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: cg->type = type;
16: return 0;
17: }
19: /*
20: KSPSetUp_CGNE - Sets up the workspace needed by the CGNE method.
22: IDENTICAL TO THE CG ONE EXCEPT for one extra work vector!
23: */
24: static PetscErrorCode KSPSetUp_CGNE(KSP ksp)
25: {
26: KSP_CG *cgP = (KSP_CG *)ksp->data;
27: PetscInt maxit = ksp->max_it;
29: /* get work vectors needed by CGNE */
30: KSPSetWorkVecs(ksp, 4);
32: /*
33: If user requested computations of eigenvalues then allocate work
34: work space needed
35: */
36: if (ksp->calc_sings) {
37: /* get space to store tridiagonal matrix for Lanczos */
38: PetscMalloc4(maxit, &cgP->e, maxit, &cgP->d, maxit, &cgP->ee, maxit, &cgP->dd);
40: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
41: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
42: }
43: return 0;
44: }
46: /*
47: KSPSolve_CGNE - This routine actually applies the conjugate gradient
48: method
50: Input Parameter:
51: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
52: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
54: Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.
56: */
57: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
58: {
59: PetscInt i, stored_max_it, eigs;
60: PetscScalar dpi, a = 1.0, beta, betaold = 1.0, b = 0, *e = NULL, *d = NULL;
61: PetscReal dp = 0.0;
62: Vec X, B, Z, R, P, T;
63: KSP_CG *cg;
64: Mat Amat, Pmat;
65: PetscBool diagonalscale, transpose_pc;
67: PCGetDiagonalScale(ksp->pc, &diagonalscale);
69: PCApplyTransposeExists(ksp->pc, &transpose_pc);
71: cg = (KSP_CG *)ksp->data;
72: eigs = ksp->calc_sings;
73: stored_max_it = ksp->max_it;
74: X = ksp->vec_sol;
75: B = ksp->vec_rhs;
76: R = ksp->work[0];
77: Z = ksp->work[1];
78: P = ksp->work[2];
79: T = ksp->work[3];
81: #define VecXDot(x, y, a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x, y, a) : VecTDot(x, y, a))
83: if (eigs) {
84: e = cg->e;
85: d = cg->d;
86: e[0] = 0.0;
87: }
88: PCGetOperators(ksp->pc, &Amat, &Pmat);
90: ksp->its = 0;
91: KSP_MatMultTranspose(ksp, Amat, B, T);
92: if (!ksp->guess_zero) {
93: KSP_MatMult(ksp, Amat, X, P);
94: KSP_MatMultTranspose(ksp, Amat, P, R);
95: VecAYPX(R, -1.0, T);
96: } else {
97: VecCopy(T, R); /* r <- b (x is 0) */
98: }
99: if (transpose_pc) {
100: KSP_PCApplyTranspose(ksp, R, T);
101: } else {
102: KSP_PCApply(ksp, R, T);
103: }
104: KSP_PCApply(ksp, T, Z);
106: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
107: VecNorm(Z, NORM_2, &dp); /* dp <- z'*z */
108: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
109: VecNorm(R, NORM_2, &dp); /* dp <- r'*r */
110: } else if (ksp->normtype == KSP_NORM_NATURAL) {
111: VecXDot(Z, R, &beta);
112: KSPCheckDot(ksp, beta);
113: dp = PetscSqrtReal(PetscAbsScalar(beta));
114: } else dp = 0.0;
115: KSPLogResidualHistory(ksp, dp);
116: KSPMonitor(ksp, 0, dp);
117: ksp->rnorm = dp;
118: (*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP); /* test for convergence */
119: if (ksp->reason) return 0;
121: i = 0;
122: do {
123: ksp->its = i + 1;
124: VecXDot(Z, R, &beta); /* beta <- r'z */
125: KSPCheckDot(ksp, beta);
126: if (beta == 0.0) {
127: ksp->reason = KSP_CONVERGED_ATOL;
128: PetscInfo(ksp, "converged due to beta = 0\n");
129: break;
130: #if !defined(PETSC_USE_COMPLEX)
131: } else if (beta < 0.0) {
132: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
133: PetscInfo(ksp, "diverging due to indefinite preconditioner\n");
134: break;
135: #endif
136: }
137: if (!i) {
138: VecCopy(Z, P); /* p <- z */
139: b = 0.0;
140: } else {
141: b = beta / betaold;
142: if (eigs) {
144: e[i] = PetscSqrtReal(PetscAbsScalar(b)) / a;
145: }
146: VecAYPX(P, b, Z); /* p <- z + b* p */
147: }
148: betaold = beta;
149: KSP_MatMult(ksp, Amat, P, T);
150: KSP_MatMultTranspose(ksp, Amat, T, Z);
151: VecXDot(P, Z, &dpi); /* dpi <- z'p */
152: KSPCheckDot(ksp, dpi);
153: a = beta / dpi; /* a = beta/p'z */
154: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b)) * e[i] + 1.0 / a;
155: VecAXPY(X, a, P); /* x <- x + ap */
156: VecAXPY(R, -a, Z); /* r <- r - az */
157: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
158: if (transpose_pc) {
159: KSP_PCApplyTranspose(ksp, R, T);
160: } else {
161: KSP_PCApply(ksp, R, T);
162: }
163: KSP_PCApply(ksp, T, Z);
164: VecNorm(Z, NORM_2, &dp); /* dp <- z'*z */
165: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
166: VecNorm(R, NORM_2, &dp);
167: } else if (ksp->normtype == KSP_NORM_NATURAL) {
168: dp = PetscSqrtReal(PetscAbsScalar(beta));
169: } else dp = 0.0;
170: ksp->rnorm = dp;
171: KSPLogResidualHistory(ksp, dp);
172: KSPMonitor(ksp, i + 1, dp);
173: (*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP);
174: if (ksp->reason) break;
175: if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
176: if (transpose_pc) {
177: KSP_PCApplyTranspose(ksp, R, T);
178: } else {
179: KSP_PCApply(ksp, R, T);
180: }
181: KSP_PCApply(ksp, T, Z);
182: }
183: i++;
184: } while (i < ksp->max_it);
185: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
186: return 0;
187: }
189: /*
190: KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
191: function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)
193: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
194: */
196: /*MC
197: KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
198: without explicitly forming A^t*A
200: Options Database Keys:
201: . -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric
203: Level: beginner
205: Notes:
206: Eigenvalue computation routines including `KSPSetComputeEigenvalues()` and `KSPComputeEigenvalues()` will return information about the
207: spectrum of A^t*A, rather than A.
209: `KSPCGNE` is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
210: eigenvalues. A unitary matrix is a classic example where `KSPCGNE` converges in one iteration, but `KSPGMRES` and `KSPCGS` need N
211: iterations, see [1]. If you intend to solve least squares problems, use `KSPLSQR`.
213: This is NOT a different algorithm than used with `KSPCG`, it merely uses that algorithm with the
214: matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
216: This method requires that one be able to apply the transpose of the preconditioner and operator
217: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
218: the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
220: This only supports left preconditioning.
222: Reference:
223: . [1] - Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992
225: Developer Note:
226: This object is subclassed off of `KSPCG`
228: .seealso: [](chapter_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, 'KSPCG', `KSPLSQR', 'KSPCGLS`,
229: `KSPCGSetType()`, `KSPBICG`, `KSPSetComputeEigenvalues()`, `KSPComputeEigenvalues()`
230: M*/
232: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
233: {
234: KSP_CG *cg;
236: PetscNew(&cg);
237: #if !defined(PETSC_USE_COMPLEX)
238: cg->type = KSP_CG_SYMMETRIC;
239: #else
240: cg->type = KSP_CG_HERMITIAN;
241: #endif
242: ksp->data = (void *)cg;
243: KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3);
244: KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2);
245: KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2);
246: KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1);
248: /*
249: Sets the functions that are associated with this data structure
250: (in C++ this is the same as defining virtual functions)
251: */
252: ksp->ops->setup = KSPSetUp_CGNE;
253: ksp->ops->solve = KSPSolve_CGNE;
254: ksp->ops->destroy = KSPDestroy_CG;
255: ksp->ops->view = KSPView_CG;
256: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
257: ksp->ops->buildsolution = KSPBuildSolutionDefault;
258: ksp->ops->buildresidual = KSPBuildResidualDefault;
260: /*
261: Attach the function KSPCGSetType_CGNE() to this object. The routine
262: KSPCGSetType() checks for this attached function and calls it if it finds
263: it. (Sort of like a dynamic member function that can be added at run time
264: */
265: PetscObjectComposeFunction((PetscObject)ksp, "KSPCGSetType_C", KSPCGSetType_CGNE);
266: return 0;
267: }