Actual source code: fcg.c
petsc-master 2019-06-18
1: /*
2: This file implements the FCG (Flexible Conjugate Gradient) method
4: */
6: #include <../src/ksp/ksp/impls/fcg/fcgimpl.h>
7: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
8: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);
10: #define KSPFCG_DEFAULT_MMAX 30 /* maximum number of search directions to keep */
11: #define KSPFCG_DEFAULT_NPREALLOC 10 /* number of search directions to preallocate */
12: #define KSPFCG_DEFAULT_VECB 5 /* number of search directions to allocate each time new direction vectors are needed */
13: #define KSPFCG_DEFAULT_TRUNCSTRAT KSP_FCD_TRUNC_TYPE_NOTAY
15: static PetscErrorCode KSPAllocateVectors_FCG(KSP ksp, PetscInt nvecsneeded, PetscInt chunksize)
16: {
17: PetscErrorCode ierr;
18: PetscInt i;
19: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
20: PetscInt nnewvecs, nvecsprev;
23: /* Allocate enough new vectors to add chunksize new vectors, reach nvecsneedtotal, or to reach mmax+1, whichever is smallest */
24: if (fcg->nvecs < PetscMin(fcg->mmax+1,nvecsneeded)){
25: nvecsprev = fcg->nvecs;
26: nnewvecs = PetscMin(PetscMax(nvecsneeded-fcg->nvecs,chunksize),fcg->mmax+1-fcg->nvecs);
27: KSPCreateVecs(ksp,nnewvecs,&fcg->pCvecs[fcg->nchunks],0,NULL);
28: PetscLogObjectParents((PetscObject)ksp,nnewvecs,fcg->pCvecs[fcg->nchunks]);
29: KSPCreateVecs(ksp,nnewvecs,&fcg->pPvecs[fcg->nchunks],0,NULL);
30: PetscLogObjectParents((PetscObject)ksp,nnewvecs,fcg->pPvecs[fcg->nchunks]);
31: fcg->nvecs += nnewvecs;
32: for (i=0;i<nnewvecs;++i){
33: fcg->Cvecs[nvecsprev + i] = fcg->pCvecs[fcg->nchunks][i];
34: fcg->Pvecs[nvecsprev + i] = fcg->pPvecs[fcg->nchunks][i];
35: }
36: fcg->chunksizes[fcg->nchunks] = nnewvecs;
37: ++fcg->nchunks;
38: }
39: return(0);
40: }
42: static PetscErrorCode KSPSetUp_FCG(KSP ksp)
43: {
45: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
46: PetscInt maxit = ksp->max_it;
47: const PetscInt nworkstd = 2;
51: /* Allocate "standard" work vectors (not including the basis and transformed basis vectors) */
52: KSPSetWorkVecs(ksp,nworkstd);
54: /* Allocated space for pointers to additional work vectors
55: note that mmax is the number of previous directions, so we add 1 for the current direction,
56: and an extra 1 for the prealloc (which might be empty) */
57: PetscMalloc5(fcg->mmax+1,&fcg->Pvecs,fcg->mmax+1,&fcg->Cvecs,fcg->mmax+1,&fcg->pPvecs,fcg->mmax+1,&fcg->pCvecs,fcg->mmax+2,&fcg->chunksizes);
58: PetscLogObjectMemory((PetscObject)ksp,2*(fcg->mmax+1)*sizeof(Vec*) + 2*(fcg->mmax + 1)*sizeof(Vec**) + (fcg->mmax + 2)*sizeof(PetscInt));
60: /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
61: if(fcg->nprealloc > fcg->mmax+1){
62: PetscInfo2(NULL,"Requested nprealloc=%d is greater than m_max+1=%d. Resetting nprealloc = m_max+1.\n",fcg->nprealloc, fcg->mmax+1);
63: }
65: /* Preallocate additional work vectors */
66: KSPAllocateVectors_FCG(ksp,fcg->nprealloc,fcg->nprealloc);
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,&fcg->e,maxit,&fcg->d,maxit,&fcg->ee,maxit,&fcg->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: static PetscErrorCode KSPSolve_FCG(KSP ksp)
83: {
85: PetscInt i,k,idx,mi;
86: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
87: PetscScalar alpha=0.0,beta = 0.0,dpi,s;
88: PetscReal dp=0.0;
89: Vec B,R,Z,X,Pcurr,Ccurr;
90: Mat Amat,Pmat;
91: PetscInt eigs = ksp->calc_sings; /* Variables for eigen estimation - START*/
92: PetscInt stored_max_it = ksp->max_it;
93: PetscScalar alphaold = 0,betaold = 1.0,*e = 0,*d = 0;/* Variables for eigen estimation - FINISH */
97: #define VecXDot(x,y,a) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
98: #define VecXMDot(a,b,c,d) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecMDot(a,b,c,d) : VecMTDot(a,b,c,d))
100: X = ksp->vec_sol;
101: B = ksp->vec_rhs;
102: R = ksp->work[0];
103: Z = ksp->work[1];
105: PCGetOperators(ksp->pc,&Amat,&Pmat);
106: if (eigs) {e = fcg->e; d = fcg->d; e[0] = 0.0; }
107: /* Compute initial residual needed for convergence check*/
108: ksp->its = 0;
109: if (!ksp->guess_zero) {
110: KSP_MatMult(ksp,Amat,X,R);
111: VecAYPX(R,-1.0,B); /* r <- b - Ax */
112: } else {
113: VecCopy(B,R); /* r <- b (x is 0) */
114: }
115: switch (ksp->normtype) {
116: case KSP_NORM_PRECONDITIONED:
117: KSP_PCApply(ksp,R,Z); /* z <- Br */
118: VecNorm(Z,NORM_2,&dp); /* dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
119: KSPCheckNorm(ksp,dp);
120: break;
121: case KSP_NORM_UNPRECONDITIONED:
122: VecNorm(R,NORM_2,&dp); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e) */
123: KSPCheckNorm(ksp,dp);
124: break;
125: case KSP_NORM_NATURAL:
126: KSP_PCApply(ksp,R,Z); /* z <- Br */
127: VecXDot(R,Z,&s);
128: KSPCheckDot(ksp,s);
129: dp = PetscSqrtReal(PetscAbsScalar(s)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e) */
130: break;
131: case KSP_NORM_NONE:
132: dp = 0.0;
133: break;
134: default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
135: }
137: /* Initial Convergence Check */
138: KSPLogResidualHistory(ksp,dp);
139: KSPMonitor(ksp,0,dp);
140: ksp->rnorm = dp;
141: if (ksp->normtype == KSP_NORM_NONE) {
142: KSPConvergedSkip(ksp,0,dp,&ksp->reason,ksp->cnvP);
143: } else {
144: (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
145: }
146: if (ksp->reason) return(0);
148: /* Apply PC if not already done for convergence check */
149: if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
150: KSP_PCApply(ksp,R,Z); /* z <- Br */
151: }
153: i = 0;
154: do {
155: ksp->its = i+1;
157: /* If needbe, allocate a new chunk of vectors in P and C */
158: KSPAllocateVectors_FCG(ksp,i+1,fcg->vecb);
160: /* Note that we wrap around and start clobbering old vectors */
161: idx = i % (fcg->mmax+1);
162: Pcurr = fcg->Pvecs[idx];
163: Ccurr = fcg->Cvecs[idx];
165: /* number of old directions to orthogonalize against */
166: switch(fcg->truncstrat){
167: case KSP_FCD_TRUNC_TYPE_STANDARD:
168: mi = fcg->mmax;
169: break;
170: case KSP_FCD_TRUNC_TYPE_NOTAY:
171: mi = ((i-1) % fcg->mmax)+1;
172: break;
173: default:
174: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unrecognized Truncation Strategy");
175: }
177: /* Compute a new column of P (Currently does not support modified G-S or iterative refinement)*/
178: VecCopy(Z,Pcurr);
180: {
181: PetscInt l,ndots;
183: l = PetscMax(0,i-mi);
184: ndots = i-l;
185: if (ndots){
186: PetscInt j;
187: Vec *Pold, *Cold;
188: PetscScalar *dots;
190: PetscMalloc3(ndots,&dots,ndots,&Cold,ndots,&Pold);
191: for(k=l,j=0;j<ndots;++k,++j){
192: idx = k % (fcg->mmax+1);
193: Cold[j] = fcg->Cvecs[idx];
194: Pold[j] = fcg->Pvecs[idx];
195: }
196: VecXMDot(Z,ndots,Cold,dots);
197: for(k=0;k<ndots;++k){
198: dots[k] = -dots[k];
199: }
200: VecMAXPY(Pcurr,ndots,dots,Pold);
201: PetscFree3(dots,Cold,Pold);
202: }
203: }
205: /* Update X and R */
206: betaold = beta;
207: VecXDot(Pcurr,R,&beta); /* beta <- pi'*r */
208: KSPCheckDot(ksp,beta);
209: KSP_MatMult(ksp,Amat,Pcurr,Ccurr); /* w <- A*pi (stored in ci) */
210: VecXDot(Pcurr,Ccurr,&dpi); /* dpi <- pi'*w */
211: alphaold = alpha;
212: alpha = beta / dpi; /* alpha <- beta/dpi */
213: VecAXPY(X,alpha,Pcurr); /* x <- x + alpha * pi */
214: VecAXPY(R,-alpha,Ccurr); /* r <- r - alpha * wi */
216: /* Compute norm for convergence check */
217: switch (ksp->normtype) {
218: case KSP_NORM_PRECONDITIONED:
219: KSP_PCApply(ksp,R,Z); /* z <- Br */
220: VecNorm(Z,NORM_2,&dp); /* dp <- sqrt(z'*z) = sqrt(e'*A'*B'*B*A*e) */
221: KSPCheckNorm(ksp,dp);
222: break;
223: case KSP_NORM_UNPRECONDITIONED:
224: VecNorm(R,NORM_2,&dp); /* dp <- sqrt(r'*r) = sqrt(e'*A'*A*e) */
225: KSPCheckNorm(ksp,dp);
226: break;
227: case KSP_NORM_NATURAL:
228: KSP_PCApply(ksp,R,Z); /* z <- Br */
229: VecXDot(R,Z,&s);
230: KSPCheckDot(ksp,s);
231: dp = PetscSqrtReal(PetscAbsScalar(s)); /* dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e) */
232: break;
233: case KSP_NORM_NONE:
234: dp = 0.0;
235: break;
236: default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
237: }
239: /* Check for convergence */
240: ksp->rnorm = dp;
241: KSPLogResidualHistory(ksp,dp);
242: KSPMonitor(ksp,i+1,dp);
243: (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
244: if (ksp->reason) break;
246: /* Apply PC if not already done for convergence check */
247: if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
248: KSP_PCApply(ksp,R,Z); /* z <- Br */
249: }
251: /* Compute current C (which is W/dpi) */
252: VecScale(Ccurr,1.0/dpi); /* w <- ci/dpi */
254: if (eigs) {
255: if (i > 0) {
256: if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
257: e[i] = PetscSqrtReal(PetscAbsScalar(beta/betaold))/alphaold;
258: d[i] = PetscSqrtReal(PetscAbsScalar(beta/betaold))*e[i] + 1.0/alpha;
259: } else {
260: d[i] = PetscSqrtReal(PetscAbsScalar(beta))*e[i] + 1.0/alpha;
261: }
262: fcg->ned = ksp->its-1;
263: }
264: ++i;
265: } while (i<ksp->max_it);
266: if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
267: return(0);
268: }
270: static PetscErrorCode KSPDestroy_FCG(KSP ksp)
271: {
273: PetscInt i;
274: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
278: /* Destroy "standard" work vecs */
279: VecDestroyVecs(ksp->nwork,&ksp->work);
281: /* Destroy P and C vectors and the arrays that manage pointers to them */
282: if (fcg->nvecs){
283: for (i=0;i<fcg->nchunks;++i){
284: VecDestroyVecs(fcg->chunksizes[i],&fcg->pPvecs[i]);
285: VecDestroyVecs(fcg->chunksizes[i],&fcg->pCvecs[i]);
286: }
287: }
288: PetscFree5(fcg->Pvecs,fcg->Cvecs,fcg->pPvecs,fcg->pCvecs,fcg->chunksizes);
289: /* free space used for singular value calculations */
290: if (ksp->calc_sings) {
291: PetscFree4(fcg->e,fcg->d,fcg->ee,fcg->dd);
292: }
293: KSPDestroyDefault(ksp);
294: return(0);
295: }
297: static PetscErrorCode KSPView_FCG(KSP ksp,PetscViewer viewer)
298: {
299: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
301: PetscBool iascii,isstring;
302: const char *truncstr;
305: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
306: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
308: if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD) truncstr = "Using standard truncation strategy";
309: else if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY) truncstr = "Using Notay's truncation strategy";
310: else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Undefined FCG truncation strategy");
312: if (iascii) {
313: PetscViewerASCIIPrintf(viewer," m_max=%D\n",fcg->mmax);
314: PetscViewerASCIIPrintf(viewer," preallocated %D directions\n",PetscMin(fcg->nprealloc,fcg->mmax+1));
315: PetscViewerASCIIPrintf(viewer," %s\n",truncstr);
316: } else if (isstring) {
317: PetscViewerStringSPrintf(viewer,"m_max %D nprealloc %D %s",fcg->mmax,fcg->nprealloc,truncstr);
318: }
319: return(0);
320: }
322: /*@
323: KSPFCGSetMmax - set the maximum number of previous directions FCG will store for orthogonalization
325: Note: mmax + 1 directions are stored (mmax previous ones along with a current one)
326: and whether all are used in each iteration also depends on the truncation strategy
327: (see KSPFCGSetTruncationType())
329: Logically Collective on ksp
331: Input Parameters:
332: + ksp - the Krylov space context
333: - mmax - the maximum number of previous directions to orthogonalize againt
335: Level: intermediate
337: Options Database:
338: . -ksp_fcg_mmax <N>
340: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc()
341: @*/
342: PetscErrorCode KSPFCGSetMmax(KSP ksp,PetscInt mmax)
343: {
344: KSP_FCG *fcg = (KSP_FCG*)ksp->data;
349: fcg->mmax = mmax;
350: return(0);
351: }
353: /*@
354: KSPFCGGetMmax - get the maximum number of previous directions FCG will store
356: Note: FCG stores mmax+1 directions at most (mmax previous ones, and one current one)
358: Not Collective
360: Input Parameter:
361: . ksp - the Krylov space context
363: Output Parameter:
364: . mmax - the maximum number of previous directons allowed for orthogonalization
366: Options Database:
367: . -ksp_fcg_mmax <N>
369: Level: intermediate
371: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc(), KSPFCGSetMmax()
372: @*/
374: PetscErrorCode KSPFCGGetMmax(KSP ksp,PetscInt *mmax)
375: {
376: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
380: *mmax = fcg->mmax;
381: return(0);
382: }
384: /*@
385: KSPFCGSetNprealloc - set the number of directions to preallocate with FCG
387: Logically Collective on ksp
389: Input Parameters:
390: + ksp - the Krylov space context
391: - nprealloc - the number of vectors to preallocate
393: Level: advanced
395: Options Database:
396: . -ksp_fcg_nprealloc <N> - number of directions to preallocate
398: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc()
399: @*/
400: PetscErrorCode KSPFCGSetNprealloc(KSP ksp,PetscInt nprealloc)
401: {
402: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
407: if(nprealloc > fcg->mmax+1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Cannot preallocate more than m_max+1 vectors");
408: fcg->nprealloc = nprealloc;
409: return(0);
410: }
412: /*@
413: KSPFCGGetNprealloc - get the number of directions preallocate by FCG
415: Not Collective
417: Input Parameter:
418: . ksp - the Krylov space context
420: Output Parameter:
421: . nprealloc - the number of directions preallocated
423: Level: advanced
425: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGSetNprealloc()
426: @*/
427: PetscErrorCode KSPFCGGetNprealloc(KSP ksp,PetscInt *nprealloc)
428: {
429: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
433: *nprealloc = fcg->nprealloc;
434: return(0);
435: }
437: /*@
438: KSPFCGSetTruncationType - specify how many of its stored previous directions FCG uses during orthoganalization
440: Logically Collective on ksp
442: KSP_FCD_TRUNC_TYPE_STANDARD uses all (up to mmax) stored directions
443: KSP_FCD_TRUNC_TYPE_NOTAY uses the last max(1,mod(i,mmax)) stored directions at iteration i=0,1,..
445: Input Parameters:
446: + ksp - the Krylov space context
447: - truncstrat - the choice of strategy
449: Level: intermediate
451: Options Database:
452: . -ksp_fcg_truncation_type <standard, notay> - specify how many of its stored previous directions FCG uses during orthoganalization
454: .seealso: KSPFCDTruncationType, KSPFCGGetTruncationType
455: @*/
456: PetscErrorCode KSPFCGSetTruncationType(KSP ksp,KSPFCDTruncationType truncstrat)
457: {
458: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
463: fcg->truncstrat=truncstrat;
464: return(0);
465: }
467: /*@
468: KSPFCGGetTruncationType - get the truncation strategy employed by FCG
470: Not Collective
472: Input Parameter:
473: . ksp - the Krylov space context
475: Output Parameter:
476: . truncstrat - the strategy type
478: Level: intermediate
480: .seealso: KSPFCG, KSPFCGSetTruncationType, KSPFCDTruncationType
481: @*/
482: PetscErrorCode KSPFCGGetTruncationType(KSP ksp,KSPFCDTruncationType *truncstrat)
483: {
484: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
488: *truncstrat=fcg->truncstrat;
489: return(0);
490: }
492: static PetscErrorCode KSPSetFromOptions_FCG(PetscOptionItems *PetscOptionsObject,KSP ksp)
493: {
495: KSP_FCG *fcg=(KSP_FCG*)ksp->data;
496: PetscInt mmax,nprealloc;
497: PetscBool flg;
500: PetscOptionsHead(PetscOptionsObject,"KSP FCG Options");
501: PetscOptionsInt("-ksp_fcg_mmax","Maximum number of search directions to store","KSPFCGSetMmax",fcg->mmax,&mmax,&flg);
502: if (flg) {
503: KSPFCGSetMmax(ksp,mmax);
504: }
505: PetscOptionsInt("-ksp_fcg_nprealloc","Number of directions to preallocate","KSPFCGSetNprealloc",fcg->nprealloc,&nprealloc,&flg);
506: if (flg) {
507: KSPFCGSetNprealloc(ksp,nprealloc);
508: }
509: PetscOptionsEnum("-ksp_fcg_truncation_type","Truncation approach for directions","KSPFCGSetTruncationType",KSPFCDTruncationTypes,(PetscEnum)fcg->truncstrat,(PetscEnum*)&fcg->truncstrat,NULL);
510: PetscOptionsTail();
511: return(0);
512: }
514: /*MC
515: KSPFCG - Implements the Flexible Conjugate Gradient method (FCG)
517: Options Database Keys:
518: + -ksp_fcg_mmax <N> - maximum number of search directions
519: . -ksp_fcg_nprealloc <N> - number of directions to preallocate
520: - -ksp_fcg_truncation_type <standard,notay> - truncation approach for directions
522: Contributed by Patrick Sanan
524: Notes:
525: Supports left preconditioning only.
527: Level: beginner
529: References:
530: + 1. - Notay, Y."Flexible Conjugate Gradients", SIAM J. Sci. Comput. 22:4, 2000
531: - 2. - Axelsson, O. and Vassilevski, P. S. "A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable step Preconditioning",
532: SIAM J. Matrix Anal. Appl. 12:4, 1991
534: .seealso : KSPGCR, KSPFGMRES, KSPCG, KSPFCGSetMmax(), KSPFCGGetMmax(), KSPFCGSetNprealloc(), KSPFCGGetNprealloc(), KSPFCGSetTruncationType(), KSPFCGGetTruncationType()
536: M*/
537: PETSC_EXTERN PetscErrorCode KSPCreate_FCG(KSP ksp)
538: {
540: KSP_FCG *fcg;
543: PetscNewLog(ksp,&fcg);
544: #if !defined(PETSC_USE_COMPLEX)
545: fcg->type = KSP_CG_SYMMETRIC;
546: #else
547: fcg->type = KSP_CG_HERMITIAN;
548: #endif
549: fcg->mmax = KSPFCG_DEFAULT_MMAX;
550: fcg->nprealloc = KSPFCG_DEFAULT_NPREALLOC;
551: fcg->nvecs = 0;
552: fcg->vecb = KSPFCG_DEFAULT_VECB;
553: fcg->nchunks = 0;
554: fcg->truncstrat = KSPFCG_DEFAULT_TRUNCSTRAT;
556: ksp->data = (void*)fcg;
558: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
559: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
560: KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,1);
561: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
563: ksp->ops->setup = KSPSetUp_FCG;
564: ksp->ops->solve = KSPSolve_FCG;
565: ksp->ops->destroy = KSPDestroy_FCG;
566: ksp->ops->view = KSPView_FCG;
567: ksp->ops->setfromoptions = KSPSetFromOptions_FCG;
568: ksp->ops->buildsolution = KSPBuildSolutionDefault;
569: ksp->ops->buildresidual = KSPBuildResidualDefault;
570: return(0);
571: }