Actual source code: lsqr.c
petsc-3.5.4 2015-05-23
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 <../src/ksp/ksp/impls/lsqr/lsqr.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: PetscReal arnorm; /* Norm of the vector A.r */
17: PetscReal anorm; /* Frobenius norm of the matrix A */
18: PetscReal rhs_norm; /* Norm of the right hand side */
19: } KSP_LSQR;
21: extern PetscErrorCode VecSquare(Vec);
25: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
26: {
28: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
29: PetscBool nopreconditioner;
32: PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);
33: /* nopreconditioner =PETSC_FALSE; */
35: lsqr->nwork_m = 2;
36: if (lsqr->vwork_m) {
37: VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
38: }
39: if (nopreconditioner) lsqr->nwork_n = 4;
40: else lsqr->nwork_n = 5;
42: if (lsqr->vwork_n) {
43: VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
44: }
45: KSPGetVecs(ksp,lsqr->nwork_n,&lsqr->vwork_n,lsqr->nwork_m,&lsqr->vwork_m);
46: if (lsqr->se_flg && !lsqr->se) {
47: /* lsqr->se is not set by user, get it from pmat */
48: Vec *se;
49: KSPGetVecs(ksp,1,&se,0,NULL);
50: lsqr->se = *se;
51: PetscFree(se);
52: }
53: return(0);
54: }
58: static PetscErrorCode KSPSolve_LSQR(KSP ksp)
59: {
61: PetscInt i,size1,size2;
62: PetscScalar rho,rhobar,phi,phibar,theta,c,s,tmp,tau;
63: PetscReal beta,alpha,rnorm;
64: Vec X,B,V,V1,U,U1,TMP,W,W2,SE,Z = NULL;
65: Mat Amat,Pmat;
66: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
67: PetscBool diagonalscale,nopreconditioner;
70: PCGetDiagonalScale(ksp->pc,&diagonalscale);
71: if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
73: PCGetOperators(ksp->pc,&Amat,&Pmat);
74: PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);
76: /* nopreconditioner =PETSC_FALSE; */
77: /* Calculate norm of right hand side */
78: VecNorm(ksp->vec_rhs,NORM_2,&lsqr->rhs_norm);
80: /* mark norm of matrix with negative number to indicate it has not yet been computed */
81: lsqr->anorm = -1.0;
83: /* vectors of length m, where system size is mxn */
84: B = ksp->vec_rhs;
85: U = lsqr->vwork_m[0];
86: U1 = lsqr->vwork_m[1];
88: /* vectors of length n */
89: X = ksp->vec_sol;
90: W = lsqr->vwork_n[0];
91: V = lsqr->vwork_n[1];
92: V1 = lsqr->vwork_n[2];
93: W2 = lsqr->vwork_n[3];
94: if (!nopreconditioner) Z = lsqr->vwork_n[4];
96: /* standard error vector */
97: SE = lsqr->se;
98: if (SE) {
99: VecGetSize(SE,&size1);
100: VecGetSize(X,&size2);
101: if (size1 != size2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Standard error vector (size %d) does not match solution vector (size %d)",size1,size2);
102: VecSet(SE,0.0);
103: }
105: /* Compute initial residual, temporarily use work vector u */
106: if (!ksp->guess_zero) {
107: KSP_MatMult(ksp,Amat,X,U); /* u <- b - Ax */
108: VecAYPX(U,-1.0,B);
109: } else {
110: VecCopy(B,U); /* u <- b (x is 0) */
111: }
113: /* Test for nothing to do */
114: VecNorm(U,NORM_2,&rnorm);
115: PetscObjectSAWsTakeAccess((PetscObject)ksp);
116: ksp->its = 0;
117: ksp->rnorm = rnorm;
118: PetscObjectSAWsGrantAccess((PetscObject)ksp);
119: KSPLogResidualHistory(ksp,rnorm);
120: KSPMonitor(ksp,0,rnorm);
121: (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
122: if (ksp->reason) return(0);
124: beta = rnorm;
125: VecScale(U,1.0/beta);
126: KSP_MatMultTranspose(ksp,Amat,U,V);
127: if (nopreconditioner) {
128: VecNorm(V,NORM_2,&alpha);
129: } else {
130: PCApply(ksp->pc,V,Z);
131: VecDotRealPart(V,Z,&alpha);
132: if (alpha <= 0.0) {
133: ksp->reason = KSP_DIVERGED_BREAKDOWN;
134: return(0);
135: }
136: alpha = PetscSqrtReal(alpha);
137: VecScale(Z,1.0/alpha);
138: }
139: VecScale(V,1.0/alpha);
141: if (nopreconditioner) {
142: VecCopy(V,W);
143: } else {
144: VecCopy(Z,W);
145: }
147: lsqr->arnorm = alpha * beta;
148: phibar = beta;
149: rhobar = alpha;
150: i = 0;
151: do {
152: if (nopreconditioner) {
153: KSP_MatMult(ksp,Amat,V,U1);
154: } else {
155: KSP_MatMult(ksp,Amat,Z,U1);
156: }
157: VecAXPY(U1,-alpha,U);
158: VecNorm(U1,NORM_2,&beta);
159: if (beta > 0.0) {
160: VecScale(U1,1.0/beta); /* beta*U1 = Amat*V - alpha*U */
161: }
163: KSP_MatMultTranspose(ksp,Amat,U1,V1);
164: VecAXPY(V1,-beta,V);
165: if (nopreconditioner) {
166: VecNorm(V1,NORM_2,&alpha);
167: } else {
168: PCApply(ksp->pc,V1,Z);
169: VecDotRealPart(V1,Z,&alpha);
170: if (alpha <= 0.0) {
171: ksp->reason = KSP_DIVERGED_BREAKDOWN;
172: break;
173: }
174: alpha = PetscSqrtReal(alpha);
175: VecScale(Z,1.0/alpha);
176: }
177: VecScale(V1,1.0/alpha); /* alpha*V1 = Amat^T*U1 - beta*V */
178: rho = PetscSqrtScalar(rhobar*rhobar + beta*beta);
179: c = rhobar / rho;
180: s = beta / rho;
181: theta = s * alpha;
182: rhobar = -c * alpha;
183: phi = c * phibar;
184: phibar = s * phibar;
185: tau = s * phi;
187: VecAXPY(X,phi/rho,W); /* x <- x + (phi/rho) w */
189: if (SE) {
190: VecCopy(W,W2);
191: VecSquare(W2);
192: VecScale(W2,1.0/(rho*rho));
193: VecAXPY(SE, 1.0, W2); /* SE <- SE + (w^2/rho^2) */
194: }
195: if (nopreconditioner) {
196: VecAYPX(W,-theta/rho,V1); /* w <- v - (theta/rho) w */
197: } else {
198: VecAYPX(W,-theta/rho,Z); /* w <- z - (theta/rho) w */
199: }
201: lsqr->arnorm = alpha*PetscAbsScalar(tau);
202: rnorm = PetscRealPart(phibar);
204: PetscObjectSAWsTakeAccess((PetscObject)ksp);
205: ksp->its++;
206: ksp->rnorm = rnorm;
207: PetscObjectSAWsGrantAccess((PetscObject)ksp);
208: KSPLogResidualHistory(ksp,rnorm);
209: KSPMonitor(ksp,i+1,rnorm);
210: (*ksp->converged)(ksp,i+1,rnorm,&ksp->reason,ksp->cnvP);
211: if (ksp->reason) break;
212: SWAP(U1,U,TMP);
213: SWAP(V1,V,TMP);
215: i++;
216: } while (i<ksp->max_it);
217: if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
219: /* Finish off the standard error estimates */
220: if (SE) {
221: tmp = 1.0;
222: MatGetSize(Amat,&size1,&size2);
223: if (size1 > size2) tmp = size1 - size2;
224: tmp = rnorm / PetscSqrtScalar(tmp);
225: VecSqrtAbs(SE);
226: VecScale(SE,tmp);
227: }
228: return(0);
229: }
234: PetscErrorCode KSPDestroy_LSQR(KSP ksp)
235: {
236: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
240: /* Free work vectors */
241: if (lsqr->vwork_n) {
242: VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
243: }
244: if (lsqr->vwork_m) {
245: VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
246: }
247: if (lsqr->se_flg) {
248: VecDestroy(&lsqr->se);
249: }
250: PetscFree(ksp->data);
251: return(0);
252: }
256: PetscErrorCode KSPLSQRSetStandardErrorVec(KSP ksp, Vec se)
257: {
258: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
262: VecDestroy(&lsqr->se);
263: lsqr->se = se;
264: return(0);
265: }
269: PetscErrorCode KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
270: {
271: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
274: *se = lsqr->se;
275: return(0);
276: }
280: PetscErrorCode KSPLSQRGetArnorm(KSP ksp,PetscReal *arnorm, PetscReal *rhs_norm, PetscReal *anorm)
281: {
282: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
286: *arnorm = lsqr->arnorm;
287: if (anorm) {
288: if (lsqr->anorm < 0.0) {
289: PC pc;
290: Mat Amat;
291: KSPGetPC(ksp,&pc);
292: PCGetOperators(pc,&Amat,NULL);
293: MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm);
294: }
295: *anorm = lsqr->anorm;
296: }
297: if (rhs_norm) *rhs_norm = lsqr->rhs_norm;
298: return(0);
299: }
303: /*@C
304: KSPLSQRMonitorDefault - Print the residual norm at each iteration of the LSQR method and the norm of the residual of the normal equations A'*A x = A' b
306: Collective on KSP
308: Input Parameters:
309: + ksp - iterative context
310: . n - iteration number
311: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
312: - dummy - unused monitor context
314: Level: intermediate
316: .keywords: KSP, default, monitor, residual
318: .seealso: KSPMonitorSet(), KSPMonitorTrueResidualNorm(), KSPMonitorLGResidualNormCreate(), KSPMonitorDefault()
319: @*/
320: PetscErrorCode KSPLSQRMonitorDefault(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
321: {
323: PetscViewer viewer = dummy ? (PetscViewer) dummy : PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)ksp));
324: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
327: PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);
328: if (((PetscObject)ksp)->prefix) {
329: PetscViewerASCIIPrintf(viewer," Residual norm and norm of normal equations for %s solve.\n",((PetscObject)ksp)->prefix);
330: }
331: if (!n) {
332: PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e\n",n,rnorm);
333: } else {
334: PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e Residual norm normal equations %14.12e\n",n,rnorm,lsqr->arnorm);
335: }
336: PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);
337: return(0);
338: }
342: PetscErrorCode KSPSetFromOptions_LSQR(KSP ksp)
343: {
345: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
346: char monfilename[PETSC_MAX_PATH_LEN];
347: PetscViewer monviewer;
348: PetscBool flg;
351: PetscOptionsHead("KSP LSQR Options");
352: PetscOptionsName("-ksp_lsqr_set_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetStandardErrorVec",&lsqr->se_flg);
353: PetscOptionsString("-ksp_lsqr_monitor","Monitor residual norm and norm of residual of normal equations","KSPMonitorSet","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
354: if (flg) {
355: PetscViewerASCIIOpen(PetscObjectComm((PetscObject)ksp),monfilename,&monviewer);
356: KSPMonitorSet(ksp,KSPLSQRMonitorDefault,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
357: }
358: PetscOptionsTail();
359: return(0);
360: }
364: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
365: {
366: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
368: PetscBool iascii;
371: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
372: if (iascii) {
373: if (lsqr->se) {
374: PetscReal rnorm;
375: KSPLSQRGetStandardErrorVec(ksp,&lsqr->se);
376: VecNorm(lsqr->se,NORM_2,&rnorm);
377: PetscViewerASCIIPrintf(viewer," Norm of Standard Error %g, Iterations %D\n",(double)rnorm,ksp->its);
378: }
379: }
380: return(0);
381: }
385: /*@C
386: KSPLSQRDefaultConverged - Determines convergence of the LSQR Krylov method. This calls KSPConvergedDefault() and if that does not determine convergence then checks
387: convergence for the least squares problem.
389: Collective on KSP
391: Input Parameters:
392: + ksp - iterative context
393: . n - iteration number
394: . rnorm - 2-norm residual value (may be estimated)
395: - ctx - convergence context which must be created by KSPConvergedDefaultCreate()
397: reason is set to:
398: + positive - if the iteration has converged;
399: . negative - if residual norm exceeds divergence threshold;
400: - 0 - otherwise.
402: Notes:
403: 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.
405: Level: intermediate
407: .keywords: KSP, default, convergence, residual
409: .seealso: KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
410: KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(), KSPConvergedDefault()
411: @*/
412: PetscErrorCode KSPLSQRDefaultConverged(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
413: {
415: KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;
418: KSPConvergedDefault(ksp,n,rnorm,reason,ctx);
419: if (!n || *reason) return(0);
420: if (lsqr->arnorm/lsqr->rhs_norm < ksp->rtol) *reason = KSP_CONVERGED_RTOL_NORMAL;
421: if (lsqr->arnorm < ksp->abstol) *reason = KSP_CONVERGED_ATOL_NORMAL;
422: return(0);
423: }
427: /*MC
428: KSPLSQR - This implements LSQR
430: Options Database Keys:
431: + -ksp_lsqr_set_standard_error - Set Standard Error Estimates of Solution see KSPLSQRSetStandardErrorVec()
432: . -ksp_lsqr_monitor - Monitor residual norm and norm of residual of normal equations
433: - see KSPSolve()
435: Level: beginner
437: Notes:
438: This varient, when applied with no preconditioning is identical to the original algorithm in exact arithematic; however, in practice, with no preconditioning
439: due to inexact arithematic, it can converge differently. Hence when no preconditioner is used (PCType PCNONE) it automatically reverts to the original algorithm.
441: With the PETSc built-in preconditioners, such as ICC, one should call KSPSetOperators(ksp,A,A'*A)) since the preconditioner needs to work
442: for the normal equations A'*A.
444: Supports only left preconditioning.
446: References:The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, pp 43-71, 1982.
447: In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
448: The preconditioned varient was implemented by Bas van't Hof and is essentially a left preconditioning for the Normal Equations. It appears the implementation with preconditioner
449: track the true norm of the residual and uses that in the convergence test.
451: Developer Notes: How is this related to the KSPCGNE implementation? One difference is that KSPCGNE applies
452: the preconditioner transpose times the preconditioner, so one does not need to pass A'*A as the third argument to KSPSetOperators().
455: For least squares problems without a zero to A*x = b, there are additional convergence tests for the residual of the normal equations, A'*(b - Ax), see KSPLSQRDefaultConverged()
457: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPLSQRDefaultConverged()
459: M*/
462: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
463: {
464: KSP_LSQR *lsqr;
468: PetscNewLog(ksp,&lsqr);
469: lsqr->se = NULL;
470: lsqr->se_flg = PETSC_FALSE;
471: lsqr->arnorm = 0.0;
472: ksp->data = (void*)lsqr;
473: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);
475: ksp->ops->setup = KSPSetUp_LSQR;
476: ksp->ops->solve = KSPSolve_LSQR;
477: ksp->ops->destroy = KSPDestroy_LSQR;
478: ksp->ops->buildsolution = KSPBuildSolutionDefault;
479: ksp->ops->buildresidual = KSPBuildResidualDefault;
480: ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
481: ksp->ops->view = KSPView_LSQR;
482: ksp->converged = KSPLSQRDefaultConverged;
483: return(0);
484: }
488: PetscErrorCode VecSquare(Vec v)
489: {
491: PetscScalar *x;
492: PetscInt i, n;
495: VecGetLocalSize(v, &n);
496: VecGetArray(v, &x);
497: for (i = 0; i < n; i++) x[i] *= x[i];
498: VecRestoreArray(v, &x);
499: return(0);
500: }