Actual source code: lsqr.c
petsc-main 2021-04-20
2: /* lourens.vanzanen@shell.com contributed the standard error estimates of the solution, Jul 25, 2006 */
3: /* Bas van't Hof contributed the preconditioned aspects Feb 10, 2010 */
5: #define SWAP(a,b,c) { c = a; a = b; b = c; }
7: #include <petsc/private/kspimpl.h>
8: #include <petscdraw.h>
10: typedef struct {
11: PetscInt nwork_n,nwork_m;
12: Vec *vwork_m; /* work vectors of length m, where the system is size m x n */
13: Vec *vwork_n; /* work vectors of length n */
14: Vec se; /* Optional standard error vector */
15: PetscBool se_flg; /* flag for -ksp_lsqr_set_standard_error */
16: PetscBool exact_norm; /* flag for -ksp_lsqr_exact_mat_norm */
17: PetscReal arnorm; /* Good estimate of norm((A*inv(Pmat))'*r), where r = A*x - b, used in specific stopping criterion */
18: PetscReal anorm; /* Poor estimate of norm(A*inv(Pmat),'fro') used in specific stopping criterion */
19: /* Backup previous convergence test */
20: PetscErrorCode (*converged)(KSP,PetscInt,PetscReal,KSPConvergedReason*,void*);
21: PetscErrorCode (*convergeddestroy)(void*);
22: void *cnvP;
23: } KSP_LSQR;
25: static PetscErrorCode VecSquare(Vec v)
26: {
28: PetscScalar *x;
29: PetscInt i, n;
32: VecGetLocalSize(v, &n);
33: VecGetArray(v, &x);
34: for (i = 0; i < n; i++) x[i] *= PetscConj(x[i]);
35: VecRestoreArray(v, &x);
36: return(0);
37: }
39: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
40: {
42: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
43: PetscBool nopreconditioner;
46: PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);
48: if (lsqr->vwork_m) {
49: VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
50: }
52: if (lsqr->vwork_n) {
53: VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
54: }
56: lsqr->nwork_m = 2;
57: if (nopreconditioner) lsqr->nwork_n = 4;
58: else lsqr->nwork_n = 5;
59: KSPCreateVecs(ksp,lsqr->nwork_n,&lsqr->vwork_n,lsqr->nwork_m,&lsqr->vwork_m);
61: if (lsqr->se_flg && !lsqr->se) {
62: VecDuplicate(lsqr->vwork_n[0],&lsqr->se);
63: VecSet(lsqr->se,PETSC_INFINITY);
64: } else if (!lsqr->se_flg) {
65: VecDestroy(&lsqr->se);
66: }
67: return(0);
68: }
70: static PetscErrorCode KSPSolve_LSQR(KSP ksp)
71: {
73: PetscInt i,size1,size2;
74: PetscScalar rho,rhobar,phi,phibar,theta,c,s,tmp,tau;
75: PetscReal beta,alpha,rnorm;
76: Vec X,B,V,V1,U,U1,TMP,W,W2,Z = NULL;
77: Mat Amat,Pmat;
78: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
79: PetscBool diagonalscale,nopreconditioner;
82: PCGetDiagonalScale(ksp->pc,&diagonalscale);
83: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
85: PCGetOperators(ksp->pc,&Amat,&Pmat);
86: PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);
88: /* vectors of length m, where system size is mxn */
89: B = ksp->vec_rhs;
90: U = lsqr->vwork_m[0];
91: U1 = lsqr->vwork_m[1];
93: /* vectors of length n */
94: X = ksp->vec_sol;
95: W = lsqr->vwork_n[0];
96: V = lsqr->vwork_n[1];
97: V1 = lsqr->vwork_n[2];
98: W2 = lsqr->vwork_n[3];
99: if (!nopreconditioner) Z = lsqr->vwork_n[4];
101: /* standard error vector */
102: if (lsqr->se) {
103: VecSet(lsqr->se,0.0);
104: }
106: /* Compute initial residual, temporarily use work vector u */
107: if (!ksp->guess_zero) {
108: KSP_MatMult(ksp,Amat,X,U); /* u <- b - Ax */
109: VecAYPX(U,-1.0,B);
110: } else {
111: VecCopy(B,U); /* u <- b (x is 0) */
112: }
114: /* Test for nothing to do */
115: VecNorm(U,NORM_2,&rnorm);
116: KSPCheckNorm(ksp,rnorm);
117: PetscObjectSAWsTakeAccess((PetscObject)ksp);
118: ksp->its = 0;
119: ksp->rnorm = rnorm;
120: PetscObjectSAWsGrantAccess((PetscObject)ksp);
121: KSPLogResidualHistory(ksp,rnorm);
122: KSPMonitor(ksp,0,rnorm);
123: (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
124: if (ksp->reason) return(0);
126: beta = rnorm;
127: VecScale(U,1.0/beta);
128: KSP_MatMultTranspose(ksp,Amat,U,V);
129: if (nopreconditioner) {
130: VecNorm(V,NORM_2,&alpha);
131: KSPCheckNorm(ksp,rnorm);
132: } else {
133: /* this is an application of the preconditioner for the normal equations; not the operator, see the manual page */
134: PCApply(ksp->pc,V,Z);
135: VecDotRealPart(V,Z,&alpha);
136: if (alpha <= 0.0) {
137: ksp->reason = KSP_DIVERGED_BREAKDOWN;
138: return(0);
139: }
140: alpha = PetscSqrtReal(alpha);
141: VecScale(Z,1.0/alpha);
142: }
143: VecScale(V,1.0/alpha);
145: if (nopreconditioner) {
146: VecCopy(V,W);
147: } else {
148: VecCopy(Z,W);
149: }
151: if (lsqr->exact_norm) {
152: MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm);
153: } else lsqr->anorm = 0.0;
155: lsqr->arnorm = alpha * beta;
156: phibar = beta;
157: rhobar = alpha;
158: i = 0;
159: do {
160: if (nopreconditioner) {
161: KSP_MatMult(ksp,Amat,V,U1);
162: } else {
163: KSP_MatMult(ksp,Amat,Z,U1);
164: }
165: VecAXPY(U1,-alpha,U);
166: VecNorm(U1,NORM_2,&beta);
167: KSPCheckNorm(ksp,beta);
168: if (beta > 0.0) {
169: VecScale(U1,1.0/beta); /* beta*U1 = Amat*V - alpha*U */
170: if (!lsqr->exact_norm) {
171: lsqr->anorm = PetscSqrtScalar(PetscSqr(lsqr->anorm) + PetscSqr(alpha) + PetscSqr(beta));
172: }
173: }
175: KSP_MatMultTranspose(ksp,Amat,U1,V1);
176: VecAXPY(V1,-beta,V);
177: if (nopreconditioner) {
178: VecNorm(V1,NORM_2,&alpha);
179: KSPCheckNorm(ksp,alpha);
180: } else {
181: PCApply(ksp->pc,V1,Z);
182: VecDotRealPart(V1,Z,&alpha);
183: if (alpha <= 0.0) {
184: ksp->reason = KSP_DIVERGED_BREAKDOWN;
185: break;
186: }
187: alpha = PetscSqrtReal(alpha);
188: VecScale(Z,1.0/alpha);
189: }
190: VecScale(V1,1.0/alpha); /* alpha*V1 = Amat^T*U1 - beta*V */
191: rho = PetscSqrtScalar(rhobar*rhobar + beta*beta);
192: c = rhobar / rho;
193: s = beta / rho;
194: theta = s * alpha;
195: rhobar = -c * alpha;
196: phi = c * phibar;
197: phibar = s * phibar;
198: tau = s * phi;
200: VecAXPY(X,phi/rho,W); /* x <- x + (phi/rho) w */
202: if (lsqr->se) {
203: VecCopy(W,W2);
204: VecSquare(W2);
205: VecScale(W2,1.0/(rho*rho));
206: VecAXPY(lsqr->se, 1.0, W2); /* lsqr->se <- lsqr->se + (w^2/rho^2) */
207: }
208: if (nopreconditioner) {
209: VecAYPX(W,-theta/rho,V1); /* w <- v - (theta/rho) w */
210: } else {
211: VecAYPX(W,-theta/rho,Z); /* w <- z - (theta/rho) w */
212: }
214: lsqr->arnorm = alpha*PetscAbsScalar(tau);
215: rnorm = PetscRealPart(phibar);
217: PetscObjectSAWsTakeAccess((PetscObject)ksp);
218: ksp->its++;
219: ksp->rnorm = rnorm;
220: PetscObjectSAWsGrantAccess((PetscObject)ksp);
221: KSPLogResidualHistory(ksp,rnorm);
222: KSPMonitor(ksp,i+1,rnorm);
223: (*ksp->converged)(ksp,i+1,rnorm,&ksp->reason,ksp->cnvP);
224: if (ksp->reason) break;
225: SWAP(U1,U,TMP);
226: SWAP(V1,V,TMP);
228: i++;
229: } while (i<ksp->max_it);
230: if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
232: /* Finish off the standard error estimates */
233: if (lsqr->se) {
234: tmp = 1.0;
235: MatGetSize(Amat,&size1,&size2);
236: if (size1 > size2) tmp = size1 - size2;
237: tmp = rnorm / PetscSqrtScalar(tmp);
238: VecSqrtAbs(lsqr->se);
239: VecScale(lsqr->se,tmp);
240: }
241: return(0);
242: }
245: PetscErrorCode KSPDestroy_LSQR(KSP ksp)
246: {
247: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
251: /* Free work vectors */
252: if (lsqr->vwork_n) {
253: VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
254: }
255: if (lsqr->vwork_m) {
256: VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
257: }
258: VecDestroy(&lsqr->se);
259: /* Revert convergence test */
260: KSPSetConvergenceTest(ksp,lsqr->converged,lsqr->cnvP,lsqr->convergeddestroy);
261: /* Free the KSP_LSQR context */
262: PetscFree(ksp->data);
263: return(0);
264: }
266: /*@
267: KSPLSQRSetComputeStandardErrorVec - Compute vector of standard error estimates during KSPSolve_LSQR().
269: Not Collective
271: Input Parameters:
272: + ksp - iterative context
273: - flg - compute the vector of standard estimates or not
275: Developer notes:
276: Vaclav: I'm not sure whether this vector is useful for anything.
278: Level: intermediate
280: .seealso: KSPSolve(), KSPLSQR, KSPLSQRGetStandardErrorVec()
281: @*/
282: PetscErrorCode KSPLSQRSetComputeStandardErrorVec(KSP ksp, PetscBool flg)
283: {
284: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
287: lsqr->se_flg = flg;
288: return(0);
289: }
291: /*@
292: KSPLSQRSetExactMatNorm - Compute exact matrix norm instead of iteratively refined estimate.
294: Not Collective
296: Input Parameters:
297: + ksp - iterative context
298: - flg - compute exact matrix norm or not
300: Notes:
301: By default, flg=PETSC_FALSE. This is usually preferred to avoid possibly expensive computation of the norm.
302: For flg=PETSC_TRUE, we call MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm) which will work only for some types of explicitly assembled matrices.
303: This can affect convergence rate as KSPLSQRConvergedDefault() assumes different value of ||A|| used in normal equation stopping criterion.
305: Level: intermediate
307: .seealso: KSPSolve(), KSPLSQR, KSPLSQRGetNorms(), KSPLSQRConvergedDefault()
308: @*/
309: PetscErrorCode KSPLSQRSetExactMatNorm(KSP ksp, PetscBool flg)
310: {
311: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
314: lsqr->exact_norm = flg;
315: return(0);
316: }
318: /*@
319: KSPLSQRGetStandardErrorVec - Get vector of standard error estimates.
320: Only available if -ksp_lsqr_set_standard_error was set to true
321: or KSPLSQRSetComputeStandardErrorVec(ksp, PETSC_TRUE) was called.
322: Otherwise returns NULL.
324: Not Collective
326: Input Parameters:
327: . ksp - iterative context
329: Output Parameters:
330: . se - vector of standard estimates
332: Options Database Keys:
333: . -ksp_lsqr_set_standard_error - set standard error estimates of solution
335: Developer notes:
336: Vaclav: I'm not sure whether this vector is useful for anything.
338: Level: intermediate
340: .seealso: KSPSolve(), KSPLSQR, KSPLSQRSetComputeStandardErrorVec()
341: @*/
342: PetscErrorCode KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
343: {
344: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
347: *se = lsqr->se;
348: return(0);
349: }
351: /*@
352: KSPLSQRGetNorms - Get norm estimates that LSQR computes internally during KSPSolve().
354: Not Collective
356: Input Parameters:
357: . ksp - iterative context
359: Output Parameters:
360: + arnorm - good estimate of norm((A*inv(Pmat))'*r), where r = A*x - b, used in specific stopping criterion
361: - anorm - poor estimate of norm(A*inv(Pmat),'fro') used in specific stopping criterion
363: Notes:
364: Output parameters are meaningful only after KSPSolve().
365: These are the same quantities as normar and norma in MATLAB's lsqr(), whose output lsvec is a vector of normar / norma for all iterations.
366: If -ksp_lsqr_exact_mat_norm is set or KSPLSQRSetExactMatNorm(ksp, PETSC_TRUE) called, then anorm is exact Frobenius norm.
368: Level: intermediate
370: .seealso: KSPSolve(), KSPLSQR, KSPLSQRSetExactMatNorm()
371: @*/
372: PetscErrorCode KSPLSQRGetNorms(KSP ksp,PetscReal *arnorm, PetscReal *anorm)
373: {
374: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
377: if (arnorm) *arnorm = lsqr->arnorm;
378: if (anorm) *anorm = lsqr->anorm;
379: return(0);
380: }
382: /*@C
383: KSLSQRPMonitorResidual - Prints the residual norm, as well as the normal equation residual norm, at each iteration of an iterative solver.
385: Collective on ksp
387: Input Parameters:
388: + ksp - iterative context
389: . n - iteration number
390: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
391: - vf - The viewer context
393: Options Database Key:
394: . -ksp_lsqr_monitor - Activates KSPLSQRMonitorResidual()
396: Level: intermediate
398: .seealso: KSPMonitorSet(), KSPMonitorResidual(),KSPMonitorTrueResidualMaxNorm()
399: @*/
400: PetscErrorCode KSPLSQRMonitorResidual(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
401: {
402: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
403: PetscViewer viewer = vf->viewer;
404: PetscViewerFormat format = vf->format;
405: char normtype[256];
406: PetscInt tablevel;
407: const char *prefix;
408: PetscErrorCode ierr;
412: PetscObjectGetTabLevel((PetscObject) ksp, &tablevel);
413: PetscObjectGetOptionsPrefix((PetscObject) ksp, &prefix);
414: PetscStrncpy(normtype, KSPNormTypes[ksp->normtype], sizeof(normtype));
415: PetscStrtolower(normtype);
416: PetscViewerPushFormat(viewer, format);
417: PetscViewerASCIIAddTab(viewer, tablevel);
418: if (n == 0 && prefix) {PetscViewerASCIIPrintf(viewer, " Residual norm, norm of normal equations, and matrix norm for %s solve.\n", prefix);}
419: if (!n) {
420: PetscViewerASCIIPrintf(viewer,"%3D KSP resid norm %14.12e\n",n,(double)rnorm);
421: } else {
422: PetscViewerASCIIPrintf(viewer,"%3D KSP resid norm %14.12e normal eq resid norm %14.12e matrix norm %14.12e\n",n,(double)rnorm,(double)lsqr->arnorm,(double)lsqr->anorm);
423: }
424: PetscViewerASCIISubtractTab(viewer, tablevel);
425: PetscViewerPopFormat(viewer);
426: return(0);
427: }
429: /*@C
430: KSPLSQRMonitorResidualDrawLG - Plots the true residual norm at each iteration of an iterative solver.
432: Collective on ksp
434: Input Parameters:
435: + ksp - iterative context
436: . n - iteration number
437: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
438: - vf - The viewer context
440: Options Database Key:
441: . -ksp_lsqr_monitor draw::draw_lg - Activates KSPMonitorTrueResidualDrawLG()
443: Level: intermediate
445: .seealso: KSPMonitorSet(), KSPMonitorTrueResidual()
446: @*/
447: PetscErrorCode KSPLSQRMonitorResidualDrawLG(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
448: {
449: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
450: PetscViewer viewer = vf->viewer;
451: PetscViewerFormat format = vf->format;
452: PetscDrawLG lg = vf->lg;
453: KSPConvergedReason reason;
454: PetscReal x[2], y[2];
455: PetscErrorCode ierr;
460: PetscViewerPushFormat(viewer, format);
461: if (!n) {PetscDrawLGReset(lg);}
462: x[0] = (PetscReal) n;
463: if (rnorm > 0.0) y[0] = PetscLog10Real(rnorm);
464: else y[0] = -15.0;
465: x[1] = (PetscReal) n;
466: if (lsqr->arnorm > 0.0) y[1] = PetscLog10Real(lsqr->arnorm);
467: else y[1] = -15.0;
468: PetscDrawLGAddPoint(lg, x, y);
469: KSPGetConvergedReason(ksp, &reason);
470: if (n <= 20 || !(n % 5) || reason) {
471: PetscDrawLGDraw(lg);
472: PetscDrawLGSave(lg);
473: }
474: PetscViewerPopFormat(viewer);
475: return(0);
476: }
478: /*@C
479: KSPLSQRMonitorResidualDrawLGCreate - Creates the plotter for the LSQR residual and normal eqn residual.
481: Collective on ksp
483: Input Parameters:
484: + viewer - The PetscViewer
485: . format - The viewer format
486: - ctx - An optional user context
488: Output Parameter:
489: . vf - The viewer context
491: Level: intermediate
493: .seealso: KSPMonitorSet(), KSPLSQRMonitorResidual()
494: @*/
495: PetscErrorCode KSPLSQRMonitorResidualDrawLGCreate(PetscViewer viewer, PetscViewerFormat format, void *ctx, PetscViewerAndFormat **vf)
496: {
497: const char *names[] = {"residual", "normal eqn residual"};
501: PetscViewerAndFormatCreate(viewer, format, vf);
502: (*vf)->data = ctx;
503: KSPMonitorLGCreate(PetscObjectComm((PetscObject) viewer), NULL, NULL, "Log Residual Norm", 2, names, PETSC_DECIDE, PETSC_DECIDE, 400, 300, &(*vf)->lg);
504: return(0);
505: }
507: PetscErrorCode KSPSetFromOptions_LSQR(PetscOptionItems *PetscOptionsObject,KSP ksp)
508: {
510: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
513: PetscOptionsHead(PetscOptionsObject,"KSP LSQR Options");
514: PetscOptionsBool("-ksp_lsqr_compute_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetComputeStandardErrorVec",lsqr->se_flg,&lsqr->se_flg,NULL);
515: PetscOptionsBool("-ksp_lsqr_exact_mat_norm","Compute exact matrix norm instead of iteratively refined estimate","KSPLSQRSetExactMatNorm",lsqr->exact_norm,&lsqr->exact_norm,NULL);
516: KSPMonitorSetFromOptions(ksp, "-ksp_lsqr_monitor", "lsqr_residual", NULL);
517: PetscOptionsTail();
518: return(0);
519: }
521: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
522: {
523: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
525: PetscBool iascii;
528: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
529: if (iascii) {
530: if (lsqr->se) {
531: PetscReal rnorm;
532: VecNorm(lsqr->se,NORM_2,&rnorm);
533: PetscViewerASCIIPrintf(viewer," norm of standard error %g, iterations %d\n",(double)rnorm,ksp->its);
534: } else {
535: PetscViewerASCIIPrintf(viewer," standard error not computed\n");
536: }
537: if (lsqr->exact_norm) {
538: PetscViewerASCIIPrintf(viewer," using exact matrix norm\n");
539: } else {
540: PetscViewerASCIIPrintf(viewer," using inexact matrix norm\n");
541: }
542: }
543: return(0);
544: }
546: /*@C
547: KSPLSQRConvergedDefault - Determines convergence of the LSQR Krylov method.
549: Collective on ksp
551: Input Parameters:
552: + ksp - iterative context
553: . n - iteration number
554: . rnorm - 2-norm residual value (may be estimated)
555: - ctx - convergence context which must be created by KSPConvergedDefaultCreate()
557: reason is set to:
558: + positive - if the iteration has converged;
559: . negative - if residual norm exceeds divergence threshold;
560: - 0 - otherwise.
562: Notes:
563: KSPConvergedDefault() is called first to check for convergence in A*x=b.
564: If that does not determine convergence then checks convergence for the least squares problem, i.e. in min{|b-A*x|}.
565: Possible convergence for the least squares problem (which is based on the residual of the normal equations) are KSP_CONVERGED_RTOL_NORMAL norm and KSP_CONVERGED_ATOL_NORMAL.
566: KSP_CONVERGED_RTOL_NORMAL is returned if ||A'*r|| < rtol * ||A|| * ||r||.
567: Matrix norm ||A|| is iteratively refined estimate, see KSPLSQRGetNorms().
568: This criterion is now largely compatible with that in MATLAB lsqr().
570: Level: intermediate
572: .seealso: KSPLSQR, KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
573: KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(), KSPConvergedDefault(), KSPLSQRGetNorms(), KSPLSQRSetExactMatNorm()
574: @*/
575: PetscErrorCode KSPLSQRConvergedDefault(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
576: {
578: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
581: /* check for convergence in A*x=b */
582: KSPConvergedDefault(ksp,n,rnorm,reason,ctx);
583: if (!n || *reason) return(0);
585: /* check for convergence in min{|b-A*x|} */
586: if (lsqr->arnorm < ksp->abstol) {
587: PetscInfo3(ksp,"LSQR solver has converged. Normal equation residual %14.12e is less than absolute tolerance %14.12e at iteration %D\n",(double)lsqr->arnorm,(double)ksp->abstol,n);
588: *reason = KSP_CONVERGED_ATOL_NORMAL;
589: } else if (lsqr->arnorm < ksp->rtol * lsqr->anorm * rnorm) {
590: PetscInfo6(ksp,"LSQR solver has converged. Normal equation residual %14.12e is less than rel. tol. %14.12e times %s Frobenius norm of matrix %14.12e times residual %14.12e at iteration %D\n",(double)lsqr->arnorm,(double)ksp->rtol,lsqr->exact_norm?"exact":"approx.",(double)lsqr->anorm,(double)rnorm,n);
591: *reason = KSP_CONVERGED_RTOL_NORMAL;
592: }
593: return(0);
594: }
596: /*MC
597: KSPLSQR - This implements LSQR
599: Options Database Keys:
600: + -ksp_lsqr_set_standard_error - set standard error estimates of solution, see KSPLSQRSetComputeStandardErrorVec() and KSPLSQRGetStandardErrorVec()
601: . -ksp_lsqr_exact_mat_norm - compute exact matrix norm instead of iteratively refined estimate, see KSPLSQRSetExactMatNorm()
602: - -ksp_lsqr_monitor - monitor residual norm, norm of residual of normal equations A'*A x = A' b, and estimate of matrix norm ||A||
604: Level: beginner
606: Notes:
607: Supports non-square (rectangular) matrices.
609: This varient, when applied with no preconditioning is identical to the original algorithm in exact arithematic; however, in practice, with no preconditioning
610: due to inexact arithematic, it can converge differently. Hence when no preconditioner is used (PCType PCNONE) it automatically reverts to the original algorithm.
612: With the PETSc built-in preconditioners, such as ICC, one should call KSPSetOperators(ksp,A,A'*A)) since the preconditioner needs to work
613: for the normal equations A'*A.
615: Supports only left preconditioning.
617: For least squares problems wit nonzero residual A*x - b, there are additional convergence tests for the residual of the normal equations, A'*(b - Ax), see KSPLSQRConvergedDefault().
619: References:
620: . 1. - The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, 1982.
622: In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
623: The preconditioned variant was implemented by Bas van't Hof and is essentially a left preconditioning for the Normal Equations. It appears the implementation with preconditioner
624: track the true norm of the residual and uses that in the convergence test.
626: Developer Notes:
627: How is this related to the KSPCGNE implementation? One difference is that KSPCGNE applies
628: the preconditioner transpose times the preconditioner, so one does not need to pass A'*A as the third argument to KSPSetOperators().
632: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPSolve(), KSPLSQRConvergedDefault(), KSPLSQRSetComputeStandardErrorVec(), KSPLSQRGetStandardErrorVec(), KSPLSQRSetExactMatNorm()
634: M*/
635: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
636: {
637: KSP_LSQR *lsqr;
638: void *ctx;
642: PetscNewLog(ksp,&lsqr);
643: lsqr->se = NULL;
644: lsqr->se_flg = PETSC_FALSE;
645: lsqr->exact_norm = PETSC_FALSE;
646: lsqr->anorm = -1.0;
647: lsqr->arnorm = -1.0;
648: ksp->data = (void*)lsqr;
649: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);
651: ksp->ops->setup = KSPSetUp_LSQR;
652: ksp->ops->solve = KSPSolve_LSQR;
653: ksp->ops->destroy = KSPDestroy_LSQR;
654: ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
655: ksp->ops->view = KSPView_LSQR;
657: /* Backup current convergence test; remove destroy routine from KSP to prevent destroying the convergence context in KSPSetConvergenceTest() */
658: KSPGetAndClearConvergenceTest(ksp,&lsqr->converged,&lsqr->cnvP,&lsqr->convergeddestroy);
659: /* Override current convergence test */
660: KSPConvergedDefaultCreate(&ctx);
661: KSPSetConvergenceTest(ksp,KSPLSQRConvergedDefault,ctx,KSPConvergedDefaultDestroy);
662: return(0);
663: }