Actual source code: minres.c

  2: #include <private/kspimpl.h>

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

 10: PetscErrorCode KSPSetUp_MINRES(KSP ksp)
 11: {

 15:   if (ksp->pc_side == PC_RIGHT) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"No right preconditioning for KSPMINRES");
 16:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"No symmetric preconditioning for KSPMINRES");
 17:   KSPDefaultGetWork(ksp,9);
 18:   return(0);
 19: }


 24: PetscErrorCode  KSPSolve_MINRES(KSP ksp)
 25: {
 27:   PetscInt       i;
 28:   PetscScalar    alpha,beta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
 29:   PetscScalar    rho0,rho1,irho1,rho2,mrho2,rho3,mrho3,dp = 0.0;
 30:   PetscReal      np;
 31:   Vec            X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
 32:   Mat            Amat,Pmat;
 33:   MatStructure   pflag;
 34:   KSP_MINRES     *minres = (KSP_MINRES*)ksp->data;
 35:   PetscBool      diagonalscale;

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

 41:   X       = ksp->vec_sol;
 42:   B       = ksp->vec_rhs;
 43:   R       = ksp->work[0];
 44:   Z       = ksp->work[1];
 45:   U       = ksp->work[2];
 46:   V       = ksp->work[3];
 47:   W       = ksp->work[4];
 48:   UOLD    = ksp->work[5];
 49:   VOLD    = ksp->work[6];
 50:   WOLD    = ksp->work[7];
 51:   WOOLD   = ksp->work[8];

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

 55:   ksp->its = 0;

 57:   VecSet(UOLD,0.0);          /*     u_old  <-   0   */
 58:   VecCopy(UOLD,VOLD);         /*     v_old  <-   0   */
 59:   VecCopy(UOLD,W);            /*     w      <-   0   */
 60:   VecCopy(UOLD,WOLD);         /*     w_old  <-   0   */

 62:   if (!ksp->guess_zero) {
 63:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x    */
 64:     VecAYPX(R,-1.0,B);
 65:   } else {
 66:     VecCopy(B,R);              /*     r <- b (x is 0) */
 67:   }

 69:   KSP_PCApply(ksp,R,Z); /*     z  <- B*r       */

 71:   VecDot(R,Z,&dp);
 72:   if (PetscAbsScalar(dp) < minres->haptol) {
 73:     PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),minres->haptol);
 74:     dp = PetscAbsScalar(dp); /* tiny number, can't use 0.0, cause divided by below */
 75:     if (dp == 0.0) {
 76:       ksp->reason = KSP_CONVERGED_ATOL;
 77:       return(0);
 78:     }
 79:   }

 81: #if !defined(PETSC_USE_COMPLEX)
 82:   if (dp < 0.0) {
 83:     ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
 84:     return(0);
 85:   }
 86: #endif
 87:   dp   = PetscSqrtScalar(dp);
 88:   beta = dp;                                        /*  beta <- sqrt(r'*z  */
 89:   eta  = beta;

 91:   VecCopy(R,V);
 92:   VecCopy(Z,U);
 93:   ibeta = 1.0 / beta;
 94:   VecScale(V,ibeta);         /*    v <- r / beta     */
 95:   VecScale(U,ibeta);         /*    u <- z / beta     */

 97:   VecNorm(Z,NORM_2,&np);      /*   np <- ||z||        */

 99:   KSPLogResidualHistory(ksp,np);
100:   KSPMonitor(ksp,0,np);
101:   ksp->rnorm = np;
102:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP);  /* test for convergence */
103:   if (ksp->reason) return(0);

105:   i = 0;
106:   do {
107:      ksp->its = i+1;

109: /*   Lanczos  */

111:      KSP_MatMult(ksp,Amat,U,R);   /*      r <- A*u   */
112:      VecDot(U,R,&alpha);          /*  alpha <- r'*u  */
113:      KSP_PCApply(ksp,R,Z); /*      z <- B*r   */

115:      VecAXPY(R,-alpha,V);     /*  r <- r - alpha v     */
116:      VecAXPY(Z,-alpha,U);     /*  z <- z - alpha u     */
117:      VecAXPY(R,-beta,VOLD);   /*  r <- r - beta v_old  */
118:      VecAXPY(Z,-beta,UOLD);   /*  z <- z - beta u_old  */

120:      betaold = beta;

122:      VecDot(R,Z,&dp);
123:      if (PetscAbsScalar(dp) < minres->haptol) {
124:        PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),minres->haptol);
125:        dp = PetscAbsScalar(dp); /* tiny number, can we use 0.0? */
126:      }

128: #if !defined(PETSC_USE_COMPLEX)
129:      if (dp < 0.0) {
130:        ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
131:        break;
132:      }

134: #endif
135:      beta = PetscSqrtScalar(dp);                               /*  beta <- sqrt(r'*z)   */

137: /*    QR factorisation    */

139:      coold = cold; cold = c; soold = sold; sold = s;

141:      rho0 = cold * alpha - coold * sold * betaold;
142:      rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
143:      rho2 = sold * alpha + coold * cold * betaold;
144:      rho3 = soold * betaold;

146: /*     Givens rotation    */

148:      c = rho0 / rho1;
149:      s = beta / rho1;

151: /*    Update    */

153:      VecCopy(WOLD,WOOLD);     /*  w_oold <- w_old      */
154:      VecCopy(W,WOLD);         /*  w_old  <- w          */
155: 
156:      VecCopy(U,W);            /*  w      <- u          */
157:      mrho2 = - rho2;
158:      VecAXPY(W,mrho2,WOLD);  /*  w <- w - rho2 w_old  */
159:      mrho3 = - rho3;
160:      VecAXPY(W,mrho3,WOOLD); /*  w <- w - rho3 w_oold */
161:      irho1 = 1.0 / rho1;
162:      VecScale(W,irho1);      /*  w <- w / rho1        */

164:      ceta = c * eta;
165:      VecAXPY(X,ceta,W);      /*  x <- x + c eta w     */
166:      eta = - s * eta;

168:      VecCopy(V,VOLD);
169:      VecCopy(U,UOLD);
170:      VecCopy(R,V);
171:      VecCopy(Z,U);
172:      ibeta = 1.0 / beta;
173:      VecScale(V,ibeta);      /*  v <- r / beta       */
174:      VecScale(U,ibeta);      /*  u <- z / beta       */
175: 
176:      np = ksp->rnorm * PetscAbsScalar(s);

178:      ksp->rnorm = np;
179:      KSPLogResidualHistory(ksp,np);
180:      KSPMonitor(ksp,i+1,np);
181:      (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
182:      if (ksp->reason) break;
183:      i++;
184:   } while (i<ksp->max_it);
185:   if (i >= ksp->max_it) {
186:     ksp->reason = KSP_DIVERGED_ITS;
187:   }
188:   return(0);
189: }

191: /*MC
192:      KSPMINRES - This code implements the MINRES (Minimum Residual) method. 

194:    Options Database Keys:
195: .   see KSPSolve()

197:    Level: beginner

199:    Notes: The operator and the preconditioner must be symmetric and the preconditioner must
200:           be positive definite for this method.
201:           Supports only left preconditioning.

203:    Reference: Paige & Saunders, 1975.

205:    Contributed by: Robert Scheichl: maprs@maths.bath.ac.uk

207: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG, KSPCR
208: M*/
212: PetscErrorCode  KSPCreate_MINRES(KSP ksp)
213: {
214:   KSP_MINRES     *minres;

218:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
219:   PetscNewLog(ksp,KSP_MINRES,&minres);
220:   minres->haptol = 1.e-18;
221:   ksp->data      = (void*)minres;

223:   /*
224:        Sets the functions that are associated with this data structure 
225:        (in C++ this is the same as defining virtual functions)
226:   */
227:   ksp->ops->setup                = KSPSetUp_MINRES;
228:   ksp->ops->solve                = KSPSolve_MINRES;
229:   ksp->ops->destroy              = KSPDefaultDestroy;
230:   ksp->ops->setfromoptions       = 0;
231:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
232:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;
233:   return(0);
234: }