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251 lines
6.3 KiB
C
251 lines
6.3 KiB
C
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#ifndef GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
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#define GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
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namespace Grid {
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/////////////////////////////////////////////////////////////
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// Base classes for iterative processes based on operators
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// single input vec, single output vec.
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/////////////////////////////////////////////////////////////
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template<class Field>
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class ConjugateGradientMultiShift : public OperatorMultiFunction<Field>,
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public OperatorFunction<Field>
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{
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public:
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RealD Tolerance;
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Integer MaxIterations;
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int verbose;
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MultiShiftFunction shifts;
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ConjugateGradientMultiShift(Integer maxit,MultiShiftFunction &_shifts) :
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MaxIterations(maxit),
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shifts(_shifts)
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{
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verbose=1;
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}
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void operator() (LinearOperatorBase<Field> &Linop, const Field &src, Field &psi)
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{
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GridBase *grid = src._grid;
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int nshift = shifts.order;
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std::vector<Field> results(nshift,grid);
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(*this)(Linop,src,results);
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psi = shifts.norm*src;
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for(int i=0;i<nshift;i++){
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psi = psi + shifts.residues[i]*results[i];
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}
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return;
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}
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void operator() (LinearOperatorBase<Field> &Linop, const Field &src, std::vector<Field> &psi)
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{
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GridBase *grid = src._grid;
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////////////////////////////////////////////////////////////////////////
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// Convenience references to the info stored in "MultiShiftFunction"
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////////////////////////////////////////////////////////////////////////
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int nshift = shifts.order;
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std::vector<RealD> &mass(shifts.poles); // Make references to array in "shifts"
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std::vector<RealD> &mresidual(shifts.tolerances);
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std::vector<RealD> alpha(nshift,1.0);
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std::vector<Field> ps(nshift,grid);// Search directions
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assert(psi.size()==nshift);
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assert(mass.size()==nshift);
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assert(mresidual.size()==nshift);
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// dynamic sized arrays on stack; 2d is a pain with vector
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RealD bs[nshift];
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RealD rsq[nshift];
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RealD z[nshift][2];
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int converged[nshift];
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const int primary =0;
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//Primary shift fields CG iteration
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RealD a,b,c,d;
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RealD cp,bp,qq; //prev
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// Matrix mult fields
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Field r(grid);
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Field p(grid);
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Field tmp(grid);
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Field mmp(grid);
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// Check lightest mass
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for(int s=0;s<nshift;s++){
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assert( mass[s]>= mass[primary] );
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converged[s]=0;
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}
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// Wire guess to zero
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// Residuals "r" are src
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// First search direction "p" is also src
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cp = norm2(src);
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for(int s=0;s<nshift;s++){
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rsq[s] = cp * mresidual[s] * mresidual[s];
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std::cout<<"ConjugateGradientMultiShift: shift "<<s
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<<" target resid "<<rsq[s]<<std::endl;
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ps[s] = src;
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}
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// r and p for primary
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r=src;
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p=src;
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//MdagM+m[0]
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Linop.HermOpAndNorm(p,mmp,d,qq);
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axpy(mmp,mass[0],p,mmp);
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RealD rn = norm2(p);
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d += rn*mass[0];
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// have verified that inner product of
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// p and mmp is equal to d after this since
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// the d computation is tricky
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// qq = real(innerProduct(p,mmp));
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// std::cout << "debug equal ? qq "<<qq<<" d "<< d<<std::endl;
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b = -cp /d;
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// Set up the various shift variables
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int iz=0;
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z[0][1-iz] = 1.0;
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z[0][iz] = 1.0;
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bs[0] = b;
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for(int s=1;s<nshift;s++){
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z[s][1-iz] = 1.0;
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z[s][iz] = 1.0/( 1.0 - b*(mass[s]-mass[0]));
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bs[s] = b*z[s][iz];
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}
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// r += b[0] A.p[0]
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// c= norm(r)
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c=axpy_norm(r,b,mmp,r);
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for(int s=0;s<nshift;s++) {
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axpby(psi[s],0.,-bs[s]*alpha[s],src,src);
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}
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// Iteration loop
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int k;
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for (k=1;k<=MaxIterations;k++){
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a = c /cp;
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axpy(p,a,p,r);
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// Note to self - direction ps is iterated seperately
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// for each shift. Does not appear to have any scope
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// for avoiding linear algebra in "single" case.
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//
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// However SAME r is used. Could load "r" and update
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// ALL ps[s]. 2/3 Bandwidth saving
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// New Kernel: Load r, vector of coeffs, vector of pointers ps
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for(int s=0;s<nshift;s++){
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if ( ! converged[s] ) {
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if (s==0){
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axpy(ps[s],a,ps[s],r);
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} else{
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RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
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axpby(ps[s],z[s][iz],as,r,ps[s]);
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}
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}
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}
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cp=c;
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Linop.HermOpAndNorm(p,mmp,d,qq);
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axpy(mmp,mass[0],p,mmp);
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RealD rn = norm2(p);
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d += rn*mass[0];
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bp=b;
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b=-cp/d;
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c=axpy_norm(r,b,mmp,r);
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// Toggle the recurrence history
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bs[0] = b;
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iz = 1-iz;
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for(int s=1;s<nshift;s++){
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if((!converged[s])){
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RealD z0 = z[s][1-iz];
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RealD z1 = z[s][iz];
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z[s][iz] = z0*z1*bp
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/ (b*a*(z1-z0) + z1*bp*(1- (mass[s]-mass[0])*b));
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bs[s] = b*z[s][iz]/z0; // NB sign rel to Mike
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}
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}
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for(int s=0;s<nshift;s++){
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int ss = s;
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// Scope for optimisation here in case of "single".
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// Could load psi[0] and pull all ps[s] in.
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// if ( single ) ss=primary;
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// Bandwith saving in single case is Ls * 3 -> 2+Ls, so ~ 3x saving
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// Pipelined CG gain:
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//
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// New Kernel: Load r, vector of coeffs, vector of pointers ps
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// New Kernel: Load psi[0], vector of coeffs, vector of pointers ps
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// If can predict the coefficient bs then we can fuse these and avoid write reread cyce
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// on ps[s].
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// Before: 3 x npole + 3 x npole
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// After : 2 x npole (ps[s]) => 3x speed up of multishift CG.
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if( (!converged[s]) ) {
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axpy(psi[ss],-bs[s]*alpha[s],ps[s],psi[ss]);
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}
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}
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// Convergence checks
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int all_converged = 1;
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for(int s=0;s<nshift;s++){
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if ( (!converged[s]) ){
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RealD css = c * z[s][iz]* z[s][iz];
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if(css<rsq[s]){
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if ( ! converged[s] )
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std::cout<<"ConjugateGradientMultiShift k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
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converged[s]=1;
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} else {
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all_converged=0;
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}
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}
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}
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if ( all_converged ){
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std::cout<< "CGMultiShift: All shifts have converged iteration "<<k<<std::endl;
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std::cout<< "CGMultiShift: Checking solutions"<<std::endl;
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// Check answers
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for(int s=0; s < nshift; s++) {
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Linop.HermOpAndNorm(psi[s],mmp,d,qq);
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axpy(tmp,mass[s],psi[s],mmp);
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axpy(r,-alpha[s],src,tmp);
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RealD rn = norm2(r);
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RealD cn = norm2(src);
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std::cout<<"CGMultiShift: shift["<<s<<"] true residual "<<std::sqrt(rn/cn)<<std::endl;
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}
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return;
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}
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}
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// ugly hack
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std::cout<<"CG multi shift did not converge"<<std::endl;
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assert(0);
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}
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};
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}
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#endif
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