Actual source code: tsirm.c
1: #include <petsc/private/kspimpl.h>
3: typedef struct {
4: PetscReal tol_ls;
5: PetscInt size_ls, maxiter_ls, cgls, size, Istart, Iend;
6: Mat A, S;
7: Vec Alpha, r;
8: } KSP_TSIRM;
10: static PetscErrorCode KSPSetUp_TSIRM(KSP ksp)
11: {
12: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
14: PetscFunctionBegin;
15: /* Initialization */
16: #if defined(PETSC_USE_REAL_SINGLE)
17: tsirm->tol_ls = 1e-25;
18: #else
19: tsirm->tol_ls = 1e-50;
20: #endif
21: tsirm->size_ls = 12;
22: tsirm->maxiter_ls = 15;
23: tsirm->cgls = 0;
25: /* Matrix of the system */
26: PetscCall(KSPGetOperators(ksp, &tsirm->A, NULL)); /* Matrix of the system */
27: PetscCall(MatGetSize(tsirm->A, &tsirm->size, NULL)); /* Size of the system */
28: PetscCall(MatGetOwnershipRange(tsirm->A, &tsirm->Istart, &tsirm->Iend));
30: /* Matrix S of residuals */
31: PetscCall(MatCreate(PETSC_COMM_WORLD, &tsirm->S));
32: PetscCall(MatSetSizes(tsirm->S, tsirm->Iend - tsirm->Istart, PETSC_DECIDE, tsirm->size, tsirm->size_ls));
33: PetscCall(MatSetType(tsirm->S, MATDENSE));
34: PetscCall(MatSetUp(tsirm->S));
36: /* Residual and vector Alpha computed in the minimization step */
37: PetscCall(MatCreateVecs(tsirm->S, &tsirm->Alpha, &tsirm->r));
38: PetscFunctionReturn(PETSC_SUCCESS);
39: }
41: static PetscErrorCode KSPSolve_TSIRM(KSP ksp)
42: {
43: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
44: KSP sub_ksp;
45: PC pc;
46: Mat AS = NULL;
47: Vec x, b;
48: PetscScalar *array;
49: PetscReal norm = 20;
50: PetscInt i, *ind_row, first_iteration = 1, its = 0, total = 0, col = 0;
51: PetscInt restart = 30;
52: KSP ksp_min; /* KSP for minimization */
53: PC pc_min; /* PC for minimization */
54: PetscBool isksp;
56: PetscFunctionBegin;
57: x = ksp->vec_sol; /* Solution vector */
58: b = ksp->vec_rhs; /* Right-hand side vector */
60: /* Row indexes (these indexes are global) */
61: PetscCall(PetscMalloc1(tsirm->Iend - tsirm->Istart, &ind_row));
62: for (i = 0; i < tsirm->Iend - tsirm->Istart; i++) ind_row[i] = i + tsirm->Istart;
64: /* Inner solver */
65: PetscCall(KSPGetPC(ksp, &pc));
66: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCKSP, &isksp));
67: PetscCheck(isksp, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "PC must be of type PCKSP");
68: PetscCall(PCKSPGetKSP(pc, &sub_ksp));
69: PetscCall(KSPSetTolerances(sub_ksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, restart));
71: /* previously it seemed good but with SNES it seems not good... */
72: PetscCall(KSP_MatMult(sub_ksp, tsirm->A, x, tsirm->r));
73: PetscCall(VecAXPY(tsirm->r, -1, b));
74: PetscCall(VecNorm(tsirm->r, NORM_2, &norm));
75: KSPCheckNorm(ksp, norm);
76: ksp->its = 0;
77: PetscCall(KSPConvergedDefault(ksp, ksp->its, norm, &ksp->reason, ksp->cnvP));
78: PetscCall(KSPSetInitialGuessNonzero(sub_ksp, PETSC_TRUE));
79: do {
80: for (col = 0; col < tsirm->size_ls && ksp->reason == 0; col++) {
81: /* Solve (inner iteration) */
82: PetscCall(KSPSolve(sub_ksp, b, x));
83: PetscCall(KSPGetIterationNumber(sub_ksp, &its));
84: total += its;
86: /* Build S^T */
87: PetscCall(VecGetArray(x, &array));
88: PetscCall(MatSetValues(tsirm->S, tsirm->Iend - tsirm->Istart, ind_row, 1, &col, array, INSERT_VALUES));
89: PetscCall(VecRestoreArray(x, &array));
91: PetscCall(KSPGetResidualNorm(sub_ksp, &norm));
92: ksp->rnorm = norm;
93: ksp->its++;
94: PetscCall(KSPConvergedDefault(ksp, ksp->its, norm, &ksp->reason, ksp->cnvP));
95: PetscCall(KSPMonitor(ksp, ksp->its, norm));
96: }
98: /* Minimization step */
99: if (!ksp->reason) {
100: PetscCall(MatAssemblyBegin(tsirm->S, MAT_FINAL_ASSEMBLY));
101: PetscCall(MatAssemblyEnd(tsirm->S, MAT_FINAL_ASSEMBLY));
102: if (first_iteration) {
103: PetscCall(MatMatMult(tsirm->A, tsirm->S, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &AS));
104: first_iteration = 0;
105: } else {
106: PetscCall(MatMatMult(tsirm->A, tsirm->S, MAT_REUSE_MATRIX, PETSC_DEFAULT, &AS));
107: }
109: /* CGLS or LSQR method to minimize the residuals*/
110: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp_min));
111: if (tsirm->cgls) {
112: PetscCall(KSPSetType(ksp_min, KSPCGLS));
113: } else {
114: PetscCall(KSPSetType(ksp_min, KSPLSQR));
115: }
116: PetscCall(KSPSetOperators(ksp_min, AS, AS));
117: PetscCall(KSPSetTolerances(ksp_min, tsirm->tol_ls, PETSC_DEFAULT, PETSC_DEFAULT, tsirm->maxiter_ls));
118: PetscCall(KSPGetPC(ksp_min, &pc_min));
119: PetscCall(PCSetType(pc_min, PCNONE));
120: PetscCall(KSPSolve(ksp_min, b, tsirm->Alpha)); /* Find Alpha such that ||AS Alpha = b|| */
121: PetscCall(KSPDestroy(&ksp_min));
122: /* Apply minimization */
123: PetscCall(MatMult(tsirm->S, tsirm->Alpha, x)); /* x = S * Alpha */
124: }
125: } while (ksp->its < ksp->max_it && !ksp->reason);
126: PetscCall(MatDestroy(&AS));
127: PetscCall(PetscFree(ind_row));
128: ksp->its = total;
129: PetscFunctionReturn(PETSC_SUCCESS);
130: }
132: static PetscErrorCode KSPSetFromOptions_TSIRM(KSP ksp, PetscOptionItems *PetscOptionsObject)
133: {
134: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
136: PetscFunctionBegin;
137: PetscOptionsHeadBegin(PetscOptionsObject, "KSP TSIRM options");
138: PetscCall(PetscOptionsInt("-ksp_tsirm_cgls", "Method used for the minimization step", "", tsirm->cgls, &tsirm->cgls, NULL)); /*0:LSQR, 1:CGLS*/
139: PetscCall(PetscOptionsReal("-ksp_tsirm_tol_ls", "Tolerance threshold for the minimization step", "", tsirm->tol_ls, &tsirm->tol_ls, NULL));
140: PetscCall(PetscOptionsInt("-ksp_tsirm_max_it_ls", "Maximum number of iterations for the minimization step", "", tsirm->maxiter_ls, &tsirm->maxiter_ls, NULL));
141: PetscCall(PetscOptionsInt("-ksp_tsirm_size_ls", "Number of residuals for minimization", "", tsirm->size_ls, &tsirm->size_ls, NULL));
142: PetscOptionsHeadEnd();
143: PetscFunctionReturn(PETSC_SUCCESS);
144: }
146: static PetscErrorCode KSPDestroy_TSIRM(KSP ksp)
147: {
148: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
150: PetscFunctionBegin;
151: PetscCall(MatDestroy(&tsirm->S));
152: PetscCall(VecDestroy(&tsirm->Alpha));
153: PetscCall(VecDestroy(&tsirm->r));
154: PetscCall(PetscFree(ksp->data));
155: PetscFunctionReturn(PETSC_SUCCESS);
156: }
158: /*MC
159: KSPTSIRM - Implements the two-stage iteration with least-squares residual minimization method {cite}`couturier2016tsirm`
161: Options Database Keys:
162: + -ksp_ksp_type <solver> - the type of the inner solver (GMRES or any of its variants for instance)
163: . -ksp_pc_type <preconditioner> - the type of the preconditioner applied to the inner solver
164: . -ksp_ksp_max_it <maxits> - the maximum number of inner iterations (iterations of the inner solver)
165: . -ksp_ksp_rtol <tol> - sets the relative convergence tolerance of the inner solver
166: . -ksp_tsirm_cgls <number> - if 1 use CGLS solver in the minimization step, otherwise use LSQR solver
167: . -ksp_tsirm_max_it_ls <maxits> - the maximum number of iterations for the least-squares minimization solver
168: . -ksp_tsirm_tol_ls <tol> - sets the convergence tolerance of the least-squares minimization solver
169: - -ksp_tsirm_size_ls <size> - the number of residuals for the least-squares minimization step
171: Level: advanced
173: Notes:
174: `KSPTSIRM` is a two-stage iteration method for solving large sparse linear systems of the form $Ax=b$. The main idea behind this new
175: method is the use a least-squares residual minimization to improve the convergence of Krylov based iterative methods, typically those of GMRES variants.
176: The principle of TSIRM algorithm is to build an outer iteration over a Krylov method, called the inner solver, and to frequently store the current residual
177: computed by the given Krylov method in a matrix of residuals S. After a few outer iterations, a least-squares minimization step is applied on the matrix
178: composed by the saved residuals, in order to compute a better solution and to make new iterations if required.
179: The minimization step consists in solving the least-squares problem $\min||b-ASa||$ to find 'a' which minimizes the
180: residuals $(b-AS)$. The minimization step is performed using two solvers of linear least-squares problems: `KSPCGLS` or `KSPLSQR`. A new solution x with
181: a minimal residual is computed with $x=Sa$.
183: Contributed by:
184: Lilia Ziane Khodja
186: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`,
187: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
188: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
189: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
190: M*/
191: PETSC_EXTERN PetscErrorCode KSPCreate_TSIRM(KSP ksp)
192: {
193: KSP_TSIRM *tsirm;
195: PetscFunctionBegin;
196: PetscCall(PetscNew(&tsirm));
197: ksp->data = (void *)tsirm;
198: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 2));
199: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 1));
200: ksp->ops->setup = KSPSetUp_TSIRM;
201: ksp->ops->solve = KSPSolve_TSIRM;
202: ksp->ops->destroy = KSPDestroy_TSIRM;
203: ksp->ops->buildsolution = KSPBuildSolutionDefault;
204: ksp->ops->buildresidual = KSPBuildResidualDefault;
205: ksp->ops->setfromoptions = KSPSetFromOptions_TSIRM;
206: ksp->ops->view = NULL;
207: #if defined(PETSC_USE_COMPLEX)
208: SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "This is not supported for complex numbers");
209: #else
210: PetscFunctionReturn(PETSC_SUCCESS);
211: #endif
212: }