Actual source code: bicg.c


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

  4: static PetscErrorCode KSPSetUp_BiCG(KSP ksp)
  5: {
  6:   /* check user parameters and functions */
  9:   KSPSetWorkVecs(ksp,6);
 10:   return 0;
 11: }

 13: static PetscErrorCode  KSPSolve_BiCG(KSP ksp)
 14: {
 15:   PetscInt       i;
 16:   PetscBool      diagonalscale;
 17:   PetscScalar    dpi,a=1.0,beta,betaold=1.0,b,ma;
 18:   PetscReal      dp;
 19:   Vec            X,B,Zl,Zr,Rl,Rr,Pl,Pr;
 20:   Mat            Amat,Pmat;

 22:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

 25:   X  = ksp->vec_sol;
 26:   B  = ksp->vec_rhs;
 27:   Rl = ksp->work[0];
 28:   Zl = ksp->work[1];
 29:   Pl = ksp->work[2];
 30:   Rr = ksp->work[3];
 31:   Zr = ksp->work[4];
 32:   Pr = ksp->work[5];

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

 36:   if (!ksp->guess_zero) {
 37:     KSP_MatMult(ksp,Amat,X,Rr);      /*   r <- b - Ax       */
 38:     VecAYPX(Rr,-1.0,B);
 39:   } else {
 40:     VecCopy(B,Rr);           /*     r <- b (x is 0) */
 41:   }
 42:   VecCopy(Rr,Rl);
 43:   KSP_PCApply(ksp,Rr,Zr);     /*     z <- Br         */
 44:   KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
 45:   if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
 46:     VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
 47:   } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
 48:     VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
 49:   } else dp = 0.0;

 51:   KSPCheckNorm(ksp,dp);
 52:   KSPMonitor(ksp,0,dp);
 53:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
 54:   ksp->its   = 0;
 55:   ksp->rnorm = dp;
 56:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
 57:   KSPLogResidualHistory(ksp,dp);
 58:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
 59:   if (ksp->reason) return 0;

 61:   i = 0;
 62:   do {
 63:     VecDot(Zr,Rl,&beta);       /*     beta <- r'z     */
 64:     KSPCheckDot(ksp,beta);
 65:     if (!i) {
 66:       if (beta == 0.0) {
 67:         ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
 68:         return 0;
 69:       }
 70:       VecCopy(Zr,Pr);       /*     p <- z          */
 71:       VecCopy(Zl,Pl);
 72:     } else {
 73:       b    = beta/betaold;
 74:       VecAYPX(Pr,b,Zr);  /*     p <- z + b* p   */
 75:       b    = PetscConj(b);
 76:       VecAYPX(Pl,b,Zl);
 77:     }
 78:     betaold = beta;
 79:     KSP_MatMult(ksp,Amat,Pr,Zr); /*     z <- Kp         */
 80:     KSP_MatMultHermitianTranspose(ksp,Amat,Pl,Zl);
 81:     VecDot(Zr,Pl,&dpi);            /*     dpi <- z'p      */
 82:     KSPCheckDot(ksp,dpi);
 83:     a       = beta/dpi;                           /*     a = beta/p'z    */
 84:     VecAXPY(X,a,Pr);    /*     x <- x + ap     */
 85:     ma      = -a;
 86:     VecAXPY(Rr,ma,Zr);
 87:     ma      = PetscConj(ma);
 88:     VecAXPY(Rl,ma,Zl);
 89:     if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
 90:       KSP_PCApply(ksp,Rr,Zr);  /*     z <- Br         */
 91:       KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
 92:       VecNorm(Zr,NORM_2,&dp);  /*    dp <- z'*z       */
 93:     } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
 94:       VecNorm(Rr,NORM_2,&dp);  /*    dp <- r'*r       */
 95:     } else dp = 0.0;

 97:     KSPCheckNorm(ksp,dp);
 98:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
 99:     ksp->its   = i+1;
100:     ksp->rnorm = dp;
101:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
102:     KSPLogResidualHistory(ksp,dp);
103:     KSPMonitor(ksp,i+1,dp);
104:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
105:     if (ksp->reason) break;
106:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
107:       KSP_PCApply(ksp,Rr,Zr);  /* z <- Br  */
108:       KSP_PCApplyHermitianTranspose(ksp,Rl,Zl);
109:     }
110:     i++;
111:   } while (i<ksp->max_it);
112:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
113:   return 0;
114: }

116: /*MC
117:      KSPBICG - Implements the Biconjugate gradient method (similar to running the conjugate
118:          gradient on the normal equations).

120:    Options Database Keys:
121:    see KSPSolve()

123:    Level: beginner

125:    Notes:
126:     this method requires that one be apply to apply the transpose of the preconditioner and operator
127:          as well as the operator and preconditioner.
128:          Supports only left preconditioning

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

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

135: M*/
136: PETSC_EXTERN PetscErrorCode KSPCreate_BiCG(KSP ksp)
137: {
138:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
139:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
140:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

142:   ksp->ops->setup          = KSPSetUp_BiCG;
143:   ksp->ops->solve          = KSPSolve_BiCG;
144:   ksp->ops->destroy        = KSPDestroyDefault;
145:   ksp->ops->view           = NULL;
146:   ksp->ops->setfromoptions = NULL;
147:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
148:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
149:   return 0;
150: }