Date: 2015-10-02T22:21:34+00:00

Actual source code: minres.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/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(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No right preconditioning for KSPMINRES");
     16:   else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No symmetric preconditioning for KSPMINRES");
     17:   KSPSetWorkVecs(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:   KSP_MINRES     *minres = (KSP_MINRES*)ksp->data;
     34:   PetscBool      diagonalscale;

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

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

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

     54:   ksp->its = 0;

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

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

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

     70:   VecDot(R,Z,&dp);
     71:   if (PetscRealPart(dp) < 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:   dp   = PetscAbsScalar(dp);
     78:   dp   = PetscSqrtScalar(dp);
     79:   beta = dp;                                        /*  beta <- sqrt(r'*z  */
     80:   eta  = beta;

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

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

     90:   KSPLogResidualHistory(ksp,np);
     91:   KSPMonitor(ksp,0,np);
     92:   ksp->rnorm = np;
     93:   (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP); /* test for convergence */
     94:   if (ksp->reason) return(0);

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

    100: /*   Lanczos  */

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

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

    111:     betaold = beta;

    113:     VecDot(R,Z,&dp);
    114:     if ( PetscRealPart(dp) < minres->haptol) {
    115:       PetscInfo2(ksp,"Detected indefinite operator %g tolerance %g\n",(double)PetscRealPart(dp),(double)minres->haptol);
    116:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
    117:       break;
    118:     }

    120:     dp   = PetscAbsScalar(dp);
    121:     beta = PetscSqrtScalar(dp);                               /*  beta <- sqrt(r'*z)   */

    123: /*    QR factorisation    */

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

    127:     rho0 = cold * alpha - coold * sold * betaold;
    128:     rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
    129:     rho2 = sold * alpha + coold * cold * betaold;
    130:     rho3 = soold * betaold;

    132: /*     Givens rotation    */

    134:     c = rho0 / rho1;
    135:     s = beta / rho1;

    137: /*    Update    */

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

    142:     VecCopy(U,W);           /*  w      <- u          */
    143:     mrho2 = -rho2;
    144:     VecAXPY(W,mrho2,WOLD); /*  w <- w - rho2 w_old  */
    145:     mrho3 = -rho3;
    146:     VecAXPY(W,mrho3,WOOLD); /*  w <- w - rho3 w_oold */
    147:     irho1 = 1.0 / rho1;
    148:     VecScale(W,irho1);     /*  w <- w / rho1        */

    150:     ceta = c * eta;
    151:     VecAXPY(X,ceta,W);      /*  x <- x + c eta w     */
    152:     eta  = -s * eta;

    154:     VecCopy(V,VOLD);
    155:     VecCopy(U,UOLD);
    156:     VecCopy(R,V);
    157:     VecCopy(Z,U);
    158:     ibeta = 1.0 / beta;
    159:     VecScale(V,ibeta);     /*  v <- r / beta       */
    160:     VecScale(U,ibeta);     /*  u <- z / beta       */

    162:     np = ksp->rnorm * PetscAbsScalar(s);

    164:     ksp->rnorm = np;
    165:     KSPLogResidualHistory(ksp,np);
    166:     KSPMonitor(ksp,i+1,np);
    167:     (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
    168:     if (ksp->reason) break;
    169:     i++;
    170:   } while (i<ksp->max_it);
    171:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    172:   return(0);
    173: }

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

    178:    Options Database Keys:
    179: .   see KSPSolve()

    181:    Level: beginner

    183:    Notes: The operator and the preconditioner must be symmetric and the preconditioner must
    184:           be positive definite for this method.
    185:           Supports only left preconditioning.

    187:    Reference: Paige & Saunders, 1975.

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

    191: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG, KSPCR
    192: M*/
    195: PETSC_EXTERN PetscErrorCode KSPCreate_MINRES(KSP ksp)
    196: {
    197:   KSP_MINRES     *minres;

    201:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    202:   PetscNewLog(ksp,&minres);
    203:   minres->haptol = 1.e-50;
    204:   ksp->data      = (void*)minres;

    206:   /*
    207:        Sets the functions that are associated with this data structure
    208:        (in C++ this is the same as defining virtual functions)
    209:   */
    210:   ksp->ops->setup          = KSPSetUp_MINRES;
    211:   ksp->ops->solve          = KSPSolve_MINRES;
    212:   ksp->ops->destroy        = KSPDestroyDefault;
    213:   ksp->ops->setfromoptions = 0;
    214:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    215:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    216:   return(0);
    217: }