Actual source code: cg.c
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
15: are actually called via 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>
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: */
54: static PetscErrorCode KSPSetUp_CG(KSP ksp)
55: {
56: KSP_CG *cgP = (KSP_CG*)ksp->data;
57: PetscInt maxit = ksp->max_it,nwork = 3;
59: /* get work vectors needed by CG */
60: if (cgP->singlereduction) nwork += 2;
61: KSPSetWorkVecs(ksp,nwork);
63: /*
64: If user requested computations of eigenvalues then allocate
65: work space needed
66: */
67: if (ksp->calc_sings) {
68: PetscFree4(cgP->e,cgP->d,cgP->ee,cgP->dd);
69: PetscMalloc4(maxit,&cgP->e,maxit,&cgP->d,maxit,&cgP->ee,maxit,&cgP->dd);
70: PetscLogObjectMemory((PetscObject)ksp,2*maxit*(sizeof(PetscScalar)+sizeof(PetscReal)));
72: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
73: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_CG;
74: }
75: return 0;
76: }
78: /*
79: A macro used in the following KSPSolve_CG and KSPSolve_CG_SingleReduction routines
80: */
81: #define VecXDot(x,y,a) (((cg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
83: /*
84: KSPSolve_CG - This routine actually applies the conjugate gradient method
86: Note : this routine can be replaced with another one (see below) which implements
87: another variant of CG.
89: Input Parameter:
90: . ksp - the Krylov space object that was set to use conjugate gradient, by, for
91: example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPCG);
92: */
93: static PetscErrorCode KSPSolve_CG(KSP ksp)
94: {
95: PetscInt i,stored_max_it,eigs;
96: PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL,dpiold;
97: PetscReal dp = 0.0;
98: Vec X,B,Z,R,P,W;
99: KSP_CG *cg;
100: Mat Amat,Pmat;
101: PetscBool diagonalscale;
103: PCGetDiagonalScale(ksp->pc,&diagonalscale);
106: cg = (KSP_CG*)ksp->data;
107: eigs = ksp->calc_sings;
108: stored_max_it = ksp->max_it;
109: X = ksp->vec_sol;
110: B = ksp->vec_rhs;
111: R = ksp->work[0];
112: Z = ksp->work[1];
113: P = ksp->work[2];
114: W = Z;
116: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
117: PCGetOperators(ksp->pc,&Amat,&Pmat);
119: ksp->its = 0;
120: if (!ksp->guess_zero) {
121: KSP_MatMult(ksp,Amat,X,R); /* r <- b - Ax */
122: VecAYPX(R,-1.0,B);
123: } else {
124: VecCopy(B,R); /* r <- b (x is 0) */
125: }
126: /* This may be true only on a subset of MPI ranks; setting it here so it will be detected by the first norm computation below */
127: if (ksp->reason == KSP_DIVERGED_PC_FAILED) {
128: VecSetInf(R);
129: }
131: switch (ksp->normtype) {
132: case KSP_NORM_PRECONDITIONED:
133: KSP_PCApply(ksp,R,Z); /* z <- Br */
134: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A*e */
135: KSPCheckNorm(ksp,dp);
136: break;
137: case KSP_NORM_UNPRECONDITIONED:
138: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
139: KSPCheckNorm(ksp,dp);
140: break;
141: case KSP_NORM_NATURAL:
142: KSP_PCApply(ksp,R,Z); /* z <- Br */
143: VecXDot(Z,R,&beta); /* beta <- z'*r */
144: KSPCheckDot(ksp,beta);
145: dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
146: break;
147: case KSP_NORM_NONE:
148: dp = 0.0;
149: break;
150: default: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
151: }
152: KSPLogResidualHistory(ksp,dp);
153: KSPMonitor(ksp,0,dp);
154: ksp->rnorm = dp;
156: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
157: if (ksp->reason) return 0;
159: if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
160: KSP_PCApply(ksp,R,Z); /* z <- Br */
161: }
162: if (ksp->normtype != KSP_NORM_NATURAL) {
163: VecXDot(Z,R,&beta); /* beta <- z'*r */
164: KSPCheckDot(ksp,beta);
165: }
167: i = 0;
168: do {
169: ksp->its = i+1;
170: if (beta == 0.0) {
171: ksp->reason = KSP_CONVERGED_ATOL;
172: PetscInfo(ksp,"converged due to beta = 0\n");
173: break;
174: #if !defined(PETSC_USE_COMPLEX)
175: } else if ((i > 0) && (beta*betaold < 0.0)) {
177: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
178: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
179: break;
180: #endif
181: }
182: if (!i) {
183: VecCopy(Z,P); /* p <- z */
184: b = 0.0;
185: } else {
186: b = beta/betaold;
187: if (eigs) {
189: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
190: }
191: VecAYPX(P,b,Z); /* p <- z + b* p */
192: }
193: dpiold = dpi;
194: KSP_MatMult(ksp,Amat,P,W); /* w <- Ap */
195: VecXDot(P,W,&dpi); /* dpi <- p'w */
196: KSPCheckDot(ksp,dpi);
197: betaold = beta;
199: if ((dpi == 0.0) || ((i > 0) && ((PetscSign(PetscRealPart(dpi))*PetscSign(PetscRealPart(dpiold))) < 0.0))) {
201: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
202: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
203: break;
204: }
205: a = beta/dpi; /* a = beta/p'w */
206: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
207: VecAXPY(X,a,P); /* x <- x + ap */
208: VecAXPY(R,-a,W); /* r <- r - aw */
209: if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
210: KSP_PCApply(ksp,R,Z); /* z <- Br */
211: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
212: KSPCheckNorm(ksp,dp);
213: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
214: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
215: KSPCheckNorm(ksp,dp);
216: } else if (ksp->normtype == KSP_NORM_NATURAL) {
217: KSP_PCApply(ksp,R,Z); /* z <- Br */
218: VecXDot(Z,R,&beta); /* beta <- r'*z */
219: KSPCheckDot(ksp,beta);
220: dp = PetscSqrtReal(PetscAbsScalar(beta));
221: } else {
222: dp = 0.0;
223: }
224: ksp->rnorm = dp;
225: KSPLogResidualHistory(ksp,dp);
226: KSPMonitor(ksp,i+1,dp);
227: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
228: if (ksp->reason) break;
230: if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
231: KSP_PCApply(ksp,R,Z); /* z <- Br */
232: }
233: if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
234: VecXDot(Z,R,&beta); /* beta <- z'*r */
235: KSPCheckDot(ksp,beta);
236: }
238: i++;
239: } while (i<ksp->max_it);
240: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
241: return 0;
242: }
244: /*
245: KSPSolve_CG_SingleReduction
247: This variant of CG is identical in exact arithmetic to the standard algorithm,
248: but is rearranged to use only a single reduction stage per iteration, using additional
249: intermediate vectors.
251: See KSPCGUseSingleReduction_CG()
253: */
254: static PetscErrorCode KSPSolve_CG_SingleReduction(KSP ksp)
255: {
256: PetscInt i,stored_max_it,eigs;
257: PetscScalar dpi = 0.0,a = 1.0,beta,betaold = 1.0,b = 0,*e = NULL,*d = NULL,delta,dpiold,tmp[2];
258: PetscReal dp = 0.0;
259: Vec X,B,Z,R,P,S,W,tmpvecs[2];
260: KSP_CG *cg;
261: Mat Amat,Pmat;
262: PetscBool diagonalscale;
264: PCGetDiagonalScale(ksp->pc,&diagonalscale);
267: cg = (KSP_CG*)ksp->data;
268: eigs = ksp->calc_sings;
269: stored_max_it = ksp->max_it;
270: X = ksp->vec_sol;
271: B = ksp->vec_rhs;
272: R = ksp->work[0];
273: Z = ksp->work[1];
274: P = ksp->work[2];
275: S = ksp->work[3];
276: W = ksp->work[4];
278: if (eigs) {e = cg->e; d = cg->d; e[0] = 0.0; }
279: PCGetOperators(ksp->pc,&Amat,&Pmat);
281: ksp->its = 0;
282: if (!ksp->guess_zero) {
283: KSP_MatMult(ksp,Amat,X,R); /* r <- b - Ax */
284: VecAYPX(R,-1.0,B);
285: } else {
286: VecCopy(B,R); /* r <- b (x is 0) */
287: }
289: switch (ksp->normtype) {
290: case KSP_NORM_PRECONDITIONED:
291: KSP_PCApply(ksp,R,Z); /* z <- Br */
292: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z = e'*A'*B'*B*A'*e' */
293: KSPCheckNorm(ksp,dp);
294: break;
295: case KSP_NORM_UNPRECONDITIONED:
296: VecNorm(R,NORM_2,&dp); /* dp <- r'*r = e'*A'*A*e */
297: KSPCheckNorm(ksp,dp);
298: break;
299: case KSP_NORM_NATURAL:
300: KSP_PCApply(ksp,R,Z); /* z <- Br */
301: KSP_MatMult(ksp,Amat,Z,S);
302: VecXDot(Z,S,&delta); /* delta <- z'*A*z = r'*B*A*B*r */
303: VecXDot(Z,R,&beta); /* beta <- z'*r */
304: KSPCheckDot(ksp,beta);
305: dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
306: break;
307: case KSP_NORM_NONE:
308: dp = 0.0;
309: break;
310: default: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
311: }
312: KSPLogResidualHistory(ksp,dp);
313: KSPMonitor(ksp,0,dp);
314: ksp->rnorm = dp;
316: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP); /* test for convergence */
317: if (ksp->reason) return 0;
319: if (ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) {
320: KSP_PCApply(ksp,R,Z); /* z <- Br */
321: }
322: if (ksp->normtype != KSP_NORM_NATURAL) {
323: KSP_MatMult(ksp,Amat,Z,S);
324: VecXDot(Z,S,&delta); /* delta <- z'*A*z = r'*B*A*B*r */
325: VecXDot(Z,R,&beta); /* beta <- z'*r */
326: KSPCheckDot(ksp,beta);
327: }
329: i = 0;
330: do {
331: ksp->its = i+1;
332: if (beta == 0.0) {
333: ksp->reason = KSP_CONVERGED_ATOL;
334: PetscInfo(ksp,"converged due to beta = 0\n");
335: break;
336: #if !defined(PETSC_USE_COMPLEX)
337: } else if ((i > 0) && (beta*betaold < 0.0)) {
339: ksp->reason = KSP_DIVERGED_INDEFINITE_PC;
340: PetscInfo(ksp,"diverging due to indefinite preconditioner\n");
341: break;
342: #endif
343: }
344: if (!i) {
345: VecCopy(Z,P); /* p <- z */
346: b = 0.0;
347: } else {
348: b = beta/betaold;
349: if (eigs) {
351: e[i] = PetscSqrtReal(PetscAbsScalar(b))/a;
352: }
353: VecAYPX(P,b,Z); /* p <- z + b* p */
354: }
355: dpiold = dpi;
356: if (!i) {
357: KSP_MatMult(ksp,Amat,P,W); /* w <- Ap */
358: VecXDot(P,W,&dpi); /* dpi <- p'w */
359: } else {
360: VecAYPX(W,beta/betaold,S); /* w <- Ap */
361: dpi = delta - beta*beta*dpiold/(betaold*betaold); /* dpi <- p'w */
362: }
363: betaold = beta;
364: KSPCheckDot(ksp,beta);
366: if ((dpi == 0.0) || ((i > 0) && (PetscRealPart(dpi*dpiold) <= 0.0))) {
368: ksp->reason = KSP_DIVERGED_INDEFINITE_MAT;
369: PetscInfo(ksp,"diverging due to indefinite or negative definite matrix\n");
370: break;
371: }
372: a = beta/dpi; /* a = beta/p'w */
373: if (eigs) d[i] = PetscSqrtReal(PetscAbsScalar(b))*e[i] + 1.0/a;
374: VecAXPY(X,a,P); /* x <- x + ap */
375: VecAXPY(R,-a,W); /* r <- r - aw */
376: if (ksp->normtype == KSP_NORM_PRECONDITIONED && ksp->chknorm < i+2) {
377: KSP_PCApply(ksp,R,Z); /* z <- Br */
378: KSP_MatMult(ksp,Amat,Z,S);
379: VecNorm(Z,NORM_2,&dp); /* dp <- z'*z */
380: KSPCheckNorm(ksp,dp);
381: } else if (ksp->normtype == KSP_NORM_UNPRECONDITIONED && ksp->chknorm < i+2) {
382: VecNorm(R,NORM_2,&dp); /* dp <- r'*r */
383: KSPCheckNorm(ksp,dp);
384: } else if (ksp->normtype == KSP_NORM_NATURAL) {
385: KSP_PCApply(ksp,R,Z); /* z <- Br */
386: tmpvecs[0] = S; tmpvecs[1] = R;
387: KSP_MatMult(ksp,Amat,Z,S);
388: VecMDot(Z,2,tmpvecs,tmp); /* delta <- z'*A*z = r'*B*A*B*r */
389: delta = tmp[0]; beta = tmp[1]; /* beta <- z'*r */
390: KSPCheckDot(ksp,beta);
391: dp = PetscSqrtReal(PetscAbsScalar(beta)); /* dp <- r'*z = r'*B*r = e'*A'*B*A*e */
392: } else {
393: dp = 0.0;
394: }
395: ksp->rnorm = dp;
396: KSPLogResidualHistory(ksp,dp);
397: KSPMonitor(ksp,i+1,dp);
398: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
399: if (ksp->reason) break;
401: if ((ksp->normtype != KSP_NORM_PRECONDITIONED && (ksp->normtype != KSP_NORM_NATURAL)) || (ksp->chknorm >= i+2)) {
402: KSP_PCApply(ksp,R,Z); /* z <- Br */
403: KSP_MatMult(ksp,Amat,Z,S);
404: }
405: if ((ksp->normtype != KSP_NORM_NATURAL) || (ksp->chknorm >= i+2)) {
406: tmpvecs[0] = S; tmpvecs[1] = R;
407: VecMDot(Z,2,tmpvecs,tmp);
408: delta = tmp[0]; beta = tmp[1]; /* delta <- z'*A*z = r'*B'*A*B*r */
409: KSPCheckDot(ksp,beta); /* beta <- z'*r */
410: }
412: i++;
413: } while (i<ksp->max_it);
414: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
415: return 0;
416: }
418: /*
419: KSPDestroy_CG - Frees resources allocated in KSPSetup_CG and clears function
420: compositions from KSPCreate_CG. If adding your own KSP implementation,
421: you must be sure to free all allocated resources here to prevent
422: leaks.
423: */
424: PetscErrorCode KSPDestroy_CG(KSP ksp)
425: {
426: KSP_CG *cg = (KSP_CG*)ksp->data;
428: PetscFree4(cg->e,cg->d,cg->ee,cg->dd);
429: KSPDestroyDefault(ksp);
430: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",NULL);
431: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",NULL);
432: return 0;
433: }
435: /*
436: KSPView_CG - Prints information about the current Krylov method being used.
437: If your Krylov method has special options or flags that information
438: should be printed here.
439: */
440: PetscErrorCode KSPView_CG(KSP ksp,PetscViewer viewer)
441: {
442: KSP_CG *cg = (KSP_CG*)ksp->data;
443: PetscBool iascii;
445: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
446: if (iascii) {
447: #if defined(PETSC_USE_COMPLEX)
448: PetscViewerASCIIPrintf(viewer," variant %s\n",KSPCGTypes[cg->type]);
449: #endif
450: if (cg->singlereduction) {
451: PetscViewerASCIIPrintf(viewer," using single-reduction variant\n");
452: }
453: }
454: return 0;
455: }
457: /*
458: KSPSetFromOptions_CG - Checks the options database for options related to the
459: conjugate gradient method.
460: */
461: PetscErrorCode KSPSetFromOptions_CG(PetscOptionItems *PetscOptionsObject,KSP ksp)
462: {
463: KSP_CG *cg = (KSP_CG*)ksp->data;
464: PetscBool flg;
466: PetscOptionsHead(PetscOptionsObject,"KSP CG and CGNE options");
467: #if defined(PETSC_USE_COMPLEX)
468: PetscCall(PetscOptionsEnum("-ksp_cg_type","Matrix is Hermitian or complex symmetric","KSPCGSetType",KSPCGTypes,(PetscEnum)cg->type,
469: (PetscEnum*)&cg->type,NULL));
470: #endif
471: PetscOptionsBool("-ksp_cg_single_reduction","Merge inner products into single MPI_Allreduce()","KSPCGUseSingleReduction",cg->singlereduction,&cg->singlereduction,&flg);
472: if (flg) KSPCGUseSingleReduction(ksp,cg->singlereduction);
473: PetscOptionsTail();
474: return 0;
475: }
477: /*
478: KSPCGSetType_CG - This is an option that is SPECIFIC to this particular Krylov method.
479: This routine is registered below in KSPCreate_CG() and called from the
480: routine KSPCGSetType() (see the file cgtype.c).
481: */
482: PetscErrorCode KSPCGSetType_CG(KSP ksp,KSPCGType type)
483: {
484: KSP_CG *cg = (KSP_CG*)ksp->data;
486: cg->type = type;
487: return 0;
488: }
490: /*
491: KSPCGUseSingleReduction_CG
493: This routine sets a flag to use a variant of CG. Note that (in somewhat
494: atypical fashion) it also swaps out the routine called when KSPSolve()
495: is invoked.
496: */
497: static PetscErrorCode KSPCGUseSingleReduction_CG(KSP ksp,PetscBool flg)
498: {
499: KSP_CG *cg = (KSP_CG*)ksp->data;
501: cg->singlereduction = flg;
502: if (cg->singlereduction) {
503: ksp->ops->solve = KSPSolve_CG_SingleReduction;
504: } else {
505: ksp->ops->solve = KSPSolve_CG;
506: }
507: return 0;
508: }
510: PETSC_INTERN PetscErrorCode KSPBuildResidual_CG(KSP ksp,Vec t,Vec v,Vec *V)
511: {
512: VecCopy(ksp->work[0],v);
513: *V = v;
514: return 0;
515: }
517: /*
518: KSPCreate_CG - Creates the data structure for the Krylov method CG and sets the
519: function pointers for all the routines it needs to call (KSPSolve_CG() etc)
521: It must be labeled as PETSC_EXTERN to be dynamically linkable in C++
522: */
523: /*MC
524: KSPCG - The Preconditioned Conjugate Gradient (PCG) iterative method
526: Options Database Keys:
527: + -ksp_cg_type Hermitian - (for complex matrices only) indicates the matrix is Hermitian, see KSPCGSetType()
528: . -ksp_cg_type symmetric - (for complex matrices only) indicates the matrix is symmetric
529: - -ksp_cg_single_reduction - performs both inner products needed in the algorithm with a single MPI_Allreduce() call, see KSPCGUseSingleReduction()
531: Level: beginner
533: Notes:
534: The PCG method requires both the matrix and preconditioner to be symmetric positive (or negative) (semi) definite.
536: Only left preconditioning is supported; there are several ways to motivate preconditioned CG, but they all produce the same algorithm.
537: One can interpret preconditioning A with B to mean any of the following\:
538: .n (1) Solve a left-preconditioned system BAx = Bb, using inv(B) to define an inner product in the algorithm.
539: .n (2) Solve a right-preconditioned system ABy = b, x = By, using B to define an inner product in the algorithm.
540: .n (3) Solve a symmetrically-preconditioned system, E^TAEy = E^Tb, x = Ey, where B = EE^T.
541: .n (4) Solve Ax=b with CG, but use the inner product defined by B to define the method [2].
542: .n In all cases, the resulting algorithm only requires application of B to vectors.
544: For complex numbers there are two different CG methods, one for Hermitian symmetric matrices and one for non-Hermitian symmetric matrices. Use
545: KSPCGSetType() to indicate which type you are using.
547: Developer Notes:
548: KSPSolve_CG() should actually query the matrix to determine if it is Hermitian symmetric or not and NOT require the user to
549: indicate it to the KSP object.
551: References:
552: + * - Magnus R. Hestenes and Eduard Stiefel, Methods of Conjugate Gradients for Solving Linear Systems,
553: Journal of Research of the National Bureau of Standards Vol. 49, No. 6, December 1952 Research Paper 2379
554: - * - Josef Malek and Zdenek Strakos, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs,
555: SIAM, 2014.
557: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
558: KSPCGSetType(), KSPCGUseSingleReduction(), KSPPIPECG, KSPGROPPCG
560: M*/
561: PETSC_EXTERN PetscErrorCode KSPCreate_CG(KSP ksp)
562: {
563: KSP_CG *cg;
565: PetscNewLog(ksp,&cg);
566: #if !defined(PETSC_USE_COMPLEX)
567: cg->type = KSP_CG_SYMMETRIC;
568: #else
569: cg->type = KSP_CG_HERMITIAN;
570: #endif
571: ksp->data = (void*)cg;
573: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
574: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);
575: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
576: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
578: /*
579: Sets the functions that are associated with this data structure
580: (in C++ this is the same as defining virtual functions)
581: */
582: ksp->ops->setup = KSPSetUp_CG;
583: ksp->ops->solve = KSPSolve_CG;
584: ksp->ops->destroy = KSPDestroy_CG;
585: ksp->ops->view = KSPView_CG;
586: ksp->ops->setfromoptions = KSPSetFromOptions_CG;
587: ksp->ops->buildsolution = KSPBuildSolutionDefault;
588: ksp->ops->buildresidual = KSPBuildResidual_CG;
590: /*
591: Attach the function KSPCGSetType_CG() to this object. The routine
592: KSPCGSetType() checks for this attached function and calls it if it finds
593: it. (Sort of like a dynamic member function that can be added at run time
594: */
595: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGSetType_C",KSPCGSetType_CG);
596: PetscObjectComposeFunction((PetscObject)ksp,"KSPCGUseSingleReduction_C",KSPCGUseSingleReduction_CG);
597: return 0;
598: }