Actual source code: cg.c
1: #define PETSCKSP_DLL
3: /*
4: This file implements the conjugate gradient method in PETSc as part of
5: KSP. You can use this as a starting point for implementing your own
6: Krylov method that is not provided with PETSc.
8: The following basic routines are required for each Krylov method.
9: KSPCreate_XXX() - Creates the Krylov context
10: KSPSetFromOptions_XXX() - Sets runtime options
11: KSPSolve_XXX() - Runs the Krylov method
12: KSPDestroy_XXX() - Destroys the Krylov context, freeing all
13: memory it needed
14: Here the "_XXX" denotes a particular implementation, in this case
15: we use _CG (e.g. KSPCreate_CG, KSPDestroy_CG). These routines are
16: are actually called vai the common user interface routines
17: KSPSetType(), KSPSetFromOptions(), KSPSolve(), and KSPDestroy() so the
18: application code interface remains identical for all preconditioners.
20: Other basic routines for the KSP objects include
21: KSPSetUp_XXX()
22: KSPView_XXX() - Prints details of solver being used.
24: Detailed notes:
25: By default, this code implements the CG (Conjugate Gradient) method,
26: which is valid for real symmetric (and complex Hermitian) positive
27: definite matrices. Note that for the complex Hermitian case, the
28: VecDot() arguments within the code MUST remain in the order given
29: for correct computation of inner products.
31: Reference: Hestenes and Steifel, 1952.
33: By switching to the indefinite vector inner product, VecTDot(), the
34: same code is used for the complex symmetric case as well. The user
35: must call KSPCGSetType(ksp,KSP_CG_SYMMETRIC) or use the option
36: -ksp_cg_symmetric to invoke this variant for the complex case.
37: Note, however, that the complex symmetric code is NOT valid for
38: all such matrices ... and thus we don't recommend using this method.
39: */
40: /*
41: cgctx.h defines the simple data structured used to store information
42: related to the type of matrix (e.g. complex symmetric) being solved and
43: data used during the optional Lanczo process used to compute eigenvalues
44: */
45: #include src/ksp/ksp/impls/cg/cgctx.h
46: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal *,PetscReal *);
47: EXTERN PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);
49: /*
50: KSPSetUp_CG - Sets up the workspace needed by the CG method.
52: This is called once, usually automatically by KSPSolve() or KSPSetUp()
53: but can be called directly by KSPSetUp()
54: */
57: PetscErrorCode KSPSetUp_CG(KSP ksp)
58: {
59: KSP_CG *cgP = (KSP_CG*)ksp->data;
61: PetscInt maxit = ksp->max_it;
64: /*
65: This implementation of CG only handles left preconditioning
66: so generate an error otherwise.
67: */
68: if (ksp->pc_side == PC_RIGHT) {
69: SETERRQ(PETSC_ERR_SUP,"No right preconditioning for KSPCG");
70: } else if (ksp->pc_side == PC_SYMMETRIC) {
71: SETERRQ(PETSC_ERR_SUP,"No symmetric preconditioning for KSPCG");
72: }
74: /* get work vectors needed by CG */
75: KSPDefaultGetWork(ksp,3);
77: /*
78: If user requested computations of eigenvalues then allocate work
79: work space needed
80: */
81: if (ksp->calc_sings) {
82: /* get space to store tridiagonal matrix for Lanczos */
83: PetscMalloc(2*(maxit+1)*sizeof(PetscScalar),&cgP->e);
84: PetscLogObjectMemory(ksp,2*(maxit+1)*sizeof(PetscScalar));
85: cgP->d = cgP->e + maxit + 1;
86: PetscMalloc(2*(maxit+1)*sizeof(PetscReal),&cgP->ee);
87: PetscLogObjectMemory(ksp,2*(maxit+1)*sizeof(PetscScalar));
88: cgP->dd = cgP->ee + maxit + 1;
89: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
90: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
91: }
92: return(0);
93: }
95: /*
96: KSPSolve_CG - This routine actually applies the conjugate gradient
97: method
99: Input Parameter:
100: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
101: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
102: */
105: PetscErrorCode KSPSolve_CG(KSP ksp)
106: {
108: PetscInt i,stored_max_it,eigs;
109: PetscScalar dpi,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0;
110: PetscReal dp = 0.0;
111: Vec X,B,Z,R,P;
112: KSP_CG *cg;
113: Mat Amat,Pmat;
114: MatStructure pflag;
115: PetscTruth diagonalscale;
118: PCDiagonalScale(ksp->pc,&diagonalscale);
119: if (diagonalscale) SETERRQ1(PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",ksp->type_name);
121: cg = (KSP_CG*)ksp->data;
122: eigs = ksp->calc_sings;
123: stored_max_it = ksp->max_it;
124: X = ksp->vec_sol;
125: B = ksp->vec_rhs;
126: R = ksp->work[0];
127: Z = ksp->work[1];
128: P = ksp->work[2];
130: #if !defined(PETSC_USE_COMPLEX)
131: #define VecXDot(x,y,a) VecDot(x,y,a)
132: #else
133: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
134: #endif
136: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
137: PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
139: ksp->its = 0;
140: if (!ksp->guess_zero) {
141: KSP_MatMult(ksp,Amat,X,R); /* r <- b - Ax */
142: VecAYPX(R,-1.0,B);
143: } else {
144: VecCopy(B,R); /* r <- b (x is 0) */
145: }
146: KSP_PCApply(ksp,R,Z); /* z <- Br */
147: VecXDot(Z,R,&beta);
148: if (ksp->normtype == KSP_PRECONDITIONED_NORM) {
149: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
150: } else if (ksp->normtype == KSP_UNPRECONDITIONED_NORM) {
151: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
152: } else if (ksp->normtype == KSP_NATURAL_NORM) {
153: dp = sqrt(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
154: } else dp = 0.0;
155: KSPLogResidualHistory(ksp,dp);
156: KSPMonitor(ksp,0,dp); /* call any registered monitor routines */
157: ksp->rnorm = dp;
159: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
160: if (ksp->reason) return(0);
162: i = 0;
163: do {
164: ksp->its = i+1;
165: VecXDot(Z,R,&beta); /* beta <- r'z */
166: if (beta == 0.0) {
167: ksp->reason = KSP_CONVERGED_ATOL;
168: PetscInfo(ksp,"converged due to beta = 0\n");
169: break;
170: #if !defined(PETSC_USE_COMPLEX)
171: } else if (beta < 0.0) {
172: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
173: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
174: break;
175: #endif
176: }
177: if (!i) {
178: VecCopy(Z,P); /* p <- z */
179: b = 0.0;
180: } else {
181: b = beta/betaold;
182: if (eigs) {
183: if (ksp->max_it != stored_max_it) {
184: SETERRQ(PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
185: }
186: e[i] = sqrt(PetscAbsScalar(b))/a;
187: }
188: VecAYPX(P,b,Z); /* p <- z + b* p */
189: }
190: betaold = beta;
191: KSP_MatMult(ksp,Amat,P,Z); /* z <- Kp */
192: VecXDot(P,Z,&dpi); /* dpi <- z'p */
193: if (PetscAbsScalar(dpi) <= 0.0) {
194: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
195: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
196: break;
197: }
198: a = beta/dpi; /* a = beta/p'z */
199: if (eigs) {
200: d[i] = sqrt(PetscAbsScalar(b))*e[i] + 1.0/a;
201: }
202: VecAXPY(X,a,P); /* x <- x + ap */
203: VecAXPY(R,-a,Z); /* r <- r - az */
204: if (ksp->normtype == KSP_PRECONDITIONED_NORM) {
205: KSP_PCApply(ksp,R,Z); /* z <- Br */
206: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
207: } else if (ksp->normtype == KSP_UNPRECONDITIONED_NORM) {
208: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
209: } else if (ksp->normtype == KSP_NATURAL_NORM) {
210: dp = sqrt(PetscAbsScalar(beta));
211: } else {
212: dp = 0.0;
213: }
214: ksp->rnorm = dp;
215: KSPLogResidualHistory(ksp,dp);
216: KSPMonitor(ksp,i+1,dp);
217: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
218: if (ksp->reason) break;
219: if (ksp->normtype != KSP_PRECONDITIONED_NORM) {
220: KSP_PCApply(ksp,R,Z); /* z <- Br */
221: }
222: i++;
223: } while (i<ksp->max_it);
224: if (i >= ksp->max_it) {
225: ksp->reason = KSP_DIVERGED_ITS;
226: }
227: return(0);
228: }
229: /*
230: KSPDestroy_CG - Frees all memory space used by the Krylov method
232: */
235: PetscErrorCode KSPDestroy_CG(KSP ksp)
236: {
237: KSP_CG *cg = (KSP_CG*)ksp->data;
241: /* free space used for singular value calculations */
242: if (ksp->calc_sings) {
243: PetscFree(cg->e);
244: PetscFree(cg->ee);
245: }
247: KSPDefaultFreeWork(ksp);
248:
249: /* free the context variable */
250: PetscFree(cg);
251: return(0);
252: }
254: /*
255: KSPView_CG - Prints information about the current Krylov method being used
257: Currently this only prints information to a file (or stdout) about the
258: symmetry of the problem. If your Krylov method has special options or
259: flags that information should be printed here.
261: */
264: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
265: {
266: #if defined(PETSC_USE_COMPLEX)
267: KSP_CG *cg = (KSP_CG *)ksp->data;
269: PetscTruth iascii;
272: PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
273: if (iascii) {
274: PetscViewerASCIIPrintf(viewer," CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
275: } else {
276: SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP cg",((PetscObject)viewer)->type_name);
277: }
278: #endif
279: return(0);
280: }
282: /*
283: KSPSetFromOptions_CG - Checks the options database for options related to the
284: conjugate gradient method.
285: */
288: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)
289: {
290: #if defined(PETSC_USE_COMPLEX)
292: KSP_CG *cg = (KSP_CG *)ksp->data;
293: #endif
296: #if defined(PETSC_USE_COMPLEX)
297: PetscOptionsHead("KSP CG and CGNE options");
298: PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
299: (PetscEnum*)&cg->type,PETSC_NULL);
300: PetscOptionsTail();
301: #endif
302: return(0);
303: }
305: /*
306: KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
307: This routine is registered below in KSPCreate_CG() and called from the
308: routine KSPCGSetType() (see the file cgtype.c).
311: */
315: PetscErrorCode PETSCKSP_DLLEXPORT KSPCGSetType_CG(KSP ksp,KSPCGType type)
316: {
317: KSP_CG *cg;
320: cg = (KSP_CG *)ksp->data;
321: cg->type = type;
322: return(0);
323: }
326: /*
327: KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
328: function pointers for all the routines it needs to call (KSPSolve_CG() etc)
331: */
332: /*MC
333: KSPCG - The preconditioned conjugate gradient (PCG) iterative method
335: Options Database Keys:
336: + -ksp_cg_Hermitian - (for complex matrices only) indicates the matrix is Hermitian
337: - -ksp_cg_symmetric - (for complex matrices only) indicates the matrix is symmetric
339: Level: beginner
341: Notes: The PCG method requires both the matrix and preconditioner to
342: be symmetric positive (semi) definite
344: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
345: KSPCGSetType()
347: M*/
351: PetscErrorCode PETSCKSP_DLLEXPORT KSPCreate_CG(KSP ksp)
352: {
354: KSP_CG *cg;
357: PetscNew(KSP_CG,&cg);
358: PetscLogObjectMemory(ksp,sizeof(KSP_CG));
359: #if !defined(PETSC_USE_COMPLEX)
360: cg->type = KSP_CG_SYMMETRIC;
361: #else
362: cg->type = KSP_CG_HERMITIAN;
363: #endif
364: ksp->data = (void*)cg;
365: ksp->pc_side = PC_LEFT;
367: /*
368: Sets the functions that are associated with this data structure
369: (in C++ this is the same as defining virtual functions)
370: */
371: ksp->ops->setup = KSPSetUp_CG;
372: ksp->ops->solve = KSPSolve_CG;
373: ksp->ops->destroy = KSPDestroy_CG;
374: ksp->ops->view = KSPView_CG;
375: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
376: ksp->ops->buildsolution = KSPDefaultBuildSolution;
377: ksp->ops->buildresidual = KSPDefaultBuildResidual;
379: /*
380: Attach the function KSPCGSetType_CG() to this object. The routine
381: KSPCGSetType() checks for this attached function and calls it if it finds
382: it. (Sort of like a dynamic member function that can be added at run time
383: */
384: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C","KSPCGSetType_CG",
385: KSPCGSetType_CG);
386: return(0);
387: }