Date: 2021-03-03T22:27:25+00:00

Actual source code: minres.c
petsc-3.14.5 2021-03-03
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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:   KSPCheckNorm(ksp,np);
     67:   VecDot(R,Z,&dp);
     68:   KSPCheckDot(ksp,dp);

     70:   if (PetscRealPart(dp) < minres->haptol && np > minres->haptol) {
     71:     if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Detected indefinite operator %g tolerance %g",(double)PetscRealPart(dp),(double)minres->haptol);
     72:     PetscInfo2(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
     73:     ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
     74:     return(0);
     75:   }

     77:   ksp->rnorm = 0.0;
     78:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = np;
     79:   KSPLogResidualHistory(ksp,ksp->rnorm);
     80:   KSPMonitor(ksp,0,ksp->rnorm);
     81:   (*ksp->converged)(ksp,0,ksp->rnorm,&ksp->reason,ksp->cnvP); /* test for convergence */
     82:   if (ksp->reason) return(0);

     84:   dp   = PetscAbsScalar(dp);
     85:   dp   = PetscSqrtScalar(dp);
     86:   beta = dp;                                        /*  beta <- sqrt(r'*z  */
     87:   eta  = beta;

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

     95:   i = 0;
     96:   do {
     97:     ksp->its = i+1;

     99:     /*   Lanczos  */

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

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

    110:     betaold = beta;

    112:     VecDot(R,Z,&dp);
    113:     KSPCheckDot(ksp,dp);
    114:     dp   = PetscAbsScalar(dp);
    115:     beta = PetscSqrtScalar(dp);                               /*  beta <- sqrt(r'*z)   */

    117:     /*    QR factorisation    */

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

    121:     rho0 = cold * alpha - coold * sold * betaold;
    122:     rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
    123:     rho2 = sold * alpha + coold * cold * betaold;
    124:     rho3 = soold * betaold;

    126:     /*     Givens rotation    */

    128:     c = rho0 / rho1;
    129:     s = beta / rho1;

    131:     /*    Update    */

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

    136:     VecCopy(U,W);           /*  w      <- u          */
    137:     VecAXPY(W,-rho2,WOLD); /*  w <- w - rho2 w_old  */
    138:     VecAXPY(W,-rho3,WOOLD); /*  w <- w - rho3 w_oold */
    139:     irho1 = 1.0 / rho1;
    140:     VecScale(W,irho1);     /*  w <- w / rho1        */

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

    145:     /*
    146:         when dp is really small we have either convergence or an indefinite operator so compute true
    147:         residual norm to check for convergence
    148:     */
    149:     if (PetscRealPart(dp) < minres->haptol) {
    150:       PetscInfo2(ksp,"Possible indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    151:       KSP_MatMult(ksp,Amat,X,VOLD);
    152:       VecAXPY(VOLD,none,B);
    153:       VecNorm(VOLD,NORM_2,&np);
    154:       KSPCheckNorm(ksp,np);
    155:     } else {
    156:       /* otherwise compute new residual norm via recurrence relation */
    157:       np *= PetscAbsScalar(s);
    158:     }

    160:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = np;
    161:     KSPLogResidualHistory(ksp,ksp->rnorm);
    162:     KSPMonitor(ksp,i+1,ksp->rnorm);
    163:     (*ksp->converged)(ksp,i+1,ksp->rnorm,&ksp->reason,ksp->cnvP); /* test for convergence */
    164:     if (ksp->reason) break;

    166:     if (PetscRealPart(dp) < minres->haptol) {
    167:       if (ksp->errorifnotconverged) SETERRQ2(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Detected indefinite operator %g tolerance %g",(double)PetscRealPart(dp),(double)minres->haptol);
    168:       PetscInfo2(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    169:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    170:       break;
    171:     }

    173:     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       */

    182:     i++;
    183:   } while (i<ksp->max_it);
    184:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    185:   return(0);
    186: }

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

    191:    Options Database Keys:
    192: .   see KSPSolve()

    194:    Level: beginner

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

    201:    Reference: Paige & Saunders, 1975.

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

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

    213:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    214:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
    215:   PetscNewLog(ksp,&minres);

    217:   /* this parameter is arbitrary; but e-50 didn't work for __float128 in one example */
    218: #if defined(PETSC_USE_REAL___FLOAT128)
    219:   minres->haptol = 1.e-100;
    220: #elif defined(PETSC_USE_REAL_SINGLE)
    221:   minres->haptol = 1.e-25;
    222: #else
    223:   minres->haptol = 1.e-50;
    224: #endif
    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        = KSPDestroyDefault;
    234:   ksp->ops->setfromoptions = NULL;
    235:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    236:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    237:   return(0);
    238: }