Actual source code: cgne.c
1: /*
2: cgimpl.h defines the simple data structured used to store information
3: related to the type of matrix (e.g. complex symmetric) being solved and
4: data used during the optional Lanczos process used to compute eigenvalues
5: */
6: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
7: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP, PetscReal *, PetscReal *);
8: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP, PetscInt, PetscReal *, PetscReal *, PetscInt *);
10: static PetscErrorCode KSPCGSetType_CGNE(KSP ksp, KSPCGType type)
11: {
12: KSP_CG *cg = (KSP_CG *)ksp->data;
14: PetscFunctionBegin;
15: cg->type = type;
16: PetscFunctionReturn(PETSC_SUCCESS);
17: }
19: static PetscErrorCode KSPSetUp_CGNE(KSP ksp)
20: {
21: KSP_CG *cgP = (KSP_CG *)ksp->data;
22: PetscInt maxit = ksp->max_it;
24: PetscFunctionBegin;
25: /* get work vectors needed by CGNE */
26: PetscCall(KSPSetWorkVecs(ksp, 4));
28: /*
29: If user requested computations of eigenvalues then allocate work space needed
30: */
31: if (ksp->calc_sings) {
32: /* get space to store tridiagonal matrix for Lanczos */
33: PetscCall(PetscMalloc4(maxit, &cgP->e, maxit, &cgP->d, maxit, &cgP->ee, maxit, &cgP->dd));
35: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
36: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
37: }
38: PetscFunctionReturn(PETSC_SUCCESS);
39: }
41: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
42: {
43: PetscInt i, stored_max_it, eigs;
44: PetscScalar dpi, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL;
45: PetscReal dp = 0.0;
46: Vec X, B, Z, R, P, T;
47: KSP_CG *cg;
48: Mat Amat, Pmat;
49: PetscBool diagonalscale, transpose_pc;
51: PetscFunctionBegin;
52: PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
53: PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
54: PetscCall(PCApplyTransposeExists(ksp->pc, &transpose_pc));
56: cg = (KSP_CG *)ksp->data;
57: eigs = ksp->calc_sings;
58: stored_max_it = ksp->max_it;
59: X = ksp->vec_sol;
60: B = ksp->vec_rhs;
61: R = ksp->work[0];
62: Z = ksp->work[1];
63: P = ksp->work[2];
64: T = ksp->work[3];
66: #define VecXDot(x, y, a) (cg->type == KSP_CG_HERMITIAN ? VecDot(x, y, a) : VecTDot(x, y, a))
68: if (eigs) {
69: e = cg->e;
70: d = cg->d;
71: e[0] = 0.0;
72: }
73: PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
75: ksp->its = 0;
76: PetscCall(KSP_MatMultTranspose(ksp, Amat, B, T));
77: if (!ksp->guess_zero) {
78: PetscCall(KSP_MatMult(ksp, Amat, X, P));
79: PetscCall(KSP_MatMultTranspose(ksp, Amat, P, R));
80: PetscCall(VecAYPX(R, -1.0, T));
81: } else {
82: PetscCall(VecCopy(T, R)); /* r <- b (x is 0) */
83: }
84: if (transpose_pc) {
85: PetscCall(KSP_PCApplyTranspose(ksp, R, T));
86: } else {
87: PetscCall(KSP_PCApply(ksp, R, T));
88: }
89: PetscCall(KSP_PCApply(ksp, T, Z));
91: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
92: PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- z'*z */
93: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
94: PetscCall(VecNorm(R, NORM_2, &dp)); /* dp <- r'*r */
95: } else if (ksp->normtype == KSP_NORM_NATURAL) {
96: PetscCall(VecXDot(Z, R, &beta));
97: KSPCheckDot(ksp, beta);
98: dp = PetscSqrtReal(PetscAbsScalar(beta));
99: } else dp = 0.0;
100: PetscCall(KSPLogResidualHistory(ksp, dp));
101: PetscCall(KSPMonitor(ksp, 0, dp));
102: ksp->rnorm = dp;
103: PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP)); /* test for convergence */
104: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
106: i = 0;
107: do {
108: ksp->its = i + 1;
109: PetscCall(VecXDot(Z, R, &beta)); /* beta <- r'z */
110: KSPCheckDot(ksp, beta);
111: if (beta == 0.0) {
112: ksp->reason = KSP_CONVERGED_ATOL;
113: PetscCall(PetscInfo(ksp, "converged due to beta = 0\n"));
114: break;
115: #if !defined(PETSC_USE_COMPLEX)
116: } else if (beta < 0.0) {
117: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
118: PetscCall(PetscInfo(ksp, "diverging due to indefinite preconditioner\n"));
119: break;
120: #endif
121: }
122: if (!i) {
123: PetscCall(VecCopy(Z, P)); /* p <- z */
124: b = 0.0;
125: } else {
126: b = beta / betaold;
127: if (eigs) {
128: PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
129: e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
130: }
131: PetscCall(VecAYPX(P, b, Z)); /* p <- z + b* p */
132: }
133: betaold = beta;
134: PetscCall(KSP_MatMult(ksp, Amat, P, T));
135: PetscCall(KSP_MatMultTranspose(ksp, Amat, T, Z));
136: PetscCall(VecXDot(P, Z, &dpi)); /* dpi <- z'p */
137: KSPCheckDot(ksp, dpi);
138: a = beta / dpi; /* a = beta/p'z */
139: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
140: PetscCall(VecAXPY(X, a, P)); /* x <- x + ap */
141: PetscCall(VecAXPY(R, -a, Z)); /* r <- r - az */
142: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
143: if (transpose_pc) {
144: PetscCall(KSP_PCApplyTranspose(ksp, R, T));
145: } else {
146: PetscCall(KSP_PCApply(ksp, R, T));
147: }
148: PetscCall(KSP_PCApply(ksp, T, Z));
149: PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- z'*z */
150: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
151: PetscCall(VecNorm(R, NORM_2, &dp));
152: } else if (ksp->normtype == KSP_NORM_NATURAL) {
153: dp = PetscSqrtReal(PetscAbsScalar(beta));
154: } else dp = 0.0;
155: ksp->rnorm = dp;
156: PetscCall(KSPLogResidualHistory(ksp, dp));
157: PetscCall(KSPMonitor(ksp, i + 1, dp));
158: PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
159: if (ksp->reason) break;
160: if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
161: if (transpose_pc) {
162: PetscCall(KSP_PCApplyTranspose(ksp, R, T));
163: } else {
164: PetscCall(KSP_PCApply(ksp, R, T));
165: }
166: PetscCall(KSP_PCApply(ksp, T, Z));
167: }
168: i++;
169: } while (i < ksp->max_it);
170: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
171: PetscFunctionReturn(PETSC_SUCCESS);
172: }
174: /*
175: KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
176: function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)
178: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
179: */
181: /*MC
182: KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
183: without explicitly forming $A^T*A$
185: Options Database Key:
186: . -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric
188: Level: beginner
190: Notes:
191: Eigenvalue computation routines including `KSPSetComputeEigenvalues()` and `KSPComputeEigenvalues()` will return information about the
192: spectrum of $A^T*A$, rather than $A$.
194: `KSPCGNE` is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
195: eigenvalues. A unitary matrix is a classic example where `KSPCGNE` converges in one iteration, but `KSPGMRES` and `KSPCGS` need N
196: iterations, see {cite}`nachtigal90`. If you intend to solve least squares problems, use `KSPLSQR`.
198: This is NOT a different algorithm than used with `KSPCG`, it merely uses that algorithm with the
199: matrix defined by $A^T*A$ and preconditioner defined by $B^T*B$ where $B$ is the preconditioner for $A$.
201: This method requires that one be able to apply the transpose of the preconditioner and operator
202: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
203: the preconditioner is used in its place so one ends up preconditioning $A^T*A$ with $B*B$. Seems odd?
205: This only supports left preconditioning.
207: Developer Note:
208: This object is subclassed off of `KSPCG`, see the source code in src/ksp/ksp/impls/cg for comments on the structure of the code
210: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPCG`, `KSPLSQR`, `KSPCGLS`,
211: `KSPCGSetType()`, `KSPBICG`, `KSPSetComputeEigenvalues()`, `KSPComputeEigenvalues()`
212: M*/
214: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
215: {
216: KSP_CG *cg;
218: PetscFunctionBegin;
219: PetscCall(PetscNew(&cg));
220: #if !defined(PETSC_USE_COMPLEX)
221: cg->type = KSP_CG_SYMMETRIC;
222: #else
223: cg->type = KSP_CG_HERMITIAN;
224: #endif
225: ksp->data = (void *)cg;
226: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
227: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
228: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
229: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
231: /*
232: Sets the functions that are associated with this data structure
233: (in C++ this is the same as defining virtual functions)
234: */
235: ksp->ops->setup = KSPSetUp_CGNE;
236: ksp->ops->solve = KSPSolve_CGNE;
237: ksp->ops->destroy = KSPDestroy_CG;
238: ksp->ops->view = KSPView_CG;
239: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
240: ksp->ops->buildsolution = KSPBuildSolutionDefault;
241: ksp->ops->buildresidual = KSPBuildResidualDefault;
243: /*
244: Attach the function KSPCGSetType_CGNE() to this object. The routine
245: KSPCGSetType() checks for this attached function and calls it if it finds
246: it. (Sort of like a dynamic member function that can be added at run time
247: */
248: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", KSPCGSetType_CGNE));
249: PetscFunctionReturn(PETSC_SUCCESS);
250: }