Actual source code: minres.c

  1: #include "src/ksp/ksp/kspimpl.h"

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

  9: PetscErrorCode KSPSetUp_MINRES(KSP ksp)
 10: {

 14:   if (ksp->pc_side == PC_RIGHT) {
 15:     SETERRQ(2,"No right preconditioning for KSPMINRES");
 16:   } else if (ksp->pc_side == PC_SYMMETRIC) {
 17:     SETERRQ(2,"No symmetric preconditioning for KSPMINRES");
 18:   }
 19:   KSPDefaultGetWork(ksp,9);
 20:   return(0);
 21: }


 26: PetscErrorCode  KSPSolve_MINRES(KSP ksp)
 27: {
 29:   PetscInt       i;
 30:   PetscScalar    alpha,malpha,beta,mbeta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
 31:   PetscScalar    rho0,rho1,irho1,rho2,mrho2,rho3,mrho3,mone = -1.0,zero = 0.0,dp = 0.0;
 32:   PetscReal      np;
 33:   Vec            X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
 34:   Mat            Amat,Pmat;
 35:   MatStructure   pflag;
 36:   KSP_MINRES     *minres = (KSP_MINRES*)ksp->data;
 37:   PetscTruth     diagonalscale;

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

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

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

 57:   ksp->its = 0;

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

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

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

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

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

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

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

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

107:   i = 0;
108:   do {
109:      ksp->its = i+1;

111: /*   Lanczos  */

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

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

124:      betaold = beta;

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

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

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

141: /*    QR factorisation    */

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

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

150: /*     Givens rotation    */

152:      c = rho0 / rho1;
153:      s = beta / rho1;

155: /*    Update    */

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

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

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

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

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

198:    Options Database Keys:
199: .   see KSPSolve()

201:    Level: beginner

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

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

208: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG
209: M*/
213: PetscErrorCode KSPCreate_MINRES(KSP ksp)
214: {
215:   KSP_MINRES     *minres;


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

225:   /*
226:        Sets the functions that are associated with this data structure 
227:        (in C++ this is the same as defining virtual functions)
228:   */
229:   ksp->ops->setup                = KSPSetUp_MINRES;
230:   ksp->ops->solve                = KSPSolve_MINRES;
231:   ksp->ops->destroy              = KSPDefaultDestroy;
232:   ksp->ops->setfromoptions       = 0;
233:   ksp->ops->buildsolution        = KSPDefaultBuildSolution;
234:   ksp->ops->buildresidual        = KSPDefaultBuildResidual;
235:   return(0);
236: }