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: {
 10:   KSPSetWorkVecs(ksp, 9);
 11:   return 0;
 12: }

 14: static PetscErrorCode KSPSolve_MINRES(KSP ksp)
 15: {
 16:   PetscInt          i;
 17:   PetscScalar       alpha, beta, ibeta, betaold, eta, c = 1.0, ceta, cold = 1.0, coold, s = 0.0, sold = 0.0, soold;
 18:   PetscScalar       rho0, rho1, irho1, rho2, rho3, dp = 0.0;
 19:   const PetscScalar none = -1.0;
 20:   PetscReal         np;
 21:   Vec               X, B, R, Z, U, V, W, UOLD, VOLD, WOLD, WOOLD;
 22:   Mat               Amat, Pmat;
 23:   KSP_MINRES       *minres = (KSP_MINRES *)ksp->data;
 24:   PetscBool         diagonalscale;

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

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

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

 43:   ksp->its = 0;

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

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

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

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

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

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

 87:   i = 0;
 88:   do {
 89:     ksp->its = i + 1;

 91:     /*   Lanczos  */

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

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

102:     betaold = beta;

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

109:     /*    QR factorisation    */

111:     coold = cold;
112:     cold  = c;
113:     soold = sold;
114:     sold  = s;

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

121:     /*     Givens rotation    */

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

126:     /*    Update    */

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

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

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

140:     /*
141:         when dp is really small we have either convergence or an indefinite operator so compute true
142:         residual norm to check for convergence
143:     */
144:     if (PetscRealPart(dp) < minres->haptol) {
145:       PetscInfo(ksp, "Possible indefinite operator %g tolerance %g\n", (double)PetscRealPart(dp), (double)minres->haptol);
146:       KSP_MatMult(ksp, Amat, X, VOLD);
147:       VecAXPY(VOLD, none, B);
148:       VecNorm(VOLD, NORM_2, &np);
149:       KSPCheckNorm(ksp, np);
150:     } else {
151:       /* otherwise compute new residual norm via recurrence relation */
152:       np *= PetscAbsScalar(s);
153:     }

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

161:     if (PetscRealPart(dp) < minres->haptol) {
163:       PetscInfo(ksp, "Detected indefinite operator %g tolerance %g\n", (double)PetscRealPart(dp), (double)minres->haptol);
164:       ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
165:       break;
166:     }

168:     eta = -s * eta;
169:     VecCopy(V, VOLD);
170:     VecCopy(U, UOLD);
171:     VecCopy(R, V);
172:     VecCopy(Z, U);
173:     ibeta = 1.0 / beta;
174:     VecScale(V, ibeta); /*  v <- r / beta       */
175:     VecScale(U, ibeta); /*  u <- z / beta       */

177:     i++;
178:   } while (i < ksp->max_it);
179:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
180:   return 0;
181: }

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

186:    Level: beginner

188:    Notes:
189:    The operator and the preconditioner must be symmetric and the preconditioner must be positive definite for this method.

191:    Supports only left preconditioning.

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

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

199: .seealso: [](chapter_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `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:   PetscNew(&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: }