Actual source code: symmlq.c

petsc-3.5.0 2014-06-30
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  2: #include <petsc-private/kspimpl.h>

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

 10: PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp)
 11: {

 15:   KSPSetWorkVecs(ksp,9);
 16:   return(0);
 17: }

 21: PetscErrorCode  KSPSolve_SYMMLQ(KSP ksp)
 22: {
 24:   PetscInt       i;
 25:   PetscScalar    alpha,beta,ibeta,betaold,beta1,ceta = 0,ceta_oold = 0.0, ceta_old = 0.0,ceta_bar;
 26:   PetscScalar    c  = 1.0,cold=1.0,s=0.0,sold=0.0,coold,soold,rho0,rho1,rho2,rho3;
 27:   PetscScalar    dp = 0.0;
 28:   PetscReal      np,s_prod;
 29:   Vec            X,B,R,Z,U,V,W,UOLD,VOLD,Wbar;
 30:   Mat            Amat,Pmat;
 31:   KSP_SYMMLQ     *symmlq = (KSP_SYMMLQ*)ksp->data;
 32:   PetscBool      diagonalscale;

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

 38:   X    = ksp->vec_sol;
 39:   B    = ksp->vec_rhs;
 40:   R    = ksp->work[0];
 41:   Z    = ksp->work[1];
 42:   U    = ksp->work[2];
 43:   V    = ksp->work[3];
 44:   W    = ksp->work[4];
 45:   UOLD = ksp->work[5];
 46:   VOLD = ksp->work[6];
 47:   Wbar = ksp->work[7];

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

 51:   ksp->its = 0;

 53:   VecSet(UOLD,0.0);           /* u_old <- zeros;  */
 54:   VecCopy(UOLD,VOLD);          /* v_old <- u_old;  */
 55:   VecCopy(UOLD,W);             /* w     <- u_old;  */
 56:   VecCopy(UOLD,Wbar);          /* w_bar <- u_old;  */
 57:   if (!ksp->guess_zero) {
 58:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x */
 59:     VecAYPX(R,-1.0,B);
 60:   } else {
 61:     VecCopy(B,R);              /*     r <- b (x is 0) */
 62:   }

 64:   KSP_PCApply(ksp,R,Z); /* z  <- B*r       */
 65:   VecDot(R,Z,&dp);             /* dp = r'*z;      */
 66:   if (PetscAbsScalar(dp) < symmlq->haptol) {
 67:     PetscInfo2(ksp,"Detected happy breakdown %g tolerance %g\n",(double)PetscAbsScalar(dp),(double)symmlq->haptol);
 68:     ksp->rnorm  = 0.0;  /* what should we really put here? */
 69:     ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;  /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */
 70:     return(0);
 71:   }

 73: #if !defined(PETSC_USE_COMPLEX)
 74:   if (dp < 0.0) {
 75:     ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
 76:     return(0);
 77:   }
 78: #endif
 79:   dp     = PetscSqrtScalar(dp);
 80:   beta   = dp;                         /*  beta <- sqrt(r'*z)  */
 81:   beta1  = beta;
 82:   s_prod = PetscAbsScalar(beta1);

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

 97:   i = 0; ceta = 0.;
 98:   do {
 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; */

106:       VecCopy(R,V);
107:       VecScale(V,1.0/beta); /* v <- ibeta*r; */
108:       VecCopy(Z,U);
109:       VecScale(U,1.0/beta); /* u <- ibeta*z; */

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

118:       ceta_oold = ceta_old;
119:       ceta_old  = ceta;
120:     }

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

127:     VecAXPY(R,-alpha,V);   /*  r <- r - alpha* v;  */
128:     VecAXPY(Z,-alpha,U);   /*  z <- z - alpha* u;  */
129:     VecAXPY(R,-beta,VOLD); /*  r <- r - beta * v_old; */
130:     VecAXPY(Z,-beta,UOLD); /*  z <- z - beta * u_old; */
131:     betaold = beta;                                /* beta_k                  */
132:     VecDot(R,Z,&dp);       /* dp <- r'*z;             */
133:     if (PetscAbsScalar(dp) < symmlq->haptol) {
134:       PetscInfo2(ksp,"Detected happy breakdown %g tolerance %g\n",(double)PetscAbsScalar(dp),(double)symmlq->haptol);
135:       dp   = 0.0;
136:     }

138: #if !defined(PETSC_USE_COMPLEX)
139:     if (dp < 0.0) {
140:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
141:       break;
142:     }
143: #endif
144:     beta = PetscSqrtScalar(dp);                    /*  beta = sqrt(dp); */

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

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

156:     if (ksp->its==1) ceta = beta1/rho1;
157:     else ceta = -(rho2*ceta_old + rho3*ceta_oold)/rho1;

159:     s_prod = s_prod*PetscAbsScalar(s);
160:     if (c == 0.0) np = s_prod*1.e16;
161:     else np = s_prod/PetscAbsScalar(c);       /* residual norm for xc_k (CGNORM) */

163:     ksp->rnorm = np;
164:     KSPLogResidualHistory(ksp,np);
165:     KSPMonitor(ksp,i+1,np);
166:     (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
167:     if (ksp->reason) break;
168:     i++;
169:   } while (i<ksp->max_it);

171:   /* move to the CG point: xc_(k+1) */
172:   if (c == 0.0) ceta_bar = ceta*1.e15;
173:   else ceta_bar = ceta/c;

175:   VecAXPY(X,ceta_bar,Wbar); /* x <- x + ceta_bar*w_bar */

177:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
178:   return(0);
179: }

181: /*MC
182:      KSPSYMMLQ -  This code implements the SYMMLQ method.

184:    Options Database Keys:
185: .   see KSPSolve()

187:    Level: beginner

189:    Notes: The operator and the preconditioner must be symmetric for this method. The
190:           preconditioner must be POSITIVE-DEFINITE.

192:           Supports only left preconditioning.

194:    Reference: Paige & Saunders, 1975.

196: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP
197: M*/
200: PETSC_EXTERN PetscErrorCode KSPCreate_SYMMLQ(KSP ksp)
201: {
202:   KSP_SYMMLQ     *symmlq;

206:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);

208:   PetscNewLog(ksp,&symmlq);
209:   symmlq->haptol = 1.e-18;
210:   ksp->data      = (void*)symmlq;

212:   /*
213:        Sets the functions that are associated with this data structure
214:        (in C++ this is the same as defining virtual functions)
215:   */
216:   ksp->ops->setup          = KSPSetUp_SYMMLQ;
217:   ksp->ops->solve          = KSPSolve_SYMMLQ;
218:   ksp->ops->destroy        = KSPDestroyDefault;
219:   ksp->ops->setfromoptions = 0;
220:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
221:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
222:   return(0);
223: }