portelli/Grid
1
0
Fork 0
mirror of https://github.com/paboyle/Grid.git synced 2025-06-12 12:17:05 +01:00
Code Releases Activity

Merge remote-tracking branch 'upstream/develop' into feature/wilsonmg

Browse Source
This commit is contained in:
Daniel Richtmann
2018-03-23 21:13:50 +01:00
parent 3c3ec4e267 f290b2e908
commit afdcbf79d1
37 changed files with 1129 additions and 551 deletions
Download Patch File Download Diff File Expand all files Collapse all files

1
lib/algorithms/Algorithms.h
View File

@ -39,6 +39,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
#include <Grid/algorithms/approx/MultiShiftFunction.h>
#include <Grid/algorithms/approx/Forecast.h>
#include <Grid/algorithms/iterative/Deflation.h>
#include <Grid/algorithms/iterative/ConjugateGradient.h>
#include <Grid/algorithms/iterative/ConjugateResidual.h>
#include <Grid/algorithms/iterative/NormalEquations.h>

101
lib/algorithms/iterative/Deflation.h Normal file
View File

@ -0,0 +1,101 @@
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
Copyright (C) 2015
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
#ifndef GRID_DEFLATION_H
#define GRID_DEFLATION_H
namespace Grid {
struct ZeroGuesser {
public:
template<class Field>
void operator()(const Field &src,Field &guess) { guess = Zero(); };
};
struct SourceGuesser {
public:
template<class Field>
void operator()(const Field &src,Field &guess) { guess = src; };
};
////////////////////////////////
// Fine grid deflation
////////////////////////////////
template<class Field>
struct DeflatedGuesser {
private:
const std::vector<Field> &evec;
const std::vector<RealD> &eval;
public:
DeflatedGuesser(const std::vector<Field> & _evec,const std::vector<RealD> & _eval) : evec(_evec), eval(_eval) {};
void operator()(const Field &src,Field &guess) {
guess = zero;
assert(evec.size()==eval.size());
auto N = evec.size();
for (int i=0;i<N;i++) {
const Field& tmp = evec[i];
axpy(guess,TensorRemove(innerProduct(tmp,src)) / eval[i],tmp,guess);
}
}
};
template<class FineField, class CoarseField>
class LocalCoherenceDeflatedGuesser {
private:
const std::vector<FineField> &subspace;
const std::vector<CoarseField> &evec_coarse;
const std::vector<RealD> &eval_coarse;
public:
LocalCoherenceDeflatedGuesser(const std::vector<FineField> &_subspace,
const std::vector<CoarseField> &_evec_coarse,
const std::vector<RealD> &_eval_coarse)
: subspace(_subspace),
evec_coarse(_evec_coarse),
eval_coarse(_eval_coarse)
{
}
void operator()(const FineField &src,FineField &guess) {
int N = (int)evec_coarse.size();
CoarseField src_coarse(evec_coarse[0]._grid);
CoarseField guess_coarse(evec_coarse[0]._grid); guess_coarse = zero;
blockProject(src_coarse,src,subspace);
for (int i=0;i<N;i++) {
const CoarseField & tmp = evec_coarse[i];
axpy(guess_coarse,TensorRemove(innerProduct(tmp,src_coarse)) / eval_coarse[i],tmp,guess_coarse);
}
blockPromote(guess_coarse,guess,subspace);
};
};
}
#endif

15
lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
View File

@ -149,19 +149,6 @@ void basisSortInPlace(std::vector<Field> & _v,std::vector<RealD>& sort_vals, boo
basisReorderInPlace(_v,sort_vals,idx);
}
// PAB: faster to compute the inner products first then fuse loops.
// If performance critical can improve.
template<class Field>
void basisDeflate(const std::vector<Field> &_v,const std::vector<RealD>& eval,const Field& src_orig,Field& result) {
result = zero;
assert(_v.size()==eval.size());
int N = (int)_v.size();
for (int i=0;i<N;i++) {
Field& tmp = _v[i];
axpy(result,TensorRemove(innerProduct(tmp,src_orig)) / eval[i],tmp,result);
}
}
/////////////////////////////////////////////////////////////
// Implicitly restarted lanczos
/////////////////////////////////////////////////////////////
@ -181,6 +168,7 @@ enum IRLdiagonalisation {
template<class Field> class ImplicitlyRestartedLanczosHermOpTester : public ImplicitlyRestartedLanczosTester<Field>
{
public:
LinearFunction<Field> &_HermOp;
ImplicitlyRestartedLanczosHermOpTester(LinearFunction<Field> &HermOp) : _HermOp(HermOp) { };
int ReconstructEval(int j,RealD resid,Field &B, RealD &eval,RealD evalMaxApprox)
@ -243,6 +231,7 @@ class ImplicitlyRestartedLanczos {
/////////////////////////
public:
//////////////////////////////////////////////////////////////////
// PAB:
//////////////////////////////////////////////////////////////////

175
lib/algorithms/iterative/LocalCoherenceLanczos.h
View File

@ -28,7 +28,10 @@ Author: paboyle <paboyle@ph.ed.ac.uk>
/* END LEGAL */
#ifndef GRID_LOCAL_COHERENCE_IRL_H
#define GRID_LOCAL_COHERENCE_IRL_H
namespace Grid {
struct LanczosParams : Serializable {
public:
GRID_SERIALIZABLE_CLASS_MEMBERS(LanczosParams,
@ -70,21 +73,24 @@ public:
typedef Lattice<Fobj> FineField;
LinearOperatorBase<FineField> &_Linop;
Aggregation<Fobj,CComplex,nbasis> &_Aggregate;
std::vector<FineField> &subspace;
ProjectedHermOp(LinearOperatorBase<FineField>& linop, Aggregation<Fobj,CComplex,nbasis> &aggregate) :
_Linop(linop),
_Aggregate(aggregate) { };
ProjectedHermOp(LinearOperatorBase<FineField>& linop, std::vector<FineField> & _subspace) :
_Linop(linop), subspace(_subspace)
{
assert(subspace.size() >0);
};
void operator()(const CoarseField& in, CoarseField& out) {
GridBase *FineGrid = subspace[0]._grid;
int checkerboard = subspace[0].checkerboard;
FineField fin (FineGrid); fin.checkerboard= checkerboard;
FineField fout(FineGrid); fout.checkerboard = checkerboard;
GridBase *FineGrid = _Aggregate.FineGrid;
FineField fin(FineGrid);
FineField fout(FineGrid);
_Aggregate.PromoteFromSubspace(in,fin); std::cout<<GridLogIRL<<"ProjectedHermop : Promote to fine"<<std::endl;
_Linop.HermOp(fin,fout); std::cout<<GridLogIRL<<"ProjectedHermop : HermOp (fine) "<<std::endl;
_Aggregate.ProjectToSubspace(out,fout); std::cout<<GridLogIRL<<"ProjectedHermop : Project to coarse "<<std::endl;
blockPromote(in,fin,subspace); std::cout<<GridLogIRL<<"ProjectedHermop : Promote to fine"<<std::endl;
_Linop.HermOp(fin,fout); std::cout<<GridLogIRL<<"ProjectedHermop : HermOp (fine) "<<std::endl;
blockProject(out,fout,subspace); std::cout<<GridLogIRL<<"ProjectedHermop : Project to coarse "<<std::endl;
}
};
@ -99,24 +105,27 @@ public:
OperatorFunction<FineField> & _poly;
LinearOperatorBase<FineField> &_Linop;
Aggregation<Fobj,CComplex,nbasis> &_Aggregate;
std::vector<FineField> &subspace;
ProjectedFunctionHermOp(OperatorFunction<FineField> & poly,LinearOperatorBase<FineField>& linop,
Aggregation<Fobj,CComplex,nbasis> &aggregate) :
ProjectedFunctionHermOp(OperatorFunction<FineField> & poly,
LinearOperatorBase<FineField>& linop,
std::vector<FineField> & _subspace) :
_poly(poly),
_Linop(linop),
_Aggregate(aggregate) { };
subspace(_subspace)
{ };
void operator()(const CoarseField& in, CoarseField& out) {
GridBase *FineGrid = _Aggregate.FineGrid;
FineField fin(FineGrid) ;fin.checkerboard =_Aggregate.checkerboard;
FineField fout(FineGrid);fout.checkerboard =_Aggregate.checkerboard;
_Aggregate.PromoteFromSubspace(in,fin); std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Promote to fine"<<std::endl;
GridBase *FineGrid = subspace[0]._grid;
int checkerboard = subspace[0].checkerboard;
FineField fin (FineGrid); fin.checkerboard =checkerboard;
FineField fout(FineGrid);fout.checkerboard =checkerboard;
blockPromote(in,fin,subspace); std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Promote to fine"<<std::endl;
_poly(_Linop,fin,fout); std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Poly "<<std::endl;
_Aggregate.ProjectToSubspace(out,fout); std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Project to coarse "<<std::endl;
blockProject(out,fout,subspace); std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Project to coarse "<<std::endl;
}
};
@ -132,19 +141,23 @@ class ImplicitlyRestartedLanczosSmoothedTester : public ImplicitlyRestartedLanc
LinearFunction<CoarseField> & _Poly;
OperatorFunction<FineField> & _smoother;
LinearOperatorBase<FineField> &_Linop;
Aggregation<Fobj,CComplex,nbasis> &_Aggregate;
RealD _coarse_relax_tol;
RealD _coarse_relax_tol;
std::vector<FineField> &_subspace;
ImplicitlyRestartedLanczosSmoothedTester(LinearFunction<CoarseField> &Poly,
OperatorFunction<FineField> &smoother,
LinearOperatorBase<FineField> &Linop,
Aggregation<Fobj,CComplex,nbasis> &Aggregate,
std::vector<FineField> &subspace,
RealD coarse_relax_tol=5.0e3)
: _smoother(smoother), _Linop(Linop),_Aggregate(Aggregate), _Poly(Poly), _coarse_relax_tol(coarse_relax_tol) { };
: _smoother(smoother), _Linop(Linop), _Poly(Poly), _subspace(subspace),
_coarse_relax_tol(coarse_relax_tol)
{ };
int TestConvergence(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
{
CoarseField v(B);
RealD eval_poly = eval;
// Apply operator
_Poly(B,v);
@ -168,14 +181,13 @@ class ImplicitlyRestartedLanczosSmoothedTester : public ImplicitlyRestartedLanc
}
int ReconstructEval(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
{
GridBase *FineGrid = _Aggregate.FineGrid;
int checkerboard = _Aggregate.checkerboard;
GridBase *FineGrid = _subspace[0]._grid;
int checkerboard = _subspace[0].checkerboard;
FineField fB(FineGrid);fB.checkerboard =checkerboard;
FineField fv(FineGrid);fv.checkerboard =checkerboard;
_Aggregate.PromoteFromSubspace(B,fv);
blockPromote(B,fv,_subspace);
_smoother(_Linop,fv,fB);
RealD eval_poly = eval;
@ -217,27 +229,65 @@ protected:
int _checkerboard;
LinearOperatorBase<FineField> & _FineOp;
// FIXME replace Aggregation with vector of fine; the code reuse is too small for
// the hassle and complexity of cross coupling.
Aggregation<Fobj,CComplex,nbasis> _Aggregate;
std::vector<RealD> evals_fine;
std::vector<RealD> evals_coarse;
std::vector<CoarseField> evec_coarse;
std::vector<RealD> &evals_fine;
std::vector<RealD> &evals_coarse;
std::vector<FineField> &subspace;
std::vector<CoarseField> &evec_coarse;
private:
std::vector<RealD> _evals_fine;
std::vector<RealD> _evals_coarse;
std::vector<FineField> _subspace;
std::vector<CoarseField> _evec_coarse;
public:
LocalCoherenceLanczos(GridBase *FineGrid,
GridBase *CoarseGrid,
LinearOperatorBase<FineField> &FineOp,
int checkerboard) :
GridBase *CoarseGrid,
LinearOperatorBase<FineField> &FineOp,
int checkerboard) :
_CoarseGrid(CoarseGrid),
_FineGrid(FineGrid),
_Aggregate(CoarseGrid,FineGrid,checkerboard),
_FineOp(FineOp),
_checkerboard(checkerboard)
_checkerboard(checkerboard),
evals_fine (_evals_fine),
evals_coarse(_evals_coarse),
subspace (_subspace),
evec_coarse(_evec_coarse)
{
evals_fine.resize(0);
evals_coarse.resize(0);
};
void Orthogonalise(void ) { _Aggregate.Orthogonalise(); }
//////////////////////////////////////////////////////////////////////////
// Alternate constructore, external storage for use by Hadrons module
//////////////////////////////////////////////////////////////////////////
LocalCoherenceLanczos(GridBase *FineGrid,
GridBase *CoarseGrid,
LinearOperatorBase<FineField> &FineOp,
int checkerboard,
std::vector<FineField> &ext_subspace,
std::vector<CoarseField> &ext_coarse,
std::vector<RealD> &ext_eval_fine,
std::vector<RealD> &ext_eval_coarse
) :
_CoarseGrid(CoarseGrid),
_FineGrid(FineGrid),
_FineOp(FineOp),
_checkerboard(checkerboard),
evals_fine (ext_eval_fine),
evals_coarse(ext_eval_coarse),
subspace (ext_subspace),
evec_coarse (ext_coarse)
{
evals_fine.resize(0);
evals_coarse.resize(0);
};
void Orthogonalise(void ) {
CoarseScalar InnerProd(_CoarseGrid);
blockOrthogonalise(InnerProd,subspace);std::cout << GridLogMessage <<" Gramm-Schmidt pass 1"<<std::endl;
blockOrthogonalise(InnerProd,subspace);std::cout << GridLogMessage <<" Gramm-Schmidt pass 2"<<std::endl;
};
template<typename T> static RealD normalise(T& v)
{
@ -246,43 +296,44 @@ public:
v = v * (1.0/nn);
return nn;
}
/*
void fakeFine(void)
{
int Nk = nbasis;
_Aggregate.subspace.resize(Nk,_FineGrid);
_Aggregate.subspace[0]=1.0;
_Aggregate.subspace[0].checkerboard=_checkerboard;
normalise(_Aggregate.subspace[0]);
subspace.resize(Nk,_FineGrid);
subspace[0]=1.0;
subspace[0].checkerboard=_checkerboard;
normalise(subspace[0]);
PlainHermOp<FineField> Op(_FineOp);
for(int k=1;k<Nk;k++){
_Aggregate.subspace[k].checkerboard=_checkerboard;
Op(_Aggregate.subspace[k-1],_Aggregate.subspace[k]);
normalise(_Aggregate.subspace[k]);
subspace[k].checkerboard=_checkerboard;
Op(subspace[k-1],subspace[k]);
normalise(subspace[k]);
}
}
*/
void testFine(RealD resid)
{
assert(evals_fine.size() == nbasis);
assert(_Aggregate.subspace.size() == nbasis);
assert(subspace.size() == nbasis);
PlainHermOp<FineField> Op(_FineOp);
ImplicitlyRestartedLanczosHermOpTester<FineField> SimpleTester(Op);
for(int k=0;k<nbasis;k++){
assert(SimpleTester.ReconstructEval(k,resid,_Aggregate.subspace[k],evals_fine[k],1.0)==1);
assert(SimpleTester.ReconstructEval(k,resid,subspace[k],evals_fine[k],1.0)==1);
}
}
void testCoarse(RealD resid,ChebyParams cheby_smooth,RealD relax)
{
assert(evals_fine.size() == nbasis);
assert(_Aggregate.subspace.size() == nbasis);
assert(subspace.size() == nbasis);
//////////////////////////////////////////////////////////////////////////////////////////////////
// create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
//////////////////////////////////////////////////////////////////////////////////////////////////
Chebyshev<FineField> ChebySmooth(cheby_smooth);
ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (ChebySmooth,_FineOp,_Aggregate);
ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,_Aggregate,relax);
ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (ChebySmooth,_FineOp,_subspace);
ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
for(int k=0;k<evec_coarse.size();k++){
if ( k < nbasis ) {
@ -302,34 +353,34 @@ public:
PlainHermOp<FineField> Op(_FineOp);
evals_fine.resize(Nm);
_Aggregate.subspace.resize(Nm,_FineGrid);
subspace.resize(Nm,_FineGrid);
ImplicitlyRestartedLanczos<FineField> IRL(ChebyOp,Op,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
FineField src(_FineGrid); src=1.0; src.checkerboard = _checkerboard;
int Nconv;
IRL.calc(evals_fine,_Aggregate.subspace,src,Nconv,false);
IRL.calc(evals_fine,subspace,src,Nconv,false);
// Shrink down to number saved
assert(Nstop>=nbasis);
assert(Nconv>=nbasis);
evals_fine.resize(nbasis);
_Aggregate.subspace.resize(nbasis,_FineGrid);
subspace.resize(nbasis,_FineGrid);
}
void calcCoarse(ChebyParams cheby_op,ChebyParams cheby_smooth,RealD relax,
int Nstop, int Nk, int Nm,RealD resid,
RealD MaxIt, RealD betastp, int MinRes)
{
Chebyshev<FineField> Cheby(cheby_op);
ProjectedHermOp<Fobj,CComplex,nbasis> Op(_FineOp,_Aggregate);
ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,_Aggregate);
ProjectedHermOp<Fobj,CComplex,nbasis> Op(_FineOp,_subspace);
ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,_subspace);
//////////////////////////////////////////////////////////////////////////////////////////////////
// create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
//////////////////////////////////////////////////////////////////////////////////////////////////
Chebyshev<FineField> ChebySmooth(cheby_smooth);
ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,_Aggregate,relax);
ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,_subspace,relax);
evals_coarse.resize(Nm);
evec_coarse.resize(Nm,_CoarseGrid);

33
lib/algorithms/iterative/SchurRedBlack.h
View File

@ -107,7 +107,12 @@ namespace Grid {
};
template<class Matrix>
void operator() (Matrix & _Matrix,const Field &in, Field &out){
void operator() (Matrix & _Matrix,const Field &in, Field &out){
ZeroGuesser guess;
(*this)(_Matrix,in,out,guess);
}
template<class Matrix, class Guesser>
void operator() (Matrix & _Matrix,const Field &in, Field &out, Guesser &guess){
// FIXME CGdiagonalMee not implemented virtual function
// FIXME use CBfactorise to control schur decomp
@ -129,7 +134,6 @@ namespace Grid {
pickCheckerboard(Odd ,src_o,in);
pickCheckerboard(Even,sol_e,out);
pickCheckerboard(Odd ,sol_o,out);
std::cout << GridLogMessage << " SchurRedBlackStaggeredSolve checkerboards picked" <<std::endl;
/////////////////////////////////////////////////////
@ -146,6 +150,7 @@ namespace Grid {
// Call the red-black solver
//////////////////////////////////////////////////////////////
std::cout<<GridLogMessage << "SchurRedBlackStaggeredSolver calling the Mpc solver" <<std::endl;
guess(src_o,sol_o);
_HermitianRBSolver(_HermOpEO,src_o,sol_o); assert(sol_o.checkerboard==Odd);
std::cout<<GridLogMessage << "SchurRedBlackStaggeredSolver called the Mpc solver" <<std::endl;
@ -189,7 +194,12 @@ namespace Grid {
CBfactorise=cb;
};
template<class Matrix>
void operator() (Matrix & _Matrix,const Field &in, Field &out){
void operator() (Matrix & _Matrix,const Field &in, Field &out){
ZeroGuesser guess;
(*this)(_Matrix,in,out,guess);
}
template<class Matrix, class Guesser>
void operator() (Matrix & _Matrix,const Field &in, Field &out,Guesser &guess){
// FIXME CGdiagonalMee not implemented virtual function
// FIXME use CBfactorise to control schur decomp
@ -225,6 +235,7 @@ namespace Grid {
// Call the red-black solver
//////////////////////////////////////////////////////////////
std::cout<<GridLogMessage << "SchurRedBlack solver calling the MpcDagMp solver" <<std::endl;
guess(src_o,sol_o);
_HermitianRBSolver(_HermOpEO,src_o,sol_o); assert(sol_o.checkerboard==Odd);
///////////////////////////////////////////////////
@ -268,7 +279,12 @@ namespace Grid {
};
template<class Matrix>
void operator() (Matrix & _Matrix,const Field &in, Field &out){
void operator() (Matrix & _Matrix,const Field &in, Field &out){
ZeroGuesser guess;
(*this)(_Matrix,in,out,guess);
}
template<class Matrix,class Guesser>
void operator() (Matrix & _Matrix,const Field &in, Field &out,Guesser &guess){
// FIXME CGdiagonalMee not implemented virtual function
// FIXME use CBfactorise to control schur decomp
@ -305,6 +321,7 @@ namespace Grid {
//////////////////////////////////////////////////////////////
std::cout<<GridLogMessage << "SchurRedBlack solver calling the MpcDagMp solver" <<std::endl;
// _HermitianRBSolver(_HermOpEO,src_o,sol_o); assert(sol_o.checkerboard==Odd);
guess(src_o,tmp);
_HermitianRBSolver(_HermOpEO,src_o,tmp); assert(tmp.checkerboard==Odd);
_Matrix.MooeeInv(tmp,sol_o); assert( sol_o.checkerboard ==Odd);
@ -347,7 +364,12 @@ namespace Grid {
};
template<class Matrix>
void operator() (Matrix & _Matrix,const Field &in, Field &out){
void operator() (Matrix & _Matrix,const Field &in, Field &out){
ZeroGuesser guess;
(*this)(_Matrix,in,out,guess);
}
template<class Matrix, class Guesser>
void operator() (Matrix & _Matrix,const Field &in, Field &out,Guesser &guess){
// FIXME CGdiagonalMee not implemented virtual function
// FIXME use CBfactorise to control schur decomp
@ -385,6 +407,7 @@ namespace Grid {
std::cout<<GridLogMessage << "SchurRedBlack solver calling the MpcDagMp solver" <<std::endl;
// _HermitianRBSolver(_HermOpEO,src_o,sol_o); assert(sol_o.checkerboard==Odd);
// _HermitianRBSolver(_HermOpEO,src_o,tmp); assert(tmp.checkerboard==Odd);
guess(src_o,tmp);
_HermitianRBSolver(src_o,tmp); assert(tmp.checkerboard==Odd);
_Matrix.MooeeInv(tmp,sol_o); assert( sol_o.checkerboard ==Odd);