Actual source code: symmlq.c


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

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

  8: PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp)
  9: {
 10:   PetscFunctionBegin;
 11:   PetscCall(KSPSetWorkVecs(ksp, 9));
 12:   PetscFunctionReturn(PETSC_SUCCESS);
 13: }

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

 27:   PetscFunctionBegin;
 28:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
 29:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

 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:   Wbar = ksp->work[7];

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

 44:   ksp->its = 0;

 46:   PetscCall(VecSet(UOLD, 0.0));   /* u_old <- zeros;  */
 47:   PetscCall(VecCopy(UOLD, VOLD)); /* v_old <- u_old;  */
 48:   PetscCall(VecCopy(UOLD, W));    /* w     <- u_old;  */
 49:   PetscCall(VecCopy(UOLD, Wbar)); /* w_bar <- u_old;  */
 50:   if (!ksp->guess_zero) {
 51:     PetscCall(KSP_MatMult(ksp, Amat, X, R)); /*     r <- b - A*x */
 52:     PetscCall(VecAYPX(R, -1.0, B));
 53:   } else {
 54:     PetscCall(VecCopy(B, R)); /*     r <- b (x is 0) */
 55:   }

 57:   PetscCall(KSP_PCApply(ksp, R, Z)); /* z  <- B*r       */
 58:   PetscCall(VecDot(R, Z, &dp));      /* dp = r'*z;      */
 59:   KSPCheckDot(ksp, dp);
 60:   if (PetscAbsScalar(dp) < symmlq->haptol) {
 61:     PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol));
 62:     ksp->rnorm  = 0.0;                           /* what should we really put here? */
 63:     ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN; /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */
 64:     PetscFunctionReturn(PETSC_SUCCESS);
 65:   }

 67: #if !defined(PETSC_USE_COMPLEX)
 68:   if (dp < 0.0) {
 69:     ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
 70:     PetscFunctionReturn(PETSC_SUCCESS);
 71:   }
 72: #endif
 73:   dp     = PetscSqrtScalar(dp);
 74:   beta   = dp; /*  beta <- sqrt(r'*z)  */
 75:   beta1  = beta;
 76:   s_prod = PetscAbsScalar(beta1);

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

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

 99:     /*    Update    */
100:     if (ksp->its > 1) {
101:       PetscCall(VecCopy(V, VOLD)); /* v_old <- v; */
102:       PetscCall(VecCopy(U, UOLD)); /* u_old <- u; */

104:       PetscCall(VecCopy(R, V));
105:       PetscCall(VecScale(V, 1.0 / beta)); /* v <- ibeta*r; */
106:       PetscCall(VecCopy(Z, U));
107:       PetscCall(VecScale(U, 1.0 / beta)); /* u <- ibeta*z; */

109:       PetscCall(VecCopy(Wbar, W));
110:       PetscCall(VecScale(W, c));
111:       PetscCall(VecAXPY(W, s, U)); /* w  <- c*w_bar + s*u;    (w_k) */
112:       PetscCall(VecScale(Wbar, -s));
113:       PetscCall(VecAXPY(Wbar, c, U)); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */
114:       PetscCall(VecAXPY(X, ceta, W)); /* x <- x + ceta * w;       (xL_k)  */

116:       ceta_oold = ceta_old;
117:       ceta_old  = ceta;
118:     }

120:     /*   Lanczos  */
121:     PetscCall(KSP_MatMult(ksp, Amat, U, R)); /*  r     <- Amat*u; */
122:     PetscCall(VecDot(U, R, &alpha));         /*  alpha <- u'*r;   */
123:     PetscCall(KSP_PCApply(ksp, R, Z));       /*      z <- B*r;    */

125:     PetscCall(VecAXPY(R, -alpha, V));   /*  r <- r - alpha* v;  */
126:     PetscCall(VecAXPY(Z, -alpha, U));   /*  z <- z - alpha* u;  */
127:     PetscCall(VecAXPY(R, -beta, VOLD)); /*  r <- r - beta * v_old; */
128:     PetscCall(VecAXPY(Z, -beta, UOLD)); /*  z <- z - beta * u_old; */
129:     betaold = beta;                     /* beta_k                  */
130:     PetscCall(VecDot(R, Z, &dp));       /* dp <- r'*z;             */
131:     KSPCheckDot(ksp, dp);
132:     if (PetscAbsScalar(dp) < symmlq->haptol) {
133:       PetscCall(PetscInfo(ksp, "Detected happy breakdown %g tolerance %g\n", (double)PetscAbsScalar(dp), (double)symmlq->haptol));
134:       dp = 0.0;
135:     }

137: #if !defined(PETSC_USE_COMPLEX)
138:     if (dp < 0.0) {
139:       ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
140:       break;
141:     }
142: #endif
143:     beta = PetscSqrtScalar(dp); /*  beta = sqrt(dp); */

145:     /*    QR factorization    */
146:     coold = cold;
147:     cold  = c;
148:     soold = sold;
149:     sold  = s;
150:     rho0  = cold * alpha - coold * sold * betaold;      /* gamma_bar */
151:     rho1  = PetscSqrtScalar(rho0 * rho0 + beta * beta); /* gamma     */
152:     rho2  = sold * alpha + coold * cold * betaold;      /* delta     */
153:     rho3  = soold * betaold;                            /* epsilon   */

155:     /* Givens rotation: [c -s; s c] (different from the Reference!) */
156:     c = rho0 / rho1;
157:     s = beta / rho1;

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

162:     s_prod = s_prod * PetscAbsScalar(s);
163:     if (c == 0.0) np = s_prod * 1.e16;
164:     else np = s_prod / PetscAbsScalar(c); /* residual norm for xc_k (CGNORM) */

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

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

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

181:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
182:   PetscFunctionReturn(PETSC_SUCCESS);
183: }

185: /*MC
186:      KSPSYMMLQ -  This code implements the SYMMLQ method.

188:    Level: beginner

190:    Notes:
191:    The operator and the preconditioner must be symmetric for this method.

193:    The preconditioner must be POSITIVE-DEFINITE.

195:    Supports only left preconditioning.

197:    Reference:
198: . * - Paige & Saunders, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal. 12, 1975.

200: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`
201: M*/
202: PETSC_EXTERN PetscErrorCode KSPCreate_SYMMLQ(KSP ksp)
203: {
204:   KSP_SYMMLQ *symmlq;

206:   PetscFunctionBegin;
207:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
208:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

210:   PetscCall(PetscNew(&symmlq));
211:   symmlq->haptol = 1.e-18;
212:   ksp->data      = (void *)symmlq;

214:   /*
215:        Sets the functions that are associated with this data structure
216:        (in C++ this is the same as defining virtual functions)
217:   */
218:   ksp->ops->setup          = KSPSetUp_SYMMLQ;
219:   ksp->ops->solve          = KSPSolve_SYMMLQ;
220:   ksp->ops->destroy        = KSPDestroyDefault;
221:   ksp->ops->setfromoptions = NULL;
222:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
223:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
224:   PetscFunctionReturn(PETSC_SUCCESS);
225: }