static PetscErrorCode KSPSolve_PIPEFCG(KSP ksp)
{
PetscErrorCode ierr;
KSP_PIPEFCG *pipefcg;
PetscScalar gamma;
PetscReal dp=0.0;
Vec B,R,Z,X;
Mat Amat,Pmat;
#define VecXDot(x,y,a) (((pipefcg->type) == (KSP_CG_HERMITIAN)) ? VecDot (x,y,a) : VecTDot (x,y,a))
PetscFunctionBegin;
ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
pipefcg = (KSP_PIPEFCG*)ksp->data;
X = ksp->vec_sol;
B = ksp->vec_rhs;
R = ksp->work[0];
Z = ksp->work[1];
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
/* Compute initial residual needed for convergence check*/
ksp->its = 0;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr);
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr); /* r <- b - Ax */
} else {
ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
switch (ksp->normtype) {
case KSP_NORM_PRECONDITIONED:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
break;
case KSP_NORM_UNPRECONDITIONED:
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e) */
break;
case KSP_NORM_NATURAL:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecXDot(Z,R,&gamma);CHKERRQ(ierr);
dp = PetscSqrtReal(PetscAbsScalar(gamma)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e) */
break;
case KSP_NORM_NONE:
dp = 0.0;
break;
default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
}
/* Initial Convergence Check */
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,0,dp);CHKERRQ(ierr);
ksp->rnorm = dp;
if (ksp->normtype == KSP_NORM_NONE) {
ierr = KSPConvergedSkip (ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
} else {
ierr = (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
}
if (ksp->reason) PetscFunctionReturn(0);
do {
/* A cycle is broken only if a norm breakdown occurs. If not the entire solve happens in a single cycle.
This is coded this way to allow both truncation and truncation-restart strategy
(see KSPFCDGetNumOldDirections()) */
ierr = KSPSolve_PIPEFCG_cycle(ksp);CHKERRQ(ierr);
if (ksp->reason) break;
if (pipefcg->norm_breakdown) {
pipefcg->n_restarts++;
pipefcg->norm_breakdown = PETSC_FALSE;
}
} while (ksp->its < ksp->max_it);
if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_CG(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,stored_max_it,eigs;
PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
PetscReal dp = 0.0;
Vec X,B,Z,R,P,S,W;
KSP_CG *cg;
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);
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];
if (cg->singlereduction) {
S = ksp->work[3];
W = ksp->work[4];
} else {
S = 0; /* unused */
W = Z;
}
#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;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr); /* r <- b - Ax */
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr);
} else {
ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
switch (ksp->normtype) {
case KSP_NORM_PRECONDITIONED:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
break;
case KSP_NORM_UNPRECONDITIONED:
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r = e'*A'*A*e */
break;
case KSP_NORM_NATURAL:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecXDot(Z,S,&delta);CHKERRQ(ierr);
}
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
if (PetscIsInfOrNanScalar(beta)) {
if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
break;
case KSP_NORM_NONE:
dp = 0.0;
break;
default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
}
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);
if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
}
if (ksp->normtype != KSP_NORM_NATURAL) {
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecXDot(Z,S,&delta);CHKERRQ(ierr);
}
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
if (PetscIsInfOrNanScalar(beta)) {
if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
}
i = 0;
do {
ksp->its = i+1;
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 ((i > 0) && (beta*betaold < 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 */
}
dpiold = dpi;
if (!cg->singlereduction || !i) {
ierr = KSP_MatMult(ksp,Amat,P,W);CHKERRQ(ierr); /* w <- Ap */
ierr = VecXDot(P,W,&dpi);CHKERRQ(ierr); /* dpi <- p'w */
} else {
ierr = VecAYPX(W,beta/betaold,S);CHKERRQ(ierr); /* w <- Ap */
dpi = delta - beta*beta*dpiold/(betaold*betaold); /* dpi <- p'w */
}
betaold = beta;
if (PetscIsInfOrNanScalar(dpi)) {
if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
ierr = PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");CHKERRQ(ierr);
break;
}
a = beta/dpi; /* a = beta/p'w */
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,W);CHKERRQ(ierr); /* r <- r - aw */
if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
}
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
} else if (ksp->normtype == KSP_NORM_NATURAL) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
PetscScalar tmp[2];
Vec vecs[2];
vecs[0] = S; vecs[1] = R;
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecMDot(Z,2,vecs,tmp);CHKERRQ(ierr);
delta = tmp[0]; beta = tmp[1];
} else {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- r'*z */
}
if (PetscIsInfOrNanScalar(beta)) {
if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else {
dp = 0.0;
}
ksp->rnorm = dp;
CHKERRQ(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 && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
}
}
if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
if (cg->singlereduction) {
PetscScalar tmp[2];
Vec vecs[2];
vecs[0] = S; vecs[1] = R;
ierr = VecMDot(Z,2,vecs,tmp);CHKERRQ(ierr);
delta = tmp[0]; beta = tmp[1];
} else {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
}
if (PetscIsInfOrNanScalar(beta)) {
if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
else {
ksp->reason = KSP_DIVERGED_NANORINF;
PetscFunctionReturn(0);
}
}
}
i++;
} while (i<ksp->max_it);
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_CG(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,stored_max_it,eigs;
PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
PetscReal dp = 0.0;
Vec X,B,Z,R,P,S,W;
KSP_CG *cg;
Mat Amat,Pmat;
PetscBool diagonalscale;
/* Dingwen */
PetscInt itv_d, itv_c;
PetscScalar CKSX1,CKSZ1,CKSR1,CKSP1,CKSS1,CKSW1;
PetscScalar CKSX2,CKSZ2,CKSR2,CKSP2,CKSS2,CKSW2;
Vec CKSAmat1;
Vec CKSAmat2;
Vec C1,C2;
PetscScalar d1,d2;
PetscScalar sumX1,sumR1;
PetscScalar sumX2,sumR2;
Vec CKPX,CKPP;
PetscScalar CKPbetaold;
PetscInt CKPi;
PetscBool flag1 = PETSC_TRUE, flag2 = PETSC_TRUE;
PetscInt pos;
PetscScalar v;
VecScatter ctx;
Vec W_SEQ;
PetscScalar *_W;
/* Dingwen */
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);
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];
/* Dingwen */
CKPX = ksp->work[3];
CKPP = ksp->work[4];
CKSAmat1 = ksp->work[5];
CKSAmat2 = ksp->work[6];
C1 = ksp->work[7];
C2 = ksp->work[8];
/* Dingwen */
/* Dingwen */
int rank; /* Get MPI variables */
MPI_Comm_rank (MPI_COMM_WORLD,&rank);
/* Dingwen */
#define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
if (cg->singlereduction) {
S = ksp->work[9];
W = ksp->work[10];
} else {
S = 0; /* unused */
W = Z;
}
if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
ksp->its = 0;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr); /* r <- b - Ax */
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr);
} else {
ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
/* Dingwen */
/* checksum coefficients initialization */
PetscInt size;
ierr = VecGetSize(B,&size);
for (i=0; i<size; i++)
{
v = 1.0;
ierr = VecSetValues(C1,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
v = i;
ierr = VecSetValues(C2,1,&i,&v,INSERT_VALUES);CHKERRQ(ierr);
}
d1 = 1.0;
d2 = 2.0;
/* Dingwen */
switch (ksp->normtype) {
case KSP_NORM_PRECONDITIONED:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
break;
case KSP_NORM_UNPRECONDITIONED:
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r = e'*A'*A*e */
break;
case KSP_NORM_NATURAL:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecXDot(Z,S,&delta);CHKERRQ(ierr);
/* Dingwen */
ierr = VecXDot(C1,S,&CKSS1);CHKERRQ(ierr); /* Compute the initial checksum1(S) */
ierr = VecXDot(C2,S,&CKSS2);CHKERRQ(ierr); /* Compute the initial checksum2(S) */
/* Dingwen */
}
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
KSPCheckDot(ksp,beta);
dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
break;
case KSP_NORM_NONE:
dp = 0.0;
break;
default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
}
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);
if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
}
if (ksp->normtype != KSP_NORM_NATURAL) {
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecXDot(Z,S,&delta);CHKERRQ(ierr);
}
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
KSPCheckDot(ksp,beta);
}
/* Dingwen */
/* Checksum Initialization */
ierr = VecXDot(C1,X,&CKSX1);CHKERRQ(ierr); /* Compute the initial checksum1(X) */
ierr = VecXDot(C1,W,&CKSW1);CHKERRQ(ierr); /* Compute the initial checksum1(W) */
ierr = VecXDot(C1,R,&CKSR1);CHKERRQ(ierr); /* Compute the initial checksum1(R) */
ierr = VecXDot(C1,Z,&CKSZ1);CHKERRQ(ierr); /* Compute the initial checksum1(Z) */
ierr = VecXDot(C2,X,&CKSX2);CHKERRQ(ierr); /* Compute the initial checksum2(X) */
ierr = VecXDot(C2,W,&CKSW2);CHKERRQ(ierr); /* Compute the initial checksum2(W) */
ierr = VecXDot(C2,R,&CKSR2);CHKERRQ(ierr); /* Compute the initial checksum2(R) */
ierr = VecXDot(C2,Z,&CKSZ2);CHKERRQ(ierr); /* Compute the initial checksum2(Z) */
ierr = KSP_MatMultTranspose(ksp,Amat,C1,CKSAmat1);CHKERRQ(ierr);
ierr = VecAXPY(CKSAmat1,-d1,C1);CHKERRQ(ierr);
ierr = VecAXPY(CKSAmat1,-d2,C2);CHKERRQ(ierr); /* Compute the initial checksum1(A) */
ierr = KSP_MatMultTranspose(ksp,Amat,C2,CKSAmat2);CHKERRQ(ierr);
ierr = VecAXPY(CKSAmat2,-d2,C1);CHKERRQ(ierr);
ierr = VecAXPY(CKSAmat2,-d1,C2);CHKERRQ(ierr); /* Compute the initial checksum2(A) */
itv_c = 2;
itv_d = 10;
/* Dingwen */
i = 0;
do {
/* Dingwen */
if ((i>0) && (i%itv_d == 0))
{
ierr = VecXDot(C1,X,&sumX1);CHKERRQ(ierr);
ierr = VecXDot(C1,R,&sumR1);CHKERRQ(ierr);
if ((PetscAbsScalar(sumX1-CKSX1) > 1.0e-6) || (PetscAbsScalar(sumR1-CKSR1) > 1.0e-6))
{
/* Rollback and Recovery */
if (rank==0) printf ("Recovery start...\n");
if (rank==0) printf ("Rollback from iteration-%d to iteration-%d\n",i,CKPi);
betaold = CKPbetaold; /* Recovery scalar betaold by checkpoint*/
i = CKPi; /* Recovery integer i by checkpoint */
ierr = VecCopy(CKPP,P);CHKERRQ(ierr); /* Recovery vector P from checkpoint */
ierr = VecXDot(C1,P,&CKSP1);CHKERRQ(ierr); /* Recovery checksum1(P) by P */
ierr = VecXDot(C2,P,&CKSP2);CHKERRQ(ierr); /* Recovery checksum2(P) by P */
ierr = KSP_MatMult(ksp,Amat,P,W);CHKERRQ(ierr); /* Recovery vector W by P */
ierr = VecXDot(P,W,&dpi);CHKERRQ(ierr); /* Recovery scalar dpi by P and W */
ierr = VecCopy(CKPX,X);CHKERRQ(ierr); /* Recovery vector X from checkpoint */
ierr = VecXDot(C1,X,&CKSX1);CHKERRQ(ierr); /* Recovery checksum1(X) by X */
ierr = VecXDot(C2,X,&CKSX2);CHKERRQ(ierr); /* Recovery checksum2(X) by X */
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr); /* Recovery vector R by X */
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr);
ierr = VecXDot(C1,R,&CKSR1);CHKERRQ(ierr); /* Recovery checksum1(R) by R */
ierr = VecXDot(C2,R,&CKSR2);CHKERRQ(ierr); /* Recovery checksum2(R) by R */
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* Recovery vector Z by R */
ierr = VecXDot(C1,Z,&CKSZ1);CHKERRQ(ierr); /* Recovery checksum1(Z) by Z */
ierr = VecXDot(C2,Z,&CKSZ2);CHKERRQ(ierr); /* Recovery checksum2(Z) by Z */
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* Recovery scalar beta by Z and R */
if (rank==0) printf ("Recovery end.\n");
}
else if (i%(itv_c*itv_d) == 0)
{
if (rank==0) printf ("Checkpoint iteration-%d\n",i);
ierr = VecCopy(X,CKPX);CHKERRQ(ierr);
ierr = VecCopy(P,CKPP);CHKERRQ(ierr);
CKPbetaold = betaold;
CKPi = i;
}
}
ksp->its = i+1;
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 ((i > 0) && (beta*betaold < 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;
/* Dingwen */
ierr = VecXDot(C1,P, &CKSP1);CHKERRQ(ierr); /* Compute the initial checksum1(P) */
ierr = VecXDot(C2,P, &CKSP2);CHKERRQ(ierr); /* Compute the initial checksum2(P) */
/* Dingwen */
} 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 */
/* Dingwen */
CKSP1 = CKSZ1 + b*CKSP1; /* Update checksum1(P) = checksum1(Z) + b*checksum1(P); */
CKSP2 = CKSZ2 + b*CKSP2; /* Update checksum2(P) = checksum2(Z) + b*checksum2(P); */
/* Dingwen */
}
dpiold = dpi;
if (!cg->singlereduction || !i) {
ierr = KSP_MatMult(ksp,Amat,P,W);CHKERRQ(ierr); /* w <- Ap */ /* MVM */
ierr = VecXDot(P,W,&dpi);CHKERRQ(ierr); /* dpi <- p'w */
/* Dingwen */
ierr = VecXDot(CKSAmat1, P, &CKSW1);CHKERRQ(ierr);
CKSW1 = CKSW1 + d1*CKSP1 + d2*CKSP2; /* Update checksum1(W) = checksum1(A)P + d1*checksum1(P) + d2*checksum2(P); */
ierr = VecXDot(CKSAmat2, P, &CKSW2);CHKERRQ(ierr);
CKSW2 = CKSW2 + d2*CKSP1 + d1*CKSP2; /* Update checksum2(W) = checksum2(A)P + d2*checksum1(P) + d1*checksum2(P); */
if((i==41)&&(flag2))
{
pos = 100;
v = 1000;
ierr = VecSetValue(W,pos,v,INSERT_VALUES);CHKERRQ(ierr);
VecAssemblyBegin(W);
VecAssemblyEnd(W);
if (rank==0) printf ("Inject an error in %d-th element of vector W after MVM W=AP at iteration-%d\n", pos,i);
flag2 = PETSC_FALSE;
}
PetscScalar delta1,delta2;
PetscScalar sumW1,sumW2;
ierr = VecXDot(C1,W,&sumW1);CHKERRQ(ierr);
ierr = VecXDot(C2,W,&sumW2);CHKERRQ(ierr);
delta1 = sumW1 - CKSW1;
delta2 = sumW2 - CKSW2;
if (PetscAbsScalar(delta1) > 1.0e-6)
{
VecScatterCreateToAll(W,&ctx,&W_SEQ);
VecScatterBegin(ctx,W,W_SEQ,INSERT_VALUES,SCATTER_FORWARD);
VecScatterEnd(ctx,W,W_SEQ,INSERT_VALUES,SCATTER_FORWARD);
VecGetArray(W_SEQ,&_W);
pos = rint(delta2/delta1);
v = _W[pos];
v = v - delta1;
ierr = VecSetValues(W,1,&pos,&v,INSERT_VALUES);CHKERRQ(ierr);
if (rank==0) printf ("Correct an error of %d-th elements of vector W after MVM W=AP at iteration-%d\n", pos, i);
}
} else {
ierr = VecAYPX(W,beta/betaold,S);CHKERRQ(ierr); /* w <- Ap */
dpi = delta - beta*beta*dpiold/(betaold*betaold); /* dpi <- p'w */
/* Dingwen */
CKSW1 = beta/betaold*CKSW1 + CKSS1; /* Update checksum1(W) = checksum1(S) + beta/betaold*checksum1(W); */
CKSW2 = beta/betaold*CKSW2 + CKSS2; /* Update checksum2(W) = checksum2(S) + beta/betaold*checksum2(W); */
/* Dingwen */
}
betaold = beta;
KSPCheckDot(ksp,beta);
if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
ierr = PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");CHKERRQ(ierr);
break;
}
a = beta/dpi; /* a = beta/p'w */
if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
ierr = VecAXPY(X,a,P);CHKERRQ(ierr); /* x <- x + ap */
/* Dingwen */
CKSX1 = CKSX1 + a*CKSP1; /* Update checksum1(X) = checksum1(X) + a*checksum1(P); */
CKSX2 = CKSX2 + a*CKSP2; /* Update checksum2(X) = checksum2(X) + a*checksum2(P); */
/* Dingwen */
ierr = VecAXPY(R,-a,W);CHKERRQ(ierr); /* r <- r - aw */
/* Dingwen */
CKSR1 = CKSR1 - a*CKSW1; /* Update checksum1(R) = checksum1(R) - a*checksum1(W); */
CKSR2 = CKSR2 - a*CKSW2; /* Update checksum2(R) = checksum2(R) - a*checksum2(W); */
/* Dingwen */
if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
/* Dingwen */
ierr = VecXDot(C1,Z, &CKSZ1);CHKERRQ(ierr); /* Update checksum1(Z) */
ierr = VecXDot(C2,Z, &CKSZ2);CHKERRQ(ierr); /* Update checksum2(Z) */
/* Dingwen */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr); /* MVM */
/* Dingwen */
ierr = VecXDot(CKSAmat1, Z, &CKSS1);CHKERRQ(ierr);
CKSS1 = CKSS1 + d1*CKSZ1 + d2*CKSZ2; /* Update checksum1(S) = checksum1(A)Z + d1*chekcsum1(Z) + d2*checksum2(Z); */
ierr = VecXDot(CKSAmat2, Z, &CKSS2);CHKERRQ(ierr);
CKSS2 = CKSS2 + d2*CKSZ1 + d1*CKSZ2; /* Update checksum2(S) = checksum2(A)Z + d2*chekcsum1(Z) + d1*checksum2(Z); */
/* Dingwen */
}
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r */
} else if (ksp->normtype == KSP_NORM_NATURAL) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
/* Dingwen */
ierr = VecXDot(C1,Z, &CKSZ1);CHKERRQ(ierr); /* Update checksum1(Z) */
ierr = VecXDot(C2,Z, &CKSZ2);CHKERRQ(ierr); /* Update checksum2(Z) */
/* Dingwen */
if (cg->singlereduction) {
PetscScalar tmp[2];
Vec vecs[2];
vecs[0] = S; vecs[1] = R;
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecMDot(Z,2,vecs,tmp);CHKERRQ(ierr);
delta = tmp[0]; beta = tmp[1];
} else {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- r'*z */
}
KSPCheckDot(ksp,beta);
dp = PetscSqrtReal(PetscAbsScalar(beta));
} else {
dp = 0.0;
}
ksp->rnorm = dp;
CHKERRQ(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 && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
/* Dingwen */
ierr = VecXDot(C1,Z, &CKSZ1);CHKERRQ(ierr); /* Update checksum1(Z) */
ierr = VecXDot(C2,Z, &CKSZ2);CHKERRQ(ierr); /* Update checksum2(Z) */
/* Dingwen */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
}
}
if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
if (cg->singlereduction) {
PetscScalar tmp[2];
Vec vecs[2];
vecs[0] = S; vecs[1] = R;
ierr = VecMDot(Z,2,vecs,tmp);CHKERRQ(ierr);
delta = tmp[0]; beta = tmp[1];
} else {
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
}
KSPCheckDot(ksp,beta);
}
i++;
/* Dingwen */
/* Inject error */
if ((i==50)&&(flag1))
{
pos = 1000;
v = -1;
ierr = VecSetValues(X,1,&pos,&v,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(X);CHKERRQ(ierr);
ierr = VecAssemblyEnd(X);CHKERRQ(ierr);
flag1 = PETSC_FALSE;
if (rank==0)printf ("Inject an error in vector X at the end of iteration-%d\n", i-1);
}
/* Dingwen */
} while (i<ksp->max_it);
/* Dingwen */
ierr = VecXDot(C1,X,&sumX1);CHKERRQ(ierr);
ierr = VecXDot(C1,R,&sumR1);CHKERRQ(ierr);
ierr = VecXDot(C2,X,&sumX2);CHKERRQ(ierr);
ierr = VecXDot(C2,R,&sumR2);CHKERRQ(ierr);
if (rank==0)
{
printf ("sum1 of X = %f\n", sumX1);
printf ("checksum1(X) = %f\n", CKSX1);
printf ("sum2 of X = %f\n", sumX2);
printf ("checksum2(X) = %f\n", CKSX2);
printf ("sum1 of R = %f\n", sumR1);
printf ("checksum1(R) = %f\n", CKSR1);
printf ("sum2 of R = %f\n", sumR2);
printf ("checksum2(R) = %f\n", CKSR2);
}
VecDestroy(&W_SEQ);
VecScatterDestroy(&ctx);
/* Dingwen */
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
if (eigs) cg->ned = ksp->its;
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_FCG(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,k,idx,mi;
KSP_FCG *fcg = (KSP_FCG*)ksp->data;
PetscScalar alpha=0.0,beta = 0.0,dpi,s;
PetscReal dp=0.0;
Vec B,R,Z,X,Pcurr,Ccurr;
Mat Amat,Pmat;
PetscInt eigs = ksp->calc_sings; /* Variables for eigen estimation - START*/
PetscInt stored_max_it = ksp->max_it;
PetscScalar alphaold = 0,betaold = 1.0,*e = 0,*d = 0;/* Variables for eigen estimation - FINISH */
PetscFunctionBegin;
#define VecXDot(x,y,a) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
#define VecXMDot(a,b,c,d) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecMDot(a,b,c,d) : VecMTDot(a,b,c,d))
X = ksp->vec_sol;
B = ksp->vec_rhs;
R = ksp->work[0];
Z = ksp->work[1];
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
if (eigs) {e = fcg->e; d = fcg->d; e[0] = 0.0; }
/* Compute initial residual needed for convergence check*/
ksp->its = 0;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr);
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr); /* r <- b - Ax */
} else {
ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
switch (ksp->normtype) {
case KSP_NORM_PRECONDITIONED:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
break;
case KSP_NORM_UNPRECONDITIONED:
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e) */
break;
case KSP_NORM_NATURAL:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecXDot(R,Z,&s);CHKERRQ(ierr);
dp = PetscSqrtReal(PetscAbsScalar(s)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e) */
break;
case KSP_NORM_NONE:
dp = 0.0;
break;
default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
}
/* Initial Convergence Check */
ierr = KSPLogResidualHistory(ksp,dp);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,0,dp);CHKERRQ(ierr);
ksp->rnorm = dp;
if (ksp->normtype == KSP_NORM_NONE) {
ierr = KSPConvergedSkip(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
} else {
ierr = (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
}
if (ksp->reason) PetscFunctionReturn(0);
/* Apply PC if not already done for convergence check */
if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
}
i = 0;
do {
ksp->its = i+1;
/* If needbe, allocate a new chunk of vectors in P and C */
ierr = KSPAllocateVectors_FCG(ksp,i+1,fcg->vecb);CHKERRQ(ierr);
/* Note that we wrap around and start clobbering old vectors */
idx = i % (fcg->mmax+1);
Pcurr = fcg->Pvecs[idx];
Ccurr = fcg->Cvecs[idx];
/* Compute a new column of P (Currently does not support modified G-S or iterative refinement)*/
switch(fcg->truncstrat){
case KSP_FCG_TRUNC_TYPE_NOTAY :
mi = PetscMax(1,i%(fcg->mmax+1));
break;
case KSP_FCG_TRUNC_TYPE_STANDARD :
mi = fcg->mmax;
break;
default:
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unrecognized FCG Truncation Strategy");CHKERRQ(ierr);
}
ierr = VecCopy(Z,Pcurr);CHKERRQ(ierr);
{
PetscInt l,ndots;
l = PetscMax(0,i-mi);
ndots = i-l;
if (ndots){
PetscInt j;
Vec *Pold, *Cold;
PetscScalar *dots;
ierr = PetscMalloc3(ndots,&dots,ndots,&Cold,ndots,&Pold);CHKERRQ(ierr);
for(k=l,j=0;j<ndots;++k,++j){
idx = k % (fcg->mmax+1);
Cold[j] = fcg->Cvecs[idx];
Pold[j] = fcg->Pvecs[idx];
}
ierr = VecXMDot(Z,ndots,Cold,dots);CHKERRQ(ierr);
for(k=0;k<ndots;++k){
dots[k] = -dots[k];
}
ierr = VecMAXPY(Pcurr,ndots,dots,Pold);CHKERRQ(ierr);
ierr = PetscFree3(dots,Cold,Pold);CHKERRQ(ierr);
}
}
/* Update X and R */
betaold = beta;
ierr = VecXDot(Pcurr,R,&beta);CHKERRQ(ierr); /* beta <- pi'*r */
ierr = KSP_MatMult(ksp,Amat,Pcurr,Ccurr);CHKERRQ(ierr); /* w <- A*pi (stored in ci) */
ierr = VecXDot(Pcurr,Ccurr,&dpi);CHKERRQ(ierr); /* dpi <- pi'*w */
alphaold = alpha;
alpha = beta / dpi; /* alpha <- beta/dpi */
ierr = VecAXPY(X,alpha,Pcurr);CHKERRQ(ierr); /* x <- x + alpha * pi */
ierr = VecAXPY(R,-alpha,Ccurr);CHKERRQ(ierr); /* r <- r - alpha * wi */
/* Compute norm for convergence check */
switch (ksp->normtype) {
case KSP_NORM_PRECONDITIONED:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- sqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
break;
case KSP_NORM_UNPRECONDITIONED:
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e) */
break;
case KSP_NORM_NATURAL:
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecXDot(R,Z,&s);CHKERRQ(ierr);
dp = PetscSqrtReal(PetscAbsScalar(s)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e) */
break;
case KSP_NORM_NONE:
dp = 0.0;
break;
default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
}
/* Check for convergence */
ksp->rnorm = dp;
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;
/* Apply PC if not already done for convergence check */
if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
}
/* Compute current C (which is W/dpi) */
ierr = VecScale(Ccurr,1.0/dpi);CHKERRQ(ierr); /* w <- ci/dpi */
if (eigs) {
if (i > 0) {
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(beta/betaold))/alphaold;
d[i] = PetscSqrtReal(PetscAbsScalar(beta/betaold))*e[i] + 1.0/alpha;
} else {
d[i] = PetscSqrtReal(PetscAbsScalar(beta))*e[i] + 1.0/alpha;
}
}
++i;
} while (i<ksp->max_it);
if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
if (eigs) fcg->ned = ksp->its-1;
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_CG(KSP ksp)
{
PetscErrorCode ierr;
PetscInt i,stored_max_it,eigs;
PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
PetscReal dp = 0.0;
Vec X,B,Z,R,P,S,W;
KSP_CG *cg;
Mat Amat,Pmat;
MatStructure pflag;
PetscTruth diagonalscale;
PetscFunctionBegin;
ierr = PCDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
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];
if (cg->singlereduction) {
S = ksp->work[3];
W = ksp->work[4];
} else {
S = 0; /* unused */
W = Z;
}
#if !defined(PETSC_USE_COMPLEX)
#define VecXDot(x,y,a) VecDot(x,y,a)
#else
#define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
#endif
if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);CHKERRQ(ierr);
ksp->its = 0;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,X,R);CHKERRQ(ierr); /* r <- b - Ax */
ierr = VecAYPX(R,-1.0,B);CHKERRQ(ierr);
} else {
ierr = VecCopy(B,R);CHKERRQ(ierr); /* r <- b (x is 0) */
}
if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
ierr = VecNorm(Z,NORM_2,&dp);CHKERRQ(ierr); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
} else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(R,NORM_2,&dp);CHKERRQ(ierr); /* dp <- r'*r = e'*A'*A*e */
} else if (ksp->normtype == KSP_NORM_NATURAL) {
ierr = KSP_PCApply(ksp,R,Z);CHKERRQ(ierr); /* z <- Br */
if (cg->singlereduction) {
ierr = KSP_MatMult(ksp,Amat,Z,S);CHKERRQ(ierr);
ierr = VecXDot(Z,S,&delta);CHKERRQ(ierr);
}
ierr = VecXDot(Z,R,&beta);CHKERRQ(ierr); /* beta <- z'*r */
if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
dp = sqrt(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
} else dp = 0.0;
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);
}
