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: /* Matrix of the system */
16: PetscCall(KSPGetOperators(ksp, &tsirm->A, NULL)); /* Matrix of the system */
17: PetscCall(MatGetSize(tsirm->A, &tsirm->size, NULL)); /* Size of the system */
18: PetscCall(MatGetOwnershipRange(tsirm->A, &tsirm->Istart, &tsirm->Iend));
20: /* Matrix S of residuals */
21: PetscCall(MatCreate(PetscObjectComm((PetscObject)ksp), &tsirm->S));
22: PetscCall(MatSetSizes(tsirm->S, tsirm->Iend - tsirm->Istart, PETSC_DECIDE, tsirm->size, tsirm->size_ls));
23: PetscCall(MatSetType(tsirm->S, MATDENSE));
24: PetscCall(MatSetUp(tsirm->S));
26: /* Residual and vector Alpha computed in the minimization step */
27: PetscCall(MatCreateVecs(tsirm->S, &tsirm->Alpha, &tsirm->r));
28: PetscFunctionReturn(PETSC_SUCCESS);
29: }
31: static PetscErrorCode KSPSolve_TSIRM(KSP ksp)
32: {
33: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
34: KSP sub_ksp;
35: PC pc;
36: Mat AS = NULL;
37: Vec x, b;
38: PetscScalar *array;
39: PetscReal norm = 20;
40: PetscInt i, *ind_row, first_iteration = 1, its = 0, total = 0, col = 0;
41: KSP ksp_min; /* KSP for minimization */
42: PC pc_min; /* PC for minimization */
43: PetscBool isksp;
45: PetscFunctionBegin;
46: x = ksp->vec_sol; /* Solution vector */
47: b = ksp->vec_rhs; /* Right-hand side vector */
49: /* Row indexes (these indexes are global) */
50: PetscCall(PetscMalloc1(tsirm->Iend - tsirm->Istart, &ind_row));
51: for (i = 0; i < tsirm->Iend - tsirm->Istart; i++) ind_row[i] = i + tsirm->Istart;
53: /* Inner solver */
54: PetscCall(KSPGetPC(ksp, &pc));
55: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCKSP, &isksp));
56: PetscCheck(isksp, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "PC must be of type PCKSP");
57: PetscCall(PCKSPGetKSP(pc, &sub_ksp));
59: /* previously it seemed good but with SNES it seems not good... */
60: PetscCall(KSP_MatMult(sub_ksp, tsirm->A, x, tsirm->r));
61: PetscCall(VecAXPY(tsirm->r, -1, b));
62: PetscCall(VecNorm(tsirm->r, NORM_2, &norm));
63: KSPCheckNorm(ksp, norm);
64: ksp->its = 0;
65: PetscCall(KSPConvergedDefault(ksp, ksp->its, norm, &ksp->reason, ksp->cnvP));
66: PetscCall(KSPMonitor(ksp, ksp->its, norm));
67: PetscCall(KSPSetInitialGuessNonzero(sub_ksp, PETSC_TRUE));
68: do {
69: for (col = 0; col < tsirm->size_ls && ksp->reason == KSP_CONVERGED_ITERATING; col++) {
70: /* Solve (inner iteration) */
71: PetscCall(KSPSolve(sub_ksp, b, x));
72: PetscCall(KSPGetIterationNumber(sub_ksp, &its));
73: total += its;
75: /* Build S^T */
76: PetscCall(VecGetArray(x, &array));
77: PetscCall(MatSetValues(tsirm->S, tsirm->Iend - tsirm->Istart, ind_row, 1, &col, array, INSERT_VALUES));
78: PetscCall(VecRestoreArray(x, &array));
80: PetscCall(KSPGetResidualNorm(sub_ksp, &norm));
81: ksp->rnorm = norm;
82: ksp->its++;
83: PetscCall(KSPConvergedDefault(ksp, ksp->its, norm, &ksp->reason, ksp->cnvP));
84: PetscCall(KSPMonitor(ksp, ksp->its, norm));
85: }
87: /* Minimization step */
88: if (ksp->reason == KSP_CONVERGED_ITERATING) {
89: PetscCall(MatAssemblyBegin(tsirm->S, MAT_FINAL_ASSEMBLY));
90: PetscCall(MatAssemblyEnd(tsirm->S, MAT_FINAL_ASSEMBLY));
91: if (first_iteration) {
92: PetscCall(MatMatMult(tsirm->A, tsirm->S, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &AS));
93: first_iteration = 0;
94: } else {
95: PetscCall(MatMatMult(tsirm->A, tsirm->S, MAT_REUSE_MATRIX, PETSC_DEFAULT, &AS));
96: }
98: /* CGLS or LSQR method to minimize the residuals*/
99: PetscCall(KSPCreate(PetscObjectComm((PetscObject)ksp), &ksp_min));
100: if (tsirm->cgls) {
101: PetscCall(KSPSetType(ksp_min, KSPCGLS));
102: } else {
103: PetscCall(KSPSetType(ksp_min, KSPLSQR));
104: }
105: PetscCall(KSPSetOperators(ksp_min, AS, AS));
106: PetscCall(KSPSetTolerances(ksp_min, tsirm->tol_ls, PETSC_DEFAULT, PETSC_DEFAULT, tsirm->maxiter_ls));
107: PetscCall(KSPGetPC(ksp_min, &pc_min));
108: PetscCall(PCSetType(pc_min, PCNONE));
109: PetscCall(KSPSolve(ksp_min, b, tsirm->Alpha)); /* Find Alpha such that ||AS Alpha = b|| */
110: PetscCall(KSPDestroy(&ksp_min));
111: /* Apply minimization */
112: PetscCall(MatMult(tsirm->S, tsirm->Alpha, x)); /* x = S * Alpha */
113: }
114: } while (ksp->its < ksp->max_it && !ksp->reason);
115: PetscCall(MatDestroy(&AS));
116: PetscCall(PetscFree(ind_row));
117: ksp->its = total;
118: PetscFunctionReturn(PETSC_SUCCESS);
119: }
121: static PetscErrorCode KSPSetFromOptions_TSIRM(KSP ksp, PetscOptionItems *PetscOptionsObject)
122: {
123: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
125: PetscFunctionBegin;
126: PetscOptionsHeadBegin(PetscOptionsObject, "KSP TSIRM options");
127: PetscCall(PetscOptionsInt("-ksp_tsirm_cgls", "Method used for the minimization step", "", tsirm->cgls, &tsirm->cgls, NULL)); /*0:LSQR, 1:CGLS*/
128: PetscCall(PetscOptionsReal("-ksp_tsirm_tol_ls", "Tolerance threshold for the minimization step", "", tsirm->tol_ls, &tsirm->tol_ls, NULL));
129: PetscCall(PetscOptionsInt("-ksp_tsirm_max_it_ls", "Maximum number of iterations for the minimization step", "", tsirm->maxiter_ls, &tsirm->maxiter_ls, NULL));
130: PetscCall(PetscOptionsInt("-ksp_tsirm_size_ls", "Number of residuals for minimization", "", tsirm->size_ls, &tsirm->size_ls, NULL));
131: PetscOptionsHeadEnd();
132: PetscFunctionReturn(PETSC_SUCCESS);
133: }
135: static PetscErrorCode KSPDestroy_TSIRM(KSP ksp)
136: {
137: KSP_TSIRM *tsirm = (KSP_TSIRM *)ksp->data;
139: PetscFunctionBegin;
140: PetscCall(MatDestroy(&tsirm->S));
141: PetscCall(VecDestroy(&tsirm->Alpha));
142: PetscCall(VecDestroy(&tsirm->r));
143: PetscCall(PetscFree(ksp->data));
144: PetscFunctionReturn(PETSC_SUCCESS);
145: }
147: /*MC
148: KSPTSIRM - Implements the two-stage iteration with least-squares residual minimization method {cite}`couturier2016tsirm`
150: Options Database Keys:
151: + -ksp_ksp_type <solver> - the type of the inner solver (GMRES or any of its variants for instance)
152: . -ksp_pc_type <preconditioner> - the type of the preconditioner applied to the inner solver
153: . -ksp_ksp_max_it <maxits> - the maximum number of inner iterations (iterations of the inner solver)
154: . -ksp_ksp_rtol <tol> - sets the relative convergence tolerance of the inner solver
155: . -ksp_tsirm_cgls <number> - if 1 use CGLS solver in the minimization step, otherwise use LSQR solver
156: . -ksp_tsirm_max_it_ls <maxits> - the maximum number of iterations for the least-squares minimization solver
157: . -ksp_tsirm_tol_ls <tol> - sets the convergence tolerance of the least-squares minimization solver
158: - -ksp_tsirm_size_ls <size> - the number of residuals for the least-squares minimization step
160: Level: advanced
162: Notes:
163: `KSPTSIRM` is a two-stage iteration method for solving large sparse linear systems of the form $Ax=b$. The main idea behind this new
164: method is the use a least-squares residual minimization to improve the convergence of Krylov based iterative methods, typically those of GMRES variants.
165: 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
166: 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
167: composed by the saved residuals, in order to compute a better solution and to make new iterations if required.
168: The minimization step consists in solving the least-squares problem $\min||b-ASa||$ to find 'a' which minimizes the
169: residuals $(b-AS)$. The minimization step is performed using two solvers of linear least-squares problems: `KSPCGLS` or `KSPLSQR`. A new solution x with
170: a minimal residual is computed with $x=Sa$.
172: Defaults to 30 iterations for the inner solve, use option `-ksp_ksp_max_it <it>` to change it.
174: Contributed by:
175: Lilia Ziane Khodja
177: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPLGMRES`,
178: `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
179: `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
180: `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPSetPCSide()`
181: M*/
182: PETSC_EXTERN PetscErrorCode KSPCreate_TSIRM(KSP ksp)
183: {
184: KSP_TSIRM *tsirm;
185: PC pc;
186: KSP sub_ksp;
188: PetscFunctionBegin;
189: PetscCall(PetscNew(&tsirm));
190: ksp->data = (void *)tsirm;
191: #if defined(PETSC_USE_REAL_SINGLE)
192: tsirm->tol_ls = 1e-25;
193: #else
194: tsirm->tol_ls = 1e-50;
195: #endif
196: tsirm->size_ls = 12;
197: tsirm->maxiter_ls = 15;
198: tsirm->cgls = 0;
199: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 2));
200: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 1));
201: ksp->ops->setup = KSPSetUp_TSIRM;
202: ksp->ops->solve = KSPSolve_TSIRM;
203: ksp->ops->destroy = KSPDestroy_TSIRM;
204: ksp->ops->buildsolution = KSPBuildSolutionDefault;
205: ksp->ops->buildresidual = KSPBuildResidualDefault;
206: ksp->ops->setfromoptions = KSPSetFromOptions_TSIRM;
207: ksp->ops->view = NULL;
209: PetscCall(KSPGetPC(ksp, &pc));
210: PetscCall(PCSetType(pc, PCKSP));
211: PetscCall(PCKSPGetKSP(pc, &sub_ksp));
212: PetscCall(KSPSetTolerances(sub_ksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, 30));
213: #if defined(PETSC_USE_COMPLEX)
214: SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "This is not supported for complex numbers");
215: #else
216: PetscFunctionReturn(PETSC_SUCCESS);
217: #endif
218: }