ROL::SchurComplement Class Reference

Given a 2x2 block operator, perform the Schur reduction and return the decoupled system components. More...

#include <ROL_SchurComplement.hpp>

Public Member Functions
	SchurComplement (ROL::Ptr< OP > &A, ROL::Ptr< OP > &B, ROL::Ptr< OP > &C, ROL::Ptr< OP > &D, ROL::Ptr< V > &scratch1)
	SchurComplement (BlockOperator2< Real > &op, ROL::Ptr< Vector< Real > > &scratch1)
void	applyLower (Vector< Real > &Hv, const Vector< Real > &v, Real &tol)
void	applyLowerInverse (Vector< Real > &Hv, const Vector< Real > &v, Real &tol)
void	applyUpper (Vector< Real > &Hv, const Vector< Real > &v, Real &tol)
void	applyUpperInverse (Vector< Real > &Hv, const Vector< Real > &v, Real &tol)
ROL::Ptr< OP >	getS11 (void)
void	solve2 (Vector< Real > &Hv2, const Vector< Real > &v2, Real &tol)

Public Attributes
	A_ = op.getOperator(0,0)
	B_ = op.getOperator(0,1)
	C_ = op.getOperator(1,0)
	D_ = op.getOperator(1,1)
	U_ = ROL::makePtr<UPPER>(B_)
	L_ = ROL::makePtr<LOWER>(C_)

Private Types
typedef Vector< Real >	V
typedef PartitionedVector< Real >	PV
typedef LinearOperator< Real >	OP
typedef BlockOperator2UnitUpper	UPPER
typedef BlockOperator2UnitLower	LOWER

Private Attributes
ROL::Ptr< OP >	A_
ROL::Ptr< OP >	B_
ROL::Ptr< OP >	C_
ROL::Ptr< OP >	D_
ROL::Ptr< OP >	L_
ROL::Ptr< OP >	U_
ROL::Ptr< V >	scratch1_

Detailed Description

Given a 2x2 block operator, perform the Schur reduction and return the decoupled system components.

   Let \form#164 where 

\[ M = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \]

\[ x = \begin{pmatrix} y & z \end{pmatrix} \]

\[ b = \begin{pmayrix} u & v \end{pmatrix} \]

  The block factorization is \form#168 where 

\[ U = \begin{pmatrix} I & BD^{-1} \\ 0 & I \end{pmatrix} \]

\[ S = \begin{pmatrix} A-BD^{-1}C & 0 \\ 0 & D \end{pmatrix} \]

\[ L = \begin{pmatrix} I & 0 \\ D^{-1} C & I \]

  We can rewrite \form#172 as the block-decoupled problem \form#173
  where \form#174 and \form#175

  The expectation here is that we will solve the equation for the first decoupled
  variable iteratively. 

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Definition at line 72 of file ROL_SchurComplement.hpp.

Member Typedef Documentation

typedef Vector<Real> ROL::SchurComplement::V

private

Definition at line 74 of file ROL_SchurComplement.hpp.

typedef PartitionedVector<Real> ROL::SchurComplement::PV

private

Definition at line 75 of file ROL_SchurComplement.hpp.

typedef LinearOperator<Real> ROL::SchurComplement::OP

private

Definition at line 76 of file ROL_SchurComplement.hpp.

typedef BlockOperator2UnitUpper ROL::SchurComplement::UPPER

private

Definition at line 77 of file ROL_SchurComplement.hpp.

typedef BlockOperator2UnitLower ROL::SchurComplement::LOWER

private

Definition at line 78 of file ROL_SchurComplement.hpp.

Constructor & Destructor Documentation

ROL::SchurComplement::SchurComplement ( ROL::Ptr< OP > &  A, ROL::Ptr< OP > &  B, ROL::Ptr< OP > &  C, ROL::Ptr< OP > &  D, ROL::Ptr< V > &  scratch1  )

inline

Definition at line 91 of file ROL_SchurComplement.hpp.

References B_, and C_.

ROL::SchurComplement::SchurComplement ( BlockOperator2< Real > &  op, ROL::Ptr< Vector< Real > > &  scratch1  )

inline

Definition at line 102 of file ROL_SchurComplement.hpp.

Member Function Documentation

void ROL::SchurComplement::applyLower ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  )

inline

Definition at line 115 of file ROL_SchurComplement.hpp.

void ROL::SchurComplement::applyLowerInverse ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  )

inline

Definition at line 119 of file ROL_SchurComplement.hpp.

void ROL::SchurComplement::applyUpper ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  )

inline

Definition at line 123 of file ROL_SchurComplement.hpp.

void ROL::SchurComplement::applyUpperInverse ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  )

inline

Definition at line 127 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::getS11 ( void  )

inline

Definition at line 131 of file ROL_SchurComplement.hpp.

References A_, B_, C_, and D_.

void ROL::SchurComplement::solve2 ( Vector< Real > &  Hv2, const Vector< Real > &  v2, Real &  tol  )

inline

Definition at line 135 of file ROL_SchurComplement.hpp.

Member Data Documentation

ROL::Ptr<OP> ROL::SchurComplement::A_

private

Definition at line 82 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::B_

private

Definition at line 82 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::C_

private

Definition at line 82 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::D_

private

Definition at line 82 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::L_

private

Definition at line 84 of file ROL_SchurComplement.hpp.

ROL::Ptr<OP> ROL::SchurComplement::U_

private

Definition at line 84 of file ROL_SchurComplement.hpp.

ROL::Ptr<V> ROL::SchurComplement::scratch1_

private

Definition at line 85 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::A_ = op.getOperator(0,0)

Definition at line 107 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::B_ = op.getOperator(0,1)

Definition at line 108 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::C_ = op.getOperator(1,0)

Definition at line 109 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::D_ = op.getOperator(1,1)

Definition at line 110 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::U_ = ROL::makePtr<UPPER>(B_)

Definition at line 112 of file ROL_SchurComplement.hpp.

ROL::SchurComplement::L_ = ROL::makePtr<LOWER>(C_)

Definition at line 113 of file ROL_SchurComplement.hpp.

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The documentation for this class was generated from the following file:

• ROL_SchurComplement.hpp