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bugfixes in gmres

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jiri committed 2026-10-29 23:46:20 +01:00
1 parent e8979df1b1
commit 498636927d
1 file changed
+40 -66
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gmres.h
+40 -66
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@@ -47,6 +47,29 @@ c[k] = d[k]/R(k,k);
for (int i=k-1;i>=0;i--) c[i] = (d[i]-xdot(k-i,&R(i,i+1),1,&c[i+1],1)) / R(i,i);
}
//rotate columns 0..k of H to the triangular R (rotations 0..k), solve R c = -d and add the k+1 Krylov vectors to x
template<typename T>
void gmres_update(NRMat<T> &H, const NRVec<T> &cci, const NRVec<T> &ssi, NRVec<T> &d, NRVec<T> &c, const int k, NRVec<T> *v, AuxStorage<T> *st, const int incore, NRVec<T> &x)
{
for(int i=0;i<=k;i++)
{
T ci = cci[i], si = ssi[i];
for(int j=i;j<=k;j++)
{
T a = H(i,j);
H(i,j) = ci*a+si*H(i+1,j);
H(i+1,j) = -si*a+ci*H(i+1,j);
}
}
d *= -1.;
gmres_backsubstitute(H,c,d,k);
for(int i=0;i<=k;i++)
{
if(!incore) st->get(v[0],i);
x.axpy(c[i],v[incore?i:0]);
}
}
//x contains ev. initial guess and on return the solution
template<typename T, typename Matrix>
@@ -82,7 +105,6 @@ if(doguess)
x.normalize();
}
neustart:
for (int l=0;l<neustart;l++) // main loop for restarts
{
if(square) // r_0 = b + A x_0
@@ -106,6 +128,7 @@ for (int l=0;l<neustart;l++) // main loop for restarts
v[0] = r_k* (1./beta);
if(!incore) st->put(v[0],0);
bool updated=false;
// Iteration
for (int k=0;k<MAXIT;k++)
{
@@ -137,33 +160,16 @@ for (int l=0;l<neustart;l++) // main loop for restarts
//Schritt 4
double tmp;
H(k+1,k) = tmp= z.norm();
if(tmp < 1.e-2*eps )
bool breakdown = tmp < 1.e-2*eps; //Krylov space invariant: the solution in it is final for this restart
if(breakdown)
{
if(verbose) std::cerr <<("gmres restart performed\n");
// Abbruchbedingung, konstruiere x_k
for (int i=0;i<k;i++)
{
ci = cci[i];si = ssi[i];
for (int j=0;j<k;j++)
{
T a = H(i,j);
H(i,j) = ci*a+si*H(i+1,j);
H(i+1,j) = -si*a+ci*H(i+1,j);
if(verbose) std::cerr <<("gmres breakdown, restart performed\n");
}
}
// Loese R_k c = - d_k
d *= -1.;
gmres_backsubstitute(H,c,d,k-1);
for (int i=0;i<k-1;i++)
else
{
if(!incore) st->get(v[0],i);
x.axpy(c[i],v[incore?i:0]);
}
flag=0; goto neustart;
} // Ende Abbruch
v[incore?k+1:0] = z * (1./H(k+1,k));
if(!incore) st->put(v[0],k+1);
}
// Schritt 5 - berechne Phi_k
for (int j=0;j<k+2;j++) d[j] = H(j,k);
@@ -177,8 +183,12 @@ for (int l=0;l<neustart;l++) // main loop for restarts
}
//phi[k]= atan(d[k+1]/d[k]);
ci=hypot(d[k],d[k+1]);
if(ci==0) {cci[k]=1; ssi[k]=0;} //singular
else
{
cci[k]=d[k]/ci;
ssi[k]=d[k+1]/ci;
}
//berechne neuen d-Vektor
d= 0.;
@@ -204,53 +214,17 @@ for (int l=0;l<neustart;l++) // main loop for restarts
d_alt = abs(d[k+1]);
//*err= d_alt;
if (d_alt < eps*beta_0)
if (d_alt < eps*beta_0 || breakdown)
{
// konstruiere R_k
for (int i=0;i<k;i++)
{
ci = cci[i];
si = ssi[i];
for (int j=0;j<k;j++)
{
T a = H(i,j);
H(i,j) = ci*a+si*H(i+1,j);
H(i+1,j) = -si*a+ci*H(i+1,j);
}
}
// Loese R_k c = - d_k
d *= -1.;
gmres_backsubstitute(H,c,d,k-1);
for(int i=0;i<k;i++)
{
if(!incore) st->get(v[0],i);
x.axpy(c[i],v[incore?i:0]);
}
flag=0; goto myreturn;
gmres_update(H,cci,ssi,d,c,k,v,st,incore,x);
updated=true;
if(d_alt < eps*beta_0) {flag=0; goto myreturn;}
break; //breakdown without convergence: next restart
}
} // k-Schleife
// zum Neustart: Konstruiere R_k
for (int i=0;i<MAXIT;i++)
{
ci = cci[i];si = ssi[i];
for (int j=0;j<MAXIT;j++)
{
T a = H(i,j);
H(i,j) = ci*a+si*H(i+1,j);
H(i+1,j) = -si*a+ci*H(i+1,j);
}
}
// Loese R_k c = - d_k
d *= -1.;
gmres_backsubstitute(H,c,d,MAXIT-1);
for(int i=0;i<MAXIT;i++)
{
if(!incore) st->get(v[0],i);
x.axpy(c[i],v[incore?i:0]);
}
// zum Neustart: Konstruiere R_k und loese R_k c = - d_k
if(!updated) gmres_update(H,cci,ssi,d,c,MAXIT-1,v,st,incore,x);
} // l schleife
flag=1;