boolean DL_largematrix::conjug_gradient(DL_largevector *x, DL_largevector *b){
// Solves Ax=b using conjugate gradient
// returns if the solution was diverging |Ax-b|>|b|
static DL_largevector p,pp, r,rr, z,zz;
if ((rep==lud) || (rep==ludb)) {
DL_dsystem->get_companion()->Msg("DL_largematrix::conjug_grad not implemented for LU decomposed matrices\n");
return FALSE;
}
int j, iter=0, itmax=nrrows;
DL_Scalar ak, akden, bk, bkden=0, bknum, bnrm;
p.resize(nrrows);
pp.resize(nrrows);
r.assign(b);
rr.assign(b);
z.resize(nrrows);
zz.resize(nrrows);
bnrm=b->norm();
x->makezero();
asolve(&r,&z);
while (iter<itmax) {
++iter;
asolve(&rr,&zz);
bknum=z.inprod(&rr);
if (iter==1) {
p.assign(&z);
pp.assign(&zz);
}
else {
bk=bknum/bkden;
for (j=0;j<nrrows;j++) {
p.set(j,bk*p.get(j)+z.get(j));
pp.set(j,bk*pp.get(j)+zz.get(j));
}
}
bkden=bknum;
times(&p,&z);
akden=z.inprod(&pp);
ak=bknum/akden;
transposetimes(&pp,&zz);
for(j=0;j<nrrows;j++) { // not very nice to use the implementation
// of x, r and rr here, but += and -= are faster...
x->v[j]+=ak*p.get(j);
r.v[j]-=ak*z.get(j);
rr.v[j]-=ak*zz.get(j);
}
asolve(&r,&z);
if (r.norm()<=(TOL*bnrm)) break;
}
return (r.norm()>bnrm);
}
void PCBCGSolver::linbcg(unsigned long n, double b[], double x[], int itol, double tol,
int itmax, int *iter, double *err) {
unsigned long j;
double ak,akden,bk,bkden,bknum,bnrm,dxnrm,xnrm,zm1nrm,znrm;
double *p,*pp,*r,*rr,*z,*zz;
p=new double[n+1];
pp=new double[n+1];
r=new double[n+1];
rr=new double[n+1];
z=new double[n+1];
zz=new double[n+1];
*iter=0;
atimes(n,x,r,0);
for (j=1; j<=n; j++) {
r[j]=b[j]-r[j];
rr[j]=r[j];
}
znrm=1.0;
if (itol == 1) bnrm=snrm(n,b,itol);
else if (itol == 2) {
asolve(n,b,z,0);
bnrm=snrm(n,z,itol);
}
else if (itol == 3 || itol == 4) {
asolve(n,b,z,0);
bnrm=snrm(n,z,itol);
asolve(n,r,z,0);
znrm=snrm(n,z,itol);
} else printf("illegal itol in linbcg");
asolve(n,r,z,0);
while (*iter <= itmax) {
++(*iter);
zm1nrm=znrm;
asolve(n,rr,zz,1);
for (bknum=0.0,j=1; j<=n; j++) bknum += z[j]*rr[j];
if (*iter == 1) {
for (j=1; j<=n; j++) {
p[j]=z[j];
pp[j]=zz[j];
}
}
else {
bk=bknum/bkden;
for (j=1; j<=n; j++) {
p[j]=bk*p[j]+z[j];
pp[j]=bk*pp[j]+zz[j];
}
}
bkden=bknum;
atimes(n,p,z,0);
for (akden=0.0,j=1; j<=n; j++) akden += z[j]*pp[j];
ak=bknum/akden;
atimes(n,pp,zz,1);
for (j=1; j<=n; j++) {
x[j] += ak*p[j];
r[j] -= ak*z[j];
rr[j] -= ak*zz[j];
}
asolve(n,r,z,0);
if (itol == 1 || itol == 2) {
znrm=1.0;
*err=snrm(n,r,itol)/bnrm;
} else if (itol == 3 || itol == 4) {
znrm=snrm(n,z,itol);
if (fabs(zm1nrm-znrm) > EPS*znrm) {
dxnrm=fabs(ak)*snrm(n,p,itol);
*err=znrm/fabs(zm1nrm-znrm)*dxnrm;
} else {
*err=znrm/bnrm;
continue;
}
xnrm=snrm(n,x,itol);
if (*err <= 0.5*xnrm) *err /= xnrm;
else {
*err=znrm/bnrm;
continue;
}
}
//printf("iter=%4d err=%12.6f\n",*iter,*err);
if (*err <= tol) break;
}
delete [] p;
delete [] pp;
delete [] r;
delete [] rr;
delete [] z;
delete [] zz;
p = NULL;
pp = NULL;
r = NULL;
rr = NULL;
z = NULL;
zz = NULL;
}
void linbcg(unsigned long n, double b[], double x[], int itol, double tol,
int itmax, int *iter, double *err)
{
void asolve(unsigned long n, double b[], double x[], int itrnsp);
void atimes(unsigned long n, double x[], double r[], int itrnsp);
double snrm(unsigned long n, double sx[], int itol);
unsigned long j;
double ak,akden,bk,bkden,bknum,bnrm,dxnrm,xnrm,zm1nrm,znrm;
double *p,*pp,*r,*rr,*z,*zz;
p=dvector(1,n);
pp=dvector(1,n);
r=dvector(1,n);
rr=dvector(1,n);
z=dvector(1,n);
zz=dvector(1,n);
*iter=0;
atimes(n,x,r,0);
for (j=1;j<=n;j++) {
r[j]=b[j]-r[j];
rr[j]=r[j];
}
znrm=1.0;
if (itol == 1) bnrm=snrm(n,b,itol);
else if (itol == 2) {
asolve(n,b,z,0);
bnrm=snrm(n,z,itol);
}
else if (itol == 3 || itol == 4) {
asolve(n,b,z,0);
bnrm=snrm(n,z,itol);
asolve(n,r,z,0);
znrm=snrm(n,z,itol);
} else nrerror("illegal itol in linbcg");
asolve(n,r,z,0);
while (*iter <= itmax) {
++(*iter);
zm1nrm=znrm;
asolve(n,rr,zz,1);
for (bknum=0.0,j=1;j<=n;j++) bknum += z[j]*rr[j];
if (*iter == 1) {
for (j=1;j<=n;j++) {
p[j]=z[j];
pp[j]=zz[j];
}
}
else {
bk=bknum/bkden;
for (j=1;j<=n;j++) {
p[j]=bk*p[j]+z[j];
pp[j]=bk*pp[j]+zz[j];
}
}
bkden=bknum;
atimes(n,p,z,0);
for (akden=0.0,j=1;j<=n;j++) akden += z[j]*pp[j];
ak=bknum/akden;
atimes(n,pp,zz,1);
for (j=1;j<=n;j++) {
x[j] += ak*p[j];
r[j] -= ak*z[j];
rr[j] -= ak*zz[j];
}
asolve(n,r,z,0);
if (itol == 1 || itol == 2) {
znrm=1.0;
*err=snrm(n,r,itol)/bnrm;
} else if (itol == 3 || itol == 4) {
znrm=snrm(n,z,itol);
if (fabs(zm1nrm-znrm) > EPS*znrm) {
dxnrm=fabs(ak)*snrm(n,p,itol);
*err=znrm/fabs(zm1nrm-znrm)*dxnrm;
} else {
*err=znrm/bnrm;
continue;
}
xnrm=snrm(n,x,itol);
if (*err <= 0.5*xnrm) *err /= xnrm;
else {
*err=znrm/bnrm;
continue;
}
}
printf("iter=%4d err=%12.6f\n",*iter,*err);
if (*err <= tol) break;
}
free_dvector(p,1,n);
free_dvector(pp,1,n);
free_dvector(r,1,n);
free_dvector(rr,1,n);
free_dvector(z,1,n);
free_dvector(zz,1,n);
}
