DtV (DVectorSlice *y, const DVectorSlice &x) const
 y += D * x
void update_Q () const
 Update Q.
void assert_initialized () const
 

Private Attributes

bool maintain_original_
bool original_is_updated_
bool maintain_inverse_
bool inverse_is_updated_
VectorSpace::space_ptr_t vec_spc_
size_type n_
size_type m_
size_type m_bar_
size_type num_secant_updates_
value_type gamma_k_
multi_vec_mut_ptr_t S_
multi_vec_mut_ptr_t Y_
DMatrix STY_
DMatrix STSYTY_
bool Q_updated_
DMatrix QJ_
size_type n_max_
size_type k_bar_
DMatrix S_
DMatrix Y_
DVector work_

Public types

typedef Teuchos::RCP< const
MultiVector > 
multi_vec_ptr_t
 

Constructors and initializers

 MatrixSymPosDefLBFGS (size_type m=10, bool maintain_original=true, bool maintain_inverse=true, bool auto_rescaling=false)
 Calls this->initial_setup()
 STANDARD_MEMBER_COMPOSITION_MEMBERS (bool, auto_rescaling)
 Set whether automatic rescaling is used or not.
void initial_setup (size_type m=10, bool maintain_original=true, bool maintain_inverse=true, bool auto_rescaling=false)
 Initial setup for the matrix.
size_type m () const
 
size_type m_bar () const
 
value_type gamma_k () const
 
const multi_vec_ptr_t S () const
 
const multi_vec_ptr_t Y () const
 
bool maintain_original () const
 
bool maintain_inverse () const
 
size_type num_secant_updates () const
 Returns the total number of successful secant updates performed since this->init_identity() was called.

Overridden from MatrixOp

const VectorSpacespace_cols () const
 
std::ostream & output (std::ostream &out) const
 
MatrixOp & operator= (const MatrixOp &mwo)
 
void Vp_StMtV (VectorMutable *v_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const Vector &v_rhs2, value_type beta) const
 
std::ostream & output (std::ostream &out) const
 
MatrixOp & operator= (const MatrixOp &m)
 
void Vp_StMtV (DVectorSlice *vs_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const DVectorSlice &vs_rhs2, value_type beta) const
 

Overridden from MatrixOpNonsing

void V_InvMtV (VectorMutable *v_lhs, BLAS_Cpp::Transp trans_rhs1, const Vector &v_rhs2) const
 

Overridden from MatrixSymSecant

void init_identity (const VectorSpace &space_diag, value_type alpha)
 
void init_diagonal (const Vector &diag)
 Actually this calls init_identity( diag.space(), diag.norm_inf() ).
void secant_update (VectorMutable *s, VectorMutable *y, VectorMutable *Bs)
 
void init_identity (size_type n, value_type alpha)
 
void init_diagonal (const DVectorSlice &diag)
 Actually this calls init_identity( (&diag)->size(), norm_inf(diag) ).
void secant_update (DVectorSlice *s, DVectorSlice *y, DVectorSlice *Bs)
 

Overridden from MatrixWithOpFactorized

void V_InvMtV (DVectorSlice *v_lhs, BLAS_Cpp::Transp trans_rhs1, const DVectorSlice &vs_rhs2) const
 

Overridden from MatrixSymAddDelUpdateble

void initialize (value_type alpha, size_type max_size)
 This is fine as long as alpha > 0.0.
void initialize (const DMatrixSliceSym &A, size_type max_size, bool force_factorization, Inertia inertia, PivotTolerances pivot_tols)
 Sorry, this will throw an exception!
size_type max_size () const
 
Inertia inertia () const
 Returns (0,0,rows())
void set_uninitialized ()
 Will set rows() == 0.
void augment_update (const DVectorSlice *t, value_type alpha, bool force_refactorization, EEigenValType add_eigen_val, PivotTolerances pivot_tols)
 Augment the matrix to add a row and column.
void delete_update (size_type jd, bool force_refactorization, EEigenValType drop_eigen_val, PivotTolerances pivot_tols)
 Should always succeed unless user gives a wrong value for drop_eigen_val.

Detailed Description

Implementation of limited Memory BFGS matrix for arbitrary vector spaces.

Implementation of limited Memory BFGS matrix.

The function set_num_updates_stored() must be called first to set the maximum number of the most recent updates that can be stored. The storage requirements for this class are O( n*m + m*m ) which is O(n*m) when n >> m which is expected (where n is the dimension of the vector space and m is the maximum number of updates stored).

This implementation is based on:

Byrd, Nocedal, and Schnabel, "Representations of quasi-Newton matrices and their use in limited memory methods", Mathematical Programming, 63 (1994)

Consider BFGS updates of the form:


 ( B^{k-1}, s^{k-1}, y^{k-1} ) -> B^{k}
 
 where:
 
 B^{k} = B^{k-1} - ( (B*s)*(B*s)' / (s'*B*s) )^{k-1} + ( (y*y') / (s'*y) )^{k-1}
 
 B <: R^(n x n)
 s <: R^(n)
 y <: R^(n)
 

Now let us consider limited memory updating. For this implementation we set:


 Bo = ( 1 / gamma_k ) * I
 
 where:
               / (s^{k-1}'*y^{k-1})/(y^{k-1}'*y^{k-1})           :  if auto_rescaling() == true
     gamma_k = |
             \  1/alpha from last call to init_identity(n,alpha) :  otherwise
 
 

Now let us define the matrices S and Y that store the update vectors s^{i} and y^{i} for i = 1 ... m_bar:


 S = [ s^{1}, s^{2},...,s^{m_bar} ] <: R^(n x m)
 Y = [ y^{1}, y^{2},...,y^{m_bar} ] <: R^(n x m)
  

Here we are only storing the m_bar <= m most recent update vectors and their ordering is significant. The columns S(:,m_bar) and Y(:,m_bar) contain the most recent update vectors. This is all client needs to know in order to reconstruct the updates themselves.

This class allows matrix-vector products x = B*y and the inverse matrix-vector products x = inv(B)*y to be performed at a cost of about O(n*m_bar^2).

The function set_num_updates_stored(l) must be called first to set the maximum number of the most recent updates that can be stored. The storage requirements for this class are O( n_max*l + l*l ) which is O(n_max*l) when n_max >> l which is expected.

This implementation is based on:

Byrd, Nocedal, and Schnabel, "Representations of quasi-Newton matrices and their use in limited memory methods", Mathematical Programming, 63 (1994)

Consider BFGS updates of the form: {verbatim}

( B^{k-1}, s^{k-1}, y^{k-1} ) -> B^{k}

where:

B^{k} = B^{k-1} - ( (B*s)*(B*s)' / (s'*B*s) )^{k-1} + ( (y*y') / (s'*y) )^{k-1}

B <: R^(n x n) s <: R^(n) y <: R^(n)

{verbatim} Given that we start from the same initial matrix #Bo#, the updated matrix B^{k}# will be the same independent of the order the #(s^{i},y^{i})# updates are added.

Now let us consider limited memory updating. For this implementation we set: {verbatim}

Bo = ( 1 / gamma_k ) * I

where: / (s^{k-1}'*y^{k-1})/(y^{k-1}'*y^{k-1}) : if auto_rescaling() == true gamma_k = | \ alpha from last call to init_identity(n,alpha) : otherwise

{verbatim} Now let us define the matrices S# and Y# that store the update vectors #s^{i}# and #y^{i}# for #i = 1 ... m_bar#: {verbatim}

S = [ s^{1}, s^{2},...,s^{m_bar} ] <: R^(n x m) Y = [ y^{1}, y^{2},...,y^{m_bar} ] <: R^(n x m)

{verbatim} Here we are only storing the m_bar <= m# most recent update vectors and their ordering is arbitrary. The columns #S(:,k_bar)# and #Y(:,k_bar)# contain the most recent update vectors. The next most recent vectors are to the left (i.e. #p = k_bar-1#) and so forth until #p = 1#. Then the next most recent update vectors start at m_bar# and move to the left until you reach the oldest update vector stored at column k_bar+1#. This is all client need to know in order to reconstruct the updates themselves.

This class allows matrix vector products x = B*y and the inverse matrix vector products x = inv(B)*y to be performed at a cost of about O(n*m^2).

In addition, the class supports the MatixSymAddDelUpdateable interface with a few major restrictions. This allows the client to add and remove rows and columns from the matrix.

Definition at line 97 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.


Member Typedef Documentation

Definition at line 107 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

typedef VectorSpace::multi_vec_mut_ptr_t ConstrainedOptPack::MatrixSymPosDefLBFGS::multi_vec_mut_ptr_t [private]

Definition at line 273 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.


Constructor & Destructor Documentation

ConstrainedOptPack::MatrixSymPosDefLBFGS::MatrixSymPosDefLBFGS ( size_type  m = 10,
bool  maintain_original = true,
bool  maintain_inverse = true,
bool  auto_rescaling = false 
)

Calls this->initial_setup()

Definition at line 148 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

ConstrainedOptPack::MatrixSymPosDefLBFGS::MatrixSymPosDefLBFGS ( size_type  max_size = 0,
size_type  m = 10,
bool  maintain_original = true,
bool  maintain_inverse = true,
bool  auto_rescaling = false 
)

Calls initial_setup(,,,)


Member Function Documentation

ConstrainedOptPack::MatrixSymPosDefLBFGS::STANDARD_MEMBER_COMPOSITION_MEMBERS ( bool  ,
auto_rescaling   
)

Set whether automatic rescaling is used or not.

This function must be called before a BFGS update is performed in order for it to take effect for that update.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::initial_setup ( size_type  m = 10,
bool  maintain_original = true,
bool  maintain_inverse = true,
bool  auto_rescaling = false 
)

Initial setup for the matrix.

This function must be called before init_identity(n) is called in order for these setting to have affect. When this function is called all current updates are lost and the matrix becomes uninitialized.

Parameters:
m[in] Max number of recent update vectors s and y stored.
maintain_original[in] If true then quantities needed to compute x = Bk*y will be maintained, otherwise they will not be unless needed. This is to save computational costs in case matrix-vector products will never be needed. However, if a matrix vector product is needed then these quantities will be computed on the fly in order to satisfy the request.
maintain_inverse[in] If true then quantities needed to compute x = inv(Bk)*y = x = Hk*y will be maintained, otherwise they will not be unless needed. This is to save computational costs in case inverse matrix-vector products will never be needed. However, if the inverse product is ever needed then the needed quantities will be computed on the fly in order to satisfiy the request. Because it takes so little extra work to maintain the quantities needed for Hk it is recommended to always set this to true.
auto_rescaling[in] See intro.

Definition at line 158 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::m ( ) const [inline]

Definition at line 347 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::m_bar ( ) const [inline]

Definition at line 353 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

value_type ConstrainedOptPack::MatrixSymPosDefLBFGS::gamma_k ( ) const [inline]

Definition at line 359 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::S ( ) const [inline]

Definition at line 366 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::Y ( ) const [inline]

Definition at line 373 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

bool ConstrainedOptPack::MatrixSymPosDefLBFGS::maintain_original ( ) const [inline]

Definition at line 379 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

bool ConstrainedOptPack::MatrixSymPosDefLBFGS::maintain_inverse ( ) const [inline]

Definition at line 385 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::num_secant_updates ( ) const [inline]

Returns the total number of successful secant updates performed since this->init_identity() was called.

Definition at line 391 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

const VectorSpace & ConstrainedOptPack::MatrixSymPosDefLBFGS::space_cols ( ) const [virtual]
std::ostream & ConstrainedOptPack::MatrixSymPosDefLBFGS::output ( std::ostream &  out) const [virtual]

Reimplemented from AbstractLinAlgPack::MatrixOp.

Definition at line 190 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

MatrixOp & ConstrainedOptPack::MatrixSymPosDefLBFGS::operator= ( const MatrixOp &  mwo)

Definition at line 214 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::Vp_StMtV ( VectorMutable *  v_lhs,
value_type  alpha,
BLAS_Cpp::Transp  trans_rhs1,
const Vector v_rhs2,
value_type  beta 
) const

Definition at line 250 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::V_InvMtV ( VectorMutable *  v_lhs,
BLAS_Cpp::Transp  trans_rhs1,
const Vector v_rhs2 
) const

Definition at line 340 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::init_identity ( const VectorSpace space_diag,
value_type  alpha 
)

Definition at line 464 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::init_diagonal ( const Vector diag)

Actually this calls init_identity( diag.space(), diag.norm_inf() ).

This initialization is not convienent for this implementation. Besides, when we are using automatric rescaling (auto_rescaling == true) then this will really not matter much anyway.

Definition at line 496 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::secant_update ( VectorMutable *  s,
VectorMutable *  y,
VectorMutable *  Bs 
)

Definition at line 501 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

const DMatrixSliceTri ConstrainedOptPack::MatrixSymPosDefLBFGS::R ( ) const [inline, private]

Definition at line 98 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

const DMatrixSliceTri ConstrainedOptPack::MatrixSymPosDefLBFGS::Lb ( ) const [inline, private]

Strictly lower triangular part of L.

Definition at line 104 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::STY ( ) [inline, private]

Definition at line 110 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::STY ( ) const [inline, private]

Definition at line 116 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::STS ( ) [inline, private]

Definition at line 122 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

const DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::STS ( ) const [inline, private]

Definition at line 128 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::YTY ( ) [inline, private]

Definition at line 134 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

const DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::YTY ( ) const [inline, private]

Definition at line 140 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::V_invQtV ( DVectorSlice *  y,
const DVectorSlice &  x 
) const [private]

y = inv(Q) * x

Definition at line 793 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::Vp_DtV ( DVectorSlice *  y,
const DVectorSlice &  x 
) const [private]

y += D * x

Definition at line 663 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::update_Q ( ) const [private]

Update Q.

Definition at line 703 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::assert_initialized ( ) const [private]

Definition at line 899 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.cpp.

ConstrainedOptPack::MatrixSymPosDefLBFGS::STANDARD_MEMBER_COMPOSITION_MEMBERS ( bool  ,
auto_rescaling   
)

Set whether automatic rescaling is used or not.

This function must be called before a BFGS update is performed in order for it to take effect for that update.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::initial_setup ( size_type  max_size = 0,
size_type  m = 10,
bool  maintain_original = true,
bool  maintain_inverse = true,
bool  auto_rescaling = false 
)

Initial setup for the matrix.

This function must be called before init_identity(n) is called. When this function is called all current updates are lost and the matrix becomes uninitialized.

Parameters:
max_size[in] If max_size > 0 then this is the max size the matrix is allowed to become. If max_size == 0 then this size will be determined by one of the initialization methods.
m[in] Max number of recent update vectors stored
maintain_original[in] If true then quantities needed to compute x = Bk*y will be maintained, otherwise they will not be unless needed. This is to save computational costs in case matrix vector products will never be needed. However, if a matrix vector product is needed then these quantities will be computed on the fly in order to satisfy the request.
maintain_inverse[in] If true then quantities needed to compute x = inv(Bk)*y = x = Hk*y will be maintained , otherwise they will not be unless needed. This is to save computational costs in case inverse matrix vector products will never be needed. However, if the inverse product is ever needed then the needed quantities will be computed on the fly in order to satisfiy the request. Because it takes so little extra work to maintain the quantities needed for Hk it is recommended to always set this to true.
auto_rescaling[in] See intro.
size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::m ( ) const

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::m_bar ( ) const

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::k_bar ( ) const [inline]
value_type ConstrainedOptPack::MatrixSymPosDefLBFGS::gamma_k ( ) const

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::S ( ) const

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::Y ( ) const

bool ConstrainedOptPack::MatrixSymPosDefLBFGS::maintain_original ( ) const

bool ConstrainedOptPack::MatrixSymPosDefLBFGS::maintain_inverse ( ) const

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::num_secant_updates ( ) const

Returns the total number of successful secant updates performed.

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::rows ( ) const [virtual]

Reimplemented from AbstractLinAlgPack::MatrixBase.

std::ostream& ConstrainedOptPack::MatrixSymPosDefLBFGS::output ( std::ostream &  out) const [virtual]

Reimplemented from AbstractLinAlgPack::MatrixOp.

MatrixOp& ConstrainedOptPack::MatrixSymPosDefLBFGS::operator= ( const MatrixOp &  m)

void ConstrainedOptPack::MatrixSymPosDefLBFGS::Vp_StMtV ( DVectorSlice *  vs_lhs,
value_type  alpha,
BLAS_Cpp::Transp  trans_rhs1,
const DVectorSlice &  vs_rhs2,
value_type  beta 
) const

void ConstrainedOptPack::MatrixSymPosDefLBFGS::V_InvMtV ( DVectorSlice *  v_lhs,
BLAS_Cpp::Transp  trans_rhs1,
const DVectorSlice &  vs_rhs2 
) const

void ConstrainedOptPack::MatrixSymPosDefLBFGS::init_identity ( size_type  n,
value_type  alpha 
)

void ConstrainedOptPack::MatrixSymPosDefLBFGS::init_diagonal ( const DVectorSlice &  diag)

Actually this calls init_identity( (&diag)->size(), norm_inf(diag) ).

This initialization is not convienent for this implementation. Besides, when we are using automatric rescaling (auto_rescaling == true) then this will really not matter much anyway.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::secant_update ( DVectorSlice *  s,
DVectorSlice *  y,
DVectorSlice *  Bs 
)

void ConstrainedOptPack::MatrixSymPosDefLBFGS::initialize ( value_type  alpha,
size_type  max_size 
)

This is fine as long as alpha > 0.0.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::initialize ( const DMatrixSliceSym &  A,
size_type  max_size,
bool  force_factorization,
Inertia  inertia,
PivotTolerances  pivot_tols 
)

Sorry, this will throw an exception!

size_type ConstrainedOptPack::MatrixSymPosDefLBFGS::max_size ( ) const

Inertia ConstrainedOptPack::MatrixSymPosDefLBFGS::inertia ( ) const

Returns (0,0,rows())

void ConstrainedOptPack::MatrixSymPosDefLBFGS::set_uninitialized ( )

Will set rows() == 0.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::augment_update ( const DVectorSlice *  t,
value_type  alpha,
bool  force_refactorization,
EEigenValType  add_eigen_val,
PivotTolerances  pivot_tols 
)

Augment the matrix to add a row and column.

This function is very limited in what it will do. It will throw exceptions if alpha <= 0.0 or t != NULL or add_eigen_val == EIGEN_VAL_NEG or this->rows() == this->max_size(). The obvious postconditions for this function will only technically be satisfied if alpha == this->gamma_k().

void ConstrainedOptPack::MatrixSymPosDefLBFGS::delete_update ( size_type  jd,
bool  force_refactorization,
EEigenValType  drop_eigen_val,
PivotTolerances  pivot_tols 
)

Should always succeed unless user gives a wrong value for drop_eigen_val.

const DMatrixSliceTri ConstrainedOptPack::MatrixSymPosDefLBFGS::R ( ) const [private]

const DMatrixSliceTri ConstrainedOptPack::MatrixSymPosDefLBFGS::Lb ( ) const [private]

Strictly lower triangular part of L.

DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::STY ( ) [private]

const DMatrixSlice ConstrainedOptPack::MatrixSymPosDefLBFGS::STY ( ) const [private]

DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::STS ( ) [private]

const DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::STS ( ) const [private]

DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::YTY ( ) [private]

const DMatrixSliceSym ConstrainedOptPack::MatrixSymPosDefLBFGS::YTY ( ) const [private]

void ConstrainedOptPack::MatrixSymPosDefLBFGS::V_invQtV ( DVectorSlice *  y,
const DVectorSlice &  x 
) const [private]

y = inv(Q) * x

void ConstrainedOptPack::MatrixSymPosDefLBFGS::Vp_DtV ( DVectorSlice *  y,
const DVectorSlice &  x 
) const [private]

y += D * x

void ConstrainedOptPack::MatrixSymPosDefLBFGS::update_Q ( ) const [private]

Update Q.

void ConstrainedOptPack::MatrixSymPosDefLBFGS::assert_initialized ( ) const [private]


Member Data Documentation

Definition at line 278 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 279 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 280 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 281 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

VectorSpace::space_ptr_t ConstrainedOptPack::MatrixSymPosDefLBFGS::vec_spc_ [private]

Definition at line 284 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 286 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 286 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 286 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 286 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 291 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 294 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 294 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 298 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 298 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 304 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.

Definition at line 305 of file ConstrainedOptPack_MatrixSymPosDefLBFGS.hpp.


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