Actual source code: ibcgs.c
2: #include <petsc/private/kspimpl.h>
3: #include <petsc/private/vecimpl.h>
5: static PetscErrorCode KSPSetUp_IBCGS(KSP ksp)
6: {
7: PetscBool diagonalscale;
9: PCGetDiagonalScale(ksp->pc,&diagonalscale);
11: KSPSetWorkVecs(ksp,9);
12: return 0;
13: }
15: /*
16: The code below "cheats" from PETSc style
17: 1) VecRestoreArray() is called immediately after VecGetArray() and the array values are still accessed; the reason for the immediate
18: restore is that Vec operations are done on some of the vectors during the solve and if we did not restore immediately it would
19: generate two VecGetArray() (the second one inside the Vec operation) calls without a restore between them.
20: 2) The vector operations on done directly on the arrays instead of with VecXXXX() calls
22: For clarity in the code we name single VECTORS with two names, for example, Rn_1 and R, but they actually always
23: the exact same memory. We do this with macro defines so that compiler won't think they are
24: two different variables.
26: */
27: #define Xn_1 Xn
28: #define xn_1 xn
29: #define Rn_1 Rn
30: #define rn_1 rn
31: #define Un_1 Un
32: #define un_1 un
33: #define Vn_1 Vn
34: #define vn_1 vn
35: #define Qn_1 Qn
36: #define qn_1 qn
37: #define Zn_1 Zn
38: #define zn_1 zn
39: static PetscErrorCode KSPSolve_IBCGS(KSP ksp)
40: {
41: PetscInt i,N;
42: PetscReal rnorm = 0.0,rnormin = 0.0;
43: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
44: /* Because of possible instabilities in the algorithm (as indicated by different residual histories for the same problem
45: on the same number of processes with different runs) we support computing the inner products using Intel's 80 bit arithmetic
46: rather than just 64 bit. Thus we copy our double precision values into long doubles (hoping this keeps the 16 extra bits)
47: and tell MPI to do its ALlreduces with MPI_LONG_DOUBLE.
49: Note for developers that does not effect the code. Intel's long double is implemented by storing the 80 bits of extended double
50: precision into a 16 byte space (the rest of the space is ignored) */
51: long double insums[7],outsums[7];
52: #else
53: PetscScalar insums[7],outsums[7];
54: #endif
55: PetscScalar sigman_2, sigman_1, sigman, pin_1, pin, phin_1, phin,tmp1,tmp2;
56: PetscScalar taun_1, taun, rhon, alphan_1, alphan, omegan_1, omegan;
57: const PetscScalar *PETSC_RESTRICT r0, *PETSC_RESTRICT f0, *PETSC_RESTRICT qn, *PETSC_RESTRICT b, *PETSC_RESTRICT un;
58: PetscScalar *PETSC_RESTRICT rn, *PETSC_RESTRICT xn, *PETSC_RESTRICT vn, *PETSC_RESTRICT zn;
59: /* the rest do not have to keep n_1 values */
60: PetscScalar kappan, thetan, etan, gamman, betan, deltan;
61: const PetscScalar *PETSC_RESTRICT tn;
62: PetscScalar *PETSC_RESTRICT sn;
63: Vec R0,Rn,Xn,F0,Vn,Zn,Qn,Tn,Sn,B,Un;
64: Mat A;
68: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
69: /* since 80 bit long doubls do not fill the upper bits, we fill them initially so that
70: valgrind won't detect MPI_Allreduce() with uninitialized data */
71: PetscMemzero(insums,sizeof(insums));
72: PetscMemzero(insums,sizeof(insums));
73: #endif
75: PCGetOperators(ksp->pc,&A,NULL);
76: VecGetLocalSize(ksp->vec_sol,&N);
77: Xn = ksp->vec_sol; VecGetArray(Xn_1,(PetscScalar**)&xn_1)); PetscCall(VecRestoreArray(Xn_1,NULL);
78: B = ksp->vec_rhs; VecGetArrayRead(B,(const PetscScalar**)&b)); PetscCall(VecRestoreArrayRead(B,NULL);
79: R0 = ksp->work[0]; VecGetArrayRead(R0,(const PetscScalar**)&r0)); PetscCall(VecRestoreArrayRead(R0,NULL);
80: Rn = ksp->work[1]; VecGetArray(Rn_1,(PetscScalar**)&rn_1)); PetscCall(VecRestoreArray(Rn_1,NULL);
81: Un = ksp->work[2]; VecGetArrayRead(Un_1,(const PetscScalar**)&un_1)); PetscCall(VecRestoreArrayRead(Un_1,NULL);
82: F0 = ksp->work[3]; VecGetArrayRead(F0,(const PetscScalar**)&f0)); PetscCall(VecRestoreArrayRead(F0,NULL);
83: Vn = ksp->work[4]; VecGetArray(Vn_1,(PetscScalar**)&vn_1)); PetscCall(VecRestoreArray(Vn_1,NULL);
84: Zn = ksp->work[5]; VecGetArray(Zn_1,(PetscScalar**)&zn_1)); PetscCall(VecRestoreArray(Zn_1,NULL);
85: Qn = ksp->work[6]; VecGetArrayRead(Qn_1,(const PetscScalar**)&qn_1)); PetscCall(VecRestoreArrayRead(Qn_1,NULL);
86: Tn = ksp->work[7]; VecGetArrayRead(Tn,(const PetscScalar**)&tn)); PetscCall(VecRestoreArrayRead(Tn,NULL);
87: Sn = ksp->work[8]; VecGetArrayRead(Sn,(const PetscScalar**)&sn)); PetscCall(VecRestoreArrayRead(Sn,NULL);
89: /* r0 = rn_1 = b - A*xn_1; */
90: /* KSP_PCApplyBAorAB(ksp,Xn_1,Rn_1,Tn);
91: VecAYPX(Rn_1,-1.0,B); */
92: KSPInitialResidual(ksp,Xn_1,Tn,Sn,Rn_1,B);
93: if (ksp->normtype != KSP_NORM_NONE) {
94: VecNorm(Rn_1,NORM_2,&rnorm);
95: KSPCheckNorm(ksp,rnorm);
96: }
97: KSPMonitor(ksp,0,rnorm);
98: (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
99: if (ksp->reason) return 0;
101: VecCopy(Rn_1,R0);
103: /* un_1 = A*rn_1; */
104: KSP_PCApplyBAorAB(ksp,Rn_1,Un_1,Tn);
106: /* f0 = A'*rn_1; */
107: if (ksp->pc_side == PC_RIGHT) { /* B' A' */
108: KSP_MatMultTranspose(ksp,A,R0,Tn);
109: KSP_PCApplyTranspose(ksp,Tn,F0);
110: } else if (ksp->pc_side == PC_LEFT) { /* A' B' */
111: KSP_PCApplyTranspose(ksp,R0,Tn);
112: KSP_MatMultTranspose(ksp,A,Tn,F0);
113: }
115: /*qn_1 = vn_1 = zn_1 = 0.0; */
116: VecSet(Qn_1,0.0);
117: VecSet(Vn_1,0.0);
118: VecSet(Zn_1,0.0);
120: sigman_2 = pin_1 = taun_1 = 0.0;
122: /* the paper says phin_1 should be initialized to zero, it is actually R0'R0 */
123: VecDot(R0,R0,&phin_1);
124: KSPCheckDot(ksp,phin_1);
126: /* sigman_1 = rn_1'un_1 */
127: VecDot(R0,Un_1,&sigman_1);
129: alphan_1 = omegan_1 = 1.0;
131: for (ksp->its = 1; ksp->its<ksp->max_it+1; ksp->its++) {
132: rhon = phin_1 - omegan_1*sigman_2 + omegan_1*alphan_1*pin_1;
133: if (ksp->its == 1) deltan = rhon;
134: else deltan = rhon/taun_1;
135: betan = deltan/omegan_1;
136: taun = sigman_1 + betan*taun_1 - deltan*pin_1;
137: if (taun == 0.0) {
139: else {
140: ksp->reason = KSP_DIVERGED_NANORINF;
141: return 0;
142: }
143: }
144: alphan = rhon/taun;
145: PetscLogFlops(15.0);
147: /*
148: zn = alphan*rn_1 + (alphan/alphan_1)betan*zn_1 - alphan*deltan*vn_1
149: vn = un_1 + betan*vn_1 - deltan*qn_1
150: sn = rn_1 - alphan*vn
152: The algorithm in the paper is missing the alphan/alphan_1 term in the zn update
153: */
154: PetscLogEventBegin(VEC_Ops,0,0,0,0);
155: tmp1 = (alphan/alphan_1)*betan;
156: tmp2 = alphan*deltan;
157: for (i=0; i<N; i++) {
158: zn[i] = alphan*rn_1[i] + tmp1*zn_1[i] - tmp2*vn_1[i];
159: vn[i] = un_1[i] + betan*vn_1[i] - deltan*qn_1[i];
160: sn[i] = rn_1[i] - alphan*vn[i];
161: }
162: PetscLogFlops(3.0+11.0*N);
163: PetscLogEventEnd(VEC_Ops,0,0,0,0);
165: /*
166: qn = A*vn
167: */
168: KSP_PCApplyBAorAB(ksp,Vn,Qn,Tn);
170: /*
171: tn = un_1 - alphan*qn
172: */
173: VecWAXPY(Tn,-alphan,Qn,Un_1);
175: /*
176: phin = r0'sn
177: pin = r0'qn
178: gamman = f0'sn
179: etan = f0'tn
180: thetan = sn'tn
181: kappan = tn'tn
182: */
183: PetscLogEventBegin(VEC_ReduceArithmetic,0,0,0,0);
184: phin = pin = gamman = etan = thetan = kappan = 0.0;
185: for (i=0; i<N; i++) {
186: phin += r0[i]*sn[i];
187: pin += r0[i]*qn[i];
188: gamman += f0[i]*sn[i];
189: etan += f0[i]*tn[i];
190: thetan += sn[i]*tn[i];
191: kappan += tn[i]*tn[i];
192: }
193: PetscLogFlops(12.0*N);
194: PetscLogEventEnd(VEC_ReduceArithmetic,0,0,0,0);
196: insums[0] = phin;
197: insums[1] = pin;
198: insums[2] = gamman;
199: insums[3] = etan;
200: insums[4] = thetan;
201: insums[5] = kappan;
202: insums[6] = rnormin;
204: PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
205: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
206: if (ksp->lagnorm && ksp->its > 1) {
207: MPIU_Allreduce(insums,outsums,7,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
208: } else {
209: MPIU_Allreduce(insums,outsums,6,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
210: }
211: #else
212: if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) {
213: MPIU_Allreduce(insums,outsums,7,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
214: } else {
215: MPIU_Allreduce(insums,outsums,6,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
216: }
217: #endif
218: PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
219: phin = outsums[0];
220: pin = outsums[1];
221: gamman = outsums[2];
222: etan = outsums[3];
223: thetan = outsums[4];
224: kappan = outsums[5];
225: if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) rnorm = PetscSqrtReal(PetscRealPart(outsums[6]));
227: if (kappan == 0.0) {
229: else {
230: ksp->reason = KSP_DIVERGED_NANORINF;
231: return 0;
232: }
233: }
234: if (thetan == 0.0) {
236: else {
237: ksp->reason = KSP_DIVERGED_NANORINF;
238: return 0;
239: }
240: }
241: omegan = thetan/kappan;
242: sigman = gamman - omegan*etan;
244: /*
245: rn = sn - omegan*tn
246: xn = xn_1 + zn + omegan*sn
247: */
248: PetscLogEventBegin(VEC_Ops,0,0,0,0);
249: rnormin = 0.0;
250: for (i=0; i<N; i++) {
251: rn[i] = sn[i] - omegan*tn[i];
252: rnormin += PetscRealPart(PetscConj(rn[i])*rn[i]);
253: xn[i] += zn[i] + omegan*sn[i];
254: }
255: PetscObjectStateIncrease((PetscObject)Xn);
256: PetscLogFlops(7.0*N);
257: PetscLogEventEnd(VEC_Ops,0,0,0,0);
259: if (!ksp->lagnorm && ksp->chknorm < ksp->its && ksp->normtype != KSP_NORM_NONE) {
260: PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
261: MPIU_Allreduce(&rnormin,&rnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
262: PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
263: rnorm = PetscSqrtReal(rnorm);
264: }
266: /* Test for convergence */
267: KSPMonitor(ksp,ksp->its,rnorm);
268: (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);
269: if (ksp->reason) {
270: KSPUnwindPreconditioner(ksp,Xn,Tn);
271: return 0;
272: }
274: /* un = A*rn */
275: KSP_PCApplyBAorAB(ksp,Rn,Un,Tn);
277: /* Update n-1 locations with n locations */
278: sigman_2 = sigman_1;
279: sigman_1 = sigman;
280: pin_1 = pin;
281: phin_1 = phin;
282: alphan_1 = alphan;
283: taun_1 = taun;
284: omegan_1 = omegan;
285: }
286: if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
287: KSPUnwindPreconditioner(ksp,Xn,Tn);
288: return 0;
289: }
291: /*MC
292: KSPIBCGS - Implements the IBiCGStab (Improved Stabilized version of BiConjugate Gradient) method
293: in an alternative form to have only a single global reduction operation instead of the usual 3 (or 4)
295: Options Database Keys:
296: see KSPSolve()
298: Level: beginner
300: Notes:
301: Supports left and right preconditioning
303: See KSPBCGSL for additional stabilization
305: Unlike the Bi-CG-stab algorithm, this requires one multiplication be the transpose of the operator
306: before the iteration starts.
308: The paper has two errors in the algorithm presented, they are fixed in the code in KSPSolve_IBCGS()
310: For maximum reduction in the number of global reduction operations, this solver should be used with
311: KSPSetLagNorm().
313: This is not supported for complex numbers.
315: Reference: The Improved BiCGStab Method for Large and Sparse Unsymmetric Linear Systems on Parallel Distributed Memory
316: Architectures. L. T. Yang and R. Brent, Proceedings of the Fifth International Conference on Algorithms and
317: Architectures for Parallel Processing, 2002, IEEE.
319: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBICG, KSPBCGSL, KSPIBCGS, KSPSetLagNorm()
320: M*/
322: PETSC_EXTERN PetscErrorCode KSPCreate_IBCGS(KSP ksp)
323: {
325: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
326: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
327: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
329: ksp->ops->setup = KSPSetUp_IBCGS;
330: ksp->ops->solve = KSPSolve_IBCGS;
331: ksp->ops->destroy = KSPDestroyDefault;
332: ksp->ops->buildsolution = KSPBuildSolutionDefault;
333: ksp->ops->buildresidual = KSPBuildResidualDefault;
334: ksp->ops->setfromoptions = NULL;
335: ksp->ops->view = NULL;
336: #if defined(PETSC_USE_COMPLEX)
337: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"This is not supported for complex numbers");
338: #else
339: return 0;
340: #endif
341: }