Actual source code: symmlq.c

  1: /*$Id: symmlq.c,v 1.13 2001/03/23 23:23:49 balay Exp $*/
  2: /*                       
  3:     This code implements the SYMMLQ method. 
  4:     Reference: Paige & Saunders, 1975.
  5: */
  6: #include "src/sles/ksp/kspimpl.h"

  8: typedef struct {
  9:   double haptol;
 10: } KSP_SYMMLQ;

 12: int KSPSetUp_SYMMLQ(KSP ksp)
 13: {

 17:   if (ksp->pc_side == PC_RIGHT) {
 18:     SETERRQ(2,"No right preconditioning for KSPSYMMLQ");
 19:   } else if (ksp->pc_side == PC_SYMMETRIC) {
 20:     SETERRQ(2,"No symmetric preconditioning for KSPSYMMLQ");
 21:   }
 22:   KSPDefaultGetWork(ksp,9);
 23:   return(0);
 24: }

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

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

 43:   maxit   = ksp->max_it;
 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 %gn",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:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP);  /* test for convergence */
 93:   if (ksp->reason) {*its =  0; return(0);}
 94:   KSPLogResidualHistory(ksp,np);
 95:   KSPMonitor(ksp,0,np);            /* call any registered monitor routines */
 96:   ksp->rnorm = np;

 98:   for (i=0; i<maxit; i++){
 99:     ksp->its = i+1;

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

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

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

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

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

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

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

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

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

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

184:   if (i == maxit) {
185:     ksp->reason = KSP_DIVERGED_ITS;
186:   }
187:   *its = ksp->its;

189:   return(0);
190: }

192: EXTERN_C_BEGIN
193: int KSPCreate_SYMMLQ(KSP ksp)
194: {
195:   KSP_SYMMLQ *symmlq;


200:   ksp->pc_side                   = PC_LEFT;
201:   ksp->calc_res                  = PETSC_TRUE;

203:   ierr           = PetscNew(KSP_SYMMLQ,&symmlq);
204:   symmlq->haptol = 1.e-18;
205:   ksp->data      = (void*)symmlq;

207:   /*
208:        Sets the functions that are associated with this data structure 
209:        (in C++ this is the same as defining virtual functions)
210:   */
211:   ksp->ops->setup                = KSPSetUp_SYMMLQ;
212:   ksp->ops->solve                = KSPSolve_SYMMLQ;
213:   ksp->ops->destroy              = KSPDefaultDestroy;
214:   ksp->ops->setfromoptions       = 0;
215:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
216:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;

218:   return(0);
219: }
220: EXTERN_C_END