Actual source code: symmlq.c
petsc-3.4.5 2014-06-29
2: #include <petsc-private/kspimpl.h>
4: typedef struct {
5: PetscReal haptol;
6: } KSP_SYMMLQ;
10: PetscErrorCode KSPSetUp_SYMMLQ(KSP ksp)
11: {
15: KSPSetWorkVecs(ksp,9);
16: return(0);
17: }
21: PetscErrorCode KSPSolve_SYMMLQ(KSP ksp)
22: {
24: PetscInt i;
25: PetscScalar alpha,beta,ibeta,betaold,beta1,ceta = 0,ceta_oold = 0.0, ceta_old = 0.0,ceta_bar;
26: PetscScalar c = 1.0,cold=1.0,s=0.0,sold=0.0,coold,soold,rho0,rho1,rho2,rho3;
27: PetscScalar dp = 0.0;
28: PetscReal np,s_prod;
29: Vec X,B,R,Z,U,V,W,UOLD,VOLD,Wbar;
30: Mat Amat,Pmat;
31: MatStructure pflag;
32: KSP_SYMMLQ *symmlq = (KSP_SYMMLQ*)ksp->data;
33: PetscBool diagonalscale;
36: PCGetDiagonalScale(ksp->pc,&diagonalscale);
37: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
39: X = ksp->vec_sol;
40: B = ksp->vec_rhs;
41: R = ksp->work[0];
42: Z = ksp->work[1];
43: U = ksp->work[2];
44: V = ksp->work[3];
45: W = ksp->work[4];
46: UOLD = ksp->work[5];
47: VOLD = ksp->work[6];
48: Wbar = ksp->work[7];
50: PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
52: ksp->its = 0;
54: VecSet(UOLD,0.0); /* u_old <- zeros; */
55: VecCopy(UOLD,VOLD); /* v_old <- u_old; */
56: VecCopy(UOLD,W); /* w <- u_old; */
57: VecCopy(UOLD,Wbar); /* w_bar <- u_old; */
58: if (!ksp->guess_zero) {
59: KSP_MatMult(ksp,Amat,X,R); /* r <- b - A*x */
60: VecAYPX(R,-1.0,B);
61: } else {
62: VecCopy(B,R); /* r <- b (x is 0) */
63: }
65: KSP_PCApply(ksp,R,Z); /* z <- B*r */
66: VecDot(R,Z,&dp); /* dp = r'*z; */
67: if (PetscAbsScalar(dp) < symmlq->haptol) {
68: PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),symmlq->haptol);
69: ksp->rnorm = 0.0; /* what should we really put here? */
70: ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN; /* bugfix proposed by Lourens (lourens.vanzanen@shell.com) */
71: return(0);
72: }
74: #if !defined(PETSC_USE_COMPLEX)
75: if (dp < 0.0) {
76: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
77: return(0);
78: }
79: #endif
80: dp = PetscSqrtScalar(dp);
81: beta = dp; /* beta <- sqrt(r'*z) */
82: beta1 = beta;
83: s_prod = PetscAbsScalar(beta1);
85: VecCopy(R,V); /* v <- r; */
86: VecCopy(Z,U); /* u <- z; */
87: ibeta = 1.0 / beta;
88: VecScale(V,ibeta); /* v <- ibeta*v; */
89: VecScale(U,ibeta); /* u <- ibeta*u; */
90: VecCopy(U,Wbar); /* w_bar <- u; */
91: VecNorm(Z,NORM_2,&np); /* np <- ||z|| */
92: KSPLogResidualHistory(ksp,np);
93: KSPMonitor(ksp,0,np);
94: ksp->rnorm = np;
95: (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP); /* test for convergence */
96: if (ksp->reason) return(0);
98: i = 0; ceta = 0.;
99: do {
100: ksp->its = i+1;
102: /* Update */
103: if (ksp->its > 1) {
104: VecCopy(V,VOLD); /* v_old <- v; */
105: VecCopy(U,UOLD); /* u_old <- u; */
107: VecCopy(R,V);
108: VecScale(V,1.0/beta); /* v <- ibeta*r; */
109: VecCopy(Z,U);
110: VecScale(U,1.0/beta); /* u <- ibeta*z; */
112: VecCopy(Wbar,W);
113: VecScale(W,c);
114: VecAXPY(W,s,U); /* w <- c*w_bar + s*u; (w_k) */
115: VecScale(Wbar,-s);
116: VecAXPY(Wbar,c,U); /* w_bar <- -s*w_bar + c*u; (w_bar_(k+1)) */
117: VecAXPY(X,ceta,W); /* x <- x + ceta * w; (xL_k) */
119: ceta_oold = ceta_old;
120: ceta_old = ceta;
121: }
123: /* Lanczos */
124: KSP_MatMult(ksp,Amat,U,R); /* r <- Amat*u; */
125: VecDot(U,R,&alpha); /* alpha <- u'*r; */
126: KSP_PCApply(ksp,R,Z); /* z <- B*r; */
128: VecAXPY(R,-alpha,V); /* r <- r - alpha* v; */
129: VecAXPY(Z,-alpha,U); /* z <- z - alpha* u; */
130: VecAXPY(R,-beta,VOLD); /* r <- r - beta * v_old; */
131: VecAXPY(Z,-beta,UOLD); /* z <- z - beta * u_old; */
132: betaold = beta; /* beta_k */
133: VecDot(R,Z,&dp); /* dp <- r'*z; */
134: if (PetscAbsScalar(dp) < symmlq->haptol) {
135: PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),symmlq->haptol);
136: dp = 0.0;
137: }
139: #if !defined(PETSC_USE_COMPLEX)
140: if (dp < 0.0) {
141: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
142: break;
143: }
144: #endif
145: beta = PetscSqrtScalar(dp); /* beta = sqrt(dp); */
147: /* QR factorization */
148: coold = cold; cold = c; soold = sold; sold = s;
149: rho0 = cold * alpha - coold * sold * betaold; /* gamma_bar */
150: rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta); /* gamma */
151: rho2 = sold * alpha + coold * cold * betaold; /* delta */
152: rho3 = soold * betaold; /* epsilon */
154: /* Givens rotation: [c -s; s c] (different from the Reference!) */
155: c = rho0 / rho1; s = beta / rho1;
157: if (ksp->its==1) ceta = beta1/rho1;
158: else ceta = -(rho2*ceta_old + rho3*ceta_oold)/rho1;
160: s_prod = s_prod*PetscAbsScalar(s);
161: if (c == 0.0) np = s_prod*1.e16;
162: else np = s_prod/PetscAbsScalar(c); /* residual norm for xc_k (CGNORM) */
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);
172: /* move to the CG point: xc_(k+1) */
173: if (c == 0.0) ceta_bar = ceta*1.e15;
174: else ceta_bar = ceta/c;
176: VecAXPY(X,ceta_bar,Wbar); /* x <- x + ceta_bar*w_bar */
178: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
179: return(0);
180: }
182: /*MC
183: KSPSYMMLQ - This code implements the SYMMLQ method.
185: Options Database Keys:
186: . see KSPSolve()
188: Level: beginner
190: Notes: The operator and the preconditioner must be symmetric for this method. The
191: preconditioner must be POSITIVE-DEFINITE.
193: Supports only left preconditioning.
195: Reference: Paige & Saunders, 1975.
197: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP
198: M*/
201: PETSC_EXTERN PetscErrorCode KSPCreate_SYMMLQ(KSP ksp)
202: {
203: KSP_SYMMLQ *symmlq;
207: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
209: PetscNewLog(ksp,KSP_SYMMLQ,&symmlq);
210: symmlq->haptol = 1.e-18;
211: ksp->data = (void*)symmlq;
213: /*
214: Sets the functions that are associated with this data structure
215: (in C++ this is the same as defining virtual functions)
216: */
217: ksp->ops->setup = KSPSetUp_SYMMLQ;
218: ksp->ops->solve = KSPSolve_SYMMLQ;
219: ksp->ops->destroy = KSPDestroyDefault;
220: ksp->ops->setfromoptions = 0;
221: ksp->ops->buildsolution = KSPBuildSolutionDefault;
222: ksp->ops->buildresidual = KSPBuildResidualDefault;
223: return(0);
224: }