Even-odd and time preconditioned linear operator. More...

#include <teoprec_linop.h>

Inheritance diagram for Chroma::EvenOddTimePrecLinearOperator< T, P, Q >:

Public Member Functions
virtual	~EvenOddTimePrecLinearOperator ()
	Virtual destructor to help with cleanup;. More...

const Subset &	subset () const
	Only defined on the odd lattice. More...

virtual void	evenEvenTimeLinOp (T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the even-even block onto a source std::vector. More...

virtual void	evenEvenTimeInvLinOp (T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the inverse of the even-even block onto a source std::vector. More...

virtual void	evenOddSpaceLinOp (T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the even-odd block onto a source std::vector. More...

virtual void	oddEvenSpaceLinOp (T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the odd-even block onto a source std::vector. More...

virtual void	oddOddTimeLinOp (T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the odd-odd block onto a source std::vector. More...

virtual void	operator() (T &chi, const T &psi, enum PlusMinus isign) const
	Apply the operator onto a source std::vector. More...

virtual void	unprecLinOp (T &chi, const T &psi, enum PlusMinus isign) const
	Apply the UNPRECONDITIONED operator onto a source std::vector. More...

virtual void	derivEvenEvenTimeLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the even-even block onto a source std::vector. More...

virtual void	derivEvenOddSpaceLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the even-odd block onto a source std::vector. More...

virtual void	derivOddEvenSpaceLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the odd-even block onto a source std::vector. More...

virtual void	derivOddOddTimeLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the the odd-odd block onto a source std::vector. More...

virtual void	deriv (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Apply the derivative of the operator onto a source std::vector. More...

virtual void	derivUnprecLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const
	Apply the derivative of the UNPRECONDITIONED operator onto a source std::vector. More...

Public Member Functions inherited from Chroma::DiffLinearOperator< T, P, Q >
virtual	~DiffLinearOperator ()
	Virtual destructor to help with cleanup;. More...

virtual const FermBC< T, P, Q > &	getFermBC () const =0
	Return the fermion BC object for this linear operator. More...

virtual void	deriv (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign, const Real &epsilon) const
	Apply the derivative of the operator onto a source std::vector to some precision. More...

virtual void	derivMultipole (P &ds_u, const multi1d< T > &chi, const multi1d< T > &psi, enum PlusMinus isign) const
	Return the force for multiple poles. More...

Public Member Functions inherited from Chroma::LinearOperator< T >
virtual	~LinearOperator ()
	Virtual destructor to help with cleanup;. More...

virtual void	operator() (T &chi, const T &psi, enum PlusMinus isign, Real epsilon) const
	Apply the operator onto a source std::vector to some precision. More...

virtual unsigned long	nFlops () const

Detailed Description

template<typename T, typename P, typename Q>
class Chroma::EvenOddTimePrecLinearOperator< T, P, Q >

Even-odd and time preconditioned linear operator.

Given a matrix M written in separate time and space operators

M = D_t + D_s

The time preconditioning consists of multiplying by the inverse of the time operator to give

M'  =  1 +  D_t^(-1)*D_s

For spatial even-odd precond., this interface requires the D_t to be diagonal in spatial components - have no space-space or space-time components. Hence, this means no even-odd component. Also, the D_s must no time coupling, and no even-even or odd-odd component - e.g. all diagonal terms have been pushed into D_t.

Rewrite M' into block form:

  [      A             D        ]
  [       E,E           E,O     ]

M' = [ ] [ D A ] [ O,E O,O ]

where the E,O refer to only the spatial dimensions and

A(e,e) = 1 + D_t^(-1)(e,e) * D_s(e,e) -> 1 # D_s(e,e)=0 D(e,o) = D_t^(-1)(e,e) * D_s(e,o) # is a matrix in time-time D(o,e) = D_t^(-1)(o,o) * D_s(o,e) # is a matrix in time-time A(o,o) = 1 + D_t^(-1)(o,o) * D_s(o,o) -> 1 # D_s(o,o)=0

A(e,e)^(-1) = <diagonal in space, matrix in time-time components>

Spatial even-odd preconditioning consists of using the triangular matrices

 [      1              0        ]
 [       E,E            E,O     ]

L = [ ] [ D A^(-1) 1 ] [ O,E E,E O,O ]

and

 [      A              D       ]
 [       E,E            E,O    ]

U = [ ] [ 0 1 ] [ O,E O,O ]

The preconditioned matrix is formed from

~ M = L^-1 * M' * U^-1

where

      [      1              0        ]
      [       E,E            E,O     ]

L^(-1) = [ ] [ - D A^(-1) 1 ] [ O,E E,E O,O ]

and

      [      A^(-1)       - A^(-1) D       ]
      [       E,E            E,E    E,O    ]

U^(-1) = [ ] [ 0 1 ] [ O,E O,O ]

Resulting in a new M

 [      1                    0                      ]

~ [ E,E E,O ] M = [ ] [ 0 A - D A^(-1) D ] [ O,E O,O O,E E,E E,O ]

This class is used to implement the resulting linear operator

~ M = A(o,o) - D(o,e) * A^-1(e,e) * D(e,o) = 1 - D_t^(-1)(o,o) * D_s(o,e) * D_t^(-1)(e,e) * D_s(e,o)

~ M^dag = 1 - D_s(o,e)^dag * D_t^(-1)(e,e)^dag * D_s(e,o)^dag * D_t^(-1)(o,o)^dag

By construction, the linear operator is ONLY defined on the odd subset

The non-symmetrical nature of the daggered version means the two cases (no-dagger and dagger) must be handled separately. This is in contrast to the standard (4D) even-odd precond. case where the the daggered version has the same structure, except the dagger is pushed down into the individual pieces.

Definition at line 115 of file teoprec_linop.h.

Constructor & Destructor Documentation

◆ ~EvenOddTimePrecLinearOperator()

template<typename T , typename P , typename Q >

virtual Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::~EvenOddTimePrecLinearOperator ( )

inlinevirtual

Virtual destructor to help with cleanup;.

Definition at line 119 of file teoprec_linop.h.

Member Function Documentation

◆ deriv()

template<typename T , typename P , typename Q >

virtual void Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::deriv	(	P &	ds_u,
		const T &	chi,
		const T &	psi,
		enum PlusMinus	isign
	)		const

pure virtual

Apply the derivative of the operator onto a source std::vector.

User should make sure deriv routines do a resize

Reimplemented from Chroma::DiffLinearOperator< T, P, Q >.

Implemented in Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >.

◆ derivEvenEvenTimeLinOp()

template<typename T , typename P , typename Q >

virtual void Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivEvenEvenTimeLinOp	(	P &	ds_u,
		const T &	chi,
		const T &	psi,
		enum PlusMinus	isign
	)		const

pure virtual

Apply the even-even block onto a source std::vector.

Implemented in Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >.

Referenced by Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivUnprecLinOp().

◆ derivEvenOddSpaceLinOp()

template<typename T , typename P , typename Q >

virtual void Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivEvenOddSpaceLinOp	(	P &	ds_u,
		const T &	chi,
		const T &	psi,
		enum PlusMinus	isign
	)		const

pure virtual

Apply the the even-odd block onto a source std::vector.

Implemented in Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >.

Referenced by Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivUnprecLinOp().

◆ derivOddEvenSpaceLinOp()

template<typename T , typename P , typename Q >

virtual void Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivOddEvenSpaceLinOp	(	P &	ds_u,
		const T &	chi,
		const T &	psi,
		enum PlusMinus	isign
	)		const

pure virtual

Apply the the odd-even block onto a source std::vector.

Implemented in Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >.

Referenced by Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivUnprecLinOp().

◆ derivOddOddTimeLinOp()

template<typename T , typename P , typename Q >

virtual void Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::derivOddOddTimeLinOp	(	P &	ds_u,
		const T &	chi,
		const T &	psi,
		enum PlusMinus	isign
	)		const