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,PetscScalar,&cgP->e,maxit+1,PetscScalar,&cgP->d,maxit+1,PetscReal,&cgP->ee,maxit+1,PetscReal,&cgP->dd);
74: PetscLogObjectMemory(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: MatStructure pflag;
103: PetscBool diagonalscale;
106: PCGetDiagonalScale(ksp->pc,&diagonalscale);
107: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
109: cg = (KSP_CG*)ksp->data;
110: eigs = ksp->calc_sings;
111: stored_max_it = ksp->max_it;
112: X = ksp->vec_sol;
113: B = ksp->vec_rhs;
114: R = ksp->work[0];
115: Z = ksp->work[1];
116: P = ksp->work[2];
117: if (cg->singlereduction) {
118: S = ksp->work[3];
119: W = ksp->work[4];
120: } else {
121: S = 0; /* unused */
122: W = Z;
123: }
125: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))127: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
128: PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
130: ksp->its = 0;
131: if (!ksp->guess_zero) {
132: KSP_MatMult(ksp,Amat,X,R); /* r <- b - Ax */
133: VecAYPX(R,-1.0,B);
134: } else {
135: VecCopy(B,R); /* r <- b (x is 0) */
136: }
138: switch (ksp->normtype) {
139: case KSP_NORM_PRECONDITIONED:
140: KSP_PCApply(ksp,R,Z); /* z <- Br */
141: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
142: break;
143: case KSP_NORM_UNPRECONDITIONED:
144: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
145: break;
146: case KSP_NORM_NATURAL:
147: KSP_PCApply(ksp,R,Z); /* z <- Br */
148: if (cg->singlereduction) {
149: KSP_MatMult(ksp,Amat,Z,S);
150: VecXDot(Z,S,&delta);
151: }
152: VecXDot(Z,R,&beta); /* beta <- z'*r */
153: if (PetscIsInfOrNanScalar(beta)) {
154: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
155: else {
156: ksp->reason = KSP_DIVERGED_NANORINF;
157: return(0);
158: }
159: }
160: dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
161: break;
162: case KSP_NORM_NONE:
163: dp = 0.0;
164: break;
165: default:SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
166: }
167: KSPLogResidualHistory(ksp,dp);
168: KSPMonitor(ksp,0,dp);
169: ksp->rnorm = dp;
171: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
172: if (ksp->reason) return(0);
174: if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
175: KSP_PCApply(ksp,R,Z); /* z <- Br */
176: }
177: if (ksp->normtype != KSP_NORM_NATURAL) {
178: if (cg->singlereduction) {
179: KSP_MatMult(ksp,Amat,Z,S);
180: VecXDot(Z,S,&delta);
181: }
182: VecXDot(Z,R,&beta); /* beta <- z'*r */
183: if (PetscIsInfOrNanScalar(beta)) {
184: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
185: else {
186: ksp->reason = KSP_DIVERGED_NANORINF;
187: return(0);
188: }
189: }
190: }
192: i = 0;
193: do {
194: ksp->its = i+1;
195: if (beta == 0.0) {
196: ksp->reason = KSP_CONVERGED_ATOL;
197: PetscInfo(ksp,"converged due to beta = 0\n");
198: break;
199: #if !defined(PETSC_USE_COMPLEX)
200: } else if ((i > 0) && (beta*betaold < 0.0)) {
201: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
202: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
203: break;
204: #endif
205: }
206: if (!i) {
207: VecCopy(Z,P); /* p <- z */
208: b = 0.0;
209: } else {
210: b = beta/betaold;
211: if (eigs) {
212: if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
213: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
214: }
215: VecAYPX(P,b,Z); /* p <- z + b* p */
216: }
217: dpiold = dpi;
218: if (!cg->singlereduction || !i) {
219: KSP_MatMult(ksp,Amat,P,W); /* w <- Ap */
220: VecXDot(P,W,&dpi); /* dpi <- p'w */
221: } else {
222: VecAYPX(W,beta/betaold,S); /* w <- Ap */
223: dpi = delta - beta*beta*dpiold/(betaold*betaold); /* dpi <- p'w */
224: }
225: betaold = beta;
226: if (PetscIsInfOrNanScalar(dpi)) {
227: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
228: else {
229: ksp->reason = KSP_DIVERGED_NANORINF;
230: return(0);
231: }
232: }
234: if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
235: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
236: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
237: break;
238: }
239: a = beta/dpi; /* a = beta/p'w */
240: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
241: VecAXPY(X,a,P); /* x <- x + ap */
242: VecAXPY(R,-a,W); /* r <- r - aw */
243: if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
244: KSP_PCApply(ksp,R,Z); /* z <- Br */
245: if (cg->singlereduction) {
246: KSP_MatMult(ksp,Amat,Z,S);
247: }
248: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
249: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
250: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
251: } else if (ksp->normtype == KSP_NORM_NATURAL) {
252: KSP_PCApply(ksp,R,Z); /* z <- Br */
253: if (cg->singlereduction) {
254: PetscScalar tmp[2];
255: Vec vecs[2];
256: vecs[0] = S; vecs[1] = R;
257: KSP_MatMult(ksp,Amat,Z,S);
258: VecMDot(Z,2,vecs,tmp);
259: delta = tmp[0]; beta = tmp[1];
260: } else {
261: VecXDot(Z,R,&beta); /* beta <- r'*z */
262: }
263: if (PetscIsInfOrNanScalar(beta)) {
264: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
265: else {
266: ksp->reason = KSP_DIVERGED_NANORINF;
267: return(0);
268: }
269: }
270: dp = PetscSqrtReal(PetscAbsScalar(beta));
271: } else {
272: dp = 0.0;
273: }
274: ksp->rnorm = dp;
275: KSPLogResidualHistory(ksp,dp);
276: KSPMonitor(ksp,i+1,dp);
277: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
278: if (ksp->reason) break;
280: if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
281: KSP_PCApply(ksp,R,Z); /* z <- Br */
282: if (cg->singlereduction) {
283: KSP_MatMult(ksp,Amat,Z,S);
284: }
285: }
286: if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
287: if (cg->singlereduction) {
288: PetscScalar tmp[2];
289: Vec vecs[2];
290: vecs[0] = S; vecs[1] = R;
291: VecMDot(Z,2,vecs,tmp);
292: delta = tmp[0]; beta = tmp[1];
293: } else {
294: VecXDot(Z,R,&beta); /* beta <- z'*r */
295: }
296: if (PetscIsInfOrNanScalar(beta)) {
297: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to Nan or Inf inner product");
298: else {
299: ksp->reason = KSP_DIVERGED_NANORINF;
300: return(0);
301: }
302: }
303: }
305: i++;
306: } while (i<ksp->max_it);
307: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
308: return(0);
309: }
313: PetscErrorCode KSPDestroy_CG(KSP ksp)314: {
315: KSP_CG *cg = (KSP_CG*)ksp->data;
319: /* free space used for singular value calculations */
320: if (ksp->calc_sings) {
321: PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
322: }
323: KSPDestroyDefault(ksp);
324: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
325: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
326: return(0);
327: }
329: /*
330: KSPView_CG - Prints information about the current Krylov method being used
332: Currently this only prints information to a file (or stdout) about the
333: symmetry of the problem. If your Krylov method has special options or
334: flags that information should be printed here.
336: */
339: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)340: {
341: #if defined(PETSC_USE_COMPLEX)
342: KSP_CG *cg = (KSP_CG*)ksp->data;
344: PetscBool iascii;
347: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
348: if (iascii) {
349: PetscViewerASCIIPrintf(viewer," CG or CGNE: variant %s\n",KSPCGTypes[cg->type]);
350: }
351: #endif
352: return(0);
353: }
355: /*
356: KSPSetFromOptions_CG - Checks the options database for options related to the
357: conjugate gradient method.
358: */
361: PetscErrorCode KSPSetFromOptions_CG(KSP ksp)362: {
364: KSP_CG *cg = (KSP_CG*)ksp->data;
367: PetscOptionsHead("KSP CG and CGNE options");
368: #if defined(PETSC_USE_COMPLEX)
369: PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
370: (PetscEnum*)&cg->type,NULL);
371: #endif
372: PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()",
373: "KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,NULL);
374: PetscOptionsTail();
375: return(0);
376: }
378: /*
379: KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
380: This routine is registered below in KSPCreate_CG() and called from the
381: routine KSPCGSetType() (see the file cgtype.c).
382: */
385: static PetscErrorCode KSPCGSetType_CG(KSP ksp,KSPCGType type)386: {
387: KSP_CG *cg = (KSP_CG*)ksp->data;
390: cg->type = type;
391: return(0);
392: }
396: static PetscErrorCode KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)397: {
398: KSP_CG *cg = (KSP_CG*)ksp->data;
401: cg->singlereduction = flg;
402: return(0);
403: }
405: /*
406: KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
407: function pointers for all the routines it needs to call (KSPSolve_CG() etc)
409: It must be wrapped in EXTERN_C_BEGIN to be dynamically linkable in C++
410: */
411: /*MC
412: KSPCG - The preconditioned conjugate gradient (PCG) iterative method
414: Options Database Keys:
415: + -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
416: . -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
417: - -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPI_Allreduce() call, see KSPCGUseSingleReduction()
419: Level: beginner
421: Notes: The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite
422: Only left preconditioning is supported.
424: For complex numbers there are two different CG methods. One for Hermitian symmetric matrices and one for non-Hermitian symmetric matrices. Use
425: KSPCGSetType() to indicate which type you are using.
427: Developer Notes: KSPSolve_CG() should actually query the matrix to determine if it is Hermitian symmetric or not and NOT require the user to
428: indicate it to the KSP object.
430: References:
431: Methods of Conjugate Gradients for Solving Linear Systems, Magnus R. Hestenes and Eduard Stiefel,
432: Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
433: pp. 409--436.
435: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
436: KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG438: M*/
441: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)442: {
444: KSP_CG *cg;
447: PetscNewLog(ksp,KSP_CG,&cg);
448: #if !defined(PETSC_USE_COMPLEX)
449: cg->type = KSP_CG_SYMMETRIC;
450: #else
451: cg->type = KSP_CG_HERMITIAN;
452: #endif
453: ksp->data = (void*)cg;
455: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
456: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
457: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,1);
458: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
460: /*
461: Sets the functions that are associated with this data structure
462: (in C++ this is the same as defining virtual functions)
463: */
464: ksp->ops->setup = KSPSetUp_CG;
465: ksp->ops->solve = KSPSolve_CG;
466: ksp->ops->destroy = KSPDestroy_CG;
467: ksp->ops->view = KSPView_CG;
468: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
469: ksp->ops->buildsolution = KSPBuildSolutionDefault;
470: ksp->ops->buildresidual = KSPBuildResidualDefault;
472: /*
473: Attach the function KSPCGSetType_CG() to this object. The routine
474: KSPCGSetType() checks for this attached function and calls it if it finds
475: it. (Sort of like a dynamic member function that can be added at run time
476: */
477: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
478: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
479: return(0);
480: }