Actual source code: minres.c
petsc-3.4.5 2014-06-29
2: #include <petsc-private/kspimpl.h>
4: typedef struct {
5: PetscReal haptol;
6: } KSP_MINRES;
10: PetscErrorCode KSPSetUp_MINRES(KSP ksp)
11: {
15: if (ksp->pc_side == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No right preconditioning for KSPMINRES");
16: else if (ksp->pc_side == PC_SYMMETRIC) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"No symmetric preconditioning for KSPMINRES");
17: KSPSetWorkVecs(ksp,9);
18: return(0);
19: }
24: PetscErrorCode KSPSolve_MINRES(KSP ksp)
25: {
27: PetscInt i;
28: PetscScalar alpha,beta,ibeta,betaold,eta,c=1.0,ceta,cold=1.0,coold,s=0.0,sold=0.0,soold;
29: PetscScalar rho0,rho1,irho1,rho2,mrho2,rho3,mrho3,dp = 0.0;
30: PetscReal np;
31: Vec X,B,R,Z,U,V,W,UOLD,VOLD,WOLD,WOOLD;
32: Mat Amat,Pmat;
33: MatStructure pflag;
34: KSP_MINRES *minres = (KSP_MINRES*)ksp->data;
35: PetscBool diagonalscale;
38: PCGetDiagonalScale(ksp->pc,&diagonalscale);
39: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
41: X = ksp->vec_sol;
42: B = ksp->vec_rhs;
43: R = ksp->work[0];
44: Z = ksp->work[1];
45: U = ksp->work[2];
46: V = ksp->work[3];
47: W = ksp->work[4];
48: UOLD = ksp->work[5];
49: VOLD = ksp->work[6];
50: WOLD = ksp->work[7];
51: WOOLD = ksp->work[8];
53: PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
55: ksp->its = 0;
57: VecSet(UOLD,0.0); /* u_old <- 0 */
58: VecCopy(UOLD,VOLD); /* v_old <- 0 */
59: VecCopy(UOLD,W); /* w <- 0 */
60: VecCopy(UOLD,WOLD); /* w_old <- 0 */
62: if (!ksp->guess_zero) {
63: KSP_MatMult(ksp,Amat,X,R); /* r <- b - A*x */
64: VecAYPX(R,-1.0,B);
65: } else {
66: VecCopy(B,R); /* r <- b (x is 0) */
67: }
69: KSP_PCApply(ksp,R,Z); /* z <- B*r */
71: VecDot(R,Z,&dp);
72: if (PetscRealPart(dp) < minres->haptol) {
73: PetscInfo2(ksp,"Detected indefinite operator %G tolerance %G\n",PetscRealPart(dp),minres->haptol);
74: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
75: return(0);
76: }
78: dp = PetscAbsScalar(dp);
79: dp = PetscSqrtScalar(dp);
80: beta = dp; /* beta <- sqrt(r'*z */
81: eta = beta;
83: VecCopy(R,V);
84: VecCopy(Z,U);
85: ibeta = 1.0 / beta;
86: VecScale(V,ibeta); /* v <- r / beta */
87: VecScale(U,ibeta); /* u <- z / beta */
89: VecNorm(Z,NORM_2,&np); /* np <- ||z|| */
91: KSPLogResidualHistory(ksp,np);
92: KSPMonitor(ksp,0,np);
93: ksp->rnorm = np;
94: (*ksp->converged)(ksp,0,np,&ksp->reason,ksp->cnvP); /* test for convergence */
95: if (ksp->reason) return(0);
97: i = 0;
98: do {
99: ksp->its = i+1;
101: /* Lanczos */
103: KSP_MatMult(ksp,Amat,U,R); /* r <- A*u */
104: VecDot(U,R,&alpha); /* alpha <- r'*u */
105: KSP_PCApply(ksp,R,Z); /* z <- B*r */
107: VecAXPY(R,-alpha,V); /* r <- r - alpha v */
108: VecAXPY(Z,-alpha,U); /* z <- z - alpha u */
109: VecAXPY(R,-beta,VOLD); /* r <- r - beta v_old */
110: VecAXPY(Z,-beta,UOLD); /* z <- z - beta u_old */
112: betaold = beta;
114: VecDot(R,Z,&dp);
115: if ( PetscRealPart(dp) < minres->haptol) {
116: PetscInfo2(ksp,"Detected indefinite operator %G tolerance %G\n",PetscRealPart(dp),minres->haptol);
117: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
118: break;
119: }
121: dp = PetscAbsScalar(dp);
122: beta = PetscSqrtScalar(dp); /* beta <- sqrt(r'*z) */
124: /* QR factorisation */
126: coold = cold; cold = c; soold = sold; sold = s;
128: rho0 = cold * alpha - coold * sold * betaold;
129: rho1 = PetscSqrtScalar(rho0*rho0 + beta*beta);
130: rho2 = sold * alpha + coold * cold * betaold;
131: rho3 = soold * betaold;
133: /* Givens rotation */
135: c = rho0 / rho1;
136: s = beta / rho1;
138: /* Update */
140: VecCopy(WOLD,WOOLD); /* w_oold <- w_old */
141: VecCopy(W,WOLD); /* w_old <- w */
143: VecCopy(U,W); /* w <- u */
144: mrho2 = -rho2;
145: VecAXPY(W,mrho2,WOLD); /* w <- w - rho2 w_old */
146: mrho3 = -rho3;
147: VecAXPY(W,mrho3,WOOLD); /* w <- w - rho3 w_oold */
148: irho1 = 1.0 / rho1;
149: VecScale(W,irho1); /* w <- w / rho1 */
151: ceta = c * eta;
152: VecAXPY(X,ceta,W); /* x <- x + c eta w */
153: eta = -s * eta;
155: VecCopy(V,VOLD);
156: VecCopy(U,UOLD);
157: VecCopy(R,V);
158: VecCopy(Z,U);
159: ibeta = 1.0 / beta;
160: VecScale(V,ibeta); /* v <- r / beta */
161: VecScale(U,ibeta); /* u <- z / beta */
163: np = ksp->rnorm * PetscAbsScalar(s);
165: ksp->rnorm = np;
166: KSPLogResidualHistory(ksp,np);
167: KSPMonitor(ksp,i+1,np);
168: (*ksp->converged)(ksp,i+1,np,&ksp->reason,ksp->cnvP); /* test for convergence */
169: if (ksp->reason) break;
170: i++;
171: } while (i<ksp->max_it);
172: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
173: return(0);
174: }
176: /*MC
177: KSPMINRES - This code implements the MINRES (Minimum Residual) method.
179: Options Database Keys:
180: . see KSPSolve()
182: Level: beginner
184: Notes: The operator and the preconditioner must be symmetric and the preconditioner must
185: be positive definite for this method.
186: Supports only left preconditioning.
188: Reference: Paige & Saunders, 1975.
190: Contributed by: Robert Scheichl: maprs@maths.bath.ac.uk
192: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPCG, KSPCR
193: M*/
196: PETSC_EXTERN PetscErrorCode KSPCreate_MINRES(KSP ksp)
197: {
198: KSP_MINRES *minres;
202: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
203: PetscNewLog(ksp,KSP_MINRES,&minres);
204: minres->haptol = 1.e-18;
205: ksp->data = (void*)minres;
207: /*
208: Sets the functions that are associated with this data structure
209: (in C++ this is the same as defining virtual functions)
210: */
211: ksp->ops->setup = KSPSetUp_MINRES;
212: ksp->ops->solve = KSPSolve_MINRES;
213: ksp->ops->destroy = KSPDestroyDefault;
214: ksp->ops->setfromoptions = 0;
215: ksp->ops->buildsolution = KSPBuildSolutionDefault;
216: ksp->ops->buildresidual = KSPBuildResidualDefault;
217: return(0);
218: }