Actual source code: minres.c

      1: #define PETSCKSP_DLL

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

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

     11: PetscErrorCode KSPSetUp_MINRES(KSP ksp)
     12: {

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

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

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

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

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

     59:   ksp->its = 0;

     61:   VecSet(UOLD,zero);          /*     u_old  <-   0   */
     62:   VecCopy(UOLD,VOLD);         /*     v_old  <-   0   */
     63:   VecCopy(UOLD,W);            /*     w      <-   0   */
     64:   VecCopy(UOLD,WOLD);         /*     w_old  <-   0   */

     66:   if (!ksp->guess_zero) {
     67:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x    */
     68:     VecAYPX(R,mone,B);
     69:   } else {
     70:     VecCopy(B,R);              /*     r <- b (x is 0) */
     71:   }

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

     75:   VecDot(R,Z,&dp);
     76:   if (PetscAbsScalar(dp) < minres->haptol) {
     77:     PetscLogInfo((ksp,"KSPSolve_MINRES:Detected happy breakdown %g tolerance %g\n",PetscAbsScalar(dp),minres->haptol));
     78:     dp = PetscAbsScalar(dp); /* tiny number, can't use 0.0, cause divided by below */
     79:     if (dp == 0.0) {
     80:       ksp->reason = KSP_CONVERGED_ATOL;
     81:       return(0);
     82:     }
     83:   }

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

     95:   VecCopy(R,V);
     96:   VecCopy(Z,U);
     97:   ibeta = 1.0 / beta;
     98:   VecScale(V,ibeta);         /*    v <- r / beta     */
     99:   VecScale(U,ibeta);         /*    u <- z / beta     */

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

    103:   KSPLogResidualHistory(ksp,np);
    104:   KSPMonitor(ksp,0,np);            /* call any registered monitor routines */
    105:   ksp->rnorm = np;
    106:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP);  /* test for convergence */
    107:   if (ksp->reason) return(0);

    109:   i = 0;
    110:   do {
    111:      ksp->its = i+1;

    113: /*   Lanczos  */

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

    119:      malpha = - alpha;
    120:      VecAXPY(R,malpha,V);     /*  r <- r - alpha v     */
    121:      VecAXPY(Z,malpha,U);     /*  z <- z - alpha u     */
    122:      mbeta = - beta;
    123:      VecAXPY(R,mbeta,VOLD);   /*  r <- r - beta v_old  */
    124:      VecAXPY(Z,mbeta,UOLD);   /*  z <- z - beta u_old  */

    126:      betaold = beta;

    128:      VecDot(R,Z,&dp);
    129:      if (PetscAbsScalar(dp) < minres->haptol) {
    130:        PetscLogInfo((ksp,"KSPSolve_MINRES:Detected happy breakdown %g tolerance %g\n",PetscAbsScalar(dp),minres->haptol));
    131:        dp = PetscAbsScalar(dp); /* tiny number, can we use 0.0? */
    132:      }

    134: #if !defined(PETSC_USE_COMPLEX)
    135:      if (dp < 0.0) {
    136:        ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
    137:        break;
    138:      }

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

    143: /*    QR factorisation    */

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

    147:      rho0 = cold * alpha - coold * sold * betaold;
    148:      rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
    149:      rho2 = sold * alpha + coold * cold * betaold;
    150:      rho3 = soold * betaold;

    152: /*     Givens rotation    */

    154:      c = rho0 / rho1;
    155:      s = beta / rho1;

    157: /*    Update    */

    159:      VecCopy(WOLD,WOOLD);     /*  w_oold <- w_old      */
    160:      VecCopy(W,WOLD);         /*  w_old  <- w          */
    161:
    162:      VecCopy(U,W);            /*  w      <- u          */
    163:      mrho2 = - rho2;
    164:      VecAXPY(W,mrho2,WOLD);  /*  w <- w - rho2 w_old  */
    165:      mrho3 = - rho3;
    166:      VecAXPY(W,mrho3,WOOLD); /*  w <- w - rho3 w_oold */
    167:      irho1 = 1.0 / rho1;
    168:      VecScale(W,irho1);      /*  w <- w / rho1        */

    170:      ceta = c * eta;
    171:      VecAXPY(X,ceta,W);      /*  x <- x + c eta w     */
    172:      eta = - s * eta;

    174:      VecCopy(V,VOLD);
    175:      VecCopy(U,UOLD);
    176:      VecCopy(R,V);
    177:      VecCopy(Z,U);
    178:      ibeta = 1.0 / beta;
    179:      VecScale(V,ibeta);      /*  v <- r / beta       */
    180:      VecScale(U,ibeta);      /*  u <- z / beta       */
    181:
    182:      np = ksp->rnorm * PetscAbsScalar(s);

    184:      ksp->rnorm = np;
    185:      KSPLogResidualHistory(ksp,np);
    186:      KSPMonitor(ksp,i+1,np);
    187:      (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
    188:      if (ksp->reason) break;
    189:      i++;
    190:   } while (i<ksp->max_it);
    191:   if (i >= ksp->max_it) {
    192:     ksp->reason = KSP_DIVERGED_ITS;
    193:   }
    194:   return(0);
    195: }

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

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

    203:    Level: beginner

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

    207:    Notes: The operator and the preconditioner must be positive definite for this method
    208:           Reference: Paige & Saunders, 1975.

    210: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG
    211: M*/
    215: PetscErrorCode PETSCKSP_DLLEXPORT KSPCreate_MINRES(KSP ksp)
    216: {
    217:   KSP_MINRES     *minres;

    222:   ksp->pc_side   = PC_LEFT;
    223:   PetscNew(KSP_MINRES,&minres);
    224:   minres->haptol = 1.e-18;
    225:   ksp->data      = (void*)minres;

    227:   /*
    228:        Sets the functions that are associated with this data structure
    229:        (in C++ this is the same as defining virtual functions)
    230:   */
    231:   ksp->ops->setup                = KSPSetUp_MINRES;
    232:   ksp->ops->solve                = KSPSolve_MINRES;
    233:   ksp->ops->destroy              = KSPDefaultDestroy;
    234:   ksp->ops->setfromoptions       = 0;
    235:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
    236:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;
    237:   return(0);
    238: }