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317 lines
7.3 KiB
C++
317 lines
7.3 KiB
C++
#ifndef GRID_CHEBYSHEV_H
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#define GRID_CHEBYSHEV_H
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#include<Grid.h>
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#include<algorithms/LinearOperator.h>
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namespace Grid {
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////////////////////////////////////////////////////////////////////////////////////////////
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// Simple general polynomial with user supplied coefficients
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////////////////////////////////////////////////////////////////////////////////////////////
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template<class Field>
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class HermOpOperatorFunction : public OperatorFunction<Field> {
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void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
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Linop.HermOp(in,out);
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};
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};
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template<class Field>
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class Polynomial : public OperatorFunction<Field> {
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private:
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std::vector<RealD> Coeffs;
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public:
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Polynomial(std::vector<RealD> &_Coeffs) : Coeffs(_Coeffs) { };
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// Implement the required interface
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void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
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Field AtoN(in._grid);
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Field Mtmp(in._grid);
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AtoN = in;
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out = AtoN*Coeffs[0];
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// std::cout <<"Poly in " <<norm2(in)<<std::endl;
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// std::cout <<"0 " <<norm2(out)<<std::endl;
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for(int n=1;n<Coeffs.size();n++){
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Mtmp = AtoN;
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Linop.HermOp(Mtmp,AtoN);
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out=out+AtoN*Coeffs[n];
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// std::cout << n<<" " <<norm2(out)<<std::endl;
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}
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};
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};
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////////////////////////////////////////////////////////////////////////////////////////////
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// Generic Chebyshev approximations
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////////////////////////////////////////////////////////////////////////////////////////////
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template<class Field>
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class Chebyshev : public OperatorFunction<Field> {
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private:
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std::vector<RealD> Coeffs;
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int order;
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RealD hi;
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RealD lo;
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public:
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void csv(std::ostream &out){
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for (RealD x=lo; x<hi; x+=(hi-lo)/1000) {
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RealD f = approx(x);
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out<< x<<" "<<f<<std::endl;
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}
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return;
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}
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// Convenience for plotting the approximation
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void PlotApprox(std::ostream &out) {
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out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
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for(RealD x=lo;x<hi;x+=(hi-lo)/50.0){
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out <<x<<"\t"<<approx(x)<<std::endl;
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}
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};
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Chebyshev(){};
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Chebyshev(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD) ) {Init(_lo,_hi,_order,func);};
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////////////////////////////////////////////////////////////////////////////////////////////////////
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// c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
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////////////////////////////////////////////////////////////////////////////////////////////////////
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void Init(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD))
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{
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lo=_lo;
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hi=_hi;
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order=_order;
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if(order < 2) exit(-1);
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Coeffs.resize(order);
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for(int j=0;j<order;j++){
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RealD s=0;
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for(int k=0;k<order;k++){
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RealD y=std::cos(M_PI*(k+0.5)/order);
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RealD x=0.5*(y*(hi-lo)+(hi+lo));
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RealD f=func(x);
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s=s+f*std::cos( j*M_PI*(k+0.5)/order );
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}
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Coeffs[j] = s * 2.0/order;
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}
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};
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void JacksonSmooth(void){
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RealD M=order;
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RealD alpha = M_PI/(M+2);
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RealD lmax = std::cos(alpha);
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RealD sumUsq =0;
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std::vector<RealD> U(M);
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std::vector<RealD> a(M);
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std::vector<RealD> g(M);
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for(int n=0;n<=M;n++){
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U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
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sumUsq += U[n]*U[n];
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}
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sumUsq = std::sqrt(sumUsq);
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for(int i=1;i<=M;i++){
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a[i] = U[i]/sumUsq;
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}
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g[0] = 1.0;
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for(int m=1;m<=M;m++){
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g[m] = 0;
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for(int i=0;i<=M-m;i++){
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g[m]+= a[i]*a[m+i];
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}
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}
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for(int m=1;m<=M;m++){
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Coeffs[m]*=g[m];
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}
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}
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RealD approx(RealD x) // Convenience for plotting the approximation
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{
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RealD Tn;
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RealD Tnm;
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RealD Tnp;
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RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
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RealD T0=1;
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RealD T1=y;
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RealD sum;
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sum = 0.5*Coeffs[0]*T0;
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sum+= Coeffs[1]*T1;
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Tn =T1;
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Tnm=T0;
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for(int i=2;i<order;i++){
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Tnp=2*y*Tn-Tnm;
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Tnm=Tn;
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Tn =Tnp;
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sum+= Tn*Coeffs[i];
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}
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return sum;
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};
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// Implement the required interface
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void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
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GridBase *grid=in._grid;
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int vol=grid->gSites();
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Field T0(grid); T0 = in;
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Field T1(grid);
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Field T2(grid);
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Field y(grid);
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Field *Tnm = &T0;
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Field *Tn = &T1;
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Field *Tnp = &T2;
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std::cout<<GridLogMessage << "Chebyshev ["<<lo<<","<<hi<<"]"<< " order "<<order <<std::endl;
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// Tn=T1 = (xscale M + mscale)in
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RealD xscale = 2.0/(hi-lo);
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RealD mscale = -(hi+lo)/(hi-lo);
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Linop.HermOp(T0,y);
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T1=y*xscale+in*mscale;
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// sum = .5 c[0] T0 + c[1] T1
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out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
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for(int n=2;n<order;n++){
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Linop.HermOp(*Tn,y);
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y=xscale*y+mscale*(*Tn);
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*Tnp=2.0*y-(*Tnm);
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out=out+Coeffs[n]* (*Tnp);
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// Cycle pointers to avoid copies
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Field *swizzle = Tnm;
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Tnm =Tn;
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Tn =Tnp;
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Tnp =swizzle;
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}
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}
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};
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template<class Field>
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class ChebyshevLanczos : public Chebyshev<Field> {
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private:
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std::vector<RealD> Coeffs;
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int order;
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RealD alpha;
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RealD beta;
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RealD mu;
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public:
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ChebyshevLanczos(RealD _alpha,RealD _beta,RealD _mu,int _order) :
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alpha(_alpha),
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beta(_beta),
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mu(_mu)
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{
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order=_order;
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Coeffs.resize(order);
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for(int i=0;i<_order;i++){
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Coeffs[i] = 0.0;
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}
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Coeffs[order-1]=1.0;
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};
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void csv(std::ostream &out){
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for (RealD x=-1.2*alpha; x<1.2*alpha; x+=(2.0*alpha)/10000) {
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RealD f = approx(x);
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out<< x<<" "<<f<<std::endl;
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}
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return;
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}
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RealD approx(RealD xx) // Convenience for plotting the approximation
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{
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RealD Tn;
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RealD Tnm;
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RealD Tnp;
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Real aa = alpha * alpha;
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Real bb = beta * beta;
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RealD x = ( 2.0 * (xx-mu)*(xx-mu) - (aa+bb) ) / (aa-bb);
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RealD y= x;
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RealD T0=1;
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RealD T1=y;
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RealD sum;
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sum = 0.5*Coeffs[0]*T0;
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sum+= Coeffs[1]*T1;
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Tn =T1;
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Tnm=T0;
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for(int i=2;i<order;i++){
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Tnp=2*y*Tn-Tnm;
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Tnm=Tn;
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Tn =Tnp;
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sum+= Tn*Coeffs[i];
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}
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return sum;
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};
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// shift_Multiply in Rudy's code
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void AminusMuSq(LinearOperatorBase<Field> &Linop, const Field &in, Field &out)
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{
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GridBase *grid=in._grid;
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Field tmp(grid);
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RealD aa= alpha*alpha;
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RealD bb= beta * beta;
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Linop.HermOp(in,out);
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out = out - mu*in;
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Linop.HermOp(out,tmp);
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tmp = tmp - mu * out;
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out = (2.0/ (aa-bb) ) * tmp - ((aa+bb)/(aa-bb))*in;
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};
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// Implement the required interface
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void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
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GridBase *grid=in._grid;
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int vol=grid->gSites();
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Field T0(grid); T0 = in;
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Field T1(grid);
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Field T2(grid);
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Field y(grid);
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Field *Tnm = &T0;
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Field *Tn = &T1;
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Field *Tnp = &T2;
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// Tn=T1 = (xscale M )*in
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AminusMuSq(Linop,T0,T1);
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// sum = .5 c[0] T0 + c[1] T1
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out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
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for(int n=2;n<order;n++){
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AminusMuSq(Linop,*Tn,y);
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*Tnp=2.0*y-(*Tnm);
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out=out+Coeffs[n]* (*Tnp);
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// Cycle pointers to avoid copies
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Field *swizzle = Tnm;
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Tnm =Tn;
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Tn =Tnp;
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Tnp =swizzle;
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}
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}
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};
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}
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#endif
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