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

  4: static PetscErrorCode KSPSetUp_BiCG(KSP ksp)
  5: {

  9:   /* check user parameters and functions */
 10:   if (ksp->pc_side == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no right preconditioning for KSPBiCG");
 11:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no symmetric preconditioning for KSPBiCG");
 12:   KSPSetWorkVecs(ksp,6);
 13:   return(0);
 14: }

 16: static PetscErrorCode  KSPSolve_BiCG(KSP ksp)
 17: {
 19:   PetscInt       i;
 20:   PetscBool      diagonalscale;
 21:   PetscScalar    dpi,a=1.0,beta,betaold=1.0,b,ma;
 22:   PetscReal      dp;
 23:   Vec            X,B,Zl,Zr,Rl,Rr,Pl,Pr;
 24:   Mat            Amat,Pmat;

 27:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
 28:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

 30:   X  = ksp->vec_sol;
 31:   B  = ksp->vec_rhs;
 32:   Rl = ksp->work[0];
 33:   Zl = ksp->work[1];
 34:   Pl = ksp->work[2];
 35:   Rr = ksp->work[3];
 36:   Zr = ksp->work[4];
 37:   Pr = ksp->work[5];

 39:   PCGetOperators(ksp->pc,&Amat,&Pmat);

 41:   if (!ksp->guess_zero) {
 42:     KSP_MatMult(ksp,Amat,X,Rr);      /*   r <- b - Ax       */
 43:     VecAYPX(Rr,-1.0,B);
 44:   } else {
 45:     VecCopy(B,Rr);           /*     r <- b (x is 0) */
 46:   }
 47:   VecCopy(Rr,Rl);
 48:   KSP_PCApply(ksp,Rr,Zr);     /*     z <- Br         */
 49:   VecConjugate(Rl);
 50:   KSP_PCApplyTranspose(ksp,Rl,Zl);
 51:   VecConjugate(Rl);
 52:   VecConjugate(Zl);
 53:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
 54:     VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
 55:   } else {
 56:     VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
 57:   }
 58:   KSPMonitor(ksp,0,dp);
 59:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
 60:   ksp->its   = 0;
 61:   ksp->rnorm = dp;
 62:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
 63:   KSPLogResidualHistory(ksp,dp);
 64:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
 65:   if (ksp->reason) return(0);

 67:   i = 0;
 68:   do {
 69:     VecDot(Zr,Rl,&beta);       /*     beta <- r'z     */
 70:     if (!i) {
 71:       if (beta == 0.0) {
 72:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
 73:         return(0);
 74:       }
 75:       VecCopy(Zr,Pr);       /*     p <- z          */
 76:       VecCopy(Zl,Pl);
 77:     } else {
 78:       b    = beta/betaold;
 79:       VecAYPX(Pr,b,Zr);  /*     p <- z + b* p   */
 80:       b    = PetscConj(b);
 81:       VecAYPX(Pl,b,Zl);
 82:     }
 83:     betaold = beta;
 84:     KSP_MatMult(ksp,Amat,Pr,Zr); /*     z <- Kp         */
 85:     VecConjugate(Pl);
 86:     KSP_MatMultTranspose(ksp,Amat,Pl,Zl);
 87:     VecConjugate(Pl);
 88:     VecConjugate(Zl);
 89:     VecDot(Zr,Pl,&dpi);            /*     dpi <- z'p      */
 90:     a       = beta/dpi;                           /*     a = beta/p'z    */
 91:     VecAXPY(X,a,Pr);    /*     x <- x + ap     */
 92:     ma      = -a;
 93:     VecAXPY(Rr,ma,Zr);
 94:     ma      = PetscConj(ma);
 95:     VecAXPY(Rl,ma,Zl);
 96:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
 97:       KSP_PCApply(ksp,Rr,Zr);  /*     z <- Br         */
 98:       VecConjugate(Rl);
 99:       KSP_PCApplyTranspose(ksp,Rl,Zl);
100:       VecConjugate(Rl);
101:       VecConjugate(Zl);
102:       VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
103:     } else {
104:       VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
105:     }
106:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
107:     ksp->its   = i+1;
108:     ksp->rnorm = dp;
109:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
110:     KSPLogResidualHistory(ksp,dp);
111:     KSPMonitor(ksp,i+1,dp);
112:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
113:     if (ksp->reason) break;
114:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
115:       KSP_PCApply(ksp,Rr,Zr);  /* z <- Br  */
116:       VecConjugate(Rl);
117:       KSP_PCApplyTranspose(ksp,Rl,Zl);
118:       VecConjugate(Rl);
119:       VecConjugate(Zl);
120:     }
121:     i++;
122:   } while (i<ksp->max_it);
123:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
124:   return(0);
125: }

127: /*MC
128:      KSPBICG - Implements the Biconjugate gradient method (similar to running the conjugate
129:          gradient on the normal equations).

131:    Options Database Keys:
132: .   see KSPSolve()

134:    Level: beginner

136:    Notes:
137:     this method requires that one be apply to apply the transpose of the preconditioner and operator
138:          as well as the operator and preconditioner.
139:          Supports only left preconditioning

141:          See KSPCGNE for code that EXACTLY runs the preconditioned conjugate gradient method on the
142:          normal equations

144: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBCGS, KSPCGNE

146: M*/
147: PETSC_EXTERN PetscErrorCode KSPCreate_BiCG(KSP ksp)
148: {

152:   ksp->data = (void*)0;
153:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
154:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);

156:   ksp->ops->setup          = KSPSetUp_BiCG;
157:   ksp->ops->solve          = KSPSolve_BiCG;
158:   ksp->ops->destroy        = KSPDestroyDefault;
159:   ksp->ops->view           = 0;
160:   ksp->ops->setfromoptions = 0;
161:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
162:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
163:   return(0);
164: }