static PetscErrorCode KSPSolve_IBCGS(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,N;
PetscReal rnorm,rnormin = 0.0;
#if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
/* Because of possible instabilities in the algorithm (as indicated by different residual histories for the same problem
on the same number of processes with different runs) we support computing the inner products using Intel's 80 bit arithematic
rather than just 64 bit. Thus we copy our double precision values into long doubles (hoping this keeps the 16 extra bits)
and tell MPI to do its ALlreduces with MPI_LONG_DOUBLE.
Note for developers that does not effect the code. Intel's long double is implemented by storing the 80 bits of extended double
precision into a 16 byte space (the rest of the space is ignored) */
long double insums[7],outsums[7];
#else
PetscScalar insums[7],outsums[7];
#endif
PetscScalar sigman_2, sigman_1, sigman, pin_1, pin, phin_1, phin,tmp1,tmp2;
PetscScalar taun_1, taun, rhon, alphan_1, alphan, omegan_1, omegan;
const PetscScalar *PETSC_RESTRICT r0, *PETSC_RESTRICT f0, *PETSC_RESTRICT qn, *PETSC_RESTRICT b, *PETSC_RESTRICT un;
PetscScalar *PETSC_RESTRICT rn, *PETSC_RESTRICT xn, *PETSC_RESTRICT vn, *PETSC_RESTRICT zn;
/* the rest do not have to keep n_1 values */
PetscScalar kappan, thetan, etan, gamman, betan, deltan;
const PetscScalar *PETSC_RESTRICT tn;
PetscScalar *PETSC_RESTRICT sn;
Vec R0,Rn,Xn,F0,Vn,Zn,Qn,Tn,Sn,B,Un;
Mat A;
PetscFunctionBegin;
if (!ksp->vec_rhs->petscnative) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Only coded for PETSc vectors");
#if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
/* since 80 bit long doubls do not fill the upper bits, we fill them initially so that
valgrind won't detect MPI_Allreduce() with uninitialized data */
ierr = PetscMemzero(insums,sizeof(insums));CHKERRQ(ierr);
ierr = PetscMemzero(insums,sizeof(insums));CHKERRQ(ierr);
#endif
ierr = PCGetOperators(ksp->pc,&A,NULL);CHKERRQ(ierr);
ierr = VecGetLocalSize(ksp->vec_sol,&N);CHKERRQ(ierr);
Xn = ksp->vec_sol; ierr = VecGetArray(Xn_1,(PetscScalar**)&xn_1);CHKERRQ(ierr); ierr = VecRestoreArray(Xn_1,NULL);CHKERRQ(ierr);
B = ksp->vec_rhs; ierr = VecGetArrayRead(B,(const PetscScalar**)&b);CHKERRQ(ierr); ierr = VecRestoreArrayRead(B,NULL);CHKERRQ(ierr);
R0 = ksp->work[0]; ierr = VecGetArrayRead(R0,(const PetscScalar**)&r0);CHKERRQ(ierr); ierr = VecRestoreArrayRead(R0,NULL);CHKERRQ(ierr);
Rn = ksp->work[1]; ierr = VecGetArray(Rn_1,(PetscScalar**)&rn_1);CHKERRQ(ierr); ierr = VecRestoreArray(Rn_1,NULL);CHKERRQ(ierr);
Un = ksp->work[2]; ierr = VecGetArrayRead(Un_1,(const PetscScalar**)&un_1);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Un_1,NULL);CHKERRQ(ierr);
F0 = ksp->work[3]; ierr = VecGetArrayRead(F0,(const PetscScalar**)&f0);CHKERRQ(ierr); ierr = VecRestoreArrayRead(F0,NULL);CHKERRQ(ierr);
Vn = ksp->work[4]; ierr = VecGetArray(Vn_1,(PetscScalar**)&vn_1);CHKERRQ(ierr); ierr = VecRestoreArray(Vn_1,NULL);CHKERRQ(ierr);
Zn = ksp->work[5]; ierr = VecGetArray(Zn_1,(PetscScalar**)&zn_1);CHKERRQ(ierr); ierr = VecRestoreArray(Zn_1,NULL);CHKERRQ(ierr);
Qn = ksp->work[6]; ierr = VecGetArrayRead(Qn_1,(const PetscScalar**)&qn_1);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Qn_1,NULL);CHKERRQ(ierr);
Tn = ksp->work[7]; ierr = VecGetArrayRead(Tn,(const PetscScalar**)&tn);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Tn,NULL);CHKERRQ(ierr);
Sn = ksp->work[8]; ierr = VecGetArrayRead(Sn,(const PetscScalar**)&sn);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Sn,NULL);CHKERRQ(ierr);
/* r0 = rn_1 = b - A*xn_1; */
/* ierr = KSP_PCApplyBAorAB(ksp,Xn_1,Rn_1,Tn);CHKERRQ(ierr);
ierr = VecAYPX(Rn_1,-1.0,B);CHKERRQ(ierr); */
ierr = KSPInitialResidual(ksp,Xn_1,Tn,Sn,Rn_1,B);CHKERRQ(ierr);
ierr = VecNorm(Rn_1,NORM_2,&rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,0,rnorm);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) PetscFunctionReturn(0);
ierr = VecCopy(Rn_1,R0);CHKERRQ(ierr);
/* un_1 = A*rn_1; */
ierr = KSP_PCApplyBAorAB(ksp,Rn_1,Un_1,Tn);CHKERRQ(ierr);
/* f0 = A'*rn_1; */
if (ksp->pc_side == PC_RIGHT) { /* B' A' */
ierr = KSP_MatMultTranspose(ksp,A,R0,Tn);CHKERRQ(ierr);
ierr = KSP_PCApplyTranspose(ksp,Tn,F0);CHKERRQ(ierr);
} else if (ksp->pc_side == PC_LEFT) { /* A' B' */
ierr = KSP_PCApplyTranspose(ksp,R0,Tn);CHKERRQ(ierr);
ierr = KSP_MatMultTranspose(ksp,A,Tn,F0);CHKERRQ(ierr);
}
/*qn_1 = vn_1 = zn_1 = 0.0; */
ierr = VecSet(Qn_1,0.0);CHKERRQ(ierr);
ierr = VecSet(Vn_1,0.0);CHKERRQ(ierr);
ierr = VecSet(Zn_1,0.0);CHKERRQ(ierr);
sigman_2 = pin_1 = taun_1 = 0.0;
/* the paper says phin_1 should be initialized to zero, it is actually R0'R0 */
ierr = VecDot(R0,R0,&phin_1);CHKERRQ(ierr);
/* sigman_1 = rn_1'un_1 */
ierr = VecDot(R0,Un_1,&sigman_1);CHKERRQ(ierr);
alphan_1 = omegan_1 = 1.0;
for (ksp->its = 1; ksp->its<ksp->max_it+1; ksp->its++) {
rhon = phin_1 - omegan_1*sigman_2 + omegan_1*alphan_1*pin_1;
if (ksp->its == 1) deltan = rhon;
else deltan = rhon/taun_1;
betan = deltan/omegan_1;
taun = sigman_1 + betan*taun_1 - deltan*pin_1;
if (taun == 0.0) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to taun is zero, iteration %D",ksp->its);
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
alphan = rhon/taun;
ierr = PetscLogFlops(15.0);CHKERRQ(ierr);
/*
zn = alphan*rn_1 + (alphan/alphan_1)betan*zn_1 - alphan*deltan*vn_1
vn = un_1 + betan*vn_1 - deltan*qn_1
sn = rn_1 - alphan*vn
The algorithm in the paper is missing the alphan/alphan_1 term in the zn update
*/
ierr = PetscLogEventBegin(VEC_Ops,0,0,0,0);CHKERRQ(ierr);
tmp1 = (alphan/alphan_1)*betan;
tmp2 = alphan*deltan;
for (i=0; i<N; i++) {
zn[i] = alphan*rn_1[i] + tmp1*zn_1[i] - tmp2*vn_1[i];
vn[i] = un_1[i] + betan*vn_1[i] - deltan*qn_1[i];
sn[i] = rn_1[i] - alphan*vn[i];
}
ierr = PetscLogFlops(3.0+11.0*N);CHKERRQ(ierr);
ierr = PetscLogEventEnd(VEC_Ops,0,0,0,0);CHKERRQ(ierr);
/*
qn = A*vn
*/
ierr = KSP_PCApplyBAorAB(ksp,Vn,Qn,Tn);CHKERRQ(ierr);
/*
tn = un_1 - alphan*qn
*/
ierr = VecWAXPY(Tn,-alphan,Qn,Un_1);CHKERRQ(ierr);
/*
phin = r0'sn
pin = r0'qn
gamman = f0'sn
etan = f0'tn
thetan = sn'tn
kappan = tn'tn
*/
ierr = PetscLogEventBegin(VEC_ReduceArithmetic,0,0,0,0);CHKERRQ(ierr);
phin = pin = gamman = etan = thetan = kappan = 0.0;
for (i=0; i<N; i++) {
phin += r0[i]*sn[i];
pin += r0[i]*qn[i];
gamman += f0[i]*sn[i];
etan += f0[i]*tn[i];
thetan += sn[i]*tn[i];
kappan += tn[i]*tn[i];
}
ierr = PetscLogFlops(12.0*N);CHKERRQ(ierr);
ierr = PetscLogEventEnd(VEC_ReduceArithmetic,0,0,0,0);CHKERRQ(ierr);
insums[0] = phin;
insums[1] = pin;
insums[2] = gamman;
insums[3] = etan;
insums[4] = thetan;
insums[5] = kappan;
insums[6] = rnormin;
ierr = PetscLogEventBarrierBegin(VEC_ReduceBarrier,0,0,0,0,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
#if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
if (ksp->lagnorm && ksp->its > 1) {
ierr = MPIU_Allreduce(insums,outsums,7,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
} else {
ierr = MPIU_Allreduce(insums,outsums,6,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
}
#else
if (ksp->lagnorm && ksp->its > 1) {
ierr = MPIU_Allreduce(insums,outsums,7,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
} else {
ierr = MPIU_Allreduce(insums,outsums,6,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
}
#endif
ierr = PetscLogEventBarrierEnd(VEC_ReduceBarrier,0,0,0,0,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
phin = outsums[0];
pin = outsums[1];
gamman = outsums[2];
etan = outsums[3];
thetan = outsums[4];
kappan = outsums[5];
if (ksp->lagnorm && ksp->its > 1) rnorm = PetscSqrtReal(PetscRealPart(outsums[6]));
if (kappan == 0.0) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to kappan is zero, iteration %D",ksp->its);
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
if (thetan == 0.0) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to thetan is zero, iteration %D",ksp->its);
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
omegan = thetan/kappan;
sigman = gamman - omegan*etan;
/*
rn = sn - omegan*tn
xn = xn_1 + zn + omegan*sn
*/
ierr = PetscLogEventBegin(VEC_Ops,0,0,0,0);CHKERRQ(ierr);
rnormin = 0.0;
for (i=0; i<N; i++) {
rn[i] = sn[i] - omegan*tn[i];
rnormin += PetscRealPart(PetscConj(rn[i])*rn[i]);
xn[i] += zn[i] + omegan*sn[i];
}
ierr = PetscObjectStateIncrease((PetscObject)Xn);CHKERRQ(ierr);
ierr = PetscLogFlops(7.0*N);CHKERRQ(ierr);
ierr = PetscLogEventEnd(VEC_Ops,0,0,0,0);CHKERRQ(ierr);
if (!ksp->lagnorm && ksp->chknorm < ksp->its) {
ierr = PetscLogEventBarrierBegin(VEC_ReduceBarrier,0,0,0,0,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
ierr = MPIU_Allreduce(&rnormin,&rnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
ierr = PetscLogEventBarrierEnd(VEC_ReduceBarrier,0,0,0,0,PetscObjectComm((PetscObject)ksp));CHKERRQ(ierr);
rnorm = PetscSqrtReal(rnorm);
}
/* Test for convergence */
ierr = KSPMonitor(ksp,ksp->its,rnorm);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
/* un = A*rn */
ierr = KSP_PCApplyBAorAB(ksp,Rn,Un,Tn);CHKERRQ(ierr);
/* Update n-1 locations with n locations */
sigman_2 = sigman_1;
sigman_1 = sigman;
pin_1 = pin;
phin_1 = phin;
alphan_1 = alphan;
taun_1 = taun;
omegan_1 = omegan;
}
if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
ierr = KSPUnwindPreconditioner(ksp,Xn,Tn);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_BiCG(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i;
PetscBool diagonalscale;
PetscScalar dpi,a=1.0,beta,betaold=1.0,b,ma;
PetscReal dp;
Vec X,B,Zl,Zr,Rl,Rr,Pl,Pr;
Mat Amat,Pmat;
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);
X = ksp->vec_sol;
B = ksp->vec_rhs;
Rl = ksp->work[0];
Zl = ksp->work[1];
Pl = ksp->work[2];
Rr = ksp->work[3];
Zr = ksp->work[4];
Pr = ksp->work[5];
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,Rr);CHKERRQ(ierr); /* r <- b - Ax */
ierr = VecAYPX(Rr,-1.0,B);CHKERRQ(ierr);
} else {
ierr = VecCopy(B,Rr);CHKERRQ(ierr); /* r <- b (x is 0) */
}
ierr = VecCopy(Rr,Rl);CHKERRQ(ierr);
ierr = KSP_PCApply(ksp,Rr,Zr);CHKERRQ(ierr); /* z <- Br */
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = KSP_PCApplyTranspose(ksp,Rl,Zl);CHKERRQ(ierr);
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = VecConjugate(Zl);CHKERRQ(ierr);
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = VecNorm(Zr,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else {
ierr = VecNorm(Rr,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
}
ierr = KSPMonitor(ksp,0,dp);CHKERRQ(ierr);
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ksp->rnorm = dp;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) PetscFunctionReturn(0);
i = 0;
do {
ierr = VecDot(Zr,Rl,&beta);CHKERRQ(ierr); /* beta <- r'z */
if (!i) {
if (beta == 0.0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
PetscFunctionReturn(0);
}
ierr = VecCopy(Zr,Pr);CHKERRQ(ierr); /* p <- z */
ierr = VecCopy(Zl,Pl);CHKERRQ(ierr);
} else {
b = beta/betaold;
ierr = VecAYPX(Pr,b,Zr);CHKERRQ(ierr); /* p <- z + b* p */
b = PetscConj(b);
ierr = VecAYPX(Pl,b,Zl);CHKERRQ(ierr);
}
betaold = beta;
ierr = KSP_MatMult(ksp,Amat,Pr,Zr);CHKERRQ(ierr); /* z <- Kp */
ierr = VecConjugate(Pl);CHKERRQ(ierr);
ierr = KSP_MatMultTranspose(ksp,Amat,Pl,Zl);CHKERRQ(ierr);
ierr = VecConjugate(Pl);CHKERRQ(ierr);
ierr = VecConjugate(Zl);CHKERRQ(ierr);
ierr = VecDot(Zr,Pl,&dpi);CHKERRQ(ierr); /* dpi <- z'p */
a = beta/dpi; /* a = beta/p'z */
ierr = VecAXPY(X,a,Pr);CHKERRQ(ierr); /* x <- x + ap */
ma = -a;
ierr = VecAXPY(Rr,ma,Zr);CHKERRQ(ierr);
ma = PetscConj(ma);
ierr = VecAXPY(Rl,ma,Zl);CHKERRQ(ierr);
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = KSP_PCApply(ksp,Rr,Zr);CHKERRQ(ierr); /* z <- Br */
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = KSP_PCApplyTranspose(ksp,Rl,Zl);CHKERRQ(ierr);
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = VecConjugate(Zl);CHKERRQ(ierr);
ierr = VecNorm(Zr,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else {
ierr = VecNorm(Rr,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = i+1;
ksp->rnorm = dp;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i+1,dp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = KSP_PCApply(ksp,Rr,Zr);CHKERRQ(ierr); /* z <- Br */
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = KSP_PCApplyTranspose(ksp,Rl,Zl);CHKERRQ(ierr);
ierr = VecConjugate(Rl);CHKERRQ(ierr);
ierr = VecConjugate(Zl);CHKERRQ(ierr);
}
i++;
} while (i<ksp->max_it);
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_CGNE(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,stored_max_it,eigs;
PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
PetscReal dp = 0.0;
Vec X,B,Z,R,P,T;
KSP_CG *cg;
Mat Amat,Pmat;
PetscBool diagonalscale,transpose_pc;
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 = PCApplyTransposeExists(ksp->pc,&transpose_pc);CHKERRQ(ierr);
cg = (KSP_CG*)ksp->data;
eigs = ksp->calc_sings;
stored_max_it = ksp->max_it;
X = ksp->vec_sol;
B = ksp->vec_rhs;
R = ksp->work[0];
Z = ksp->work[1];
P = ksp->work[2];
T = ksp->work[3];
#define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
ksp->its = 0;
ierr = MatMultTranspose(Amat,B,T);CHKERRQ(ierr);
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,P);CHKERRQ(ierr);
ierr = KSP_MatMultTranspose(ksp,Amat,P,R);CHKERRQ(ierr);
ierr = VecAYPX(R,-1.0,T);CHKERRQ(ierr);
} else {
ierr = VecCopy(T,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
ierr = KSP_PCApply(ksp,R,T);CHKERRQ(ierr);
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
} else if (ksp->normtype == KSP_NORM_NATURAL) {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr);
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else dp = 0.0;
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,0,dp);CHKERRQ(ierr);
ksp->rnorm = dp;
ierr = (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr); /* test for convergence */
if (ksp->reason) PetscFunctionReturn(0);
i = 0;
do {
ksp->its = i+1;
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- r'z */
if (beta == 0.0) {
ksp->reason = KSP_CONVERGED_ATOL;
ierr = PetscInfo(ksp,"converged due to beta = 0\n");CHKERRQ(ierr);
break;
#if !defined(PETSC_USE_COMPLEX)
} else if (beta < 0.0) {
ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
ierr = PetscInfo(ksp,"diverging due to indefinite preconditioner\n");CHKERRQ(ierr);
break;
#endif
}
if (!i) {
ierr = VecCopy(Z,P);CHKERRQ(ierr); /* p <- z */
b = 0.0;
} else {
b = beta/betaold;
if (eigs) {
if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
}
ierr = VecAYPX(P,b,Z);CHKERRQ(ierr); /* p <- z + b* p */
}
betaold = beta;
ierr = MatMult(Amat,P,T);CHKERRQ(ierr);
ierr = MatMultTranspose(Amat,T,Z);CHKERRQ(ierr);
ierr = VecXDot(P,Z,&dpi);CHKERRQ(ierr); /* dpi <- z'p */
a = beta/dpi; /* a = beta/p'z */
if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
ierr = VecAXPY(X,a,P);CHKERRQ(ierr); /* x <- x + ap */
ierr = VecAXPY(R,-a,Z);CHKERRQ(ierr); /* r <- r - az */
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = KSP_PCApply(ksp,R,T);CHKERRQ(ierr);
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr);
} else if (ksp->normtype == KSP_NORM_NATURAL) {
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else {
dp = 0.0;
}
ksp->rnorm = dp;
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i+1,dp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
if (transpose_pc) {
ierr = KSP_PCApplyTranspose(ksp,T,Z);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,T,Z);CHKERRQ(ierr);
}
}
i++;
} while (i<ksp->max_it);
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
