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Namespace and formatting changes

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paboyle
2018-01-15 00:21:27 +00:00
parent fcf1ccf669
commit 21251f2e1b
6 changed files with 454 additions and 451 deletions
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652
lib/algorithms/approx/Chebyshev.h
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@@ -1,4 +1,4 @@
/*************************************************************************************
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
@@ -25,14 +25,14 @@ Author: Christoph Lehner <clehner@bnl.gov>
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 */
*************************************************************************************/
/* END LEGAL */
#ifndef GRID_CHEBYSHEV_H
#define GRID_CHEBYSHEV_H
#include <Grid/algorithms/LinearOperator.h>
namespace Grid {
NAMESPACE_BEGIN(Grid);
struct ChebyParams : Serializable {
GRID_SERIALIZABLE_CLASS_MEMBERS(ChebyParams,
@@ -41,337 +41,337 @@ struct ChebyParams : Serializable {
int, Npoly);
};
////////////////////////////////////////////////////////////////////////////////////////////
// Generic Chebyshev approximations
////////////////////////////////////////////////////////////////////////////////////////////
template<class Field>
class Chebyshev : public OperatorFunction<Field> {
private:
std::vector<RealD> Coeffs;
int order;
RealD hi;
RealD lo;
////////////////////////////////////////////////////////////////////////////////////////////
// Generic Chebyshev approximations
////////////////////////////////////////////////////////////////////////////////////////////
template<class Field>
class Chebyshev : public OperatorFunction<Field> {
private:
std::vector<RealD> Coeffs;
int order;
RealD hi;
RealD lo;
public:
void csv(std::ostream &out){
RealD diff = hi-lo;
RealD delta = (hi-lo)*1.0e-9;
for (RealD x=lo; x<hi; x+=delta) {
delta*=1.1;
RealD f = approx(x);
out<< x<<" "<<f<<std::endl;
}
return;
public:
void csv(std::ostream &out){
RealD diff = hi-lo;
RealD delta = (hi-lo)*1.0e-9;
for (RealD x=lo; x<hi; x+=delta) {
delta*=1.1;
RealD f = approx(x);
out<< x<<" "<<f<<std::endl;
}
return;
}
// Convenience for plotting the approximation
void PlotApprox(std::ostream &out) {
out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
for(RealD x=lo;x<hi;x+=(hi-lo)/50.0){
out <<x<<"\t"<<approx(x)<<std::endl;
}
};
Chebyshev(){};
Chebyshev(ChebyParams p){ Init(p.alpha,p.beta,p.Npoly);};
Chebyshev(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD) ) {Init(_lo,_hi,_order,func);};
Chebyshev(RealD _lo,RealD _hi,int _order) {Init(_lo,_hi,_order);};
////////////////////////////////////////////////////////////////////////////////////////////////////
// c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
////////////////////////////////////////////////////////////////////////////////////////////////////
// CJ: the one we need for Lanczos
void Init(RealD _lo,RealD _hi,int _order)
{
lo=_lo;
hi=_hi;
order=_order;
if(order < 2) exit(-1);
Coeffs.resize(order);
Coeffs.assign(0.,order);
Coeffs[order-1] = 1.;
};
void Init(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD))
{
lo=_lo;
hi=_hi;
order=_order;
if(order < 2) exit(-1);
Coeffs.resize(order);
for(int j=0;j<order;j++){
RealD s=0;
for(int k=0;k<order;k++){
RealD y=std::cos(M_PI*(k+0.5)/order);
RealD x=0.5*(y*(hi-lo)+(hi+lo));
RealD f=func(x);
s=s+f*std::cos( j*M_PI*(k+0.5)/order );
}
Coeffs[j] = s * 2.0/order;
}
};
void JacksonSmooth(void){
RealD M=order;
RealD alpha = M_PI/(M+2);
RealD lmax = std::cos(alpha);
RealD sumUsq =0;
std::vector<RealD> U(M);
std::vector<RealD> a(M);
std::vector<RealD> g(M);
for(int n=0;n<=M;n++){
U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
sumUsq += U[n]*U[n];
}
sumUsq = std::sqrt(sumUsq);
for(int i=1;i<=M;i++){
a[i] = U[i]/sumUsq;
}
g[0] = 1.0;
for(int m=1;m<=M;m++){
g[m] = 0;
for(int i=0;i<=M-m;i++){
g[m]+= a[i]*a[m+i];
}
}
for(int m=1;m<=M;m++){
Coeffs[m]*=g[m];
}
}
RealD approx(RealD x) // Convenience for plotting the approximation
{
RealD Tn;
RealD Tnm;
RealD Tnp;
RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
RealD T0=1;
RealD T1=y;
RealD sum;
sum = 0.5*Coeffs[0]*T0;
sum+= Coeffs[1]*T1;
Tn =T1;
Tnm=T0;
for(int i=2;i<order;i++){
Tnp=2*y*Tn-Tnm;
Tnm=Tn;
Tn =Tnp;
sum+= Tn*Coeffs[i];
}
return sum;
};
RealD approxD(RealD x)
{
RealD Un;
RealD Unm;
RealD Unp;
RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
RealD U0=1;
RealD U1=2*y;
RealD sum;
sum = Coeffs[1]*U0;
sum+= Coeffs[2]*U1*2.0;
Un =U1;
Unm=U0;
for(int i=2;i<order-1;i++){
Unp=2*y*Un-Unm;
Unm=Un;
Un =Unp;
sum+= Un*Coeffs[i+1]*(i+1.0);
}
return sum/(0.5*(hi-lo));
};
RealD approxInv(RealD z, RealD x0, int maxiter, RealD resid) {
RealD x = x0;
RealD eps;
int i;
for (i=0;i<maxiter;i++) {
eps = approx(x) - z;
if (fabs(eps / z) < resid)
return x;
x = x - eps / approxD(x);
}
return std::numeric_limits<double>::quiet_NaN();
}
// Implement the required interface
void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
GridBase *grid=in._grid;
// std::cout << "Chevyshef(): in._grid="<<in._grid<<std::endl;
//std::cout <<" Linop.Grid()="<<Linop.Grid()<<"Linop.RedBlackGrid()="<<Linop.RedBlackGrid()<<std::endl;
int vol=grid->gSites();
Field T0(grid); T0 = in;
Field T1(grid);
Field T2(grid);
Field y(grid);
Field *Tnm = &T0;
Field *Tn = &T1;
Field *Tnp = &T2;
// Tn=T1 = (xscale M + mscale)in
RealD xscale = 2.0/(hi-lo);
RealD mscale = -(hi+lo)/(hi-lo);
Linop.HermOp(T0,y);
T1=y*xscale+in*mscale;
// sum = .5 c[0] T0 + c[1] T1
out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
for(int n=2;n<order;n++){
Linop.HermOp(*Tn,y);
y=xscale*y+mscale*(*Tn);
*Tnp=2.0*y-(*Tnm);
out=out+Coeffs[n]* (*Tnp);
// Cycle pointers to avoid copies
Field *swizzle = Tnm;
Tnm =Tn;
Tn =Tnp;
Tnp =swizzle;
}
// Convenience for plotting the approximation
void PlotApprox(std::ostream &out) {
out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
for(RealD x=lo;x<hi;x+=(hi-lo)/50.0){
out <<x<<"\t"<<approx(x)<<std::endl;
}
};
Chebyshev(){};
Chebyshev(ChebyParams p){ Init(p.alpha,p.beta,p.Npoly);};
Chebyshev(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD) ) {Init(_lo,_hi,_order,func);};
Chebyshev(RealD _lo,RealD _hi,int _order) {Init(_lo,_hi,_order);};
template<class Field>
class ChebyshevLanczos : public Chebyshev<Field> {
private:
std::vector<RealD> Coeffs;
int order;
RealD alpha;
RealD beta;
RealD mu;
////////////////////////////////////////////////////////////////////////////////////////////////////
// c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
////////////////////////////////////////////////////////////////////////////////////////////////////
// CJ: the one we need for Lanczos
void Init(RealD _lo,RealD _hi,int _order)
{
lo=_lo;
hi=_hi;
order=_order;
if(order < 2) exit(-1);
Coeffs.resize(order);
Coeffs.assign(0.,order);
Coeffs[order-1] = 1.;
};
public:
ChebyshevLanczos(RealD _alpha,RealD _beta,RealD _mu,int _order) :
void Init(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD))
{
lo=_lo;
hi=_hi;
order=_order;
if(order < 2) exit(-1);
Coeffs.resize(order);
for(int j=0;j<order;j++){
RealD s=0;
for(int k=0;k<order;k++){
RealD y=std::cos(M_PI*(k+0.5)/order);
RealD x=0.5*(y*(hi-lo)+(hi+lo));
RealD f=func(x);
s=s+f*std::cos( j*M_PI*(k+0.5)/order );
}
Coeffs[j] = s * 2.0/order;
}
};
void JacksonSmooth(void){
RealD M=order;
RealD alpha = M_PI/(M+2);
RealD lmax = std::cos(alpha);
RealD sumUsq =0;
std::vector<RealD> U(M);
std::vector<RealD> a(M);
std::vector<RealD> g(M);
for(int n=0;n<=M;n++){
U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
sumUsq += U[n]*U[n];
}
sumUsq = std::sqrt(sumUsq);
for(int i=1;i<=M;i++){
a[i] = U[i]/sumUsq;
}
g[0] = 1.0;
for(int m=1;m<=M;m++){
g[m] = 0;
for(int i=0;i<=M-m;i++){
g[m]+= a[i]*a[m+i];
}
}
for(int m=1;m<=M;m++){
Coeffs[m]*=g[m];
}
}
RealD approx(RealD x) // Convenience for plotting the approximation
{
RealD Tn;
RealD Tnm;
RealD Tnp;
RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
RealD T0=1;
RealD T1=y;
RealD sum;
sum = 0.5*Coeffs[0]*T0;
sum+= Coeffs[1]*T1;
Tn =T1;
Tnm=T0;
for(int i=2;i<order;i++){
Tnp=2*y*Tn-Tnm;
Tnm=Tn;
Tn =Tnp;
sum+= Tn*Coeffs[i];
}
return sum;
};
RealD approxD(RealD x)
{
RealD Un;
RealD Unm;
RealD Unp;
RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
RealD U0=1;
RealD U1=2*y;
RealD sum;
sum = Coeffs[1]*U0;
sum+= Coeffs[2]*U1*2.0;
Un =U1;
Unm=U0;
for(int i=2;i<order-1;i++){
Unp=2*y*Un-Unm;
Unm=Un;
Un =Unp;
sum+= Un*Coeffs[i+1]*(i+1.0);
}
return sum/(0.5*(hi-lo));
};
RealD approxInv(RealD z, RealD x0, int maxiter, RealD resid) {
RealD x = x0;
RealD eps;
int i;
for (i=0;i<maxiter;i++) {
eps = approx(x) - z;
if (fabs(eps / z) < resid)
return x;
x = x - eps / approxD(x);
}
return std::numeric_limits<double>::quiet_NaN();
}
// Implement the required interface
void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
GridBase *grid=in._grid;
// std::cout << "Chevyshef(): in._grid="<<in._grid<<std::endl;
//std::cout <<" Linop.Grid()="<<Linop.Grid()<<"Linop.RedBlackGrid()="<<Linop.RedBlackGrid()<<std::endl;
int vol=grid->gSites();
Field T0(grid); T0 = in;
Field T1(grid);
Field T2(grid);
Field y(grid);
Field *Tnm = &T0;
Field *Tn = &T1;
Field *Tnp = &T2;
// Tn=T1 = (xscale M + mscale)in
RealD xscale = 2.0/(hi-lo);
RealD mscale = -(hi+lo)/(hi-lo);
Linop.HermOp(T0,y);
T1=y*xscale+in*mscale;
// sum = .5 c[0] T0 + c[1] T1
out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
for(int n=2;n<order;n++){
Linop.HermOp(*Tn,y);
y=xscale*y+mscale*(*Tn);
*Tnp=2.0*y-(*Tnm);
out=out+Coeffs[n]* (*Tnp);
// Cycle pointers to avoid copies
Field *swizzle = Tnm;
Tnm =Tn;
Tn =Tnp;
Tnp =swizzle;
}
}
};
template<class Field>
class ChebyshevLanczos : public Chebyshev<Field> {
private:
std::vector<RealD> Coeffs;
int order;
RealD alpha;
RealD beta;
RealD mu;
public:
ChebyshevLanczos(RealD _alpha,RealD _beta,RealD _mu,int _order) :
alpha(_alpha),
beta(_beta),
mu(_mu)
{
order=_order;
Coeffs.resize(order);
for(int i=0;i<_order;i++){
Coeffs[i] = 0.0;
}
Coeffs[order-1]=1.0;
};
void csv(std::ostream &out){
for (RealD x=-1.2*alpha; x<1.2*alpha; x+=(2.0*alpha)/10000) {
RealD f = approx(x);
out<< x<<" "<<f<<std::endl;
}
return;
}
RealD approx(RealD xx) // Convenience for plotting the approximation
{
RealD Tn;
RealD Tnm;
RealD Tnp;
Real aa = alpha * alpha;
Real bb = beta * beta;
RealD x = ( 2.0 * (xx-mu)*(xx-mu) - (aa+bb) ) / (aa-bb);
RealD y= x;
RealD T0=1;
RealD T1=y;
RealD sum;
sum = 0.5*Coeffs[0]*T0;
sum+= Coeffs[1]*T1;
Tn =T1;
Tnm=T0;
for(int i=2;i<order;i++){
Tnp=2*y*Tn-Tnm;
Tnm=Tn;
Tn =Tnp;
sum+= Tn*Coeffs[i];
}
return sum;
};
// shift_Multiply in Rudy's code
void AminusMuSq(LinearOperatorBase<Field> &Linop, const Field &in, Field &out)
{
GridBase *grid=in._grid;
Field tmp(grid);
RealD aa= alpha*alpha;
RealD bb= beta * beta;
Linop.HermOp(in,out);
out = out - mu*in;
Linop.HermOp(out,tmp);
tmp = tmp - mu * out;
out = (2.0/ (aa-bb) ) * tmp - ((aa+bb)/(aa-bb))*in;
};
// Implement the required interface
void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
GridBase *grid=in._grid;
int vol=grid->gSites();
Field T0(grid); T0 = in;
Field T1(grid);
Field T2(grid);
Field y(grid);
Field *Tnm = &T0;
Field *Tn = &T1;
Field *Tnp = &T2;
// Tn=T1 = (xscale M )*in
AminusMuSq(Linop,T0,T1);
// sum = .5 c[0] T0 + c[1] T1
out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
for(int n=2;n<order;n++){
AminusMuSq(Linop,*Tn,y);
*Tnp=2.0*y-(*Tnm);
out=out+Coeffs[n]* (*Tnp);
// Cycle pointers to avoid copies
Field *swizzle = Tnm;
Tnm =Tn;
Tn =Tnp;
Tnp =swizzle;
}
beta(_beta),
mu(_mu)
{
order=_order;
Coeffs.resize(order);
for(int i=0;i<_order;i++){
Coeffs[i] = 0.0;
}
Coeffs[order-1]=1.0;
};
}
void csv(std::ostream &out){
for (RealD x=-1.2*alpha; x<1.2*alpha; x+=(2.0*alpha)/10000) {
RealD f = approx(x);
out<< x<<" "<<f<<std::endl;
}
return;
}
RealD approx(RealD xx) // Convenience for plotting the approximation
{
RealD Tn;
RealD Tnm;
RealD Tnp;
Real aa = alpha * alpha;
Real bb = beta * beta;
RealD x = ( 2.0 * (xx-mu)*(xx-mu) - (aa+bb) ) / (aa-bb);
RealD y= x;
RealD T0=1;
RealD T1=y;
RealD sum;
sum = 0.5*Coeffs[0]*T0;
sum+= Coeffs[1]*T1;
Tn =T1;
Tnm=T0;
for(int i=2;i<order;i++){
Tnp=2*y*Tn-Tnm;
Tnm=Tn;
Tn =Tnp;
sum+= Tn*Coeffs[i];
}
return sum;
};
// shift_Multiply in Rudy's code
void AminusMuSq(LinearOperatorBase<Field> &Linop, const Field &in, Field &out)
{
GridBase *grid=in._grid;
Field tmp(grid);
RealD aa= alpha*alpha;
RealD bb= beta * beta;
Linop.HermOp(in,out);
out = out - mu*in;
Linop.HermOp(out,tmp);
tmp = tmp - mu * out;
out = (2.0/ (aa-bb) ) * tmp - ((aa+bb)/(aa-bb))*in;
};
// Implement the required interface
void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
GridBase *grid=in._grid;
int vol=grid->gSites();
Field T0(grid); T0 = in;
Field T1(grid);
Field T2(grid);
Field y(grid);
Field *Tnm = &T0;
Field *Tn = &T1;
Field *Tnp = &T2;
// Tn=T1 = (xscale M )*in
AminusMuSq(Linop,T0,T1);
// sum = .5 c[0] T0 + c[1] T1
out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
for(int n=2;n<order;n++){
AminusMuSq(Linop,*Tn,y);
*Tnp=2.0*y-(*Tnm);
out=out+Coeffs[n]* (*Tnp);
// Cycle pointers to avoid copies
Field *swizzle = Tnm;
Tnm =Tn;
Tn =Tnp;
Tnp =swizzle;
}
}
};
NAMESPACE_END(Grid);
#endif

228
lib/algorithms/approx/Forecast.h
View File

@@ -26,127 +26,127 @@ with this program; if not, write to the Free Software Foundation, Inc.,
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
/* END LEGAL */
#ifndef INCLUDED_FORECAST_H
#define INCLUDED_FORECAST_H
namespace Grid {
NAMESPACE_BEGIN(Grid);
// Abstract base class.
// Takes a matrix (Mat), a source (phi), and a vector of Fields (chi)
// and returns a forecasted solution to the system D*psi = phi (psi).
template<class Matrix, class Field>
class Forecast
// Abstract base class.
// Takes a matrix (Mat), a source (phi), and a vector of Fields (chi)
// and returns a forecasted solution to the system D*psi = phi (psi).
template<class Matrix, class Field>
class Forecast
{
public:
virtual Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& chi) = 0;
};
// Implementation of Brower et al.'s chronological inverter (arXiv:hep-lat/9509012),
// used to forecast solutions across poles of the EOFA heatbath.
//
// Modified from CPS (cps_pp/src/util/dirac_op/d_op_base/comsrc/minresext.C)
template<class Matrix, class Field>
class ChronoForecast : public Forecast<Matrix,Field>
{
public:
Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& prev_solns)
{
public:
virtual Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& chi) = 0;
int degree = prev_solns.size();
Field chi(phi); // forecasted solution
// Trivial cases
if(degree == 0){ chi = zero; return chi; }
else if(degree == 1){ return prev_solns[0]; }
RealD dot;
ComplexD xp;
Field r(phi); // residual
Field Mv(phi);
std::vector<Field> v(prev_solns); // orthonormalized previous solutions
std::vector<Field> MdagMv(degree,phi);
// Array to hold the matrix elements
std::vector<std::vector<ComplexD>> G(degree, std::vector<ComplexD>(degree));
// Solution and source vectors
std::vector<ComplexD> a(degree);
std::vector<ComplexD> b(degree);
// Orthonormalize the vector basis
for(int i=0; i<degree; i++){
v[i] *= 1.0/std::sqrt(norm2(v[i]));
for(int j=i+1; j<degree; j++){ v[j] -= innerProduct(v[i],v[j]) * v[i]; }
}
// Perform sparse matrix multiplication and construct rhs
for(int i=0; i<degree; i++){
b[i] = innerProduct(v[i],phi);
Mat.M(v[i],Mv);
Mat.Mdag(Mv,MdagMv[i]);
G[i][i] = innerProduct(v[i],MdagMv[i]);
}
// Construct the matrix
for(int j=0; j<degree; j++){
for(int k=j+1; k<degree; k++){
G[j][k] = innerProduct(v[j],MdagMv[k]);
G[k][j] = std::conj(G[j][k]);
}}
// Gauss-Jordan elimination with partial pivoting
for(int i=0; i<degree; i++){
// Perform partial pivoting
int k = i;
for(int j=i+1; j<degree; j++){ if(std::abs(G[j][j]) > std::abs(G[k][k])){ k = j; } }
if(k != i){
xp = b[k];
b[k] = b[i];
b[i] = xp;
for(int j=0; j<degree; j++){
xp = G[k][j];
G[k][j] = G[i][j];
G[i][j] = xp;
}
}
// Convert matrix to upper triangular form
for(int j=i+1; j<degree; j++){
xp = G[j][i]/G[i][i];
b[j] -= xp * b[i];
for(int k=0; k<degree; k++){ G[j][k] -= xp*G[i][k]; }
}
}
// Use Gaussian elimination to solve equations and calculate initial guess
chi = zero;
r = phi;
for(int i=degree-1; i>=0; i--){
a[i] = 0.0;
for(int j=i+1; j<degree; j++){ a[i] += G[i][j] * a[j]; }
a[i] = (b[i]-a[i])/G[i][i];
chi += a[i]*v[i];
r -= a[i]*MdagMv[i];
}
RealD true_r(0.0);
ComplexD tmp;
for(int i=0; i<degree; i++){
tmp = -b[i];
for(int j=0; j<degree; j++){ tmp += G[i][j]*a[j]; }
tmp = std::conj(tmp)*tmp;
true_r += std::sqrt(tmp.real());
}
RealD error = std::sqrt(norm2(r)/norm2(phi));
std::cout << GridLogMessage << "ChronoForecast: |res|/|src| = " << error << std::endl;
return chi;
};
};
// Implementation of Brower et al.'s chronological inverter (arXiv:hep-lat/9509012),
// used to forecast solutions across poles of the EOFA heatbath.
//
// Modified from CPS (cps_pp/src/util/dirac_op/d_op_base/comsrc/minresext.C)
template<class Matrix, class Field>
class ChronoForecast : public Forecast<Matrix,Field>
{
public:
Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& prev_solns)
{
int degree = prev_solns.size();
Field chi(phi); // forecasted solution
// Trivial cases
if(degree == 0){ chi = zero; return chi; }
else if(degree == 1){ return prev_solns[0]; }
RealD dot;
ComplexD xp;
Field r(phi); // residual
Field Mv(phi);
std::vector<Field> v(prev_solns); // orthonormalized previous solutions
std::vector<Field> MdagMv(degree,phi);
// Array to hold the matrix elements
std::vector<std::vector<ComplexD>> G(degree, std::vector<ComplexD>(degree));
// Solution and source vectors
std::vector<ComplexD> a(degree);
std::vector<ComplexD> b(degree);
// Orthonormalize the vector basis
for(int i=0; i<degree; i++){
v[i] *= 1.0/std::sqrt(norm2(v[i]));
for(int j=i+1; j<degree; j++){ v[j] -= innerProduct(v[i],v[j]) * v[i]; }
}
// Perform sparse matrix multiplication and construct rhs
for(int i=0; i<degree; i++){
b[i] = innerProduct(v[i],phi);
Mat.M(v[i],Mv);
Mat.Mdag(Mv,MdagMv[i]);
G[i][i] = innerProduct(v[i],MdagMv[i]);
}
// Construct the matrix
for(int j=0; j<degree; j++){
for(int k=j+1; k<degree; k++){
G[j][k] = innerProduct(v[j],MdagMv[k]);
G[k][j] = std::conj(G[j][k]);
}}
// Gauss-Jordan elimination with partial pivoting
for(int i=0; i<degree; i++){
// Perform partial pivoting
int k = i;
for(int j=i+1; j<degree; j++){ if(std::abs(G[j][j]) > std::abs(G[k][k])){ k = j; } }
if(k != i){
xp = b[k];
b[k] = b[i];
b[i] = xp;
for(int j=0; j<degree; j++){
xp = G[k][j];
G[k][j] = G[i][j];
G[i][j] = xp;
}
}
// Convert matrix to upper triangular form
for(int j=i+1; j<degree; j++){
xp = G[j][i]/G[i][i];
b[j] -= xp * b[i];
for(int k=0; k<degree; k++){ G[j][k] -= xp*G[i][k]; }
}
}
// Use Gaussian elimination to solve equations and calculate initial guess
chi = zero;
r = phi;
for(int i=degree-1; i>=0; i--){
a[i] = 0.0;
for(int j=i+1; j<degree; j++){ a[i] += G[i][j] * a[j]; }
a[i] = (b[i]-a[i])/G[i][i];
chi += a[i]*v[i];
r -= a[i]*MdagMv[i];
}
RealD true_r(0.0);
ComplexD tmp;
for(int i=0; i<degree; i++){
tmp = -b[i];
for(int j=0; j<degree; j++){ tmp += G[i][j]*a[j]; }
tmp = std::conj(tmp)*tmp;
true_r += std::sqrt(tmp.real());
}
RealD error = std::sqrt(norm2(r)/norm2(phi));
std::cout << GridLogMessage << "ChronoForecast: |res|/|src| = " << error << std::endl;
return chi;
};
};
}
NAMESPACE_END(Grid);
#endif

5
lib/algorithms/approx/MultiShiftFunction.cc
View File

@@ -27,7 +27,8 @@ Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
/* END LEGAL */
#include <Grid/GridCore.h>
namespace Grid {
NAMESPACE_BEGIN(Grid);
double MultiShiftFunction::approx(double x)
{
double a = norm;
@@ -53,4 +54,4 @@ void MultiShiftFunction::csv(std::ostream &out)
}
return;
}
}
NAMESPACE_END(Grid);

4
lib/algorithms/approx/MultiShiftFunction.h
View File

@@ -29,7 +29,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
#ifndef MULTI_SHIFT_FUNCTION
#define MULTI_SHIFT_FUNCTION
namespace Grid {
NAMESPACE_BEGIN(Grid);
class MultiShiftFunction {
public:
@@ -63,5 +63,5 @@ public:
}
};
}
NAMESPACE_END(Grid);
#endif

7
lib/algorithms/approx/Zolotarev.cc
View File

@@ -58,8 +58,8 @@
/* Compute the partial fraction expansion coefficients (alpha) from the
* factored form */
namespace Grid {
namespace Approx {
NAMESPACE_BEGIN(Grid);
NAMESPACE_BEGIN(Approx);
static void construct_partfrac(izd *z) {
int dn = z -> dn, dd = z -> dd, type = z -> type;
@@ -723,5 +723,6 @@ int main(int argc, char** argv) {
return EXIT_SUCCESS;
}
#endif /* TEST */
NAMESPACE_END(Approx);
NAMESPACE_END(Grid);

9
lib/algorithms/approx/Zolotarev.h
View File

@@ -1,13 +1,13 @@
/* -*- Mode: C; comment-column: 22; fill-column: 79; -*- */
#ifdef __cplusplus
namespace Grid {
namespace Approx {
#include <Grid/Namespace.h>
NAMESPACE_BEGIN(Grid);
NAMESPACE_BEGIN(Approx);
#endif
#define HVERSION Header Time-stamp: <14-OCT-2004 09:26:51.00 adk@MISSCONTRARY>
#ifndef ZOLOTAREV_INTERNAL
#ifndef PRECISION
#define PRECISION double
@@ -83,5 +83,6 @@ void zolotarev_free(zolotarev_data *zdata);
#endif
#ifdef __cplusplus
}}
NAMESPACE_END(Approx);
NAMESPACE_END(Grid);
#endif