This linear operator computes the inverse of a upper triangular matrix. More...

#include <Teko_BlockUpperTriInverseOp.hpp>

Inheritance diagram for Teko::BlockUpperTriInverseOp:

Public Member Functions
	BlockUpperTriInverseOp (BlockedLinearOp &U, const std::vector< LinearOp > &invDiag)
	This constructor explicitly takes an upper triangular matrix and inverse diagonal operators and builds a back substitution operator. More...

Inherited methods from Thyra::LinearOpBase
virtual VectorSpace	range () const
	Range space of this operator. More...

virtual VectorSpace	domain () const
	Domain space of this operator. More...

virtual void	implicitApply (const BlockedMultiVector &x, BlockedMultiVector &y, const double alpha=1.0, const double beta=0.0) const
	Perform a matrix vector multiply with this operator. More...

virtual void	implicitApply (const Thyra::EOpTransp M_trans, const BlockedMultiVector &x, BlockedMultiVector &y, const double alpha=1.0, const double beta=0.0) const
	Perform a matrix vector multiply with this implicitly defined blocked operator. More...

Protected Attributes
const BlockedLinearOp	U_
	operator More...

std::vector< LinearOp >	invDiag_
	(Approximate) Inverses of the diagonal operators More...

Teuchos::RCP< const Thyra::ProductVectorSpaceBase < double > >	productRange_
	Range vector space. More...

Teuchos::RCP< const Thyra::ProductVectorSpaceBase < double > >	productDomain_
	Domain vector space. More...

Additional Inherited Members
Protected Member Functions inherited from Teko::BlockImplicitLinearOp
virtual bool	opSupportedImpl (const Thyra::EOpTransp M_trans) const
	Functions required by Thyra::LinearOpBase. More...

Detailed Description

This linear operator computes the inverse of a upper triangular matrix.

This linear operator computes the inverse of an upper triangular matrix. This requires, the upper triangular blocks, as well as the inverse of the operators on the diagonal.

Definition at line 26 of file Teko_BlockUpperTriInverseOp.hpp.

Constructor & Destructor Documentation

Teko::BlockUpperTriInverseOp::BlockUpperTriInverseOp	(	BlockedLinearOp &	U,
		const std::vector< LinearOp > &	invDiag
	)

This constructor explicitly takes an upper triangular matrix and inverse diagonal operators and builds a back substitution operator.

This constructor explicitly takes the parts of $ A $ required to build the inverse operator.

This constructor explicitly takes an upper triangular matrix and inverse diagonal operators and builds a back substitution operator.

Parameters

[in]	U	Upper triangular matrix object
[in]	invDiag	Vector containing the inverse of the diagonal blocks

This constructor explicitly takes the parts of $ A $ required to build the inverse operator.

Parameters

[in]	A	The block $2 \times 2$ operator.
[in]	invA00	An approximate inverse of $A_{00}$ .
[in]	invS	An approximate inverse of $S = -A_{11} + A_{10} A_{00}^{-1} A_{01}$ .

Definition at line 28 of file Teko_BlockUpperTriInverseOp.cpp.

Member Function Documentation

virtual VectorSpace Teko::BlockUpperTriInverseOp::range ( ) const

inlinevirtual

Range space of this operator.

Implements Teko::BlockImplicitLinearOp.

Definition at line 43 of file Teko_BlockUpperTriInverseOp.hpp.

virtual VectorSpace Teko::BlockUpperTriInverseOp::domain ( ) const

inlinevirtual

Domain space of this operator.

Implements Teko::BlockImplicitLinearOp.

Definition at line 46 of file Teko_BlockUpperTriInverseOp.hpp.

void Teko::BlockUpperTriInverseOp::implicitApply	(	const BlockedMultiVector &	x,
		BlockedMultiVector &	y,
		const double	alpha = `1.0`,
		const double	beta = `0.0`
	)		const

virtual

Perform a matrix vector multiply with this operator.

The apply function takes one vector as input and applies the inverse $ LDU $ decomposition. The result is returned in $y$ . If this operator is reprsented as $M$ then $y = \alpha M x + \beta y$ (ignoring conjugation!).

Parameters

[in]	x
[in,out]	y
[in]	alpha	(default=1)
[in]	beta	(default=0)

Implements Teko::BlockImplicitLinearOp.

Definition at line 47 of file Teko_BlockUpperTriInverseOp.cpp.

void Teko::BlockUpperTriInverseOp::implicitApply	(	const Thyra::EOpTransp	M_trans,
		const BlockedMultiVector &	src,
		BlockedMultiVector &	dst,
		const double	alpha = `1.0`,
		const double	beta = `0.0`
	)		const

virtual

Perform a matrix vector multiply with this implicitly defined blocked operator.

Perform a matrix vector multiply with this operator.

The apply function takes one vector as input and applies a linear operator. The result is returned in $y$ . If this operator is reprsented as $M$ then $y = \alpha M x + \beta y$

Parameters

[in]	x
[in,out]	y
[in]	alpha	(default=1)
[in]	beta	(default=0)

The apply function takes one vector as input and applies the inverse $ LDU $ decomposition. The result is returned in $y$ . If this operator is reprsented as $M$ then $y = \alpha M x + \beta y$ (ignoring conjugation!).

Parameters