PetscErrorCode KSPSolve_Chebyshev(KSP ksp)
{
KSP_Chebyshev *cheb = (KSP_Chebyshev*)ksp->data;
PetscErrorCode ierr;
PetscInt k,kp1,km1,maxit,ktmp,i;
PetscScalar alpha,omegaprod,mu,omega,Gamma,c[3],scale;
PetscReal rnorm = 0.0;
Vec sol_orig,b,p[3],r;
Mat Amat,Pmat;
PetscBool diagonalscale;
PetscFunctionBegin;
ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
if (cheb->kspest && !cheb->estimate_current) {
PetscReal max=0.0,min=0.0;
Vec X,B;
X = ksp->work[0];
if (cheb->random) {
B = ksp->work[1];
ierr = VecSetRandom(B,cheb->random);CHKERRQ(ierr);
} else {
B = ksp->vec_rhs;
}
ierr = KSPSolve(cheb->kspest,B,X);CHKERRQ(ierr);
if (ksp->guess_zero) {
ierr = VecZeroEntries(X);CHKERRQ(ierr);
}
ierr = KSPChebyshevComputeExtremeEigenvalues_Private(cheb->kspest,&min,&max);CHKERRQ(ierr);
cheb->emin = cheb->tform[0]*min + cheb->tform[1]*max;
cheb->emax = cheb->tform[2]*min + cheb->tform[3]*max;
cheb->estimate_current = PETSC_TRUE;
}
ksp->its = 0;
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
maxit = ksp->max_it;
/* These three point to the three active solutions, we
rotate these three at each solution update */
km1 = 0; k = 1; kp1 = 2;
sol_orig = ksp->vec_sol; /* ksp->vec_sol will be asigned to rotating vector p[k], thus save its address */
b = ksp->vec_rhs;
p[km1] = sol_orig;
p[k] = ksp->work[0];
p[kp1] = ksp->work[1];
r = ksp->work[2];
/* use scale*B as our preconditioner */
scale = 2.0/(cheb->emax + cheb->emin);
/* -alpha <= scale*lambda(B^{-1}A) <= alpha */
alpha = 1.0 - scale*(cheb->emin);
Gamma = 1.0;
mu = 1.0/alpha;
omegaprod = 2.0/alpha;
c[km1] = 1.0;
c[k] = mu;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,p[km1],r);CHKERRQ(ierr); /* r = b - A*p[km1] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
} else {
ierr = VecCopy(b,r);CHKERRQ(ierr);
}
ierr = KSP_PCApply(ksp,r,p[k]);CHKERRQ(ierr); /* p[k] = scale B^{-1}r + p[km1] */
ierr = VecAYPX(p[k],scale,p[km1]);CHKERRQ(ierr);
for (i=0; i<maxit; i++) {
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
c[kp1] = 2.0*mu*c[k] - c[km1];
omega = omegaprod*c[k]/c[kp1];
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ksp->vec_sol = p[k];
/* calculate residual norm if requested */
if (ksp->normtype != KSP_NORM_NONE || ksp->numbermonitors) {
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
}
/* y^{k+1} = omega(y^{k} - y^{k-1} + Gamma*r^{k}) + y^{k-1} */
ierr = VecAXPBYPCZ(p[kp1],1.0-omega,omega,omega*Gamma*scale,p[km1],p[k]);CHKERRQ(ierr);
ktmp = km1;
km1 = k;
k = kp1;
kp1 = ktmp;
}
if (!ksp->reason) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->vec_sol = p[k];
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
}
if (ksp->its >= ksp->max_it) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
} else ksp->reason = KSP_CONVERGED_ITS;
}
}
/* make sure solution is in vector x */
ksp->vec_sol = sol_orig;
if (k) {
ierr = VecCopy(p[k],sol_orig);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode KSPSolve_Chebyshev(KSP ksp)
{
KSP_Chebyshev *cheb = (KSP_Chebyshev*)ksp->data;
PetscErrorCode ierr;
PetscInt k,kp1,km1,maxit,ktmp,i;
PetscScalar alpha,omegaprod,mu,omega,Gamma,c[3],scale;
PetscReal rnorm = 0.0;
Vec sol_orig,b,p[3],r;
Mat Amat,Pmat;
PetscBool diagonalscale;
PetscFunctionBegin;
ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
if (cheb->kspest) {
PetscObjectId amatid, pmatid;
PetscObjectState amatstate, pmatstate;
ierr = PetscObjectGetId((PetscObject)Amat,&amatid);CHKERRQ(ierr);
ierr = PetscObjectGetId((PetscObject)Pmat,&pmatid);CHKERRQ(ierr);
ierr = PetscObjectStateGet((PetscObject)Amat,&amatstate);CHKERRQ(ierr);
ierr = PetscObjectStateGet((PetscObject)Pmat,&pmatstate);CHKERRQ(ierr);
if (amatid != cheb->amatid || pmatid != cheb->pmatid || amatstate != cheb->amatstate || pmatstate != cheb->pmatstate) {
PetscReal max=0.0,min=0.0;
Vec B;
KSPConvergedReason reason;
if (cheb->userandom) {
B = ksp->work[1];
if (!cheb->random) {
ierr = PetscRandomCreate(PetscObjectComm((PetscObject)B),&cheb->random);CHKERRQ(ierr);
}
ierr = VecSetRandom(B,cheb->random);CHKERRQ(ierr);
} else {
B = ksp->vec_rhs;
}
ierr = KSPSolve(cheb->kspest,B,ksp->work[0]);CHKERRQ(ierr);
ierr = KSPGetConvergedReason(cheb->kspest,&reason);CHKERRQ(ierr);
if (reason < 0) {
if (reason == KSP_DIVERGED_ITS) {
ierr = PetscInfo(ksp,"Eigen estimator ran for prescribed number of iterations\n");CHKERRQ(ierr);
} else {
PetscInt its;
ierr = KSPGetIterationNumber(cheb->kspest,&its);CHKERRQ(ierr);
SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB,"Eigen estimator failed: %s at iteration %D",KSPConvergedReasons[reason],its);
}
} else if (reason==KSP_CONVERGED_RTOL ||reason==KSP_CONVERGED_ATOL) {
ierr = PetscInfo(ksp,"Eigen estimator converged prematurely. Should not happen except for small or low rank problem\n");CHKERRQ(ierr);
} else {
ierr = PetscInfo1(ksp,"Eigen estimator did not converge by iteration: %s\n",KSPConvergedReasons[reason]);CHKERRQ(ierr);
}
ierr = KSPChebyshevComputeExtremeEigenvalues_Private(cheb->kspest,&min,&max);CHKERRQ(ierr);
cheb->emin = cheb->tform[0]*min + cheb->tform[1]*max;
cheb->emax = cheb->tform[2]*min + cheb->tform[3]*max;
cheb->amatid = amatid;
cheb->pmatid = pmatid;
cheb->amatstate = amatstate;
cheb->pmatstate = pmatstate;
}
}
ksp->its = 0;
maxit = ksp->max_it;
/* These three point to the three active solutions, we
rotate these three at each solution update */
km1 = 0; k = 1; kp1 = 2;
sol_orig = ksp->vec_sol; /* ksp->vec_sol will be asigned to rotating vector p[k], thus save its address */
b = ksp->vec_rhs;
p[km1] = sol_orig;
p[k] = ksp->work[0];
p[kp1] = ksp->work[1];
r = ksp->work[2];
/* use scale*B as our preconditioner */
scale = 2.0/(cheb->emax + cheb->emin);
/* -alpha <= scale*lambda(B^{-1}A) <= alpha */
alpha = 1.0 - scale*(cheb->emin);
Gamma = 1.0;
mu = 1.0/alpha;
omegaprod = 2.0/alpha;
c[km1] = 1.0;
c[k] = mu;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,p[km1],r);CHKERRQ(ierr); /* r = b - A*p[km1] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
} else {
ierr = VecCopy(b,r);CHKERRQ(ierr);
}
ierr = KSP_PCApply(ksp,r,p[k]);CHKERRQ(ierr); /* p[k] = scale B^{-1}r + p[km1] */
ierr = VecAYPX(p[k],scale,p[km1]);CHKERRQ(ierr);
for (i=0; i<maxit; i++) {
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
c[kp1] = 2.0*mu*c[k] - c[km1];
omega = omegaprod*c[k]/c[kp1];
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ksp->vec_sol = p[k];
/* calculate residual norm if requested */
if (ksp->normtype != KSP_NORM_NONE || ksp->numbermonitors) {
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
}
/* y^{k+1} = omega(y^{k} - y^{k-1} + Gamma*r^{k}) + y^{k-1} */
ierr = VecAXPBYPCZ(p[kp1],1.0-omega,omega,omega*Gamma*scale,p[km1],p[k]);CHKERRQ(ierr);
ktmp = km1;
km1 = k;
k = kp1;
kp1 = ktmp;
}
if (!ksp->reason) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->vec_sol = p[k];
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
}
if (ksp->its >= ksp->max_it) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
} else ksp->reason = KSP_CONVERGED_ITS;
}
}
/* make sure solution is in vector x */
ksp->vec_sol = sol_orig;
if (k) {
ierr = VecCopy(p[k],sol_orig);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
