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);
39: PetscLogObjectMemory((PetscObject)ksp,2*maxit*(sizeof(PetscScalar)+sizeof(PetscReal)));
41: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
42: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
43: }
44: return 0;
45: }
47: /*
48: KSPSolve_CGNE - This routine actually applies the conjugate gradient
49: method
51: Input Parameter:
52: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
53: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
55: Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.
57: */
58: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
59: {
60: PetscInt i,stored_max_it,eigs;
61: PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL;
62: PetscReal dp = 0.0;
63: Vec X,B,Z,R,P,T;
64: KSP_CG *cg;
65: Mat Amat,Pmat;
66: PetscBool diagonalscale,transpose_pc;
68: PCGetDiagonalScale(ksp->pc,&diagonalscale);
70: PCApplyTransposeExists(ksp->pc,&transpose_pc);
72: cg = (KSP_CG*)ksp->data;
73: eigs = ksp->calc_sings;
74: stored_max_it = ksp->max_it;
75: X = ksp->vec_sol;
76: B = ksp->vec_rhs;
77: R = ksp->work[0];
78: Z = ksp->work[1];
79: P = ksp->work[2];
80: T = ksp->work[3];
82: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
84: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
85: PCGetOperators(ksp->pc,&Amat,&Pmat);
87: ksp->its = 0;
88: KSP_MatMultTranspose(ksp,Amat,B,T);
89: if (!ksp->guess_zero) {
90: KSP_MatMult(ksp,Amat,X,P);
91: KSP_MatMultTranspose(ksp,Amat,P,R);
92: VecAYPX(R,-1.0,T);
93: } else {
94: VecCopy(T,R); /* r <- b (x is 0) */
95: }
96: if (transpose_pc) {
97: KSP_PCApplyTranspose(ksp,R,T);
98: } else {
99: KSP_PCApply(ksp,R,T);
100: }
101: KSP_PCApply(ksp,T,Z);
103: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
104: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
105: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
106: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
107: } else if (ksp->normtype == KSP_NORM_NATURAL) {
108: VecXDot(Z,R,&beta);
109: KSPCheckDot(ksp,beta);
110: dp = PetscSqrtReal(PetscAbsScalar(beta));
111: } else dp = 0.0;
112: KSPLogResidualHistory(ksp,dp);
113: KSPMonitor(ksp,0,dp);
114: ksp->rnorm = dp;
115: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
116: if (ksp->reason) return 0;
118: i = 0;
119: do {
120: ksp->its = i+1;
121: VecXDot(Z,R,&beta); /* beta <- r'z */
122: KSPCheckDot(ksp,beta);
123: if (beta == 0.0) {
124: ksp->reason = KSP_CONVERGED_ATOL;
125: PetscInfo(ksp,"converged due to beta = 0\n");
126: break;
127: #if !defined(PETSC_USE_COMPLEX)
128: } else if (beta < 0.0) {
129: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
130: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
131: break;
132: #endif
133: }
134: if (!i) {
135: VecCopy(Z,P); /* p <- z */
136: b = 0.0;
137: } else {
138: b = beta/betaold;
139: if (eigs) {
141: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
142: }
143: VecAYPX(P,b,Z); /* p <- z + b* p */
144: }
145: betaold = beta;
146: KSP_MatMult(ksp,Amat,P,T);
147: KSP_MatMultTranspose(ksp,Amat,T,Z);
148: VecXDot(P,Z,&dpi); /* dpi <- z'p */
149: KSPCheckDot(ksp,dpi);
150: a = beta/dpi; /* a = beta/p'z */
151: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
152: VecAXPY(X,a,P); /* x <- x + ap */
153: VecAXPY(R,-a,Z); /* r <- r - az */
154: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
155: if (transpose_pc) {
156: KSP_PCApplyTranspose(ksp,R,T);
157: } else {
158: KSP_PCApply(ksp,R,T);
159: }
160: KSP_PCApply(ksp,T,Z);
161: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
162: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
163: VecNorm(R,NORM_2,&dp);
164: } else if (ksp->normtype == KSP_NORM_NATURAL) {
165: dp = PetscSqrtReal(PetscAbsScalar(beta));
166: } else dp = 0.0;
167: ksp->rnorm = dp;
168: KSPLogResidualHistory(ksp,dp);
169: KSPMonitor(ksp,i+1,dp);
170: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
171: if (ksp->reason) break;
172: if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
173: if (transpose_pc) {
174: KSP_PCApplyTranspose(ksp,R,T);
175: } else {
176: KSP_PCApply(ksp,R,T);
177: }
178: KSP_PCApply(ksp,T,Z);
179: }
180: i++;
181: } while (i<ksp->max_it);
182: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
183: return 0;
184: }
186: /*
187: KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
188: function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)
190: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
191: */
193: /*MC
194: KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
195: without explicitly forming A^t*A
197: Options Database Keys:
198: . -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric
200: Level: beginner
202: Notes:
203: eigenvalue computation routines will return information about the
204: spectrum of A^t*A, rather than A.
206: CGNE is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
207: eigenvalues. A unitary matrix is a classic example where CGNE converges in one iteration, but GMRES and CGS need N
208: iterations (see Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992). If you intend
209: to solve least squares problems, use KSPLSQR.
211: This is NOT a different algorithm than used with KSPCG, it merely uses that algorithm with the
212: matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
214: This method requires that one be able to apply the transpose of the preconditioner and operator
215: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
216: the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
218: This only supports left preconditioning.
220: This object is subclassed off of KSPCG
222: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
223: KSPCGSetType(), KSPBICG
225: M*/
227: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
228: {
229: KSP_CG *cg;
231: PetscNewLog(ksp,&cg);
232: #if !defined(PETSC_USE_COMPLEX)
233: cg->type = KSP_CG_SYMMETRIC;
234: #else
235: cg->type = KSP_CG_HERMITIAN;
236: #endif
237: ksp->data = (void*)cg;
238: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
239: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
240: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
241: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
243: /*
244: Sets the functions that are associated with this data structure
245: (in C++ this is the same as defining virtual functions)
246: */
247: ksp->ops->setup = KSPSetUp_CGNE;
248: ksp->ops->solve = KSPSolve_CGNE;
249: ksp->ops->destroy = KSPDestroy_CG;
250: ksp->ops->view = KSPView_CG;
251: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
252: ksp->ops->buildsolution = KSPBuildSolutionDefault;
253: ksp->ops->buildresidual = KSPBuildResidualDefault;
255: /*
256: Attach the function KSPCGSetType_CGNE() to this object. The routine
257: KSPCGSetType() checks for this attached function and calls it if it finds
258: it. (Sort of like a dynamic member function that can be added at run time
259: */
260: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
261: return 0;
262: }