Even-odd and time preconditioned linear operator. More...
#include <teoprec_logdet_linop.h>
Public Member Functions | |
| virtual | ~EvenOddTimePrecLogDetLinearOperator () |
| Virtual destructor to help with cleanup;. More... | |
| const Subset & | subset () const |
| Only defined on the odd lattice. More... | |
| virtual void | deriv (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const |
| Apply the derivative of the operator onto a source std::vector. More... | |
| virtual void | derivEvenEvenTimeLinOp (P &ds_u, const T &chi, const T &psi, enum PlusMinus isign) const |
| 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 |
| 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 |
| 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 |
| Apply the the odd-odd block onto a source std::vector. More... | |
 Public Member Functions inherited from Chroma::EvenOddTimePrecLinearOperator< T, P, Q > | |
| virtual | ~EvenOddTimePrecLinearOperator () |
| Virtual destructor to help with cleanup;. 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 | 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::EvenOddTimePrecLogDetLinearOperator< 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.
Here A^{-1}_{ee} does depend on the gauge fields but we can exactly simulate the determinant without pseudofermion fields since we know det A_{ee} and can write it in the action as exp( log det A ) = exp( Tr Ln A )
Since we can explicitly evaluate Tr Ln A for the action, we can also evaluate the force contribution
d/dt ( Tr Ln A ) = Tr ( (d/dt)A A^{-1} )
and d/dt ( A^{-1} ) = A^{-1} [ (d/dt)A ] A^{-1}
hence we have functions logDetEvenEvenLinOp() and derivEvenEvenLinOp() and derivLogDetEvenEvenLinOp()
Definition at line 131 of file teoprec_logdet_linop.h.
Constructor & Destructor Documentation
◆ ~EvenOddTimePrecLogDetLinearOperator()
|
inlinevirtual |
Virtual destructor to help with cleanup;.
Definition at line 135 of file teoprec_logdet_linop.h.
Member Function Documentation
◆ deriv()
|
inlinevirtual |
Apply the derivative of the operator onto a source std::vector.
User should make sure deriv routines do a resize
Implements Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 142 of file teoprec_logdet_linop.h.
References Chroma::chi(), Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >::derivEvenEvenTimeLinOp(), Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >::derivOddOddTimeLinOp(), Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::evenEvenTimeInvLinOp(), Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::evenOddSpaceLinOp(), Chroma::isign, Chroma::MINUS, Chroma::EvenOddTimePrecLinearOperator< T, P, Q >::oddEvenSpaceLinOp(), Chroma::PLUS, Chroma::psi, tmp2, and tmp3.
◆ derivEvenEvenTimeLinOp()
|
inlinevirtual |
Apply the even-even block onto a source std::vector.
Implements Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 238 of file teoprec_logdet_linop.h.
Referenced by Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >::deriv().
◆ derivEvenOddSpaceLinOp()
|
inlinevirtual |
Apply the the even-odd block onto a source std::vector.
Implements Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 246 of file teoprec_logdet_linop.h.
◆ derivOddEvenSpaceLinOp()
|
inlinevirtual |
Apply the the odd-even block onto a source std::vector.
Implements Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 254 of file teoprec_logdet_linop.h.
◆ derivOddOddTimeLinOp()
|
inlinevirtual |
Apply the the odd-odd block onto a source std::vector.
Implements Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 262 of file teoprec_logdet_linop.h.
Referenced by Chroma::EvenOddTimePrecLogDetLinearOperator< T, P, Q >::deriv().
◆ subset()
|
inlinevirtual |
Only defined on the odd lattice.
Reimplemented from Chroma::EvenOddTimePrecLinearOperator< T, P, Q >.
Definition at line 138 of file teoprec_logdet_linop.h.
The documentation for this class was generated from the following file:
