Actual source code: cgne.c
petsc-3.9.4 2018-09-11
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);
59: Virtually identical to the KSPSolve_CG, it should definitely reuse the same code.
61: */
62: static PetscErrorCode KSPSolve_CGNE(KSP ksp)
63: {
65: PetscInt i,stored_max_it,eigs;
66: PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
67: PetscReal dp = 0.0;
68: Vec X,B,Z,R,P,T;
69: KSP_CG *cg;
70: Mat Amat,Pmat;
71: PetscBool diagonalscale,transpose_pc;
74: PCGetDiagonalScale(ksp->pc,&diagonalscale);
75: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
76: PCApplyTransposeExists(ksp->pc,&transpose_pc);
78: cg = (KSP_CG*)ksp->data;
79: eigs = ksp->calc_sings;
80: stored_max_it = ksp->max_it;
81: X = ksp->vec_sol;
82: B = ksp->vec_rhs;
83: R = ksp->work[0];
84: Z = ksp->work[1];
85: P = ksp->work[2];
86: T = ksp->work[3];
88: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
90: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
91: PCGetOperators(ksp->pc,&Amat,&Pmat);
93: ksp->its = 0;
94: KSP_MatMultTranspose(ksp,Amat,B,T);
95: if (!ksp->guess_zero) {
96: KSP_MatMult(ksp,Amat,X,P);
97: KSP_MatMultTranspose(ksp,Amat,P,R);
98: VecAYPX(R,-1.0,T);
99: } else {
100: VecCopy(T,R); /* r <- b (x is 0) */
101: }
102: if (transpose_pc) {
103: KSP_PCApplyTranspose(ksp,R,T);
104: } else {
105: KSP_PCApply(ksp,R,T);
106: }
107: KSP_PCApply(ksp,T,Z);
109: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
110: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
111: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
112: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
113: } else if (ksp->normtype == KSP_NORM_NATURAL) {
114: VecXDot(Z,R,&beta);
115: KSPCheckDot(ksp,beta);
116: dp = PetscSqrtReal(PetscAbsScalar(beta));
117: } else dp = 0.0;
118: KSPLogResidualHistory(ksp,dp);
119: KSPMonitor(ksp,0,dp);
120: ksp->rnorm = dp;
121: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
122: if (ksp->reason) return(0);
124: i = 0;
125: do {
126: ksp->its = i+1;
127: VecXDot(Z,R,&beta); /* beta <- r'z */
128: KSPCheckDot(ksp,beta);
129: if (beta == 0.0) {
130: ksp->reason = KSP_CONVERGED_ATOL;
131: 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: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
137: break;
138: #endif
139: }
140: if (!i) {
141: VecCopy(Z,P); /* p <- z */
142: b = 0.0;
143: } else {
144: b = beta/betaold;
145: if (eigs) {
146: if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
147: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
148: }
149: VecAYPX(P,b,Z); /* p <- z + b* p */
150: }
151: betaold = beta;
152: KSP_MatMult(ksp,Amat,P,T);
153: KSP_MatMultTranspose(ksp,Amat,T,Z);
154: 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: VecAXPY(X,a,P); /* x <- x + ap */
159: VecAXPY(R,-a,Z); /* r <- r - az */
160: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
161: if (transpose_pc) {
162: KSP_PCApplyTranspose(ksp,R,T);
163: } else {
164: KSP_PCApply(ksp,R,T);
165: }
166: KSP_PCApply(ksp,T,Z);
167: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
168: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
169: VecNorm(R,NORM_2,&dp);
170: } else if (ksp->normtype == KSP_NORM_NATURAL) {
171: dp = PetscSqrtReal(PetscAbsScalar(beta));
172: } else {
173: dp = 0.0;
174: }
175: ksp->rnorm = dp;
176: KSPLogResidualHistory(ksp,dp);
177: if (eigs) cg->ned = ksp->its;
178: KSPMonitor(ksp,i+1,dp);
179: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
180: if (ksp->reason) break;
181: if (ksp->normtype != KSP_NORM_PRECONDITIONED) {
182: if (transpose_pc) {
183: KSP_PCApplyTranspose(ksp,R,T);
184: } else {
185: KSP_PCApply(ksp,R,T);
186: }
187: KSP_PCApply(ksp,T,Z);
188: }
189: i++;
190: } while (i<ksp->max_it);
191: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
192: return(0);
193: }
195: /*
196: KSPCreate_CGNE - Creates the data structure for the Krylov method CGNE and sets the
197: function pointers for all the routines it needs to call (KSPSolve_CGNE() etc)
199: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
200: */
202: /*MC
203: KSPCGNE - Applies the preconditioned conjugate gradient method to the normal equations
204: without explicitly forming A^t*A
206: Options Database Keys:
207: . -ksp_cg_type <Hermitian or symmetric - (for complex matrices only) indicates the matrix is Hermitian or symmetric
210: Level: beginner
212: Notes: eigenvalue computation routines will return information about the
213: spectrum of A^t*A, rather than A.
216: CGNE is a general-purpose non-symmetric method. It works well when the singular values are much better behaved than
217: eigenvalues. A unitary matrix is a classic example where CGNE converges in one iteration, but GMRES and CGS need N
218: iterations (see Nachtigal, Reddy, and Trefethen, "How fast are nonsymmetric matrix iterations", 1992). If you intend
219: to solve least squares problems, use KSPLSQR.
221: This is NOT a different algorithm than used with KSPCG, it merely uses that algorithm with the
222: matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
224: This method requires that one be able to apply the transpose of the preconditioner and operator
225: as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
226: the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
228: This only supports left preconditioning.
230: This object is subclassed off of KSPCG
232: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
233: KSPCGSetType(), KSPBICG
235: M*/
237: PETSC_EXTERN PetscErrorCode KSPCreate_CGNE(KSP ksp)
238: {
240: KSP_CG *cg;
243: PetscNewLog(ksp,&cg);
244: #if !defined(PETSC_USE_COMPLEX)
245: cg->type = KSP_CG_SYMMETRIC;
246: #else
247: cg->type = KSP_CG_HERMITIAN;
248: #endif
249: ksp->data = (void*)cg;
250: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
251: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
252: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
254: /*
255: Sets the functions that are associated with this data structure
256: (in C++ this is the same as defining virtual functions)
257: */
258: ksp->ops->setup = KSPSetUp_CGNE;
259: ksp->ops->solve = KSPSolve_CGNE;
260: ksp->ops->destroy = KSPDestroy_CG;
261: ksp->ops->view = KSPView_CG;
262: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
263: ksp->ops->buildsolution = KSPBuildSolutionDefault;
264: ksp->ops->buildresidual = KSPBuildResidualDefault;
266: /*
267: Attach the function KSPCGSetType_CGNE() to this object. The routine
268: KSPCGSetType() checks for this attached function and calls it if it finds
269: it. (Sort of like a dynamic member function that can be added at run time
270: */
271: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CGNE);
272: return(0);
273: }