Even-odd preconditioned linear operator. More...

#include <seoprec_linop.h>

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

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

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

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

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

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

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

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

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

virtual void	evenOddLinOp (T &chi, const T &psi, enum PlusMinus isign) const
	Apply the EvenOdd Linop for which we have a category default) More...

virtual void	oddEvenLinOp (T &chi, const T &psi, enum PlusMinus isign) const

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

virtual void	jacobiOp (T &chi, const T &psi, enum PlusMinus isign) const
	Apply the Jacobi Operator. 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	derivEvenOddLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Compute force coming from EvenOdd (A^{-1}_ee D_eo) term. More...

virtual void	derivOddEvenLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const =0
	Compute force coming from OddEven (A^{-1}_oo D_oe ) term. More...

virtual void	deriv (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const
	Deriv. More...

virtual void	derivMultipole (P &ds_u, const multi1d< T > &chi, const multi1d< T > &psi, enum PlusMinus isign) const
	Apply the derivative of the 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 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...

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::SymEvenOddPrecLinearOperator< T, P, Q >

Even-odd preconditioned linear operator.

Support for even-odd preconditioned linear operators Given a matrix M written in block form:

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

The preconditioning consists of factorizing as

 M_unprec = M_diag x M'


M_diag = [   A_E,E    0   ]
         [   0      A_O,O ]

         [ 1        M_E,O ]
M' =     [                ]
         [ M_O,E      1   ]


M_E,O = A^{-1}_E,E D_E,O
M_O,E = A^{-1}_O,O D_E,O

We then do a schur precondition of M'

as M' = L M R

L  =   [  1      0  ]
       [            ]
       [  M_O,E  1  ]



R  =   [  1    M_E,O ]
       [             ]
       [  0      1   ]


M  =   [   1                0     ]
       [                          ]
       [   0                S     ]

where S = 1 - ( M_O,E )( M_E,O )

L^{-1} = [ 1 0 ] [ ] [- M_O,E 1 ]

R^{-1} = [ 1 - M_E,O ] [ ] [ 0 1 ]

For props we need to solve:

  M  x' = L^{-1} (M_diag)^{-1} b

and then x = R^{-1} x' (backsubstitution)

for HMC we have det(L)=1 det(R)=1 det(M_diag) is handled by TraceLog/LogDet calls to clover and we pseudofermionize only the 'S' operators

Structure: capture D_oe, D_eo, A_ee, A_oo, A^{-1}_oo and A^{-1}_ee as unprecEvenOddLinOp unprecOddEvenLinOp unprecEvenEvenLinOp unprecOddOddLinOp unprecOddOddInvLinOp unprecEvenEvenInvLinOp

then we can write category defaults for:

then evenOddLinOp is M_eo = A^{-1}_ee D_eo or h.c. oddEvenLinOp is M_oe = A^{-1}_oo D_oe or h.c.

the so called Jacobi Operator: [ 1 M_eo ] [ M_oe 1 ]

the Schur Operator: S = 1 - M_oe M_eo

the Unprec Operator: diag( A_ee A_oo ) M_jacobi

We can also write category default for the forces in terms of derivEvenOddLinOp and derivOddEvenLinOp

Const-detness or log-det ness will depend on how the derivEvenOdd and derivOddEven operators are coded

ConstDet will treat A as a constant (muliplicative factor) LogDet will evaluate chain rule in derivEvenOddLinOp and also provide lodDet terms and TraceLog forces

Definition at line 131 of file seoprec_linop.h.

Constructor & Destructor Documentation

◆ ~SymEvenOddPrecLinearOperator()

template<typename T , typename P , typename Q >

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

inlinevirtual

Virtual destructor to help with cleanup;.

Definition at line 135 of file seoprec_linop.h.

Member Function Documentation

◆ deriv()

template<typename T , typename P , typename Q >

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

inlinevirtual

Deriv.

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

Reimplemented in Chroma::SymEvenOddPrecCloverLinOp.

Definition at line 292 of file seoprec_linop.h.

References chi, Chroma::isign, Chroma::MINUS, Nd, Chroma::PLUS, psi, and Chroma::zero.

◆ derivEvenOddLinOp()

template<typename T , typename P , typename Q >

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

pure virtual

Compute force coming from EvenOdd (A^{-1}_ee D_eo) term.

Implemented in Chroma::SymEvenOddPrecLogDetLinearOperator< T, P, Q >, Chroma::SymEvenOddPrecConstDetLinearOperator< T, P, Q >, and Chroma::SymEvenOddPrecLogDetLinearOperator< LatticeFermion, multi1d< LatticeColorMatrix >, multi1d< LatticeColorMatrix > >.

◆ derivMultipole()

template<typename T , typename P , typename Q >

virtual void Chroma::SymEvenOddPrecLinearOperator< T, P, Q >::derivMultipole	(	P &	ds_u,
		const multi1d< T > &	chi,
		const multi1d< T > &	psi,
		enum PlusMinus	isign
	)		const