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;
16: cg->type = type;
17: return(0);
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;
29: PetscInt maxit = ksp->max_it;
32: /* get work vectors needed by CGNE */
33: KSPSetWorkVecs(ksp,4);
35: /*
36: If user requested computations of eigenvalues then allocate work
37: work space needed
38: */
39: if (ksp->calc_sings) {
40: /* get space to store tridiagonal matrix for Lanczos */
41: PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
42: PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));
44: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
45: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
46: }
47: return(0);
48: }
50: /*
51: KSPSolve_CGNE - This routine actually applies the conjugate gradient
52: method
54: Input Parameter:
55: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
56: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
58: Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.
60: */
61: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
62: {
64: PetscInt i,stored_max_it,eigs;
65: PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL;
66: PetscReal dp = 0.0;
67: Vec X,B,Z,R,P,T;
68: KSP_CG *cg;
69: Mat Amat,Pmat;
70: PetscBool diagonalscale,transpose_pc;
73: PCGetDiagonalScale(ksp->pc,&diagonalscale);
74: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
75: PCApplyTransposeExists(ksp->pc,&transpose_pc);
77: cg = (KSP_CG*)ksp->data;
78: eigs = ksp->calc_sings;
79: stored_max_it = ksp->max_it;
80: X = ksp->vec_sol;
81: B = ksp->vec_rhs;
82: R = ksp->work[0];
83: Z = ksp->work[1];
84: P = ksp->work[2];
85: T = ksp->work[3];
87: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
89: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
90: PCGetOperators(ksp->pc,&Amat,&Pmat);
92: ksp->its = 0;
93: KSP_MatMultTranspose(ksp,Amat,B,T);
94: if (!ksp->guess_zero) {
95: KSP_MatMult(ksp,Amat,X,P);
96: KSP_MatMultTranspose(ksp,Amat,P,R);
97: VecAYPX(R,-1.0,T);
98: } else {
99: VecCopy(T,R); /* r <- b (x is 0) */
100: }
101: if (transpose_pc) {
102: KSP_PCApplyTranspose(ksp,R,T);
103: } else {
104: KSP_PCApply(ksp,R,T);
105: }
106: KSP_PCApply(ksp,T,Z);
108: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
109: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
110: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
111: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
112: } else if (ksp->normtype == KSP_NORM_NATURAL) {
113: VecXDot(Z,R,&beta);
114: KSPCheckDot(ksp,beta);
115: dp = PetscSqrtReal(PetscAbsScalar(beta));
116: } else dp = 0.0;
117: KSPLogResidualHistory(ksp,dp);
118: KSPMonitor(ksp,0,dp);
119: ksp->rnorm = dp;
120: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
121: if (ksp->reason) return(0);
123: i = 0;
124: do {
125: ksp->its = i+1;
126: VecXDot(Z,R,&beta); /* beta <- r'z */
127: KSPCheckDot(ksp,beta);
128: if (beta == 0.0) {
129: ksp->reason = KSP_CONVERGED_ATOL;
130: PetscInfo(ksp,"converged due to beta = 0\n");
131: break;
132: #if !defined(PETSC_USE_COMPLEX)
133: } else if (beta < 0.0) {
134: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
135: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
136: break;
137: #endif
138: }
139: if (!i) {
140: VecCopy(Z,P); /* p <- z */
141: b = 0.0;
142: } else {
143: b = beta/betaold;
144: if (eigs) {
145: if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
146: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
147: }
148: VecAYPX(P,b,Z); /* p <- z + b* p */
149: }
150: betaold = beta;
151: KSP_MatMult(ksp,Amat,P,T);
152: KSP_MatMultTranspose(ksp,Amat,T,Z);
153: VecXDot(P,Z,&dpi); /* dpi <- z'p */
154: KSPCheckDot(ksp,dpi);
155: a = beta/dpi; /* a = beta/p'z */
156: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
157: VecAXPY(X,a,P); /* x <- x + ap */
158: VecAXPY(R,-a,Z); /* r <- r - az */
159: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
160: if (transpose_pc) {
161: KSP_PCApplyTranspose(ksp,R,T);
162: } else {
163: KSP_PCApply(ksp,R,T);
164: }
165: KSP_PCApply(ksp,T,Z);
166: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
167: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
168: VecNorm(R,NORM_2,&dp);
169: } else if (ksp->normtype == KSP_NORM_NATURAL) {
170: dp = PetscSqrtReal(PetscAbsScalar(beta));
171: } else dp = 0.0;
172: ksp->rnorm = dp;
173: KSPLogResidualHistory(ksp,dp);
174: if (eigs) cg->ned = ksp->its;
175: KSPMonitor(ksp,i+1,dp);
176: (*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: KSP_PCApplyTranspose(ksp,R,T);
181: } else {
182: KSP_PCApply(ksp,R,T);
183: }
184: 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: return(0);
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 will return information about the
210: spectrum of A^t*A, rather than A.
212: CGNE 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 CGNE converges in one iteration, but GMRES and CGS need N
214: iterations (see Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992). If you intend
215: to solve least squares problems, use KSPLSQR.
217: This is NOT a different algorithm than used with KSPCG, it merely uses that algorithm with the
218: matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
220: This method requires that one be able to apply the transpose of the preconditioner and operator
221: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
222: the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
224: This only supports left preconditioning.
226: This object is subclassed off of KSPCG
228: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
229: KSPCGSetType(), KSPBICG
231: M*/
233: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
234: {
236: KSP_CG *cg;
239: PetscNewLog(ksp,&cg);
240: #if !defined(PETSC_USE_COMPLEX)
241: cg->type = KSP_CG_SYMMETRIC;
242: #else
243: cg->type = KSP_CG_HERMITIAN;
244: #endif
245: ksp->data = (void*)cg;
246: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
247: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
248: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
249: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
251: /*
252: Sets the functions that are associated with this data structure
253: (in C++ this is the same as defining virtual functions)
254: */
255: ksp->ops->setup = KSPSetUp_CGNE;
256: ksp->ops->solve = KSPSolve_CGNE;
257: ksp->ops->destroy = KSPDestroy_CG;
258: ksp->ops->view = KSPView_CG;
259: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
260: ksp->ops->buildsolution = KSPBuildSolutionDefault;
261: ksp->ops->buildresidual = KSPBuildResidualDefault;
263: /*
264: Attach the function KSPCGSetType_CGNE() to this object. The routine
265: KSPCGSetType() checks for this attached function and calls it if it finds
266: it. (Sort of like a dynamic member function that can be added at run time
267: */
268: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
269: return(0);
270: }