2: #include <petsc-private/kspimpl.h>

  6: static PetscErrorCode KSPSetUp_TFQMR(KSP ksp)
  7: {

 11:   if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"no symmetric preconditioning for KSPTFQMR");
 12:   KSPDefaultGetWork(ksp,9);
 13:   return(0);
 14: }

 18: static PetscErrorCode  KSPSolve_TFQMR(KSP ksp)
 19: {
 21:   PetscInt       i,m;
 22:   PetscScalar    rho,rhoold,a,s,b,eta,etaold,psiold,cf;
 23:   PetscReal      dp,dpold,w,dpest,tau,psi,cm;
 24:   Vec            X,B,V,P,R,RP,T,T1,Q,U,D,AUQ;

 27:   X        = ksp->vec_sol;
 28:   B        = ksp->vec_rhs;
 29:   R        = ksp->work[0];
 30:   RP       = ksp->work[1];
 31:   V        = ksp->work[2];
 32:   T        = ksp->work[3];
 33:   Q        = ksp->work[4];
 34:   P        = ksp->work[5];
 35:   U        = ksp->work[6];
 36:   D        = ksp->work[7];
 37:   T1       = ksp->work[8];
 38:   AUQ      = V;

 40:   /* Compute initial preconditioned residual */
 41:   KSPInitialResidual(ksp,X,V,T,R,B);

 43:   /* Test for nothing to do */
 44:   VecNorm(R,NORM_2,&dp);
 45:   PetscObjectTakeAccess(ksp);
 46:   ksp->rnorm  = dp;
 47:   ksp->its    = 0;
 48:   PetscObjectGrantAccess(ksp);
 49:   KSPMonitor(ksp,0,dp);
 50:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
 51:   if (ksp->reason) return(0);

 53:   /* Make the initial Rp == R */
 54:   VecCopy(R,RP);

 56:   /* Set the initial conditions */
 57:   etaold = 0.0;
 58:   psiold = 0.0;
 59:   tau    = dp;
 60:   dpold  = dp;

 62:   VecDot(R,RP,&rhoold);       /* rhoold = (r,rp)     */
 63:   VecCopy(R,U);
 64:   VecCopy(R,P);
 65:   KSP_PCApplyBAorAB(ksp,P,V,T);
 66:   VecSet(D,0.0);

 68:   i=0;
 69:   do {
 70:     PetscObjectTakeAccess(ksp);
 71:     ksp->its++;
 72:     PetscObjectGrantAccess(ksp);
 73:     VecDot(V,RP,&s);          /* s <- (v,rp)          */
 74:     a = rhoold / s;                                 /* a <- rho / s         */
 75:     VecWAXPY(Q,-a,V,U);  /* q <- u - a v         */
 76:     VecWAXPY(T,1.0,U,Q);     /* t <- u + q           */
 77:     KSP_PCApplyBAorAB(ksp,T,AUQ,T1);
 78:     VecAXPY(R,-a,AUQ);      /* r <- r - a K (u + q) */
 79:     VecNorm(R,NORM_2,&dp);
 80:     for (m=0; m<2; m++) {
 81:       if (!m) {
 82:         w = PetscSqrtReal(dp*dpold);
 83:       } else {
 84:         w = dp;
 85:       }
 86:       psi = w / tau;
 87:       cm  = 1.0 / PetscSqrtReal(1.0 + psi * psi);
 88:       tau = tau * psi * cm;
 89:       eta = cm * cm * a;
 90:       cf  = psiold * psiold * etaold / a;
 91:       if (!m) {
 92:         VecAYPX(D,cf,U);
 93:       } else {
 94:         VecAYPX(D,cf,Q);
 95:       }
 96:       VecAXPY(X,eta,D);

 98:       dpest = PetscSqrtReal(m + 1.0) * tau;
 99:       PetscObjectTakeAccess(ksp);
100:       ksp->rnorm                                    = dpest;
101:       PetscObjectGrantAccess(ksp);
102:       KSPLogResidualHistory(ksp,dpest);
103:       KSPMonitor(ksp,i+1,dpest);
104:       (*ksp->converged)(ksp,i+1,dpest,&ksp->reason,ksp->cnvP);
105:       if (ksp->reason) break;

107:       etaold = eta;
108:       psiold = psi;
109:     }
110:     if (ksp->reason) break;

112:     VecDot(R,RP,&rho);        /* rho <- (r,rp)       */
113:     b = rho / rhoold;                               /* b <- rho / rhoold   */
114:     VecWAXPY(U,b,Q,R);       /* u <- r + b q        */
115:     VecAXPY(Q,b,P);
116:     VecWAXPY(P,b,Q,U);       /* p <- u + b(q + b p) */
117:     KSP_PCApplyBAorAB(ksp,P,V,Q); /* v <- K p  */

119:     rhoold = rho;
120:     dpold  = dp;

122:     i++;
123:   } while (i<ksp->max_it);
124:   if (i >= ksp->max_it) {
125:     ksp->reason = KSP_DIVERGED_ITS;
126:   }

128:   KSPUnwindPreconditioner(ksp,X,T);
129:   return(0);
130: }

132: /*MC
133:      KSPTFQMR - A transpose free QMR (quasi minimal residual), 

135:    Options Database Keys:
136: .   see KSPSolve()

138:    Level: beginner

140:    Notes: Supports left and right preconditioning, but not symmetric

142:           The "residual norm" computed in this algorithm is actually just an upper bound on the actual residual norm.
143:           That is for left preconditioning it is a bound on the preconditioned residual and for right preconditioning 
144:           it is a bound on the true residual.

146:    References: Freund, 1993

148: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPTCQMR
149: M*/
150: EXTERN_C_BEGIN
153: PetscErrorCode  KSPCreate_TFQMR(KSP ksp)
154: {

158:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
159:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,1);
160:   ksp->data                      = (void*)0;
161:   ksp->ops->setup                = KSPSetUp_TFQMR;
162:   ksp->ops->solve                = KSPSolve_TFQMR;
163:   ksp->ops->destroy              = KSPDefaultDestroy;
164:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
165:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;
166:   ksp->ops->setfromoptions       = 0;
167:   ksp->ops->view                 = 0;
168:   return(0);
169: }
170: EXTERN_C_END