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

  6: PetscErrorCode KSPSetUp_BiCG(KSP ksp)
  7: {

 11:   /* check user parameters and functions */
 12:   if (ksp->pc_side == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no right preconditioning for KSPBiCG");
 13:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"no symmetric preconditioning for KSPBiCG");
 14:   KSPSetWorkVecs(ksp,6);
 15:   return(0);
 16: }

 20: PetscErrorCode  KSPSolve_BiCG(KSP ksp)
 21: {
 23:   PetscInt       i;
 24:   PetscBool      diagonalscale;
 25:   PetscScalar    dpi,a=1.0,beta,betaold=1.0,b,ma;
 26:   PetscReal      dp;
 27:   Vec            X,B,Zl,Zr,Rl,Rr,Pl,Pr;
 28:   Mat            Amat,Pmat;
 29:   MatStructure   pflag;

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

 35:   X  = ksp->vec_sol;
 36:   B  = ksp->vec_rhs;
 37:   Rl = ksp->work[0];
 38:   Zl = ksp->work[1];
 39:   Pl = ksp->work[2];
 40:   Rr = ksp->work[3];
 41:   Zr = ksp->work[4];
 42:   Pr = ksp->work[5];

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

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

 72:   i = 0;
 73:   do {
 74:     VecDot(Zr,Rl,&beta);       /*     beta <- r'z     */
 75:     if (!i) {
 76:       if (beta == 0.0) {
 77:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
 78:         return(0);
 79:       }
 80:       VecCopy(Zr,Pr);       /*     p <- z          */
 81:       VecCopy(Zl,Pl);
 82:     } else {
 83:       b    = beta/betaold;
 84:       VecAYPX(Pr,b,Zr);  /*     p <- z + b* p   */
 85:       b    = PetscConj(b);
 86:       VecAYPX(Pl,b,Zl);
 87:     }
 88:     betaold = beta;
 89:     KSP_MatMult(ksp,Amat,Pr,Zr); /*     z <- Kp         */
 90:     VecConjugate(Pl);
 91:     KSP_MatMultTranspose(ksp,Amat,Pl,Zl);
 92:     VecConjugate(Pl);
 93:     VecConjugate(Zl);
 94:     VecDot(Zr,Pl,&dpi);            /*     dpi <- z'p      */
 95:     a       = beta/dpi;                           /*     a = beta/p'z    */
 96:     VecAXPY(X,a,Pr);    /*     x <- x + ap     */
 97:     ma      = -a;
 98:     VecAXPY(Rr,ma,Zr);
 99:     ma      = PetscConj(ma);
100:     VecAXPY(Rl,ma,Zl);
101:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
102:       KSP_PCApply(ksp,Rr,Zr);  /*     z <- Br         */
103:       VecConjugate(Rl);
104:       KSP_PCApplyTranspose(ksp,Rl,Zl);
105:       VecConjugate(Rl);
106:       VecConjugate(Zl);
107:       VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
108:     } else {
109:       VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
110:     }
111:     PetscObjectAMSTakeAccess((PetscObject)ksp);
112:     ksp->its   = i+1;
113:     ksp->rnorm = dp;
114:     PetscObjectAMSGrantAccess((PetscObject)ksp);
115:     KSPLogResidualHistory(ksp,dp);
116:     KSPMonitor(ksp,i+1,dp);
117:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
118:     if (ksp->reason) break;
119:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
120:       KSP_PCApply(ksp,Rr,Zr);  /* z <- Br  */
121:       VecConjugate(Rl);
122:       KSP_PCApplyTranspose(ksp,Rl,Zl);
123:       VecConjugate(Rl);
124:       VecConjugate(Zl);
125:     }
126:     i++;
127:   } while (i<ksp->max_it);
128:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
129:   return(0);
130: }

132: /*MC
133:      KSPBICG - Implements the Biconjugate gradient method (similar to running the conjugate
134:          gradient on the normal equations).

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

139:    Level: beginner

141:    Notes: this method requires that one be apply to apply the transpose of the preconditioner and operator
142:          as well as the operator and preconditioner.
143:          Supports only left preconditioning

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

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

150: M*/
153: PETSC_EXTERN PetscErrorCode KSPCreate_BiCG(KSP ksp)
154: {

158:   ksp->data = (void*)0;
159:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
160:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);

162:   ksp->ops->setup          = KSPSetUp_BiCG;
163:   ksp->ops->solve          = KSPSolve_BiCG;
164:   ksp->ops->destroy        = KSPDestroyDefault;
165:   ksp->ops->view           = 0;
166:   ksp->ops->setfromoptions = 0;
167:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
168:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
169:   return(0);
170: }