Actual source code: symmlq.c

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

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

 10: PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp)
 11: {

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

 26: PetscErrorCode  KSPSolve_SYMMLQ(KSP ksp)
 27: {
 29:   PetscInt       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->pc,&diagonalscale);
 42:   if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"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->pc,&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,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) {
 79:     ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
 80:     return(0);
 81:   }
 82: #endif
 83:   dp = PetscSqrtScalar(dp);
 84:   beta = dp;                         /*  beta <- sqrt(r'*z)  */
 85:   beta1 = beta;
 86:   s_prod = PetscAbsScalar(beta1);

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

101:   i = 0;
102:   do {
103:     ksp->its = i+1;

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

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

124:       ceta_oold = ceta_old;
125:       ceta_old  = ceta;
126:     }

128:     /*   Lanczos  */
129:     KSP_MatMult(ksp,Amat,U,R);   /*  r     <- Amat*u; */
130:     VecDot(U,R,&alpha);          /*  alpha <- u'*r;   */
131:     KSP_PCApply(ksp,R,Z); /*      z <- B*r;    */

133:     malpha = - alpha;
134:     VecAXPY(&malpha,V,R);     /*  r <- r - alpha* v;  */
135:     VecAXPY(&malpha,U,Z);     /*  z <- z - alpha* u;  */
136:     mbeta = - beta;
137:     VecAXPY(&mbeta,VOLD,R);   /*  r <- r - beta * v_old; */
138:     VecAXPY(&mbeta,UOLD,Z);   /*  z <- z - beta * u_old; */
139:     betaold = beta;                                /* beta_k                  */
140:     VecDot(R,Z,&dp);          /* dp <- r'*z;             */
141:     if (PetscAbsScalar(dp) < symmlq->haptol) {
142:       PetscLogInfo(ksp,"KSPSolve_SYMMLQ:Detected happy breakdown %g tolerance %g\n",PetscAbsScalar(dp),symmlq->haptol);
143:       dp = 0.0;
144:     }

146: #if !defined(PETSC_USE_COMPLEX)
147:     if (dp < 0.0) {
148:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
149:       break;
150:     }
151: #endif
152:     beta = PetscSqrtScalar(dp);                    /*  beta = sqrt(dp); */

154:     /*    QR factorization    */
155:     coold = cold; cold = c; soold = sold; sold = s;
156:     rho0 = cold * alpha - coold * sold * betaold;    /* gamma_bar */
157:     rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);   /* gamma     */
158:     rho2 = sold * alpha + coold * cold * betaold;    /* delta     */
159:     rho3 = soold * betaold;                          /* epsilon   */

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

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

184:   /* move to the CG point: xc_(k+1) */
185:   if (c == 0.0){
186:     ceta_bar = ceta*1.e15;
187:   } else {
188:     ceta_bar = ceta/c;
189:   }
190:   VecAXPY(&ceta_bar,Wbar,X); /* x <- x + ceta_bar*w_bar */

192:   if (i >= ksp->max_it) {
193:     ksp->reason = KSP_DIVERGED_ITS;
194:   }
195:   return(0);
196: }

198: /*MC
199:      KSPSYMMLQ -  This code implements the SYMMLQ method. 

201:    Options Database Keys:
202: .   see KSPSolve()

204:    Level: beginner

206:    Notes: Reference: Paige & Saunders, 1975.

208: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP
209: M*/
213: PetscErrorCode KSPCreate_SYMMLQ(KSP ksp)
214: {
215:   KSP_SYMMLQ     *symmlq;

219:   ksp->pc_side                   = PC_LEFT;

221:   PetscNew(KSP_SYMMLQ,&symmlq);
222:   symmlq->haptol = 1.e-18;
223:   ksp->data      = (void*)symmlq;

225:   /*
226:        Sets the functions that are associated with this data structure 
227:        (in C++ this is the same as defining virtual functions)
228:   */
229:   ksp->ops->setup                = KSPSetUp_SYMMLQ;
230:   ksp->ops->solve                = KSPSolve_SYMMLQ;
231:   ksp->ops->destroy              = KSPDefaultDestroy;
232:   ksp->ops->setfromoptions       = 0;
233:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
234:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;
235:   return(0);
236: }