Actual source code: minres.c
1: #define PETSCKSP_DLL
3: #include src/ksp/ksp/kspimpl.h
5: typedef struct {
6: PetscReal haptol;
7: } KSP_MINRES;
11: PetscErrorCode KSPSetUp_MINRES(KSP ksp)
12: {
16: if (ksp->pc_side == PC_RIGHT) {
17: SETERRQ(PETSC_ERR_SUP,"No right preconditioning for KSPMINRES");
18: } else if (ksp->pc_side == PC_SYMMETRIC) {
19: SETERRQ(PETSC_ERR_SUP,"No symmetric preconditioning for KSPMINRES");
20: }
21: KSPDefaultGetWork(ksp,9);
22: return(0);
23: }
28: PetscErrorCode KSPSolve_MINRES(KSP ksp)
29: {
31: PetscInt i;
32: PetscScalar alpha,beta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
33: PetscScalar rho0,rho1,irho1,rho2,mrho2,rho3,mrho3,dp = 0.0;
34: PetscReal np;
35: Vec X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
36: Mat Amat,Pmat;
37: MatStructure pflag;
38: KSP_MINRES *minres = (KSP_MINRES*)ksp->data;
39: PetscTruth diagonalscale;
42: PCDiagonalScale(ksp->pc,&diagonalscale);
43: if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",ksp->type_name);
45: X = ksp->vec_sol;
46: B = ksp->vec_rhs;
47: R = ksp->work[0];
48: Z = ksp->work[1];
49: U = ksp->work[2];
50: V = ksp->work[3];
51: W = ksp->work[4];
52: UOLD = ksp->work[5];
53: VOLD = ksp->work[6];
54: WOLD = ksp->work[7];
55: WOOLD = ksp->work[8];
57: PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
59: ksp->its = 0;
61: VecSet(UOLD,0.0); /* u_old <- 0 */
62: VecCopy(UOLD,VOLD); /* v_old <- 0 */
63: VecCopy(UOLD,W); /* w <- 0 */
64: VecCopy(UOLD,WOLD); /* w_old <- 0 */
66: if (!ksp->guess_zero) {
67: KSP_MatMult(ksp,Amat,X,R); /* r <- b - A*x */
68: VecAYPX(R,-1.0,B);
69: } else {
70: VecCopy(B,R); /* r <- b (x is 0) */
71: }
73: KSP_PCApply(ksp,R,Z); /* z <- B*r */
75: VecDot(R,Z,&dp);
76: if (PetscAbsScalar(dp) < minres->haptol) {
77: PetscInfo2(ksp,"Detected happy breakdown %G tolerance %G\n",PetscAbsScalar(dp),minres->haptol);
78: dp = PetscAbsScalar(dp); /* tiny number, can't use 0.0, cause divided by below */
79: if (dp == 0.0) {
80: ksp->reason = KSP_CONVERGED_ATOL;
81: return(0);
82: }
83: }
85: #if !defined(PETSC_USE_COMPLEX)
86: if (dp < 0.0) {
87: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
88: return(0);
89: }
90: #endif
91: dp = PetscSqrtScalar(dp);
92: beta = dp; /* beta <- sqrt(r'*z */
93: eta = beta;
95: VecCopy(R,V);
96: VecCopy(Z,U);
97: ibeta = 1.0 / beta;
98: VecScale(V,ibeta); /* v <- r / beta */
99: VecScale(U,ibeta); /* u <- z / beta */
101: VecNorm(Z,NORM_2,&np); /* np <- ||z|| */
103: KSPLogResidualHistory(ksp,np);
104: KSPMonitor(ksp,0,np); /* call any registered monitor routines */
105: ksp->rnorm = np;
106: (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP); /* test for convergence */
107: if (ksp->reason) return(0);
109: i = 0;
110: do {
111: ksp->its = i+1;
113: /* Lanczos */
115: KSP_MatMult(ksp,Amat,U,R); /* r <- A*u */
116: VecDot(U,R,&alpha); /* alpha <- r'*u */
117: KSP_PCApply(ksp,R,Z); /* z <- B*r */
119: VecAXPY(R,-alpha,V); /* r <- r - alpha v */
120: VecAXPY(Z,-alpha,U); /* z <- z - alpha u */
121: VecAXPY(R,-beta,VOLD); /* r <- r - beta v_old */
122: VecAXPY(Z,-beta,UOLD); /* z <- z - beta u_old */
124: betaold = beta;
126: VecDot(R,Z,&dp);
127: if (PetscAbsScalar(dp) < minres->haptol) {
128: PetscInfo2(ksp,"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(W,mrho2,WOLD); /* w <- w - rho2 w_old */
163: mrho3 = - rho3;
164: VecAXPY(W,mrho3,WOOLD); /* w <- w - rho3 w_oold */
165: irho1 = 1.0 / rho1;
166: VecScale(W,irho1); /* w <- w / rho1 */
168: ceta = c * eta;
169: VecAXPY(X,ceta,W); /* 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(V,ibeta); /* v <- r / beta */
178: VecScale(U,ibeta); /* 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: }