Actual source code: minres.c
petsc-3.10.5 2019-03-28
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      2:  #include <petsc/private/kspimpl.h>

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

      8: static PetscErrorCode KSPSetUp_MINRES(KSP ksp)
      9: {

     13:   if (ksp->pc_side == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No right preconditioning for KSPMINRES");
     14:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No symmetric preconditioning for KSPMINRES");
     15:   KSPSetWorkVecs(ksp,9);
     16:   return(0);
     17: }

     20: static PetscErrorCode  KSPSolve_MINRES(KSP ksp)
     21: {
     22:   PetscErrorCode    ierr;
     23:   PetscInt          i;
     24:   PetscScalar       alpha,beta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
     25:   PetscScalar       rho0,rho1,irho1,rho2,rho3,dp = 0.0;
     26:   const PetscScalar none = -1.0;
     27:   PetscReal         np;
     28:   Vec               X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
     29:   Mat               Amat,Pmat;
     30:   KSP_MINRES        *minres = (KSP_MINRES*)ksp->data;
     31:   PetscBool         diagonalscale;

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

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

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

     51:   ksp->its = 0;

     53:   VecSet(UOLD,0.0);          /*     u_old  <-   0   */
     54:   VecSet(VOLD,0.0);         /*     v_old  <-   0   */
     55:   VecSet(W,0.0);            /*     w      <-   0   */
     56:   VecSet(WOLD,0.0);         /*     w_old  <-   0   */

     58:   if (!ksp->guess_zero) {
     59:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x    */
     60:     VecAYPX(R,-1.0,B);
     61:   } else {
     62:     VecCopy(B,R);              /*     r <- b (x is 0) */
     63:   }
     64:   KSP_PCApply(ksp,R,Z);       /*     z  <- B*r       */
     65:   VecNorm(Z,NORM_2,&np);      /*   np <- ||z||        */
     66:   VecDot(R,Z,&dp);

     68:   if (PetscRealPart(dp) < minres->haptol && np > minres->haptol) {
     69:     if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Detected indefinite operator %g tolerance %g",(double)PetscRealPart(dp),(double)minres->haptol);
     70:     PetscInfo2(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
     71:     ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
     72:     return(0);
     73:   }

     75:   KSPLogResidualHistory(ksp,np);
     76:   KSPMonitor(ksp,0,np);
     77:   ksp->rnorm = np;
     78:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP); /* test for convergence */
     79:   if (ksp->reason) return(0);

     81:   dp   = PetscAbsScalar(dp);
     82:   dp   = PetscSqrtScalar(dp);
     83:   beta = dp;                                        /*  beta <- sqrt(r'*z  */
     84:   eta  = beta;

     86:   VecCopy(R,V);
     87:   VecCopy(Z,U);
     88:   ibeta = 1.0 / beta;
     89:   VecScale(V,ibeta);        /*    v <- r / beta     */
     90:   VecScale(U,ibeta);        /*    u <- z / beta     */

     92:   i = 0;
     93:   do {
     94:     ksp->its = i+1;

     96:     /*   Lanczos  */

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

    102:     VecAXPY(R,-alpha,V);     /*  r <- r - alpha v     */
    103:     VecAXPY(Z,-alpha,U);     /*  z <- z - alpha u     */
    104:     VecAXPY(R,-beta,VOLD);   /*  r <- r - beta v_old  */
    105:     VecAXPY(Z,-beta,UOLD);   /*  z <- z - beta u_old  */

    107:     betaold = beta;

    109:     VecDot(R,Z,&dp);
    110:     dp   = PetscAbsScalar(dp);
    111:     beta = PetscSqrtScalar(dp);                               /*  beta <- sqrt(r'*z)   */

    113:     /*    QR factorisation    */

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

    117:     rho0 = cold * alpha - coold * sold * betaold;
    118:     rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
    119:     rho2 = sold * alpha + coold * cold * betaold;
    120:     rho3 = soold * betaold;

    122:     /*     Givens rotation    */

    124:     c = rho0 / rho1;
    125:     s = beta / rho1;

    127:     /*    Update    */

    129:     VecCopy(WOLD,WOOLD);     /*  w_oold <- w_old      */
    130:     VecCopy(W,WOLD);         /*  w_old  <- w          */

    132:     VecCopy(U,W);           /*  w      <- u          */
    133:     VecAXPY(W,-rho2,WOLD); /*  w <- w - rho2 w_old  */
    134:     VecAXPY(W,-rho3,WOOLD); /*  w <- w - rho3 w_oold */
    135:     irho1 = 1.0 / rho1;
    136:     VecScale(W,irho1);     /*  w <- w / rho1        */

    138:     ceta = c * eta;
    139:     VecAXPY(X,ceta,W);      /*  x <- x + c eta w     */

    141:     /*
    142:         when dp is really small we have either convergence or an indefinite operator so compute true
    143:         residual norm to check for convergence
    144:     */
    145:     if (PetscRealPart(dp) < minres->haptol) {
    146:       PetscInfo2(ksp,"Possible indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    147:       KSP_MatMult(ksp,Amat,X,VOLD);
    148:       VecAXPY(VOLD,none,B);
    149:       VecNorm(VOLD,NORM_2,&np);
    150:     } else {
    151:       /* otherwise compute new residual norm via recurrence relation */
    152:       np = ksp->rnorm * PetscAbsScalar(s);
    153:     }

    155:     ksp->rnorm = np;
    156:     KSPLogResidualHistory(ksp,np);
    157:     KSPMonitor(ksp,i+1,np);
    158:     (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
    159:     if (ksp->reason) break;

    161:     if (PetscRealPart(dp) < minres->haptol) {
    162:       if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Detected indefinite operator %g tolerance %g",(double)PetscRealPart(dp),(double)minres->haptol);
    163:       PetscInfo2(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    164:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    165:       break;
    166:     }

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

    177:     i++;
    178:   } while (i<ksp->max_it);
    179:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    180:   return(0);
    181: }

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

    186:    Options Database Keys:
    187: .   see KSPSolve()

    189:    Level: beginner

    191:    Notes:
    192:     The operator and the preconditioner must be symmetric and the preconditioner must
    193:           be positive definite for this method.
    194:           Supports only left preconditioning.

    196:    Reference: Paige & Saunders, 1975.

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

    200: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG, KSPCR
    201: M*/
    202: PETSC_EXTERN PetscErrorCode KSPCreate_MINRES(KSP ksp)
    203: {
    204:   KSP_MINRES     *minres;

    208:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    209:   PetscNewLog(ksp,&minres);

    211:   /* this parameter is arbitrary; but e-50 didn't work for __float128 in one example */
    212: #if defined(PETSC_USE_REAL___FLOAT128)
    213:   minres->haptol = 1.e-100;
    214: #elif defined(PETSC_USE_REAL_SINGLE)
    215:   minres->haptol = 1.e-25;
    216: #else
    217:   minres->haptol = 1.e-50;
    218: #endif
    219:   ksp->data      = (void*)minres;

    221:   /*
    222:        Sets the functions that are associated with this data structure
    223:        (in C++ this is the same as defining virtual functions)
    224:   */
    225:   ksp->ops->setup          = KSPSetUp_MINRES;
    226:   ksp->ops->solve          = KSPSolve_MINRES;
    227:   ksp->ops->destroy        = KSPDestroyDefault;
    228:   ksp->ops->setfromoptions = 0;
    229:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    230:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    231:   return(0);
    232: }