Actual source code: ibcgs.c
1: #include <petsc/private/kspimpl.h>
2: #include <petsc/private/vecimpl.h>
4: static PetscErrorCode KSPSetUp_IBCGS(KSP ksp)
5: {
6: PetscBool diagonalscale;
8: PetscFunctionBegin;
9: PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
10: PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
11: PetscCall(KSPSetWorkVecs(ksp, 9));
12: PetscFunctionReturn(PETSC_SUCCESS);
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;
66: PetscFunctionBegin;
67: PetscCheck(ksp->vec_rhs->petscnative, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Only coded for PETSc vectors");
69: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
70: /* since 80 bit long doubls do not fill the upper bits, we fill them initially so that
71: valgrind won't detect MPI_Allreduce() with uninitialized data */
72: PetscCall(PetscMemzero(insums, sizeof(insums)));
73: PetscCall(PetscMemzero(insums, sizeof(insums)));
74: #endif
76: PetscCall(PCGetOperators(ksp->pc, &A, NULL));
77: PetscCall(VecGetLocalSize(ksp->vec_sol, &N));
78: Xn = ksp->vec_sol;
79: PetscCall(VecGetArray(Xn_1, (PetscScalar **)&xn_1));
80: PetscCall(VecRestoreArray(Xn_1, NULL));
81: B = ksp->vec_rhs;
82: PetscCall(VecGetArrayRead(B, (const PetscScalar **)&b));
83: PetscCall(VecRestoreArrayRead(B, NULL));
84: R0 = ksp->work[0];
85: PetscCall(VecGetArrayRead(R0, (const PetscScalar **)&r0));
86: PetscCall(VecRestoreArrayRead(R0, NULL));
87: Rn = ksp->work[1];
88: PetscCall(VecGetArray(Rn_1, (PetscScalar **)&rn_1));
89: PetscCall(VecRestoreArray(Rn_1, NULL));
90: Un = ksp->work[2];
91: PetscCall(VecGetArrayRead(Un_1, (const PetscScalar **)&un_1));
92: PetscCall(VecRestoreArrayRead(Un_1, NULL));
93: F0 = ksp->work[3];
94: PetscCall(VecGetArrayRead(F0, (const PetscScalar **)&f0));
95: PetscCall(VecRestoreArrayRead(F0, NULL));
96: Vn = ksp->work[4];
97: PetscCall(VecGetArray(Vn_1, (PetscScalar **)&vn_1));
98: PetscCall(VecRestoreArray(Vn_1, NULL));
99: Zn = ksp->work[5];
100: PetscCall(VecGetArray(Zn_1, (PetscScalar **)&zn_1));
101: PetscCall(VecRestoreArray(Zn_1, NULL));
102: Qn = ksp->work[6];
103: PetscCall(VecGetArrayRead(Qn_1, (const PetscScalar **)&qn_1));
104: PetscCall(VecRestoreArrayRead(Qn_1, NULL));
105: Tn = ksp->work[7];
106: PetscCall(VecGetArrayRead(Tn, (const PetscScalar **)&tn));
107: PetscCall(VecRestoreArrayRead(Tn, NULL));
108: Sn = ksp->work[8];
109: PetscCall(VecGetArrayRead(Sn, (const PetscScalar **)&sn));
110: PetscCall(VecRestoreArrayRead(Sn, NULL));
112: /* r0 = rn_1 = b - A*xn_1; */
113: /* PetscCall(KSP_PCApplyBAorAB(ksp,Xn_1,Rn_1,Tn));
114: PetscCall(VecAYPX(Rn_1,-1.0,B)); */
115: PetscCall(KSPInitialResidual(ksp, Xn_1, Tn, Sn, Rn_1, B));
116: if (ksp->normtype != KSP_NORM_NONE) {
117: PetscCall(VecNorm(Rn_1, NORM_2, &rnorm));
118: KSPCheckNorm(ksp, rnorm);
119: }
120: PetscCall(KSPMonitor(ksp, 0, rnorm));
121: PetscCall((*ksp->converged)(ksp, 0, rnorm, &ksp->reason, ksp->cnvP));
122: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
124: PetscCall(VecCopy(Rn_1, R0));
126: /* un_1 = A*rn_1; */
127: PetscCall(KSP_PCApplyBAorAB(ksp, Rn_1, Un_1, Tn));
129: /* f0 = A'*rn_1; */
130: if (ksp->pc_side == PC_RIGHT) { /* B' A' */
131: PetscCall(KSP_MatMultTranspose(ksp, A, R0, Tn));
132: PetscCall(KSP_PCApplyTranspose(ksp, Tn, F0));
133: } else if (ksp->pc_side == PC_LEFT) { /* A' B' */
134: PetscCall(KSP_PCApplyTranspose(ksp, R0, Tn));
135: PetscCall(KSP_MatMultTranspose(ksp, A, Tn, F0));
136: }
138: /*qn_1 = vn_1 = zn_1 = 0.0; */
139: PetscCall(VecSet(Qn_1, 0.0));
140: PetscCall(VecSet(Vn_1, 0.0));
141: PetscCall(VecSet(Zn_1, 0.0));
143: sigman_2 = pin_1 = taun_1 = 0.0;
145: /* the paper says phin_1 should be initialized to zero, it is actually R0'R0 */
146: PetscCall(VecDot(R0, R0, &phin_1));
147: KSPCheckDot(ksp, phin_1);
149: /* sigman_1 = rn_1'un_1 */
150: PetscCall(VecDot(R0, Un_1, &sigman_1));
152: alphan_1 = omegan_1 = 1.0;
154: for (ksp->its = 1; ksp->its < ksp->max_it + 1; ksp->its++) {
155: rhon = phin_1 - omegan_1 * sigman_2 + omegan_1 * alphan_1 * pin_1;
156: if (ksp->its == 1) deltan = rhon;
157: else deltan = rhon / taun_1;
158: betan = deltan / omegan_1;
159: taun = sigman_1 + betan * taun_1 - deltan * pin_1;
160: if (taun == 0.0) {
161: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to taun is zero, iteration %" PetscInt_FMT, ksp->its);
162: ksp->reason = KSP_DIVERGED_NANORINF;
163: PetscFunctionReturn(PETSC_SUCCESS);
164: }
165: alphan = rhon / taun;
166: PetscCall(PetscLogFlops(15.0));
168: /*
169: zn = alphan*rn_1 + (alphan/alphan_1)betan*zn_1 - alphan*deltan*vn_1
170: vn = un_1 + betan*vn_1 - deltan*qn_1
171: sn = rn_1 - alphan*vn
173: The algorithm in the paper is missing the alphan/alphan_1 term in the zn update
174: */
175: PetscCall(PetscLogEventBegin(VEC_Ops, 0, 0, 0, 0));
176: tmp1 = (alphan / alphan_1) * betan;
177: tmp2 = alphan * deltan;
178: for (i = 0; i < N; i++) {
179: zn[i] = alphan * rn_1[i] + tmp1 * zn_1[i] - tmp2 * vn_1[i];
180: vn[i] = un_1[i] + betan * vn_1[i] - deltan * qn_1[i];
181: sn[i] = rn_1[i] - alphan * vn[i];
182: }
183: PetscCall(PetscLogFlops(3.0 + 11.0 * N));
184: PetscCall(PetscLogEventEnd(VEC_Ops, 0, 0, 0, 0));
186: /*
187: qn = A*vn
188: */
189: PetscCall(KSP_PCApplyBAorAB(ksp, Vn, Qn, Tn));
191: /*
192: tn = un_1 - alphan*qn
193: */
194: PetscCall(VecWAXPY(Tn, -alphan, Qn, Un_1));
196: /*
197: phin = r0'sn
198: pin = r0'qn
199: gamman = f0'sn
200: etan = f0'tn
201: thetan = sn'tn
202: kappan = tn'tn
203: */
204: PetscCall(PetscLogEventBegin(VEC_ReduceArithmetic, 0, 0, 0, 0));
205: phin = pin = gamman = etan = thetan = kappan = 0.0;
206: for (i = 0; i < N; i++) {
207: phin += r0[i] * sn[i];
208: pin += r0[i] * qn[i];
209: gamman += f0[i] * sn[i];
210: etan += f0[i] * tn[i];
211: thetan += sn[i] * tn[i];
212: kappan += tn[i] * tn[i];
213: }
214: PetscCall(PetscLogFlops(12.0 * N));
215: PetscCall(PetscLogEventEnd(VEC_ReduceArithmetic, 0, 0, 0, 0));
217: insums[0] = phin;
218: insums[1] = pin;
219: insums[2] = gamman;
220: insums[3] = etan;
221: insums[4] = thetan;
222: insums[5] = kappan;
223: insums[6] = rnormin;
225: PetscCall(PetscLogEventBegin(VEC_ReduceCommunication, 0, 0, 0, 0));
226: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
227: if (ksp->lagnorm && ksp->its > 1) {
228: PetscCallMPI(MPIU_Allreduce(insums, outsums, 7, MPI_LONG_DOUBLE, MPI_SUM, PetscObjectComm((PetscObject)ksp)));
229: } else {
230: PetscCallMPI(MPIU_Allreduce(insums, outsums, 6, MPI_LONG_DOUBLE, MPI_SUM, PetscObjectComm((PetscObject)ksp)));
231: }
232: #else
233: if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) {
234: PetscCallMPI(MPIU_Allreduce(insums, outsums, 7, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)ksp)));
235: } else {
236: PetscCallMPI(MPIU_Allreduce(insums, outsums, 6, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)ksp)));
237: }
238: #endif
239: PetscCall(PetscLogEventEnd(VEC_ReduceCommunication, 0, 0, 0, 0));
240: phin = outsums[0];
241: pin = outsums[1];
242: gamman = outsums[2];
243: etan = outsums[3];
244: thetan = outsums[4];
245: kappan = outsums[5];
246: if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) rnorm = PetscSqrtReal(PetscRealPart(outsums[6]));
248: if (kappan == 0.0) {
249: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to kappan is zero, iteration %" PetscInt_FMT, ksp->its);
250: ksp->reason = KSP_DIVERGED_NANORINF;
251: PetscFunctionReturn(PETSC_SUCCESS);
252: }
253: if (thetan == 0.0) {
254: PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has not converged due to thetan is zero, iteration %" PetscInt_FMT, ksp->its);
255: ksp->reason = KSP_DIVERGED_NANORINF;
256: PetscFunctionReturn(PETSC_SUCCESS);
257: }
258: omegan = thetan / kappan;
259: sigman = gamman - omegan * etan;
261: /*
262: rn = sn - omegan*tn
263: xn = xn_1 + zn + omegan*sn
264: */
265: PetscCall(PetscLogEventBegin(VEC_Ops, 0, 0, 0, 0));
266: rnormin = 0.0;
267: for (i = 0; i < N; i++) {
268: rn[i] = sn[i] - omegan * tn[i];
269: rnormin += PetscRealPart(PetscConj(rn[i]) * rn[i]);
270: xn[i] += zn[i] + omegan * sn[i];
271: }
272: PetscCall(PetscObjectStateIncrease((PetscObject)Xn));
273: PetscCall(PetscLogFlops(7.0 * N));
274: PetscCall(PetscLogEventEnd(VEC_Ops, 0, 0, 0, 0));
276: if (!ksp->lagnorm && ksp->chknorm < ksp->its && ksp->normtype != KSP_NORM_NONE) {
277: PetscCall(PetscLogEventBegin(VEC_ReduceCommunication, 0, 0, 0, 0));
278: PetscCallMPI(MPIU_Allreduce(&rnormin, &rnorm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)ksp)));
279: PetscCall(PetscLogEventEnd(VEC_ReduceCommunication, 0, 0, 0, 0));
280: rnorm = PetscSqrtReal(rnorm);
281: }
283: /* Test for convergence */
284: PetscCall(KSPMonitor(ksp, ksp->its, rnorm));
285: PetscCall((*ksp->converged)(ksp, ksp->its, rnorm, &ksp->reason, ksp->cnvP));
286: if (ksp->reason) {
287: PetscCall(KSPUnwindPreconditioner(ksp, Xn, Tn));
288: PetscFunctionReturn(PETSC_SUCCESS);
289: }
291: /* un = A*rn */
292: PetscCall(KSP_PCApplyBAorAB(ksp, Rn, Un, Tn));
294: /* Update n-1 locations with n locations */
295: sigman_2 = sigman_1;
296: sigman_1 = sigman;
297: pin_1 = pin;
298: phin_1 = phin;
299: alphan_1 = alphan;
300: taun_1 = taun;
301: omegan_1 = omegan;
302: }
303: if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
304: PetscCall(KSPUnwindPreconditioner(ksp, Xn, Tn));
305: PetscFunctionReturn(PETSC_SUCCESS);
306: }
308: /*MC
309: KSPIBCGS - Implements the IBiCGStab (Improved Stabilized version of BiConjugate Gradient) method {cite}`yang:brent:2002`
310: in an alternative form to have only a single global reduction operation instead of the usual 3 (or 4)
312: Level: beginner
314: Notes:
315: Supports left and right preconditioning
317: See `KSPBCGSL` for additional stabilization
319: Unlike the Bi-CG-stab algorithm, this requires one multiplication be the transpose of the operator
320: before the iteration starts.
322: The paper has two errors in the algorithm presented, they are fixed in the code in `KSPSolve_IBCGS()`
324: For maximum reduction in the number of global reduction operations, this solver should be used with
325: `KSPSetLagNorm()`.
327: This is not supported for complex numbers.
329: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBICG`, `KSPBCGSL`, `KSPIBCGS`, `KSPSetLagNorm()`
330: M*/
332: PETSC_EXTERN PetscErrorCode KSPCreate_IBCGS(KSP ksp)
333: {
334: PetscFunctionBegin;
335: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
336: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
337: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
339: ksp->ops->setup = KSPSetUp_IBCGS;
340: ksp->ops->solve = KSPSolve_IBCGS;
341: ksp->ops->destroy = KSPDestroyDefault;
342: ksp->ops->buildsolution = KSPBuildSolutionDefault;
343: ksp->ops->buildresidual = KSPBuildResidualDefault;
344: ksp->ops->setfromoptions = NULL;
345: ksp->ops->view = NULL;
346: #if defined(PETSC_USE_COMPLEX)
347: SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "This is not supported for complex numbers");
348: #else
349: PetscFunctionReturn(PETSC_SUCCESS);
350: #endif
351: }