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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>
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 |
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.
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.
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Definition at line 242 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 243 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
ConstrainedOptPack::MatrixHessianSuperBasic::MatrixHessianSuperBasic | ( | ) |
Constructs to uninitialized.
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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}
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.
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Definition at line 268 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 275 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 283 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 290 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 298 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 304 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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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 |
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Definition at line 248 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 249 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 250 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 251 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 252 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 253 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 254 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 255 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 256 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 257 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 258 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 259 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.
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Definition at line 260 of file ConstrainedOptPack_MatrixHessianSuperBasic.hpp.