Actual source code: symmlq.c

  1: /*$Id: symmlq.c,v 1.16 2001/08/07 03:03:56 balay Exp $*/

 3:  #include src/ksp/ksp/kspimpl.h

  5: typedef struct {
  6:   PetscReal haptol;
  7: } KSP_SYMMLQ;

 11: int KSPSetUp_SYMMLQ(KSP ksp)
 12: {

 16:   if (ksp->pc_side == PC_RIGHT) {
 17:     SETERRQ(2,"No right preconditioning for KSPSYMMLQ");
 18:   } else if (ksp->pc_side == PC_SYMMETRIC) {
 19:     SETERRQ(2,"No symmetric preconditioning for KSPSYMMLQ");
 20:   }
 21:   KSPDefaultGetWork(ksp,9);
 22:   return(0);
 23: }

 27: int  KSPSolve_SYMMLQ(KSP ksp)
 28: {
 29:   int          ierr,i;
 30:   PetscScalar  alpha,malpha,beta,mbeta,ibeta,betaold,beta1,ceta,ceta_oold = 0.0, ceta_old = 0.0,ceta_bar;
 31:   PetscScalar  c=1.0,cold=1.0,s=0.0,sold=0.0,coold,soold,ms,rho0,rho1,rho2,rho3;
 32:   PetscScalar  mone = -1.0,zero = 0.0,dp = 0.0;
 33:   PetscReal    np,s_prod;
 34:   Vec          X,B,R,Z,U,V,W,UOLD,VOLD,Wbar;
 35:   Mat          Amat,Pmat;
 36:   MatStructure pflag;
 37:   KSP_SYMMLQ   *symmlq = (KSP_SYMMLQ*)ksp->data;
 38:   PetscTruth   diagonalscale;

 41:   PCDiagonalScale(ksp->B,&diagonalscale);
 42:   if (diagonalscale) SETERRQ1(1,"Krylov method %s does not support diagonal scaling",ksp->type_name);

 44:   X       = ksp->vec_sol;
 45:   B       = ksp->vec_rhs;
 46:   R       = ksp->work[0];
 47:   Z       = ksp->work[1];
 48:   U       = ksp->work[2];
 49:   V       = ksp->work[3];
 50:   W       = ksp->work[4];
 51:   UOLD    = ksp->work[5];
 52:   VOLD    = ksp->work[6];
 53:   Wbar    = ksp->work[7];
 54: 
 55:   PCGetOperators(ksp->B,&Amat,&Pmat,&pflag);

 57:   ksp->its = 0;

 59:   VecSet(&zero,UOLD);          /* u_old <- zeros;  */
 60:   VecCopy(UOLD,VOLD);          /* v_old <- u_old;  */
 61:   VecCopy(UOLD,W);             /* w     <- u_old;  */
 62:   VecCopy(UOLD,Wbar);          /* w_bar <- u_old;  */
 63:   if (!ksp->guess_zero) {
 64:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x */
 65:     VecAYPX(&mone,B,R);
 66:   } else {
 67:     VecCopy(B,R);              /*     r <- b (x is 0) */
 68:   }

 70:   KSP_PCApply(ksp,ksp->B,R,Z); /* z  <- B*r       */
 71:   VecDot(R,Z,&dp);             /* dp = r'*z;      */
 72:   if (PetscAbsScalar(dp) < symmlq->haptol) {
 73:     PetscLogInfo(ksp,"KSPSolve_SYMMLQ:Detected happy breakdown %g tolerance %g\n",PetscAbsScalar(dp),symmlq->haptol);
 74:     dp = 0.0;
 75:   }

 77: #if !defined(PETSC_USE_COMPLEX)
 78:   if (dp < 0.0) SETERRQ(PETSC_ERR_KSP_BRKDWN,"Indefinite preconditioner");
 79: #endif
 80:   dp = PetscSqrtScalar(dp);
 81:   beta = dp;                         /*  beta <- sqrt(r'*z)  */
 82:   beta1 = beta;
 83:   s_prod = PetscAbsScalar(beta1);

 85:   VecCopy(R,V);  /* v <- r; */
 86:   VecCopy(Z,U);  /* u <- z; */
 87:   ibeta = 1.0 / beta;
 88:   VecScale(&ibeta,V);     /* v <- ibeta*v; */
 89:   VecScale(&ibeta,U);     /* u <- ibeta*u; */
 90:   VecCopy(U,Wbar);        /* w_bar <- u;   */
 91:   VecNorm(Z,NORM_2,&np);      /*   np <- ||z||        */
 92:   KSPLogResidualHistory(ksp,np);
 93:   KSPMonitor(ksp,0,np);            /* call any registered monitor routines */
 94:   ksp->rnorm = np;
 95:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP);  /* test for convergence */
 96:   if (ksp->reason) return(0);

 98:   i = 0;
 99:   do {
100:     ksp->its = i+1;

102:     /*    Update    */
103:     if (ksp->its > 1){
104:       VecCopy(V,VOLD);  /* v_old <- v; */
105:       VecCopy(U,UOLD);  /* u_old <- u; */
106: 
107:       ibeta = 1.0 / beta;
108:       VecCopy(R,V);
109:       VecScale(&ibeta,V); /* v <- ibeta*r; */
110:       VecCopy(Z,U);
111:       VecScale(&ibeta,U); /* u <- ibeta*z; */

113:       VecCopy(Wbar,W);
114:       VecScale(&c,W);
115:       VecAXPY(&s,U,W);   /* w  <- c*w_bar + s*u;    (w_k) */
116:       ms = -s;
117:       VecScale(&ms,Wbar);
118:       VecAXPY(&c,U,Wbar); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */
119:       VecAXPY(&ceta,W,X); /* x <- x + ceta * w;       (xL_k)  */

121:       ceta_oold = ceta_old;
122:       ceta_old  = ceta;
123:     }

125:     /*   Lanczos  */
126:     KSP_MatMult(ksp,Amat,U,R);   /*  r     <- Amat*u; */
127:     VecDot(U,R,&alpha);          /*  alpha <- u'*r;   */
128:     KSP_PCApply(ksp,ksp->B,R,Z); /*      z <- B*r;    */

130:     malpha = - alpha;
131:     VecAXPY(&malpha,V,R);     /*  r <- r - alpha* v;  */
132:     VecAXPY(&malpha,U,Z);     /*  z <- z - alpha* u;  */
133:     mbeta = - beta;
134:     VecAXPY(&mbeta,VOLD,R);   /*  r <- r - beta * v_old; */
135:     VecAXPY(&mbeta,UOLD,Z);   /*  z <- z - beta * u_old; */
136:     betaold = beta;                                /* beta_k                  */
137:     VecDot(R,Z,&dp);          /* dp <- r'*z;             */
138:     if (PetscAbsScalar(dp) < symmlq->haptol) {
139:       PetscLogInfo(ksp,"KSPSolve_SYMMLQ:Detected happy breakdown %g tolerance %g\n",PetscAbsScalar(dp),symmlq->haptol);
140:       dp = 0.0;
141:     }

143: #if !defined(PETSC_USE_COMPLEX)
144:      if (dp < 0.0) SETERRQ(PETSC_ERR_KSP_BRKDWN,"Indefinite preconditioner");
145: #endif
146:      beta = PetscSqrtScalar(dp);                    /*  beta = sqrt(dp); */

148:      /*    QR factorization    */
149:      coold = cold; cold = c; soold = sold; sold = s;
150:      rho0 = cold * alpha - coold * sold * betaold;    /* gamma_bar */
151:      rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);   /* gamma     */
152:      rho2 = sold * alpha + coold * cold * betaold;    /* delta     */
153:      rho3 = soold * betaold;                          /* epsilon   */

155:      /* Givens rotation: [c -s; s c] (different from the Reference!) */
156:      c = rho0 / rho1; s = beta / rho1;

158:      if (ksp->its==1){
159:        ceta = beta1/rho1;
160:      } else {
161:        ceta = -(rho2*ceta_old + rho3*ceta_oold)/rho1;
162:      }
163: 
164:      s_prod = s_prod*PetscAbsScalar(s);
165:      if (c == 0.0){
166:        np = s_prod*1.e16;
167:      } else {
168:        np = s_prod/PetscAbsScalar(c);       /* residual norm for xc_k (CGNORM) */
169:      }
170:      ksp->rnorm = np;
171:      KSPLogResidualHistory(ksp,np);
172:      KSPMonitor(ksp,i+1,np);
173:      (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
174:      if (ksp->reason) break;
175:      i++;
176:   } while (i<ksp->max_it);

178:   /* move to the CG point: xc_(k+1) */
179:   if (c == 0.0){
180:     ceta_bar = ceta*1.e15;
181:   } else {
182:     ceta_bar = ceta/c;
183:   }
184:   VecAXPY(&ceta_bar,Wbar,X); /* x <- x + ceta_bar*w_bar */

186:   if (i == ksp->max_it) {
187:     ksp->reason = KSP_DIVERGED_ITS;
188:   }
189:   return(0);
190: }

192: /*MC
193:      KSPSYMMLQ -  This code implements the SYMMLQ method. 
194:                  Reference: Paige & Saunders, 1975.

196:    Options Database Keys:
197: .   see KSPSolve()

199:    Level: beginner

201: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP

203: M*/

205: EXTERN_C_BEGIN
208: int KSPCreate_SYMMLQ(KSP ksp)
209: {
210:   KSP_SYMMLQ *symmlq;


215:   ksp->pc_side                   = PC_LEFT;

217:   PetscNew(KSP_SYMMLQ,&symmlq);
218:   symmlq->haptol = 1.e-18;
219:   ksp->data      = (void*)symmlq;

221:   /*
222:        Sets the functions that are associated with this data structure 
223:        (in C++ this is the same as defining virtual functions)
224:   */
225:   ksp->ops->setup                = KSPSetUp_SYMMLQ;
226:   ksp->ops->solve                = KSPSolve_SYMMLQ;
227:   ksp->ops->destroy              = KSPDefaultDestroy;
228:   ksp->ops->setfromoptions       = 0;
229:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
230:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;

232:   return(0);
233: }
234: EXTERN_C_END