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_type 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",((PetscObject)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: }
147: if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
148: KSP_PCApply(ksp,R,Z); /* z <- Br */
149: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
150: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
151: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
152: } else if (ksp->normtype == KSP_NORM_NATURAL) {
153: KSP_PCApply(ksp,R,Z); /* z <- Br */
154: VecXDot(Z,R,&beta); /* beta <- z'*r */
155: if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
156: dp = sqrt(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
157: } else dp = 0.0;
158: KSPLogResidualHistory(ksp,dp);
159: KSPMonitor(ksp,0,dp); /* call any registered monitor routines */
160: ksp->rnorm = dp;
162: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
163: if (ksp->reason) return(0);
165: if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)){
166: KSP_PCApply(ksp,R,Z); /* z <- Br */
167: }
168: if (ksp->normtype != KSP_NORM_NATURAL){
169: VecXDot(Z,R,&beta); /* beta <- z'*r */
170: if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
171: }
173: i = 0;
174: do {
175: ksp->its = i+1;
176: if (beta == 0.0) {
177: ksp->reason = KSP_CONVERGED_ATOL;
178: PetscInfo(ksp,"converged due to beta = 0\n");
179: break;
180: #if !defined(PETSC_USE_COMPLEX)
181: } else if (beta < 0.0) {
182: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
183: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
184: break;
185: #endif
186: }
187: if (!i) {
188: VecCopy(Z,P); /* p <- z */
189: b = 0.0;
190: } else {
191: b = beta/betaold;
192: if (eigs) {
193: if (ksp->max_it != stored_max_it) {
194: SETERRQ(PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
195: }
196: e[i] = sqrt(PetscAbsScalar(b))/a;
197: }
198: VecAYPX(P,b,Z); /* p <- z + b* p */
199: }
200: betaold = beta;
201: KSP_MatMult(ksp,Amat,P,Z); /* z <- Kp */
202: VecXDot(P,Z,&dpi); /* dpi <- z'p */
203: if PetscIsInfOrNanScalar(dpi) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
205: if (PetscRealPart(dpi) <= 0.0) {
206: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
207: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
208: break;
209: }
210: a = beta/dpi; /* a = beta/p'z */
211: if (eigs) {
212: d[i] = sqrt(PetscAbsScalar(b))*e[i] + 1.0/a;
213: }
214: VecAXPY(X,a,P); /* x <- x + ap */
215: VecAXPY(R,-a,Z); /* r <- r - az */
216: if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
217: KSP_PCApply(ksp,R,Z); /* z <- Br */
218: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
219: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
220: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
221: } else if (ksp->normtype == KSP_NORM_NATURAL) {
222: KSP_PCApply(ksp,R,Z); /* z <- Br */
223: VecXDot(Z,R,&beta); /* beta <- r'*z */
224: if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
225: dp = sqrt(PetscAbsScalar(beta));
226: } else {
227: dp = 0.0;
228: }
229: ksp->rnorm = dp;
230: KSPLogResidualHistory(ksp,dp);
231: KSPMonitor(ksp,i+1,dp);
232: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
233: if (ksp->reason) break;
235: if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)){
236: KSP_PCApply(ksp,R,Z); /* z <- Br */
237: }
238: if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)){
239: VecXDot(Z,R,&beta); /* beta <- z'*r */
240: if PetscIsInfOrNanScalar(beta) SETERRQ(PETSC_ERR_FP,"Infinite or not-a-number generated in dot product");
241: }
243: i++;
244: } while (i<ksp->max_it);
245: if (i >= ksp->max_it) {
246: ksp->reason = KSP_DIVERGED_ITS;
247: }
248: return(0);
249: }
250: /*
251: KSPDestroy_CG - Frees all memory space used by the Krylov method
253: */
256: PetscErrorCode KSPDestroy_CG(KSP ksp)
257: {
258: KSP_CG *cg = (KSP_CG*)ksp->data;
262: /* free space used for singular value calculations */
263: if (ksp->calc_sings) {
264: PetscFree(cg->e);
265: PetscFree(cg->ee);
266: }
267: KSPDefaultDestroy(ksp);
268: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C","",PETSC_NULL);
269: return(0);
270: }
272: /*
273: KSPView_CG - Prints information about the current Krylov method being used
275: Currently this only prints information to a file (or stdout) about the
276: symmetry of the problem. If your Krylov method has special options or
277: flags that information should be printed here.
279: */
282: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
283: {
284: #if defined(PETSC_USE_COMPLEX)
285: KSP_CG *cg = (KSP_CG *)ksp->data;
287: PetscTruth iascii;
290: PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
291: if (iascii) {
292: PetscViewerASCIIPrintf(viewer," CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
293: } else {
294: SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP cg",((PetscObject)viewer)->type_name);
295: }
296: #endif
297: return(0);
298: }
300: /*
301: KSPSetFromOptions_CG - Checks the options database for options related to the
302: conjugate gradient method.
303: */
306: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)
307: {
308: #if defined(PETSC_USE_COMPLEX)
310: KSP_CG *cg = (KSP_CG *)ksp->data;
311: #endif
314: #if defined(PETSC_USE_COMPLEX)
315: PetscOptionsHead("KSP CG and CGNE options");
316: PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
317: (PetscEnum*)&cg->type,PETSC_NULL);
318: PetscOptionsTail();
319: #endif
320: return(0);
321: }
323: /*
324: KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
325: This routine is registered below in KSPCreate_CG() and called from the
326: routine KSPCGSetType() (see the file cgtype.c).
329: */
333: PetscErrorCode KSPCGSetType_CG(KSP ksp,KSPCGType type)
334: {
335: KSP_CG *cg;
338: cg = (KSP_CG *)ksp->data;
339: cg->type = type;
340: return(0);
341: }
344: /*
345: KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
346: function pointers for all the routines it needs to call (KSPSolve_CG() etc)
349: */
350: /*MC
351: KSPCG - The preconditioned conjugate gradient (PCG) iterative method
353: Options Database Keys:
354: + -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian
355: - -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
357: Level: beginner
359: Notes: The PCG method requires both the matrix and preconditioner to
360: be symmetric positive (semi) definite
362: References:
363: Methods of Conjugate Gradients for Solving Linear Systems, Magnus R. Hestenes and Eduard Stiefel,
364: Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
365: pp. 409--436.
367: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
368: KSPCGSetType()
370: M*/
374: PetscErrorCode KSPCreate_CG(KSP ksp)
375: {
377: KSP_CG *cg;
380: PetscNewLog(ksp,KSP_CG,&cg);
381: #if !defined(PETSC_USE_COMPLEX)
382: cg->type = KSP_CG_SYMMETRIC;
383: #else
384: cg->type = KSP_CG_HERMITIAN;
385: #endif
386: ksp->data = (void*)cg;
387: ksp->pc_side = PC_LEFT;
389: /*
390: Sets the functions that are associated with this data structure
391: (in C++ this is the same as defining virtual functions)
392: */
393: ksp->ops->setup = KSPSetUp_CG;
394: ksp->ops->solve = KSPSolve_CG;
395: ksp->ops->destroy = KSPDestroy_CG;
396: ksp->ops->view = KSPView_CG;
397: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
398: ksp->ops->buildsolution = KSPDefaultBuildSolution;
399: ksp->ops->buildresidual = KSPDefaultBuildResidual;
401: /*
402: Attach the function KSPCGSetType_CG() to this object. The routine
403: KSPCGSetType() checks for this attached function and calls it if it finds
404: it. (Sort of like a dynamic member function that can be added at run time
405: */
406: PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPCGSetType_C",
407: "KSPCGSetType_CG",
408: KSPCGSetType_CG);
409: return(0);
410: }