Actual source code: ibcgs.c
petsc-3.13.6 2020-09-29
2: #include <petsc/private/kspimpl.h>
3: #include <petsc/private/vecimpl.h>
5: static PetscErrorCode KSPSetUp_IBCGS(KSP ksp)
6: {
8: PetscBool diagonalscale;
11: PCGetDiagonalScale(ksp->pc,&diagonalscale);
12: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
13: KSPSetWorkVecs(ksp,9);
14: return(0);
15: }
17: /*
18: The code below "cheats" from PETSc style
19: 1) VecRestoreArray() is called immediately after VecGetArray() and the array values are still accessed; the reason for the immediate
20: restore is that Vec operations are done on some of the vectors during the solve and if we did not restore immediately it would
21: generate two VecGetArray() (the second one inside the Vec operation) calls without a restore between them.
22: 2) The vector operations on done directly on the arrays instead of with VecXXXX() calls
24: For clarity in the code we name single VECTORS with two names, for example, Rn_1 and R, but they actually always
25: the exact same memory. We do this with macro defines so that compiler won't think they are
26: two different variables.
28: */
29: #define Xn_1 Xn
30: #define xn_1 xn
31: #define Rn_1 Rn
32: #define rn_1 rn
33: #define Un_1 Un
34: #define un_1 un
35: #define Vn_1 Vn
36: #define vn_1 vn
37: #define Qn_1 Qn
38: #define qn_1 qn
39: #define Zn_1 Zn
40: #define zn_1 zn
41: static PetscErrorCode KSPSolve_IBCGS(KSP ksp)
42: {
44: PetscInt i,N;
45: PetscReal rnorm,rnormin = 0.0;
46: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
47: /* Because of possible instabilities in the algorithm (as indicated by different residual histories for the same problem
48: on the same number of processes with different runs) we support computing the inner products using Intel's 80 bit arithematic
49: rather than just 64 bit. Thus we copy our double precision values into long doubles (hoping this keeps the 16 extra bits)
50: and tell MPI to do its ALlreduces with MPI_LONG_DOUBLE.
52: Note for developers that does not effect the code. Intel's long double is implemented by storing the 80 bits of extended double
53: precision into a 16 byte space (the rest of the space is ignored) */
54: long double insums[7],outsums[7];
55: #else
56: PetscScalar insums[7],outsums[7];
57: #endif
58: PetscScalar sigman_2, sigman_1, sigman, pin_1, pin, phin_1, phin,tmp1,tmp2;
59: PetscScalar taun_1, taun, rhon, alphan_1, alphan, omegan_1, omegan;
60: const PetscScalar *PETSC_RESTRICT r0, *PETSC_RESTRICT f0, *PETSC_RESTRICT qn, *PETSC_RESTRICT b, *PETSC_RESTRICT un;
61: PetscScalar *PETSC_RESTRICT rn, *PETSC_RESTRICT xn, *PETSC_RESTRICT vn, *PETSC_RESTRICT zn;
62: /* the rest do not have to keep n_1 values */
63: PetscScalar kappan, thetan, etan, gamman, betan, deltan;
64: const PetscScalar *PETSC_RESTRICT tn;
65: PetscScalar *PETSC_RESTRICT sn;
66: Vec R0,Rn,Xn,F0,Vn,Zn,Qn,Tn,Sn,B,Un;
67: Mat A;
70: if (!ksp->vec_rhs->petscnative) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Only coded for PETSc vectors");
72: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
73: /* since 80 bit long doubls do not fill the upper bits, we fill them initially so that
74: valgrind won't detect MPI_Allreduce() with uninitialized data */
75: PetscMemzero(insums,sizeof(insums));
76: PetscMemzero(insums,sizeof(insums));
77: #endif
79: PCGetOperators(ksp->pc,&A,NULL);
80: VecGetLocalSize(ksp->vec_sol,&N);
81: Xn = ksp->vec_sol; VecGetArray(Xn_1,(PetscScalar**)&xn_1); VecRestoreArray(Xn_1,NULL);
82: B = ksp->vec_rhs; VecGetArrayRead(B,(const PetscScalar**)&b); VecRestoreArrayRead(B,NULL);
83: R0 = ksp->work[0]; VecGetArrayRead(R0,(const PetscScalar**)&r0); VecRestoreArrayRead(R0,NULL);
84: Rn = ksp->work[1]; VecGetArray(Rn_1,(PetscScalar**)&rn_1); VecRestoreArray(Rn_1,NULL);
85: Un = ksp->work[2]; VecGetArrayRead(Un_1,(const PetscScalar**)&un_1); VecRestoreArrayRead(Un_1,NULL);
86: F0 = ksp->work[3]; VecGetArrayRead(F0,(const PetscScalar**)&f0); VecRestoreArrayRead(F0,NULL);
87: Vn = ksp->work[4]; VecGetArray(Vn_1,(PetscScalar**)&vn_1); VecRestoreArray(Vn_1,NULL);
88: Zn = ksp->work[5]; VecGetArray(Zn_1,(PetscScalar**)&zn_1); VecRestoreArray(Zn_1,NULL);
89: Qn = ksp->work[6]; VecGetArrayRead(Qn_1,(const PetscScalar**)&qn_1); VecRestoreArrayRead(Qn_1,NULL);
90: Tn = ksp->work[7]; VecGetArrayRead(Tn,(const PetscScalar**)&tn); VecRestoreArrayRead(Tn,NULL);
91: Sn = ksp->work[8]; VecGetArrayRead(Sn,(const PetscScalar**)&sn); VecRestoreArrayRead(Sn,NULL);
93: /* r0 = rn_1 = b - A*xn_1; */
94: /* KSP_PCApplyBAorAB(ksp,Xn_1,Rn_1,Tn);
95: VecAYPX(Rn_1,-1.0,B); */
96: KSPInitialResidual(ksp,Xn_1,Tn,Sn,Rn_1,B);
98: VecNorm(Rn_1,NORM_2,&rnorm);
99: KSPCheckNorm(ksp,rnorm);
100: KSPMonitor(ksp,0,rnorm);
101: (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
102: if (ksp->reason) return(0);
104: VecCopy(Rn_1,R0);
106: /* un_1 = A*rn_1; */
107: KSP_PCApplyBAorAB(ksp,Rn_1,Un_1,Tn);
109: /* f0 = A'*rn_1; */
110: if (ksp->pc_side == PC_RIGHT) { /* B' A' */
111: KSP_MatMultTranspose(ksp,A,R0,Tn);
112: KSP_PCApplyTranspose(ksp,Tn,F0);
113: } else if (ksp->pc_side == PC_LEFT) { /* A' B' */
114: KSP_PCApplyTranspose(ksp,R0,Tn);
115: KSP_MatMultTranspose(ksp,A,Tn,F0);
116: }
118: /*qn_1 = vn_1 = zn_1 = 0.0; */
119: VecSet(Qn_1,0.0);
120: VecSet(Vn_1,0.0);
121: VecSet(Zn_1,0.0);
123: sigman_2 = pin_1 = taun_1 = 0.0;
125: /* the paper says phin_1 should be initialized to zero, it is actually R0'R0 */
126: VecDot(R0,R0,&phin_1);
127: KSPCheckDot(ksp,phin_1);
129: /* sigman_1 = rn_1'un_1 */
130: VecDot(R0,Un_1,&sigman_1);
132: alphan_1 = omegan_1 = 1.0;
134: for (ksp->its = 1; ksp->its<ksp->max_it+1; ksp->its++) {
135: rhon = phin_1 - omegan_1*sigman_2 + omegan_1*alphan_1*pin_1;
136: if (ksp->its == 1) deltan = rhon;
137: else deltan = rhon/taun_1;
138: betan = deltan/omegan_1;
139: taun = sigman_1 + betan*taun_1 - deltan*pin_1;
140: if (taun == 0.0) {
141: if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to taun is zero, iteration %D",ksp->its);
142: else {
143: ksp->reason = KSP_DIVERGED_NANORINF;
144: return(0);
145: }
146: }
147: alphan = rhon/taun;
148: PetscLogFlops(15.0);
150: /*
151: zn = alphan*rn_1 + (alphan/alphan_1)betan*zn_1 - alphan*deltan*vn_1
152: vn = un_1 + betan*vn_1 - deltan*qn_1
153: sn = rn_1 - alphan*vn
155: The algorithm in the paper is missing the alphan/alphan_1 term in the zn update
156: */
157: PetscLogEventBegin(VEC_Ops,0,0,0,0);
158: tmp1 = (alphan/alphan_1)*betan;
159: tmp2 = alphan*deltan;
160: for (i=0; i<N; i++) {
161: zn[i] = alphan*rn_1[i] + tmp1*zn_1[i] - tmp2*vn_1[i];
162: vn[i] = un_1[i] + betan*vn_1[i] - deltan*qn_1[i];
163: sn[i] = rn_1[i] - alphan*vn[i];
164: }
165: PetscLogFlops(3.0+11.0*N);
166: PetscLogEventEnd(VEC_Ops,0,0,0,0);
168: /*
169: qn = A*vn
170: */
171: KSP_PCApplyBAorAB(ksp,Vn,Qn,Tn);
173: /*
174: tn = un_1 - alphan*qn
175: */
176: VecWAXPY(Tn,-alphan,Qn,Un_1);
179: /*
180: phin = r0'sn
181: pin = r0'qn
182: gamman = f0'sn
183: etan = f0'tn
184: thetan = sn'tn
185: kappan = tn'tn
186: */
187: PetscLogEventBegin(VEC_ReduceArithmetic,0,0,0,0);
188: phin = pin = gamman = etan = thetan = kappan = 0.0;
189: for (i=0; i<N; i++) {
190: phin += r0[i]*sn[i];
191: pin += r0[i]*qn[i];
192: gamman += f0[i]*sn[i];
193: etan += f0[i]*tn[i];
194: thetan += sn[i]*tn[i];
195: kappan += tn[i]*tn[i];
196: }
197: PetscLogFlops(12.0*N);
198: PetscLogEventEnd(VEC_ReduceArithmetic,0,0,0,0);
200: insums[0] = phin;
201: insums[1] = pin;
202: insums[2] = gamman;
203: insums[3] = etan;
204: insums[4] = thetan;
205: insums[5] = kappan;
206: insums[6] = rnormin;
208: PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
209: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
210: if (ksp->lagnorm && ksp->its > 1) {
211: MPIU_Allreduce(insums,outsums,7,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
212: } else {
213: MPIU_Allreduce(insums,outsums,6,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
214: }
215: #else
216: if (ksp->lagnorm && ksp->its > 1) {
217: MPIU_Allreduce(insums,outsums,7,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
218: } else {
219: MPIU_Allreduce(insums,outsums,6,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
220: }
221: #endif
222: PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
223: phin = outsums[0];
224: pin = outsums[1];
225: gamman = outsums[2];
226: etan = outsums[3];
227: thetan = outsums[4];
228: kappan = outsums[5];
229: if (ksp->lagnorm && ksp->its > 1) rnorm = PetscSqrtReal(PetscRealPart(outsums[6]));
231: if (kappan == 0.0) {
232: if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to kappan is zero, iteration %D",ksp->its);
233: else {
234: ksp->reason = KSP_DIVERGED_NANORINF;
235: return(0);
236: }
237: }
238: if (thetan == 0.0) {
239: if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to thetan is zero, iteration %D",ksp->its);
240: else {
241: ksp->reason = KSP_DIVERGED_NANORINF;
242: return(0);
243: }
244: }
245: omegan = thetan/kappan;
246: sigman = gamman - omegan*etan;
248: /*
249: rn = sn - omegan*tn
250: xn = xn_1 + zn + omegan*sn
251: */
252: PetscLogEventBegin(VEC_Ops,0,0,0,0);
253: rnormin = 0.0;
254: for (i=0; i<N; i++) {
255: rn[i] = sn[i] - omegan*tn[i];
256: rnormin += PetscRealPart(PetscConj(rn[i])*rn[i]);
257: xn[i] += zn[i] + omegan*sn[i];
258: }
259: PetscObjectStateIncrease((PetscObject)Xn);
260: PetscLogFlops(7.0*N);
261: PetscLogEventEnd(VEC_Ops,0,0,0,0);
263: if (!ksp->lagnorm && ksp->chknorm < ksp->its) {
264: PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
265: MPIU_Allreduce(&rnormin,&rnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
266: PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
267: rnorm = PetscSqrtReal(rnorm);
268: }
270: /* Test for convergence */
271: KSPMonitor(ksp,ksp->its,rnorm);
272: (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);
273: if (ksp->reason) break;
275: /* un = A*rn */
276: KSP_PCApplyBAorAB(ksp,Rn,Un,Tn);
278: /* Update n-1 locations with n locations */
279: sigman_2 = sigman_1;
280: sigman_1 = sigman;
281: pin_1 = pin;
282: phin_1 = phin;
283: alphan_1 = alphan;
284: taun_1 = taun;
285: omegan_1 = omegan;
286: }
287: if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
288: KSPUnwindPreconditioner(ksp,Xn,Tn);
289: return(0);
290: }
293: /*MC
294: KSPIBCGS - Implements the IBiCGStab (Improved Stabilized version of BiConjugate Gradient) method
295: in an alternative form to have only a single global reduction operation instead of the usual 3 (or 4)
297: Options Database Keys:
298: . see KSPSolve()
300: Level: beginner
302: Notes:
303: Supports left and right preconditioning
305: See KSPBCGSL for additional stabilization
307: Unlike the Bi-CG-stab algorithm, this requires one multiplication be the transpose of the operator
308: before the iteration starts.
310: The paper has two errors in the algorithm presented, they are fixed in the code in KSPSolve_IBCGS()
312: For maximum reduction in the number of global reduction operations, this solver should be used with
313: KSPSetLagNorm().
315: This is not supported for complex numbers.
317: Reference: The Improved BiCGStab Method for Large and Sparse Unsymmetric Linear Systems on Parallel Distributed Memory
318: Architectures. L. T. Yang and R. Brent, Proceedings of the Fifth International Conference on Algorithms and
319: Architectures for Parallel Processing, 2002, IEEE.
321: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBICG, KSPBCGSL, KSPIBCGS, KSPSetLagNorm()
322: M*/
324: PETSC_EXTERN PetscErrorCode KSPCreate_IBCGS(KSP ksp)
325: {
329: ksp->data = (void*)0;
331: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
332: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
334: ksp->ops->setup = KSPSetUp_IBCGS;
335: ksp->ops->solve = KSPSolve_IBCGS;
336: ksp->ops->destroy = KSPDestroyDefault;
337: ksp->ops->buildsolution = KSPBuildSolutionDefault;
338: ksp->ops->buildresidual = KSPBuildResidualDefault;
339: ksp->ops->setfromoptions = 0;
340: ksp->ops->view = 0;
341: #if defined(PETSC_USE_COMPLEX)
342: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"This is not supported for complex numbers");
343: #endif
344: return(0);
345: }