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114 lines
4.2 KiB
C++
114 lines
4.2 KiB
C++
#ifndef GRID_SCHUR_RED_BLACK_H
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#define GRID_SCHUR_RED_BLACK_H
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/*
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* Red black Schur decomposition
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*
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* M = (Mee Meo) = (1 0 ) (Mee 0 ) (1 Mee^{-1} Meo)
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* (Moe Moo) (Moe Mee^-1 1 ) (0 Moo-Moe Mee^-1 Meo) (0 1 )
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* = L D U
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*
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* L^-1 = (1 0 )
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* (-MoeMee^{-1} 1 )
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* L^{dag} = ( 1 Mee^{-dag} Moe^{dag} )
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* ( 0 1 )
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* L^{-d} = ( 1 -Mee^{-dag} Moe^{dag} )
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* ( 0 1 )
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*
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* U^-1 = (1 -Mee^{-1} Meo)
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* (0 1 )
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* U^{dag} = ( 1 0)
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* (Meo^dag Mee^{-dag} 1)
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* U^{-dag} = ( 1 0)
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* (-Meo^dag Mee^{-dag} 1)
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***********************
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* M psi = eta
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***********************
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*Odd
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* i) (D_oo)^{\dag} D_oo psi_o = (D_oo)^dag L^{-1} eta_o
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* eta_o' = (D_oo)^dag (eta_o - Moe Mee^{-1} eta_e)
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*Even
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* ii) Mee psi_e + Meo psi_o = src_e
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*
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* => sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
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*
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*/
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namespace Grid {
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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// Take a matrix and form a Red Black solver calling a Herm solver
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// Use of RB info prevents making SchurRedBlackSolve conform to standard interface
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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template<class Field> class SchurRedBlackSolve {
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private:
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HermitianOperatorFunction<Field> & _HermitianRBSolver;
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int CBfactorise;
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public:
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/////////////////////////////////////////////////////
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// Wrap the usual normal equations Schur trick
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/////////////////////////////////////////////////////
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SchurRedBlackSolve(HermitianOperatorFunction<Field> &HermitianRBSolver) :
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_HermitianRBSolver(HermitianRBSolver)
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{
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CBfactorise=0;
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};
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template<class Matrix>
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void operator() (Matrix & _Matrix,const Field &in, Field &out){
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// FIXME CGdiagonalMee not implemented virtual function
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// FIXME use CBfactorise to control schur decomp
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GridBase *grid = _Matrix._cbgrid;
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GridBase *fgrid= _Matrix._grid;
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Field src_e(grid);
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Field src_o(grid);
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Field sol_e(grid);
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Field sol_o(grid);
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Field tmp(grid);
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Field Mtmp(grid);
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Field resid(fgrid);
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pickCheckerboard(Even,src_e,in);
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pickCheckerboard(Odd ,src_o,in);
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/////////////////////////////////////////////////////
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// src_o = Mdag * (source_o - Moe MeeInv source_e)
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/////////////////////////////////////////////////////
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_Matrix.MooeeInv(src_e,tmp); assert( tmp.checkerboard ==Even);
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_Matrix.Meooe (tmp,Mtmp); assert( Mtmp.checkerboard ==Odd);
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tmp=src_o-Mtmp; assert( tmp.checkerboard ==Odd);
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_Matrix.MpcDag(tmp,src_o); assert(src_o.checkerboard ==Odd);
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//////////////////////////////////////////////////////////////
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// Call the red-black solver
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//////////////////////////////////////////////////////////////
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HermitianCheckerBoardedOperator<Matrix,Field> _HermOpEO(_Matrix);
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std::cout << "SchurRedBlack solver calling the MpcDagMp solver" <<std::endl;
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_HermitianRBSolver(_HermOpEO,src_o,sol_o); assert(sol_o.checkerboard==Odd);
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///////////////////////////////////////////////////
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// sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
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///////////////////////////////////////////////////
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_Matrix.Meooe(sol_o,tmp); assert( tmp.checkerboard ==Even);
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src_e = src_e-tmp; assert( src_e.checkerboard ==Even);
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_Matrix.MooeeInv(src_e,sol_e); assert( sol_e.checkerboard ==Even);
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setCheckerboard(out,sol_e); assert( sol_e.checkerboard ==Even);
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setCheckerboard(out,sol_o); assert( sol_o.checkerboard ==Odd );
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// Verify the unprec residual
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_Matrix.M(out,resid);
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resid = resid-in;
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RealD ns = norm2(in);
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RealD nr = norm2(resid);
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std::cout << "SchurRedBlack solver true unprec resid "<< sqrt(nr/ns) <<" nr "<< nr <<" ns "<<ns << std::endl;
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}
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};
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}
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#endif
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