Matrix class that represents a hessian matrix where only the super submatrix for the super basic variables need be nonsingular. More...

#include <ConstrainedOptPack_MatrixHessianSuperBasic.hpp>

Inheritance diagram for ConstrainedOptPack::MatrixHessianSuperBasic:

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Public Types
typedef Teuchos::RCP< const MatrixSymWithOpFactorized >	B_RR_ptr_t

typedef Teuchos::RCP< const MatrixOp >	B_RX_ptr_t

typedef Teuchos::RCP< const MatrixSymOp >	B_XX_ptr_t

typedef std::vector< EBounds >	bnd_fixed_t

Public Member Functions
	MatrixHessianSuperBasic ()
	Constructs to uninitialized. More...

virtual void	initialize (size_type n, size_type n_R, const size_type i_x_free[], const size_type i_x_fixed[], const EBounds bnd_fixed[], const B_RR_ptr_t &B_RR_ptr, const B_RX_ptr_t &B_RX_ptr, BLAS_Cpp::Transp B_RX_trans, const B_XX_ptr_t &B_XX_ptr)
	Initialize the matrix. More...

Protected Member Functions
void	assert_initialized () const

Private Types
typedef std::vector< size_type >	row_i_t

typedef std::vector< size_type >	col_j_t

Private Attributes
size_type	n_

size_type	n_R_

GenPermMatrixSlice	Q_R_

row_i_t	Q_R_row_i_

col_j_t	Q_R_col_j_

GenPermMatrixSlice	Q_X_

row_i_t	Q_X_row_i_

col_j_t	Q_X_col_j_

bnd_fixed_t	bnd_fixed_

B_RR_ptr_t	B_RR_ptr_

B_RX_ptr_t	B_RX_ptr_

BLAS_Cpp::Transp	B_RX_trans_

B_XX_ptr_t	B_XX_ptr_

Provide access to constituent members
const GenPermMatrixSlice &	Q_R () const

const GenPermMatrixSlice &	Q_X () const

const bnd_fixed_t &	bnd_fixed () const

const B_RR_ptr_t &	B_RR_ptr () const

const B_RX_ptr_t &	B_RX_ptr () const

BLAS_Cpp::Transp	B_RX_trans () const

const B_XX_ptr_t &	B_XX_ptr () const

Overridden from Matrix
size_type	rows () const

Overridden from MatrixOp
void	Vp_StMtV (DVectorSlice *vs_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const DVectorSlice &vs_rhs2, value_type beta) const

void	Vp_StMtV (DVectorSlice *vs_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const SpVectorSlice &sv_rhs2, value_type beta) const

void	Vp_StPtMtV (DVectorSlice *vs_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_rhs2_trans, const DVectorSlice &sv_rhs3, value_type beta) const

value_type	transVtMtV (const SpVectorSlice &sv_rhs1, BLAS_Cpp::Transp trans_rhs2, const SpVectorSlice &sv_rhs3) const

Detailed Description

Matrix class that represents a hessian matrix where only the super submatrix for the super basic variables need be nonsingular.

Given a Hessian matrix B# and a partitioning of the variables #Q = [ Q_R Q_X ]# into free (superbasic) Q_R'*x# and fixed (nonbasic) Q_X'*x# variables, this class represents the following matrix: {verbatim} [n,n] == size(B) [n,n] == size(Q), Q is an othogonal permutation matrix (i.e. Q*Q' = Q'*Q = I) [n,n_R] == size(Q_R) [n,n_X] == size(Q_X)

B = Q*Q'*B*Q*Q' = [ Q_R Q_X ] * [ Q_R'*B*Q_R Q_R'*B*Q_X ] * [ Q_R' ] [ Q_X'*B*Q_R Q_X'*B*Q_X ] [ Q_X' ]

= [ Q_R Q_X ] * [ B_RR op(B_RX) ] * [ Q_R' ] [ op(B_RX') B_XX ] [ Q_X' ]

= Q_R*B_RR*Q_R' + Q_R*op(B_RX)*Q_X' + Q_X*op(B_RX')*Q_R + Q_X*B_XX*Q_X' {verbatim} Above, we allow the prepresentation of #op(B_RX) = Q_R'*B*Q_X# to be transposed to allow for more flexibility. Since #B_RR# and #B_XX# are symmetric, we do not need to worry about transpose or not. For this class the matrix #B_RR# is required to be symmetric and nonsingular (#MatrixSymWithOpFactorized# interface), but not necessarily positive definite. This is the condition necessary for the Hessian when projected into the active constraints at the solution for an NLP. The other matrices hold no other special properties other than #B_XX# being symmetric of course.

The default compiler generated constructors are allowed and initialize the matrix to uninitialized by default.

Definition at line 87 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

Member Typedef Documentation

typedef Teuchos::RCP<const MatrixSymWithOpFactorized> ConstrainedOptPack::MatrixHessianSuperBasic::B_RR_ptr_t

Definition at line 94 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

typedef Teuchos::RCP<const MatrixOp> ConstrainedOptPack::MatrixHessianSuperBasic::B_RX_ptr_t

Definition at line 97 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

typedef Teuchos::RCP<const MatrixSymOp> ConstrainedOptPack::MatrixHessianSuperBasic::B_XX_ptr_t

Definition at line 100 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

typedef std::vector<EBounds> ConstrainedOptPack::MatrixHessianSuperBasic::bnd_fixed_t

Definition at line 103 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

typedef std::vector<size_type> ConstrainedOptPack::MatrixHessianSuperBasic::row_i_t

private

Definition at line 242 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

typedef std::vector<size_type> ConstrainedOptPack::MatrixHessianSuperBasic::col_j_t

private

Definition at line 243 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

Constructor & Destructor Documentation

ConstrainedOptPack::MatrixHessianSuperBasic::MatrixHessianSuperBasic ( )

Constructs to uninitialized.

Member Function Documentation

virtual void ConstrainedOptPack::MatrixHessianSuperBasic::initialize	(	size_type	n,
		size_type	n_R,
		const size_type	i_x_free[],
		const size_type	i_x_fixed[],
		const EBounds	bnd_fixed[],
		const B_RR_ptr_t &	B_RR_ptr,
		const B_RX_ptr_t &	B_RX_ptr,
		BLAS_Cpp::Transp	B_RX_trans,
		const B_XX_ptr_t &	B_XX_ptr
	)

virtual

Initialize the matrix.

Preconditions:{itemize} [#i_x_free != NULL#] #0 < i_x_free[l-1] <= n, l = 1...n_R# (throw ???) [#i_x_fixed != NULL#]#0 < i_x_fixed[l-1] <= n, l = 1...n-n_R# (throw ???) [#i_x_free != NULL && i_x_fixed != NULL#] #i_x_free[l-1] != i_x_fixed[p-1], l = 1...n_R, p = 1...n-n_X# (throw ???) [#n_R > 0#] #B_RR_ptr.get() != NULL && B_RR_ptr->rows() == n_R && B_RR_ptr->cols() == n_R# (throw #std::invalid_argument#) [#n_R == 0#] #B_RR_ptr.get() == NULL# (throw #std::invalid_argument#) [#n_R < n && B_RX_ptr.get() != NULL && B_RX_trans == no_trans#] B_RX_ptr->rows() == n_R && B_RX_ptr->cols() == n-n_R# (throw #std::invalid_argument#) [#n_R < n && B_RX_ptr.get() != NULL && B_RX_trans == trans#] B_RX_ptr->rows() == n-n_R && B_RX_ptr->cols() == n_R# (throw #std::invalid_argument#) [#n_R == n#] #B_RX_ptr.get() == NULL# (throw ##std::invalid_argument#) [#n_R < n#] #B_XX_ptr.get() != NULL && B_XX_ptr->rows() == n-n_R && B_XX_ptr->cols() == n-n_R# (throw #std::invalid_argument#) [#n_R == n#] #B_XX_ptr.get() == NULL# (throw ##std::invalid_argument#) {itemize}

Parameters

n	[in] number of variables (used for consistency checking)
n_R	[in] number of initially free variables (used for consistency checking)
i_x_free	[in] array (size #n_R#): #i_x_free[l-1], l = 1...n_R# defines the matrix Q_R# as:\ #Q_R(:,l) = e(i_x_free[l-1]), l = 1...n_R#\ The ordering of these indices is significant. If n == n_R# then #i_x_free == NULL# is allowed in which case it is assumed to be identity. If #n_R == 0# then of course #i_x_free == NULL# is allowed.
i_x_fixed	[in] array (size #n_X = n - n_R#): #i_x_fixed[l-1], l = 1...n_X# defines the matrix Q_X# as:\ #Q_X(:,l) = e(i_x_fixed[l-1]), l = 1...n_X#\ The ordering of these indices is significant. If #n_R==0# then #i_x_fixed == NULL# is allowed in which case it is assumed to be identity. If #n_R == n# then of course #i_x_fixed == NULL# is allowed.
bnd_fixed	[in] array (size #n_X#): bnd_fixed[l-1], l = 1...n_X# defines what bound the variables in #i_x_fixed[l-1], l = 1...n_X# are fixed at: LOWER#, UPPER# or EQUALITY#. If #n_R == n# then of course bnd_fixed == NULL# is allowed.
B_RR_ptr	[in] Smart pointer to matrix #B_RR# (size #n_R x n_R#) for the free (super basic) variables. #B_RR_ptr.get() != NULL# must be true if #n_R > # or an exception will be thrown. if #n_R == 0# then #B_RR_ptr.get() == NULL# may be true.
B_RX_ptr	[in] Smart pointer to matrix #B_RX# (size #n_R x n_X# if B_RX_trans==no_trans# or #n_X x n_R# if B_RX_trans==trans#) for the cross terms of free (super basic) and fixed (nonbasic) variables. It is allowed for #B_RX_ptr.get() == NULL#.
B_RX_trans	[in] Determines if op(B_RX) = B_RX (#no_trans#) or op(B_RX) = B_RX' (#trans#). Ignored if #n_R == n#.
B_XX_ptr	[in] Smart pointer to matrix B_XX (size #n_X x n_X#) for the fixed (nonbasic) variables. #B_XX_ptr.get() != NULL# must be true if #n_R < n# or an exception will be thrown. If #n_R == n# then #B_XX_ptr.get() == NULL# may be true.

Reimplemented in ConstrainedOptPack::MatrixHessianSuperBasicInitDiagonal.

const GenPermMatrixSlice & ConstrainedOptPack::MatrixHessianSuperBasic::Q_R ( ) const

inline

Definition at line 268 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

const GenPermMatrixSlice & ConstrainedOptPack::MatrixHessianSuperBasic::Q_X ( ) const

inline

Definition at line 275 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

const MatrixHessianSuperBasic::bnd_fixed_t & ConstrainedOptPack::MatrixHessianSuperBasic::bnd_fixed ( ) const

inline

Definition at line 283 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

const MatrixHessianSuperBasic::B_RR_ptr_t & ConstrainedOptPack::MatrixHessianSuperBasic::B_RR_ptr ( ) const

inline

Definition at line 290 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

const MatrixHessianSuperBasic::B_RX_ptr_t & ConstrainedOptPack::MatrixHessianSuperBasic::B_RX_ptr ( ) const

inline

Definition at line 298 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

BLAS_Cpp::Transp ConstrainedOptPack::MatrixHessianSuperBasic::B_RX_trans ( ) const

inline

Definition at line 304 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

const MatrixHessianSuperBasic::B_XX_ptr_t & ConstrainedOptPack::MatrixHessianSuperBasic::B_XX_ptr ( ) const

inline

Definition at line 312 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.

size_type ConstrainedOptPack::MatrixHessianSuperBasic::rows ( ) const

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

void ConstrainedOptPack::MatrixHessianSuperBasic::Vp_StMtV	(	DVectorSlice *	vs_lhs,
		value_type	alpha,
		BLAS_Cpp::Transp	trans_rhs1,
		const SpVectorSlice &	sv_rhs2,
		value_type	beta
	)		const

void ConstrainedOptPack::MatrixHessianSuperBasic::Vp_StPtMtV	(	DVectorSlice *	vs_lhs,
		value_type	alpha,
		const GenPermMatrixSlice &	P_rhs1,
		BLAS_Cpp::Transp	P_rhs1_trans,
		BLAS_Cpp::Transp	M_rhs2_trans,
		const DVectorSlice &	sv_rhs3,
		value_type	beta
	)		const

value_type ConstrainedOptPack::MatrixHessianSuperBasic::transVtMtV	(	const SpVectorSlice &	sv_rhs1,
		BLAS_Cpp::Transp	trans_rhs2,
		const SpVectorSlice &	sv_rhs3
	)		const