Actual source code: symmlq.c

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

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

  7: static PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp)
  8: {
  9:   PetscFunctionBegin;
 10:   PetscCall(KSPSetWorkVecs(ksp, 9));
 11:   PetscFunctionReturn(PETSC_SUCCESS);
 12: }

 14: static PetscErrorCode KSPSolve_SYMMLQ(KSP ksp)
 15: {
 16:   PetscInt    i;
 17:   PetscScalar alpha, beta, ibeta, betaold, beta1, ceta = 0, ceta_oold = 0.0, ceta_old = 0.0, ceta_bar;
 18:   PetscScalar c = 1.0, cold = 1.0, s = 0.0, sold = 0.0, coold, soold, rho0, rho1, rho2, rho3;
 19:   PetscScalar dp = 0.0;
 20:   PetscReal   np = 0.0, s_prod;
 21:   Vec         X, B, R, Z, U, V, W, UOLD, VOLD, Wbar;
 22:   Mat         Amat, Pmat;
 23:   KSP_SYMMLQ *symmlq = (KSP_SYMMLQ *)ksp->data;

 25:   PetscFunctionBegin;
 26:   X    = ksp->vec_sol;
 27:   B    = ksp->vec_rhs;
 28:   R    = ksp->work[0];
 29:   Z    = ksp->work[1];
 30:   U    = ksp->work[2];
 31:   V    = ksp->work[3];
 32:   W    = ksp->work[4];
 33:   UOLD = ksp->work[5];
 34:   VOLD = ksp->work[6];
 35:   Wbar = ksp->work[7];

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

 39:   ksp->its = 0;

 41:   PetscCall(VecSet(UOLD, 0.0));   /* u_old <- zeros;  */
 42:   PetscCall(VecCopy(UOLD, VOLD)); /* v_old <- u_old;  */
 43:   PetscCall(VecCopy(UOLD, W));    /* w     <- u_old;  */
 44:   PetscCall(VecCopy(UOLD, Wbar)); /* w_bar <- u_old;  */
 45:   if (!ksp->guess_zero) {
 46:     PetscCall(KSP_MatMult(ksp, Amat, X, R)); /*     r <- b - A*x */
 47:     PetscCall(VecAYPX(R, -1.0, B));
 48:   } else {
 49:     PetscCall(VecCopy(B, R)); /*     r <- b (x is 0) */
 50:   }

 52:   PetscCall(KSP_PCApply(ksp, R, Z)); /* z  <- B*r       */
 53:   PetscCall(VecDot(R, Z, &dp));      /* dp = r'*z;      */
 54:   KSPCheckDot(ksp, dp);
 55:   if (PetscAbsScalar(dp) < symmlq->haptol) {
 56:     PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol));
 57:     ksp->rnorm  = 0.0;                           /* what should we really put here? */
 58:     ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN; /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */
 59:     PetscFunctionReturn(PETSC_SUCCESS);
 60:   }

 62: #if !PetscDefined(USE_COMPLEX)
 63:   if (dp < 0.0) {
 64:     ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
 65:     PetscFunctionReturn(PETSC_SUCCESS);
 66:   }
 67: #endif
 68:   dp     = PetscSqrtScalar(dp);
 69:   beta   = dp; /*  beta <- sqrt(r'*z)  */
 70:   beta1  = beta;
 71:   s_prod = PetscAbsScalar(beta1);

 73:   PetscCall(VecCopy(R, V)); /* v <- r; */
 74:   PetscCall(VecCopy(Z, U)); /* u <- z; */
 75:   ibeta = 1.0 / beta;
 76:   PetscCall(VecScale(V, ibeta)); /* v <- ibeta*v; */
 77:   PetscCall(VecScale(U, ibeta)); /* u <- ibeta*u; */
 78:   PetscCall(VecCopy(U, Wbar));   /* w_bar <- u;   */
 79:   if (ksp->normtype != KSP_NORM_NONE) {
 80:     PetscCall(VecNorm(Z, NORM_2, &np)); /*   np <- ||z||        */
 81:     KSPCheckNorm(ksp, np);
 82:   }
 83:   PetscCall(KSPLogResidualHistory(ksp, np));
 84:   PetscCall(KSPMonitor(ksp, 0, np));
 85:   ksp->rnorm = np;
 86:   PetscCall((*ksp->converged)(ksp, 0, np, &ksp->reason, ksp->cnvP)); /* test for convergence */
 87:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

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

 94:     /*    Update    */
 95:     if (ksp->its > 1) {
 96:       PetscCall(VecCopy(V, VOLD)); /* v_old <- v; */
 97:       PetscCall(VecCopy(U, UOLD)); /* u_old <- u; */

 99:       PetscCall(VecCopy(R, V));
100:       PetscCall(VecScale(V, 1.0 / beta)); /* v <- ibeta*r; */
101:       PetscCall(VecCopy(Z, U));
102:       PetscCall(VecScale(U, 1.0 / beta)); /* u <- ibeta*z; */

104:       PetscCall(VecCopy(Wbar, W));
105:       PetscCall(VecScale(W, c));
106:       PetscCall(VecAXPY(W, s, U)); /* w  <- c*w_bar + s*u;    (w_k) */
107:       PetscCall(VecScale(Wbar, -s));
108:       PetscCall(VecAXPY(Wbar, c, U)); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */
109:       PetscCall(VecAXPY(X, ceta, W)); /* x <- x + ceta * w;       (xL_k)  */

111:       ceta_oold = ceta_old;
112:       ceta_old  = ceta;
113:     }

115:     /*   Lanczos  */
116:     PetscCall(KSP_MatMult(ksp, Amat, U, R)); /*  r     <- Amat*u; */
117:     PetscCall(VecDot(U, R, &alpha));         /*  alpha <- u'*r;   */
118:     PetscCall(KSP_PCApply(ksp, R, Z));       /*      z <- B*r;    */

120:     PetscCall(VecAXPY(R, -alpha, V));   /*  r <- r - alpha* v;  */
121:     PetscCall(VecAXPY(Z, -alpha, U));   /*  z <- z - alpha* u;  */
122:     PetscCall(VecAXPY(R, -beta, VOLD)); /*  r <- r - beta * v_old; */
123:     PetscCall(VecAXPY(Z, -beta, UOLD)); /*  z <- z - beta * u_old; */
124:     betaold = beta;                     /* beta_k                  */
125:     PetscCall(VecDot(R, Z, &dp));       /* dp <- r'*z;             */
126:     KSPCheckDot(ksp, dp);
127:     if (PetscAbsScalar(dp) < symmlq->haptol) {
128:       PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol));
129:       dp = 0.0;
130:     }

132: #if !PetscDefined(USE_COMPLEX)
133:     if (dp < 0.0) {
134:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
135:       break;
136:     }
137: #endif
138:     beta = PetscSqrtScalar(dp); /*  beta = sqrt(dp); */

140:     /*    QR factorization    */
141:     coold = cold;
142:     cold  = c;
143:     soold = sold;
144:     sold  = s;
145:     rho0  = cold * alpha - coold * sold * betaold;      /* gamma_bar */
146:     rho1  = PetscSqrtScalar(rho0 * rho0 + beta * beta); /* gamma     */
147:     rho2  = sold * alpha + coold * cold * betaold;      /* delta     */
148:     rho3  = soold * betaold;                            /* epsilon   */

150:     /* Givens rotation: [c -s; s c] (different from the Reference!) */
151:     c = rho0 / rho1;
152:     s = beta / rho1;

154:     if (ksp->its == 1) ceta = beta1 / rho1;
155:     else ceta = -(rho2 * ceta_old + rho3 * ceta_oold) / rho1;

157:     s_prod = s_prod * PetscAbsScalar(s);
158:     if (c == 0.0) np = s_prod * 1.e16;
159:     else np = s_prod / PetscAbsScalar(c); /* residual norm for xc_k (CGNORM) */

161:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = np;
162:     else ksp->rnorm = 0.0;
163:     PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
164:     PetscCall(KSPMonitor(ksp, i + 1, ksp->rnorm));
165:     PetscCall((*ksp->converged)(ksp, i + 1, ksp->rnorm, &ksp->reason, ksp->cnvP)); /* test for convergence */
166:     if (ksp->reason) break;
167:     i++;
168:   } while (i < ksp->max_it);

170:   /* move to the CG point: xc_(k+1) */
171:   if (c == 0.0) ceta_bar = ceta * 1.e15;
172:   else ceta_bar = ceta / c;

174:   PetscCall(VecAXPY(X, ceta_bar, Wbar)); /* x <- x + ceta_bar*w_bar */

176:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
177:   PetscFunctionReturn(PETSC_SUCCESS);
178: }

180: /*MC
181:    KSPSYMMLQ - Implements the SYMMLQ method {cite}`paige.saunders:solution`.

183:    Level: beginner

185:    Notes:
186:    The operator and the preconditioner must be symmetric for this method.

188:    The preconditioner must be POSITIVE-DEFINITE.

190:    Supports only left preconditioning.

192: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`
193: M*/
194: PETSC_EXTERN PetscErrorCode KSPCreate_SYMMLQ(KSP ksp)
195: {
196:   KSP_SYMMLQ *symmlq;

198:   PetscFunctionBegin;
199:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
200:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

202:   PetscCall(PetscNew(&symmlq));
203:   symmlq->haptol = 1.e-18;
204:   ksp->data      = (void *)symmlq;

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_SYMMLQ;
211:   ksp->ops->solve          = KSPSolve_SYMMLQ;
212:   ksp->ops->destroy        = KSPDestroyDefault;
213:   ksp->ops->setfromoptions = NULL;
214:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
215:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
216:   PetscFunctionReturn(PETSC_SUCCESS);
217: }