Date: 2022-03-31T04:48:12+00:00

Actual source code: minres.c

      2: #include <petsc/private/kspimpl.h>

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

      8: static PetscErrorCode KSPSetUp_MINRES(KSP ksp)
      9: {
     12:   KSPSetWorkVecs(ksp,9);
     13:   return 0;
     14: }

     16: static PetscErrorCode  KSPSolve_MINRES(KSP ksp)
     17: {
     18:   PetscInt          i;
     19:   PetscScalar       alpha,beta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
     20:   PetscScalar       rho0,rho1,irho1,rho2,rho3,dp = 0.0;
     21:   const PetscScalar none = -1.0;
     22:   PetscReal         np;
     23:   Vec               X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
     24:   Mat               Amat,Pmat;
     25:   KSP_MINRES        *minres = (KSP_MINRES*)ksp->data;
     26:   PetscBool         diagonalscale;

     28:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

     31:   X     = ksp->vec_sol;
     32:   B     = ksp->vec_rhs;
     33:   R     = ksp->work[0];
     34:   Z     = ksp->work[1];
     35:   U     = ksp->work[2];
     36:   V     = ksp->work[3];
     37:   W     = ksp->work[4];
     38:   UOLD  = ksp->work[5];
     39:   VOLD  = ksp->work[6];
     40:   WOLD  = ksp->work[7];
     41:   WOOLD = ksp->work[8];

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

     45:   ksp->its = 0;

     47:   VecSet(UOLD,0.0);          /*     u_old  <-   0   */
     48:   VecSet(VOLD,0.0);         /*     v_old  <-   0   */
     49:   VecSet(W,0.0);            /*     w      <-   0   */
     50:   VecSet(WOLD,0.0);         /*     w_old  <-   0   */

     52:   if (!ksp->guess_zero) {
     53:     KSP_MatMult(ksp,Amat,X,R); /*     r <- b - A*x    */
     54:     VecAYPX(R,-1.0,B);
     55:   } else {
     56:     VecCopy(B,R);              /*     r <- b (x is 0) */
     57:   }
     58:   KSP_PCApply(ksp,R,Z);       /*     z  <- B*r       */
     59:   VecNorm(Z,NORM_2,&np);      /*   np <- ||z||        */
     60:   KSPCheckNorm(ksp,np);
     61:   VecDot(R,Z,&dp);
     62:   KSPCheckDot(ksp,dp);

     64:   if (PetscRealPart(dp) < minres->haptol && np > minres->haptol) {
     66:     PetscInfo(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
     67:     ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
     68:     return 0;
     69:   }

     71:   ksp->rnorm = 0.0;
     72:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = np;
     73:   KSPLogResidualHistory(ksp,ksp->rnorm);
     74:   KSPMonitor(ksp,0,ksp->rnorm);
     75:   (*ksp->converged)(ksp,0,ksp->rnorm,&ksp->reason,ksp->cnvP); /* test for convergence */
     76:   if (ksp->reason) return 0;

     78:   dp   = PetscAbsScalar(dp);
     79:   dp   = PetscSqrtScalar(dp);
     80:   beta = dp;                                        /*  beta <- sqrt(r'*z  */
     81:   eta  = beta;

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

     89:   i = 0;
     90:   do {
     91:     ksp->its = i+1;

     93:     /*   Lanczos  */

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

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

    104:     betaold = beta;

    106:     VecDot(R,Z,&dp);
    107:     KSPCheckDot(ksp,dp);
    108:     dp   = PetscAbsScalar(dp);
    109:     beta = PetscSqrtScalar(dp);                               /*  beta <- sqrt(r'*z)   */

    111:     /*    QR factorisation    */

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

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

    120:     /*     Givens rotation    */

    122:     c = rho0 / rho1;
    123:     s = beta / rho1;

    125:     /*    Update    */

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

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

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

    139:     /*
    140:         when dp is really small we have either convergence or an indefinite operator so compute true
    141:         residual norm to check for convergence
    142:     */
    143:     if (PetscRealPart(dp) < minres->haptol) {
    144:       PetscInfo(ksp,"Possible indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    145:       KSP_MatMult(ksp,Amat,X,VOLD);
    146:       VecAXPY(VOLD,none,B);
    147:       VecNorm(VOLD,NORM_2,&np);
    148:       KSPCheckNorm(ksp,np);
    149:     } else {
    150:       /* otherwise compute new residual norm via recurrence relation */
    151:       np *= PetscAbsScalar(s);
    152:     }

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

    160:     if (PetscRealPart(dp) < minres->haptol) {
    162:       PetscInfo(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    163:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    164:       break;
    165:     }

    167:     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       */

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

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

    185:    Options Database Keys:
    186:     see KSPSolve()

    188:    Level: beginner

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

    195:    Reference: Paige & Saunders, 1975.

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

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

    205:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    206:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
    207:   PetscNewLog(ksp,&minres);

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

    219:   /*
    220:        Sets the functions that are associated with this data structure
    221:        (in C++ this is the same as defining virtual functions)
    222:   */
    223:   ksp->ops->setup          = KSPSetUp_MINRES;
    224:   ksp->ops->solve          = KSPSolve_MINRES;
    225:   ksp->ops->destroy        = KSPDestroyDefault;
    226:   ksp->ops->setfromoptions = NULL;
    227:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    228:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    229:   return 0;
    230: }