Actual source code: cgne.c
2: /*
3: cgimpl.h defines the simple data structured used to store information
4: related to the type of matrix (e.g. complex symmetric) being solved and
5: data used during the optional Lanczo process used to compute eigenvalues
6: */
7: #include <../src/ksp/ksp/impls/cg/cgimpl.h>
8: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP, PetscReal *, PetscReal *);
9: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP, PetscInt, PetscReal *, PetscReal *, PetscInt *);
11: static PetscErrorCode KSPCGSetType_CGNE(KSP ksp, KSPCGType type)
12: {
13: KSP_CG *cg = (KSP_CG *)ksp->data;
15: PetscFunctionBegin;
16: cg->type = type;
17: PetscFunctionReturn(PETSC_SUCCESS);
18: }
20: /*
21: KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.
23: IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
24: */
25: static PetscErrorCode KSPSetUp_CGNE(KSP ksp)
26: {
27: KSP_CG *cgP = (KSP_CG *)ksp->data;
28: PetscInt maxit = ksp->max_it;
30: PetscFunctionBegin;
31: /* get work vectors needed by CGNE */
32: PetscCall(KSPSetWorkVecs(ksp, 4));
34: /*
35: If user requested computations of eigenvalues then allocate work
36: work space needed
37: */
38: if (ksp->calc_sings) {
39: /* get space to store tridiagonal matrix for Lanczos */
40: PetscCall(PetscMalloc4(maxit, &cgP->e, maxit, &cgP->d, maxit, &cgP->ee, maxit, &cgP->dd));
42: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
43: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
44: }
45: PetscFunctionReturn(PETSC_SUCCESS);
46: }
48: /*
49: KSPSolve_CGNE - This routine actually applies the conjugate gradient
50: method
52: Input Parameter:
53: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
54: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
56: Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.
58: */
59: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
60: {
61: PetscInt i, stored_max_it, eigs;
62: PetscScalar dpi, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL;
63: PetscReal dp = 0.0;
64: Vec X, B, Z, R, P, T;
65: KSP_CG *cg;
66: Mat Amat, Pmat;
67: PetscBool diagonalscale, transpose_pc;
69: PetscFunctionBegin;
70: PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
71: PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
72: PetscCall(PCApplyTransposeExists(ksp->pc, &transpose_pc));
74: cg = (KSP_CG *)ksp->data;
75: eigs = ksp->calc_sings;
76: stored_max_it = ksp->max_it;
77: X = ksp->vec_sol;
78: B = ksp->vec_rhs;
79: R = ksp->work[0];
80: Z = ksp->work[1];
81: P = ksp->work[2];
82: T = ksp->work[3];
84: #define VecXDot(x, y, a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x, y, a) : VecTDot(x, y, a))
86: if (eigs) {
87: e = cg->e;
88: d = cg->d;
89: e[0] = 0.0;
90: }
91: PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
93: ksp->its = 0;
94: PetscCall(KSP_MatMultTranspose(ksp, Amat, B, T));
95: if (!ksp->guess_zero) {
96: PetscCall(KSP_MatMult(ksp, Amat, X, P));
97: PetscCall(KSP_MatMultTranspose(ksp, Amat, P, R));
98: PetscCall(VecAYPX(R, -1.0, T));
99: } else {
100: PetscCall(VecCopy(T, R)); /* r <- b (x is 0) */
101: }
102: if (transpose_pc) {
103: PetscCall(KSP_PCApplyTranspose(ksp, R, T));
104: } else {
105: PetscCall(KSP_PCApply(ksp, R, T));
106: }
107: PetscCall(KSP_PCApply(ksp, T, Z));
109: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
110: PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- z'*z */
111: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
112: PetscCall(VecNorm(R, NORM_2, &dp)); /* dp <- r'*r */
113: } else if (ksp->normtype == KSP_NORM_NATURAL) {
114: PetscCall(VecXDot(Z, R, &beta));
115: KSPCheckDot(ksp, beta);
116: dp = PetscSqrtReal(PetscAbsScalar(beta));
117: } else dp = 0.0;
118: PetscCall(KSPLogResidualHistory(ksp, dp));
119: PetscCall(KSPMonitor(ksp, 0, dp));
120: ksp->rnorm = dp;
121: PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP)); /* test for convergence */
122: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
124: i = 0;
125: do {
126: ksp->its = i + 1;
127: PetscCall(VecXDot(Z, R, &beta)); /* beta <- r'z */
128: KSPCheckDot(ksp, beta);
129: if (beta == 0.0) {
130: ksp->reason = KSP_CONVERGED_ATOL;
131: PetscCall(PetscInfo(ksp, "converged due to beta = 0\n"));
132: break;
133: #if !defined(PETSC_USE_COMPLEX)
134: } else if (beta < 0.0) {
135: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
136: PetscCall(PetscInfo(ksp, "diverging due to indefinite preconditioner\n"));
137: break;
138: #endif
139: }
140: if (!i) {
141: PetscCall(VecCopy(Z, P)); /* p <- z */
142: b = 0.0;
143: } else {
144: b = beta / betaold;
145: if (eigs) {
146: PetscCheck(ksp->max_it == stored_max_it, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Can not change maxit AND calculate eigenvalues");
147: e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
148: }
149: PetscCall(VecAYPX(P, b, Z)); /* p <- z + b* p */
150: }
151: betaold = beta;
152: PetscCall(KSP_MatMult(ksp, Amat, P, T));
153: PetscCall(KSP_MatMultTranspose(ksp, Amat, T, Z));
154: PetscCall(VecXDot(P, Z, &dpi)); /* dpi <- z'p */
155: KSPCheckDot(ksp, dpi);
156: a = beta / dpi; /* a = beta/p'z */
157: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
158: PetscCall(VecAXPY(X, a, P)); /* x <- x + ap */
159: PetscCall(VecAXPY(R, -a, Z)); /* r <- r - az */
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: PetscCall(VecNorm(Z, NORM_2, &dp)); /* dp <- z'*z */
168: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
169: PetscCall(VecNorm(R, NORM_2, &dp));
170: } else if (ksp->normtype == KSP_NORM_NATURAL) {
171: dp = PetscSqrtReal(PetscAbsScalar(beta));
172: } else dp = 0.0;
173: ksp->rnorm = dp;
174: PetscCall(KSPLogResidualHistory(ksp, dp));
175: PetscCall(KSPMonitor(ksp, i + 1, dp));
176: PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
177: if (ksp->reason) break;
178: if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
179: if (transpose_pc) {
180: PetscCall(KSP_PCApplyTranspose(ksp, R, T));
181: } else {
182: PetscCall(KSP_PCApply(ksp, R, T));
183: }
184: PetscCall(KSP_PCApply(ksp, T, Z));
185: }
186: i++;
187: } while (i < ksp->max_it);
188: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
189: PetscFunctionReturn(PETSC_SUCCESS);
190: }
192: /*
193: KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
194: function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)
196: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
197: */
199: /*MC
200: KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
201: without explicitly forming A^t*A
203: Options Database Keys:
204: . -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric
206: Level: beginner
208: Notes:
209: Eigenvalue computation routines including `KSPSetComputeEigenvalues()` and `KSPComputeEigenvalues()` will return information about the
210: spectrum of A^t*A, rather than A.
212: `KSPCGNE` is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
213: eigenvalues. A unitary matrix is a classic example where `KSPCGNE` converges in one iteration, but `KSPGMRES` and `KSPCGS` need N
214: iterations, see [1]. If you intend to solve least squares problems, use `KSPLSQR`.
216: This is NOT a different algorithm than used with `KSPCG`, it merely uses that algorithm with the
217: matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
219: This method requires that one be able to apply the transpose of the preconditioner and operator
220: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
221: the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
223: This only supports left preconditioning.
225: Reference:
226: . [1] - Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992
228: Developer Note:
229: This object is subclassed off of `KSPCG`
231: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, 'KSPCG', `KSPLSQR', 'KSPCGLS`,
232: `KSPCGSetType()`, `KSPBICG`, `KSPSetComputeEigenvalues()`, `KSPComputeEigenvalues()`
233: M*/
235: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
236: {
237: KSP_CG *cg;
239: PetscFunctionBegin;
240: PetscCall(PetscNew(&cg));
241: #if !defined(PETSC_USE_COMPLEX)
242: cg->type = KSP_CG_SYMMETRIC;
243: #else
244: cg->type = KSP_CG_HERMITIAN;
245: #endif
246: ksp->data = (void *)cg;
247: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
248: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
249: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
250: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
252: /*
253: Sets the functions that are associated with this data structure
254: (in C++ this is the same as defining virtual functions)
255: */
256: ksp->ops->setup = KSPSetUp_CGNE;
257: ksp->ops->solve = KSPSolve_CGNE;
258: ksp->ops->destroy = KSPDestroy_CG;
259: ksp->ops->view = KSPView_CG;
260: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
261: ksp->ops->buildsolution = KSPBuildSolutionDefault;
262: ksp->ops->buildresidual = KSPBuildResidualDefault;
264: /*
265: Attach the function KSPCGSetType_CGNE() to this object. The routine
266: KSPCGSetType() checks for this attached function and calls it if it finds
267: it. (Sort of like a dynamic member function that can be added at run time
268: */
269: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", KSPCGSetType_CGNE));
270: PetscFunctionReturn(PETSC_SUCCESS);
271: }