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cut at Conjugate gradient. Also copied in Remez, Zolotarev, Chebyshev from Mike Clark, Tony Kennedy and my BFM package respectively since we know we will need these. I wanted the structure of algorithms/approx algorithms/iterative etc.. to start taking shape.
107 lines
3.9 KiB
C++
107 lines
3.9 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 (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 : public OperatorFunction<Field>{
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private:
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SparseMatrixBase<Field> & _Matrix;
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OperatorFunction<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(SparseMatrixBase<Field> &Matrix, OperatorFunction<Field> &HermitianRBSolver)
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: _Matrix(Matrix), _HermitianRBSolver(HermitianRBSolver) {
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CBfactorise=0;
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};
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void operator() (const Field &in, Field &out){
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// FIXME CGdiagonalMee not implemented virtual function
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// FIXME need to make eo grid from full grid.
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// FIXME use CBfactorise to control schur decomp
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const int Even=0;
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const int Odd =1;
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// Make a cartesianRedBlack from full Grid
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GridRedBlackCartesian grid(in._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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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); // MooeeInv(source[Even],tmp,DaggerNo,Even);
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_Matrix.Meooe (tmp,Mtmp); // Meo (tmp,src,Odd,DaggerNo);
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tmp=src_o-Mtmp; // axpy (tmp,src,source[Odd],-1.0);
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_Matrix.MpcDag(tmp,src_o); // Mprec(tmp,src,Mtmp,DaggerYes);
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//////////////////////////////////////////////////////////////
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// Call the red-black solver
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//////////////////////////////////////////////////////////////
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_HermitianRBSolver(src_o,sol_o); // CGNE_prec_MdagM(solution[Odd],src);
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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); // Meo(solution[Odd],tmp,Even,DaggerNo);
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src_e = src_e-tmp; // axpy(src,tmp,source[Even],-1.0);
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_Matrix.MooeeInv(src_e,sol_e); // MooeeInv(src,solution[Even],DaggerNo,Even);
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setCheckerboard(out,sol_e);
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setCheckerboard(out,sol_o);
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}
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};
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}
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#endif
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