2: /*
3: This file implements the conjugate gradient method in PETSc as part of
4: KSP. You can use this as a starting point for implementing your own
5: Krylov method that is not provided with PETSc.
7: The following basic routines are required for each Krylov method.
8: KSPCreate_XXX() - Creates the Krylov context
9: KSPSetFromOptions_XXX() - Sets runtime options
10: KSPSolve_XXX() - Runs the Krylov method
11: KSPDestroy_XXX() - Destroys the Krylov context, freeing all
12: memory it needed
13: Here the "_XXX" denotes a particular implementation, in this case
14: we use _CG (e.g. KSPCreate_CG, KSPDestroy_CG). These routines are
15: are actually called vai the common user interface routines
16: KSPSetType(), KSPSetFromOptions(), KSPSolve(), and KSPDestroy() so the
17: application code interface remains identical for all preconditioners.
19: Other basic routines for the KSP objects include
20: KSPSetUp_XXX()
21: KSPView_XXX() - Prints details of solver being used.
23: Detailed notes:
24: By default, this code implements the CG (Conjugate Gradient) method,
25: which is valid for real symmetric (and complex Hermitian) positive
26: definite matrices. Note that for the complex Hermitian case, the
27: VecDot() arguments within the code MUST remain in the order given
28: for correct computation of inner products.
30: Reference: Hestenes and Steifel, 1952.
32: By switching to the indefinite vector inner product, VecTDot(), the
33: same code is used for the complex symmetric case as well. The user
34: must call KSPCGSetType(ksp,KSP_CG_SYMMETRIC) or use the option
35: -ksp_cg_type symmetric to invoke this variant for the complex case.
36: Note, however, that the complex symmetric code is NOT valid for
37: all such matrices ... and thus we don't recommend using this method.
38: */
39: /*
40: cgimpl.h defines the simple data structured used to store information
41: related to the type of matrix (e.g. complex symmetric) being solved and
42: data used during the optional Lanczo process used to compute eigenvalues
43: */
44: #include <../src/ksp/ksp/impls/cg/cgimpl.h> /*I "petscksp.h" I*/
45: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
46: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);
48: /*
49: KSPSetUp_CG - Sets up the workspace needed by the CG method.
51: This is called once, usually automatically by KSPSolve() or KSPSetUp()
52: but can be called directly by KSPSetUp()
53: */
56: PetscErrorCode KSPSetUp_CG(KSP ksp) 57: {
58: KSP_CG *cgP = (KSP_CG*)ksp->data;
60: PetscInt maxit = ksp->max_it,nwork = 3;
63: /* get work vectors needed by CG */
64: if (cgP->singlereduction) nwork += 2;
65: KSPSetWorkVecs(ksp,nwork);
67: /*
68: If user requested computations of eigenvalues then allocate work
69: work space needed
70: */
71: if (ksp->calc_sings) {
72: /* get space to store tridiagonal matrix for Lanczos */
73: PetscMalloc4(maxit+1,&cgP->e,maxit+1,&cgP->d,maxit+1,&cgP->ee,maxit+1,&cgP->dd);
74: PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));
76: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
77: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
78: }
79: return(0);
80: }
82: /*
83: KSPSolve_CG - This routine actually applies the conjugate gradient method
85: This routine is MUCH too messy. I has too many options (norm type and single reduction) embedded making the code confusing and likely to be buggy.
87: Input Parameter:
88: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
89: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
90: */
93: PetscErrorCode KSPSolve_CG(KSP ksp) 94: {
96: PetscInt i,stored_max_it,eigs;
97: PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = 0,*d = 0,delta,dpiold;
98: PetscReal dp = 0.0;
99: Vec X,B,Z,R,P,S,W;
100: KSP_CG *cg;
101: Mat Amat,Pmat;
102: PetscBool diagonalscale;
105: PCGetDiagonalScale(ksp->pc,&diagonalscale);
106: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
108: cg = (KSP_CG*)ksp->data;
109: eigs = ksp->calc_sings;
110: stored_max_it = ksp->max_it;
111: X = ksp->vec_sol;
112: B = ksp->vec_rhs;
113: R = ksp->work[0];
114: Z = ksp->work[1];
115: P = ksp->work[2];
116: if (cg->singlereduction) {
117: S = ksp->work[3];
118: W = ksp->work[4];
119: } else {
120: S = 0; /* unused */
121: W = Z;
122: }
124: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))126: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
127: PCGetOperators(ksp->pc,&Amat,&Pmat);
129: ksp->its = 0;
130: if (!ksp->guess_zero) {
131: KSP_MatMult(ksp,Amat,X,R); /* r <- b - Ax */
132: VecAYPX(R,-1.0,B);
133: } else {
134: VecCopy(B,R); /* r <- b (x is 0) */
135: }
137: switch (ksp->normtype) {
138: case KSP_NORM_PRECONDITIONED:
139: KSP_PCApply(ksp,R,Z); /* z <- Br */
140: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
141: break;
142: case KSP_NORM_UNPRECONDITIONED:
143: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
144: break;
145: case KSP_NORM_NATURAL:
146: KSP_PCApply(ksp,R,Z); /* z <- Br */
147: if (cg->singlereduction) {
148: KSP_MatMult(ksp,Amat,Z,S);
149: VecXDot(Z,S,&delta);
150: }
151: VecXDot(Z,R,&beta); /* beta <- z'*r */
152: KSPCheckDot(ksp,beta);
153: dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
154: break;
155: case KSP_NORM_NONE:
156: dp = 0.0;
157: break;
158: default:SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
159: }
160: KSPLogResidualHistory(ksp,dp);
161: KSPMonitor(ksp,0,dp);
162: ksp->rnorm = dp;
164: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
165: if (ksp->reason) return(0);
167: if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
168: KSP_PCApply(ksp,R,Z); /* z <- Br */
169: }
170: if (ksp->normtype != KSP_NORM_NATURAL) {
171: if (cg->singlereduction) {
172: KSP_MatMult(ksp,Amat,Z,S);
173: VecXDot(Z,S,&delta);
174: }
175: VecXDot(Z,R,&beta); /* beta <- z'*r */
176: KSPCheckDot(ksp,beta);
177: }
179: i = 0;
180: do {
181: ksp->its = i+1;
182: if (beta == 0.0) {
183: ksp->reason = KSP_CONVERGED_ATOL;
184: PetscInfo(ksp,"converged due to beta = 0\n");
185: break;
186: #if !defined(PETSC_USE_COMPLEX)
187: } else if ((i > 0) && (beta*betaold < 0.0)) {
188: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
189: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
190: break;
191: #endif
192: }
193: if (!i) {
194: VecCopy(Z,P); /* p <- z */
195: b = 0.0;
196: } else {
197: b = beta/betaold;
198: if (eigs) {
199: if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
200: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
201: }
202: VecAYPX(P,b,Z); /* p <- z + b* p */
203: }
204: dpiold = dpi;
205: if (!cg->singlereduction || !i) {
206: KSP_MatMult(ksp,Amat,P,W); /* w <- Ap */
207: VecXDot(P,W,&dpi); /* dpi <- p'w */
208: } else {
209: VecAYPX(W,beta/betaold,S); /* w <- Ap */
210: dpi = delta - beta*beta*dpiold/(betaold*betaold); /* dpi <- p'w */
211: }
212: betaold = beta;
213: KSPCheckDot(ksp,beta);
215: if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
216: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
217: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
218: break;
219: }
220: a = beta/dpi; /* a = beta/p'w */
221: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
222: VecAXPY(X,a,P); /* x <- x + ap */
223: VecAXPY(R,-a,W); /* r <- r - aw */
224: if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
225: KSP_PCApply(ksp,R,Z); /* z <- Br */
226: if (cg->singlereduction) {
227: KSP_MatMult(ksp,Amat,Z,S);
228: }
229: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
230: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
231: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
232: } else if (ksp->normtype == KSP_NORM_NATURAL) {
233: KSP_PCApply(ksp,R,Z); /* z <- Br */
234: if (cg->singlereduction) {
235: PetscScalar tmp[2];
236: Vec vecs[2];
237: vecs[0] = S; vecs[1] = R;
238: KSP_MatMult(ksp,Amat,Z,S);
239: VecMDot(Z,2,vecs,tmp);
240: delta = tmp[0]; beta = tmp[1];
241: } else {
242: VecXDot(Z,R,&beta); /* beta <- r'*z */
243: }
244: KSPCheckDot(ksp,beta);
245: dp = PetscSqrtReal(PetscAbsScalar(beta));
246: } else {
247: dp = 0.0;
248: }
249: ksp->rnorm = dp;
250: KSPLogResidualHistory(ksp,dp);
251: if (eigs) cg->ned = ksp->its;
252: KSPMonitor(ksp,i+1,dp);
253: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
254: if (ksp->reason) break;
256: if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
257: KSP_PCApply(ksp,R,Z); /* z <- Br */
258: if (cg->singlereduction) {
259: KSP_MatMult(ksp,Amat,Z,S);
260: }
261: }
262: if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
263: if (cg->singlereduction) {
264: PetscScalar tmp[2];
265: Vec vecs[2];
266: vecs[0] = S; vecs[1] = R;
267: VecMDot(Z,2,vecs,tmp);
268: delta = tmp[0]; beta = tmp[1];
269: } else {
270: VecXDot(Z,R,&beta); /* beta <- z'*r */
271: }
272: KSPCheckDot(ksp,beta);
273: }
275: i++;
276: } while (i<ksp->max_it);
277: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
278: return(0);
279: }
283: PetscErrorCode KSPDestroy_CG(KSP ksp)284: {
285: KSP_CG *cg = (KSP_CG*)ksp->data;
289: /* free space used for singular value calculations */
290: if (ksp->calc_sings) {
291: PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
292: }
293: KSPDestroyDefault(ksp);
294: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
295: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
296: return(0);
297: }
299: /*
300: KSPView_CG - Prints information about the current Krylov method being used
302: Currently this only prints information to a file (or stdout) about the
303: symmetry of the problem. If your Krylov method has special options or
304: flags that information should be printed here.
306: */
309: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)310: {
311: #if defined(PETSC_USE_COMPLEX)
312: KSP_CG *cg = (KSP_CG*)ksp->data;
314: PetscBool iascii;
317: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
318: if (iascii) {
319: PetscViewerASCIIPrintf(viewer," CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
320: }
321: #endif
322: return(0);
323: }
325: /*
326: KSPSetFromOptions_CG - Checks the options database for options related to the
327: conjugate gradient method.
328: */
331: PetscErrorCode KSPSetFromOptions_CG(PetscOptions *PetscOptionsObject,KSP ksp)332: {
334: KSP_CG *cg = (KSP_CG*)ksp->data;
337: PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
338: #if defined(PETSC_USE_COMPLEX)
339: PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
340: (PetscEnum*)&cg->type,NULL);
341: #endif
342: PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
343: PetscOptionsTail();
344: return(0);
345: }
347: /*
348: KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
349: This routine is registered below in KSPCreate_CG() and called from the
350: routine KSPCGSetType() (see the file cgtype.c).
351: */
354: static PetscErrorCode KSPCGSetType_CG(KSP ksp,KSPCGType type)355: {
356: KSP_CG *cg = (KSP_CG*)ksp->data;
359: cg->type = type;
360: return(0);
361: }
365: static PetscErrorCode KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)366: {
367: KSP_CG *cg = (KSP_CG*)ksp->data;
370: cg->singlereduction = flg;
371: return(0);
372: }
374: /*
375: KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
376: function pointers for all the routines it needs to call (KSPSolve_CG() etc)
378: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
379: */
380: /*MC
381: KSPCG - The preconditioned conjugate gradient (PCG) iterative method
383: Options Database Keys:
384: + -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
385: . -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
386: - -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPI_Allreduce() call, see KSPCGUseSingleReduction()
388: Level: beginner
390: Notes: The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite
391: Only left preconditioning is supported.
393: For complex numbers there are two different CG methods. One for Hermitian symmetric matrices and one for non-Hermitian symmetric matrices. Use
394: KSPCGSetType() to indicate which type you are using.
396: Developer Notes: KSPSolve_CG() should actually query the matrix to determine if it is Hermitian symmetric or not and NOT require the user to
397: indicate it to the KSP object.
399: References:
400: Methods of Conjugate Gradients for Solving Linear Systems, Magnus R. Hestenes and Eduard Stiefel,
401: Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
402: pp. 409--436.
404: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
405: KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG407: M*/
410: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)411: {
413: KSP_CG *cg;
416: PetscNewLog(ksp,&cg);
417: #if !defined(PETSC_USE_COMPLEX)
418: cg->type = KSP_CG_SYMMETRIC;
419: #else
420: cg->type = KSP_CG_HERMITIAN;
421: #endif
422: ksp->data = (void*)cg;
424: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
425: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
426: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
428: /*
429: Sets the functions that are associated with this data structure
430: (in C++ this is the same as defining virtual functions)
431: */
432: ksp->ops->setup = KSPSetUp_CG;
433: ksp->ops->solve = KSPSolve_CG;
434: ksp->ops->destroy = KSPDestroy_CG;
435: ksp->ops->view = KSPView_CG;
436: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
437: ksp->ops->buildsolution = KSPBuildSolutionDefault;
438: ksp->ops->buildresidual = KSPBuildResidualDefault;
440: /*
441: Attach the function KSPCGSetType_CG() to this object. The routine
442: KSPCGSetType() checks for this attached function and calls it if it finds
443: it. (Sort of like a dynamic member function that can be added at run time
444: */
445: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
446: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
447: return(0);
448: }