Actual source code: lsqr.c
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: PetscObjectComposeFunction((PetscObject)ksp,"KSPLSQRMonitorResidual_C",NULL);
264: PetscObjectComposeFunction((PetscObject)ksp,"KSPLSQRMonitorResidualDrawLG_C",NULL);
265: return(0);
266: }
268: /*@
269: KSPLSQRSetComputeStandardErrorVec - Compute vector of standard error estimates during KSPSolve_LSQR().
271: Not Collective
273: Input Parameters:
274: + ksp - iterative context
275: - flg - compute the vector of standard estimates or not
277: Developer notes:
278: Vaclav: I'm not sure whether this vector is useful for anything.
280: Level: intermediate
282: .seealso: KSPSolve(), KSPLSQR, KSPLSQRGetStandardErrorVec()
283: @*/
284: PetscErrorCode KSPLSQRSetComputeStandardErrorVec(KSP ksp, PetscBool flg)
285: {
286: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
289: lsqr->se_flg = flg;
290: return(0);
291: }
293: /*@
294: KSPLSQRSetExactMatNorm - Compute exact matrix norm instead of iteratively refined estimate.
296: Not Collective
298: Input Parameters:
299: + ksp - iterative context
300: - flg - compute exact matrix norm or not
302: Notes:
303: By default, flg=PETSC_FALSE. This is usually preferred to avoid possibly expensive computation of the norm.
304: For flg=PETSC_TRUE, we call MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm) which will work only for some types of explicitly assembled matrices.
305: This can affect convergence rate as KSPLSQRConvergedDefault() assumes different value of ||A|| used in normal equation stopping criterion.
307: Level: intermediate
309: .seealso: KSPSolve(), KSPLSQR, KSPLSQRGetNorms(), KSPLSQRConvergedDefault()
310: @*/
311: PetscErrorCode KSPLSQRSetExactMatNorm(KSP ksp, PetscBool flg)
312: {
313: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
316: lsqr->exact_norm = flg;
317: return(0);
318: }
320: /*@
321: KSPLSQRGetStandardErrorVec - Get vector of standard error estimates.
322: Only available if -ksp_lsqr_set_standard_error was set to true
323: or KSPLSQRSetComputeStandardErrorVec(ksp, PETSC_TRUE) was called.
324: Otherwise returns NULL.
326: Not Collective
328: Input Parameters:
329: . ksp - iterative context
331: Output Parameters:
332: . se - vector of standard estimates
334: Options Database Keys:
335: . -ksp_lsqr_set_standard_error - set standard error estimates of solution
337: Developer notes:
338: Vaclav: I'm not sure whether this vector is useful for anything.
340: Level: intermediate
342: .seealso: KSPSolve(), KSPLSQR, KSPLSQRSetComputeStandardErrorVec()
343: @*/
344: PetscErrorCode KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
345: {
346: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
349: *se = lsqr->se;
350: return(0);
351: }
353: /*@
354: KSPLSQRGetNorms - Get norm estimates that LSQR computes internally during KSPSolve().
356: Not Collective
358: Input Parameters:
359: . ksp - iterative context
361: Output Parameters:
362: + arnorm - good estimate of norm((A*inv(Pmat))'*r), where r = A*x - b, used in specific stopping criterion
363: - anorm - poor estimate of norm(A*inv(Pmat),'fro') used in specific stopping criterion
365: Notes:
366: Output parameters are meaningful only after KSPSolve().
367: 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.
368: If -ksp_lsqr_exact_mat_norm is set or KSPLSQRSetExactMatNorm(ksp, PETSC_TRUE) called, then anorm is exact Frobenius norm.
370: Level: intermediate
372: .seealso: KSPSolve(), KSPLSQR, KSPLSQRSetExactMatNorm()
373: @*/
374: PetscErrorCode KSPLSQRGetNorms(KSP ksp,PetscReal *arnorm, PetscReal *anorm)
375: {
376: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
379: if (arnorm) *arnorm = lsqr->arnorm;
380: if (anorm) *anorm = lsqr->anorm;
381: return(0);
382: }
384: PetscErrorCode KSPLSQRMonitorResidual_LSQR(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
385: {
386: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
387: PetscViewer viewer = vf->viewer;
388: PetscViewerFormat format = vf->format;
389: char normtype[256];
390: PetscInt tablevel;
391: const char *prefix;
392: PetscErrorCode ierr;
395: PetscObjectGetTabLevel((PetscObject) ksp, &tablevel);
396: PetscObjectGetOptionsPrefix((PetscObject) ksp, &prefix);
397: PetscStrncpy(normtype, KSPNormTypes[ksp->normtype], sizeof(normtype));
398: PetscStrtolower(normtype);
399: PetscViewerPushFormat(viewer, format);
400: PetscViewerASCIIAddTab(viewer, tablevel);
401: if (n == 0 && prefix) {PetscViewerASCIIPrintf(viewer, " Residual norm, norm of normal equations, and matrix norm for %s solve.\n", prefix);}
402: if (!n) {
403: PetscViewerASCIIPrintf(viewer,"%3D KSP resid norm %14.12e\n",n,(double)rnorm);
404: } else {
405: 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);
406: }
407: PetscViewerASCIISubtractTab(viewer, tablevel);
408: PetscViewerPopFormat(viewer);
409: return(0);
410: }
412: /*@C
413: KSPLSQRMonitorResidual - Prints the residual norm, as well as the normal equation residual norm, at each iteration of an iterative solver.
415: Collective on ksp
417: Input Parameters:
418: + ksp - iterative context
419: . n - iteration number
420: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
421: - vf - The viewer context
423: Options Database Key:
424: . -ksp_lsqr_monitor - Activates KSPLSQRMonitorResidual()
426: Level: intermediate
428: .seealso: KSPMonitorSet(), KSPMonitorResidual(),KSPMonitorTrueResidualMaxNorm()
429: @*/
430: PetscErrorCode KSPLSQRMonitorResidual(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
431: {
438: PetscTryMethod(ksp, "KSPLSQRMonitorResidual_C", (KSP,PetscInt,PetscReal,PetscViewerAndFormat*), (ksp,n,rnorm,vf));
439: return(0);
440: }
442: PetscErrorCode KSPLSQRMonitorResidualDrawLG_LSQR(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
443: {
444: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
445: PetscViewer viewer = vf->viewer;
446: PetscViewerFormat format = vf->format;
447: PetscDrawLG lg = vf->lg;
448: KSPConvergedReason reason;
449: PetscReal x[2], y[2];
450: PetscErrorCode ierr;
453: PetscViewerPushFormat(viewer, format);
454: if (!n) {PetscDrawLGReset(lg);}
455: x[0] = (PetscReal) n;
456: if (rnorm > 0.0) y[0] = PetscLog10Real(rnorm);
457: else y[0] = -15.0;
458: x[1] = (PetscReal) n;
459: if (lsqr->arnorm > 0.0) y[1] = PetscLog10Real(lsqr->arnorm);
460: else y[1] = -15.0;
461: PetscDrawLGAddPoint(lg, x, y);
462: KSPGetConvergedReason(ksp, &reason);
463: if (n <= 20 || !(n % 5) || reason) {
464: PetscDrawLGDraw(lg);
465: PetscDrawLGSave(lg);
466: }
467: PetscViewerPopFormat(viewer);
468: return(0);
469: }
471: /*@C
472: KSPLSQRMonitorResidualDrawLG - Plots the true residual norm at each iteration of an iterative solver.
474: Collective on ksp
476: Input Parameters:
477: + ksp - iterative context
478: . n - iteration number
479: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
480: - vf - The viewer context
482: Options Database Key:
483: . -ksp_lsqr_monitor draw::draw_lg - Activates KSPMonitorTrueResidualDrawLG()
485: Level: intermediate
487: .seealso: KSPMonitorSet(), KSPMonitorTrueResidual()
488: @*/
489: PetscErrorCode KSPLSQRMonitorResidualDrawLG(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
490: {
498: PetscTryMethod(ksp, "KSPLSQRMonitorResidualDrawLG_C", (KSP,PetscInt,PetscReal,PetscViewerAndFormat*), (ksp,n,rnorm,vf));
499: return(0);
500: }
502: /*@C
503: KSPLSQRMonitorResidualDrawLGCreate - Creates the plotter for the LSQR residual and normal eqn residual.
505: Collective on ksp
507: Input Parameters:
508: + viewer - The PetscViewer
509: . format - The viewer format
510: - ctx - An optional user context
512: Output Parameter:
513: . vf - The viewer context
515: Level: intermediate
517: .seealso: KSPMonitorSet(), KSPLSQRMonitorResidual()
518: @*/
519: PetscErrorCode KSPLSQRMonitorResidualDrawLGCreate(PetscViewer viewer, PetscViewerFormat format, void *ctx, PetscViewerAndFormat **vf)
520: {
521: const char *names[] = {"residual", "normal eqn residual"};
525: PetscViewerAndFormatCreate(viewer, format, vf);
526: (*vf)->data = ctx;
527: KSPMonitorLGCreate(PetscObjectComm((PetscObject) viewer), NULL, NULL, "Log Residual Norm", 2, names, PETSC_DECIDE, PETSC_DECIDE, 400, 300, &(*vf)->lg);
528: return(0);
529: }
531: PetscErrorCode KSPSetFromOptions_LSQR(PetscOptionItems *PetscOptionsObject,KSP ksp)
532: {
534: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
537: PetscOptionsHead(PetscOptionsObject,"KSP LSQR Options");
538: PetscOptionsBool("-ksp_lsqr_compute_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetComputeStandardErrorVec",lsqr->se_flg,&lsqr->se_flg,NULL);
539: PetscOptionsBool("-ksp_lsqr_exact_mat_norm","Compute exact matrix norm instead of iteratively refined estimate","KSPLSQRSetExactMatNorm",lsqr->exact_norm,&lsqr->exact_norm,NULL);
540: KSPMonitorSetFromOptions(ksp, "-ksp_lsqr_monitor", "lsqr_residual", NULL);
541: PetscOptionsTail();
542: return(0);
543: }
545: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
546: {
547: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
549: PetscBool iascii;
552: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
553: if (iascii) {
554: if (lsqr->se) {
555: PetscReal rnorm;
556: VecNorm(lsqr->se,NORM_2,&rnorm);
557: PetscViewerASCIIPrintf(viewer," norm of standard error %g, iterations %d\n",(double)rnorm,ksp->its);
558: } else {
559: PetscViewerASCIIPrintf(viewer," standard error not computed\n");
560: }
561: if (lsqr->exact_norm) {
562: PetscViewerASCIIPrintf(viewer," using exact matrix norm\n");
563: } else {
564: PetscViewerASCIIPrintf(viewer," using inexact matrix norm\n");
565: }
566: }
567: return(0);
568: }
570: /*@C
571: KSPLSQRConvergedDefault - Determines convergence of the LSQR Krylov method.
573: Collective on ksp
575: Input Parameters:
576: + ksp - iterative context
577: . n - iteration number
578: . rnorm - 2-norm residual value (may be estimated)
579: - ctx - convergence context which must be created by KSPConvergedDefaultCreate()
581: reason is set to:
582: + positive - if the iteration has converged;
583: . negative - if residual norm exceeds divergence threshold;
584: - 0 - otherwise.
586: Notes:
587: KSPConvergedDefault() is called first to check for convergence in A*x=b.
588: If that does not determine convergence then checks convergence for the least squares problem, i.e. in min{|b-A*x|}.
589: 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.
590: KSP_CONVERGED_RTOL_NORMAL is returned if ||A'*r|| < rtol * ||A|| * ||r||.
591: Matrix norm ||A|| is iteratively refined estimate, see KSPLSQRGetNorms().
592: This criterion is now largely compatible with that in MATLAB lsqr().
594: Level: intermediate
596: .seealso: KSPLSQR, KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
597: KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(), KSPConvergedDefault(), KSPLSQRGetNorms(), KSPLSQRSetExactMatNorm()
598: @*/
599: PetscErrorCode KSPLSQRConvergedDefault(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
600: {
602: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
605: /* check for convergence in A*x=b */
606: KSPConvergedDefault(ksp,n,rnorm,reason,ctx);
607: if (!n || *reason) return(0);
609: /* check for convergence in min{|b-A*x|} */
610: if (lsqr->arnorm < ksp->abstol) {
611: 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);
612: *reason = KSP_CONVERGED_ATOL_NORMAL;
613: } else if (lsqr->arnorm < ksp->rtol * lsqr->anorm * rnorm) {
614: 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);
615: *reason = KSP_CONVERGED_RTOL_NORMAL;
616: }
617: return(0);
618: }
620: /*MC
621: KSPLSQR - This implements LSQR
623: Options Database Keys:
624: + -ksp_lsqr_set_standard_error - set standard error estimates of solution, see KSPLSQRSetComputeStandardErrorVec() and KSPLSQRGetStandardErrorVec()
625: . -ksp_lsqr_exact_mat_norm - compute exact matrix norm instead of iteratively refined estimate, see KSPLSQRSetExactMatNorm()
626: - -ksp_lsqr_monitor - monitor residual norm, norm of residual of normal equations A'*A x = A' b, and estimate of matrix norm ||A||
628: Level: beginner
630: Notes:
631: Supports non-square (rectangular) matrices.
633: This varient, when applied with no preconditioning is identical to the original algorithm in exact arithematic; however, in practice, with no preconditioning
634: due to inexact arithematic, it can converge differently. Hence when no preconditioner is used (PCType PCNONE) it automatically reverts to the original algorithm.
636: With the PETSc built-in preconditioners, such as ICC, one should call KSPSetOperators(ksp,A,A'*A)) since the preconditioner needs to work
637: for the normal equations A'*A.
639: Supports only left preconditioning.
641: 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().
643: References:
644: . 1. - The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, 1982.
646: In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
647: 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
648: track the true norm of the residual and uses that in the convergence test.
650: Developer Notes:
651: How is this related to the KSPCGNE implementation? One difference is that KSPCGNE applies
652: the preconditioner transpose times the preconditioner, so one does not need to pass A'*A as the third argument to KSPSetOperators().
656: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPSolve(), KSPLSQRConvergedDefault(), KSPLSQRSetComputeStandardErrorVec(), KSPLSQRGetStandardErrorVec(), KSPLSQRSetExactMatNorm()
658: M*/
659: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
660: {
661: KSP_LSQR *lsqr;
662: void *ctx;
666: PetscNewLog(ksp,&lsqr);
667: lsqr->se = NULL;
668: lsqr->se_flg = PETSC_FALSE;
669: lsqr->exact_norm = PETSC_FALSE;
670: lsqr->anorm = -1.0;
671: lsqr->arnorm = -1.0;
672: ksp->data = (void*)lsqr;
673: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);
675: ksp->ops->setup = KSPSetUp_LSQR;
676: ksp->ops->solve = KSPSolve_LSQR;
677: ksp->ops->destroy = KSPDestroy_LSQR;
678: ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
679: ksp->ops->view = KSPView_LSQR;
681: /* Backup current convergence test; remove destroy routine from KSP to prevent destroying the convergence context in KSPSetConvergenceTest() */
682: KSPGetAndClearConvergenceTest(ksp,&lsqr->converged,&lsqr->cnvP,&lsqr->convergeddestroy);
683: /* Override current convergence test */
684: KSPConvergedDefaultCreate(&ctx);
685: KSPSetConvergenceTest(ksp,KSPLSQRConvergedDefault,ctx,KSPConvergedDefaultDestroy);
686: PetscObjectComposeFunction((PetscObject)ksp,"KSPLSQRMonitorResidual_C",KSPLSQRMonitorResidual_LSQR);
687: PetscObjectComposeFunction((PetscObject)ksp,"KSPLSQRMonitorResidualDrawLG_C",KSPLSQRMonitorResidualDrawLG_LSQR);
688: return(0);
689: }