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 \(Mx=b\) where

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

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

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

The block factorization is \( M=USL \) where

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

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

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

We can rewrite \( USLx=b\) as the block-decoupled problem \( Sw=c \) where \(w=Lx\) and \( c=U^{-1}b \)

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

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Definition at line 44 of file ROL_SchurComplement.hpp.

Member Typedef Documentation

V

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

private

Definition at line 46 of file ROL_SchurComplement.hpp.

PV

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

private

Definition at line 47 of file ROL_SchurComplement.hpp.

OP

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

private

Definition at line 48 of file ROL_SchurComplement.hpp.

UPPER

typedef BlockOperator2UnitUpper ROL::SchurComplement::UPPER

private

Definition at line 49 of file ROL_SchurComplement.hpp.

LOWER

typedef BlockOperator2UnitLower ROL::SchurComplement::LOWER

private

Definition at line 50 of file ROL_SchurComplement.hpp.

Constructor & Destructor Documentation

SchurComplement() [1/2]

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 63 of file ROL_SchurComplement.hpp.

SchurComplement() [2/2]

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

inline

Definition at line 74 of file ROL_SchurComplement.hpp.

Member Function Documentation

applyLower()

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

inline

Definition at line 87 of file ROL_SchurComplement.hpp.

applyLowerInverse()

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

inline

Definition at line 91 of file ROL_SchurComplement.hpp.

applyUpper()

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

inline

Definition at line 95 of file ROL_SchurComplement.hpp.

applyUpperInverse()

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

inline

Definition at line 99 of file ROL_SchurComplement.hpp.

getS11()

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

inline

Definition at line 103 of file ROL_SchurComplement.hpp.

solve2()

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

inline

Definition at line 107 of file ROL_SchurComplement.hpp.

Member Data Documentation

A_ [1/2]

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

private

Definition at line 54 of file ROL_SchurComplement.hpp.

B_ [1/2]

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

private

Definition at line 54 of file ROL_SchurComplement.hpp.

C_ [1/2]

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

private

Definition at line 54 of file ROL_SchurComplement.hpp.

D_ [1/2]

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

private

Definition at line 54 of file ROL_SchurComplement.hpp.

L_ [1/2]

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

private

Definition at line 56 of file ROL_SchurComplement.hpp.

U_ [1/2]

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

private

Definition at line 56 of file ROL_SchurComplement.hpp.

scratch1_

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

private

Definition at line 57 of file ROL_SchurComplement.hpp.

A_ [2/2]

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

Definition at line 79 of file ROL_SchurComplement.hpp.

B_ [2/2]

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

Definition at line 80 of file ROL_SchurComplement.hpp.

C_ [2/2]

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

Definition at line 81 of file ROL_SchurComplement.hpp.

D_ [2/2]

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

Definition at line 82 of file ROL_SchurComplement.hpp.

U_ [2/2]

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

Definition at line 84 of file ROL_SchurComplement.hpp.

L_ [2/2]

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

Definition at line 85 of file ROL_SchurComplement.hpp.

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

• ROL_SchurComplement.hpp