Actual source code: lsqr.c

  1: /* lourens.vanzanen@shell.com contributed the standard error estimates of the solution, Jul 25, 2006 */
  2: /* Bas van't Hof contributed the preconditioned aspects Feb 10, 2010 */

  4: #define SWAP(a, b, c) \
  5:   do { \
  6:     c = a; \
  7:     a = b; \
  8:     b = c; \
  9:   } while (0)

 11: #include <petsc/private/kspimpl.h>
 12: #include <petscdraw.h>

 14: typedef struct {
 15:   PetscInt  nwork_n, nwork_m;
 16:   Vec      *vwork_m;    /* work vectors of length m, where the system is size m x n */
 17:   Vec      *vwork_n;    /* work vectors of length n */
 18:   Vec       se;         /* Optional standard error vector */
 19:   PetscBool se_flg;     /* flag for -ksp_lsqr_set_standard_error */
 20:   PetscBool exact_norm; /* flag for -ksp_lsqr_exact_mat_norm */
 21:   PetscReal arnorm;     /* Good estimate of norm((A*inv(Pmat))'*r), where r = A*x - b, used in specific stopping criterion */
 22:   PetscReal anorm;      /* Poor estimate of norm(A*inv(Pmat),'fro') used in specific stopping criterion */
 23:   /* Backup previous convergence test */
 24:   PetscErrorCode (*converged)(KSP, PetscInt, PetscReal, KSPConvergedReason *, void *);
 25:   PetscErrorCode (*convergeddestroy)(void *);
 26:   void *cnvP;
 27: } KSP_LSQR;

 29: static PetscErrorCode VecSquare(Vec v)
 30: {
 31:   PetscScalar *x;
 32:   PetscInt     i, n;

 34:   PetscFunctionBegin;
 35:   PetscCall(VecGetLocalSize(v, &n));
 36:   PetscCall(VecGetArray(v, &x));
 37:   for (i = 0; i < n; i++) x[i] *= PetscConj(x[i]);
 38:   PetscCall(VecRestoreArray(v, &x));
 39:   PetscFunctionReturn(PETSC_SUCCESS);
 40: }

 42: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
 43: {
 44:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;
 45:   PetscBool nopreconditioner;

 47:   PetscFunctionBegin;
 48:   PetscCall(PetscObjectTypeCompare((PetscObject)ksp->pc, PCNONE, &nopreconditioner));

 50:   if (lsqr->vwork_m) PetscCall(VecDestroyVecs(lsqr->nwork_m, &lsqr->vwork_m));

 52:   if (lsqr->vwork_n) PetscCall(VecDestroyVecs(lsqr->nwork_n, &lsqr->vwork_n));

 54:   lsqr->nwork_m = 2;
 55:   if (nopreconditioner) lsqr->nwork_n = 4;
 56:   else lsqr->nwork_n = 5;
 57:   PetscCall(KSPCreateVecs(ksp, lsqr->nwork_n, &lsqr->vwork_n, lsqr->nwork_m, &lsqr->vwork_m));

 59:   if (lsqr->se_flg && !lsqr->se) {
 60:     PetscCall(VecDuplicate(lsqr->vwork_n[0], &lsqr->se));
 61:     PetscCall(VecSet(lsqr->se, PETSC_INFINITY));
 62:   } else if (!lsqr->se_flg) {
 63:     PetscCall(VecDestroy(&lsqr->se));
 64:   }
 65:   PetscFunctionReturn(PETSC_SUCCESS);
 66: }

 68: static PetscErrorCode KSPSolve_LSQR(KSP ksp)
 69: {
 70:   PetscInt    i, size1, size2;
 71:   PetscScalar rho, rhobar, phi, phibar, theta, c, s, tmp, tau;
 72:   PetscReal   beta, alpha, rnorm;
 73:   Vec         X, B, V, V1, U, U1, TMP, W, W2, Z = NULL;
 74:   Mat         Amat, Pmat;
 75:   KSP_LSQR   *lsqr = (KSP_LSQR *)ksp->data;
 76:   PetscBool   diagonalscale, nopreconditioner;

 78:   PetscFunctionBegin;
 79:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
 80:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

 82:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
 83:   PetscCall(PetscObjectTypeCompare((PetscObject)ksp->pc, PCNONE, &nopreconditioner));

 85:   /* vectors of length m, where system size is mxn */
 86:   B  = ksp->vec_rhs;
 87:   U  = lsqr->vwork_m[0];
 88:   U1 = lsqr->vwork_m[1];

 90:   /* vectors of length n */
 91:   X  = ksp->vec_sol;
 92:   W  = lsqr->vwork_n[0];
 93:   V  = lsqr->vwork_n[1];
 94:   V1 = lsqr->vwork_n[2];
 95:   W2 = lsqr->vwork_n[3];
 96:   if (!nopreconditioner) Z = lsqr->vwork_n[4];

 98:   /* standard error vector */
 99:   if (lsqr->se) PetscCall(VecSet(lsqr->se, 0.0));

101:   /* Compute initial residual, temporarily use work vector u */
102:   if (!ksp->guess_zero) {
103:     PetscCall(KSP_MatMult(ksp, Amat, X, U)); /*   u <- b - Ax     */
104:     PetscCall(VecAYPX(U, -1.0, B));
105:   } else {
106:     PetscCall(VecCopy(B, U)); /*   u <- b (x is 0) */
107:   }

109:   /* Test for nothing to do */
110:   PetscCall(VecNorm(U, NORM_2, &rnorm));
111:   KSPCheckNorm(ksp, rnorm);
112:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
113:   ksp->its   = 0;
114:   ksp->rnorm = rnorm;
115:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
116:   PetscCall(KSPLogResidualHistory(ksp, rnorm));
117:   PetscCall(KSPMonitor(ksp, 0, rnorm));
118:   PetscCall((*ksp->converged)(ksp, 0, rnorm, &ksp->reason, ksp->cnvP));
119:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

121:   beta = rnorm;
122:   PetscCall(VecScale(U, 1.0 / beta));
123:   PetscCall(KSP_MatMultHermitianTranspose(ksp, Amat, U, V));
124:   if (nopreconditioner) {
125:     PetscCall(VecNorm(V, NORM_2, &alpha));
126:     KSPCheckNorm(ksp, rnorm);
127:   } else {
128:     /* this is an application of the preconditioner for the normal equations; not the operator, see the manual page */
129:     PetscCall(PCApply(ksp->pc, V, Z));
130:     PetscCall(VecDotRealPart(V, Z, &alpha));
131:     if (alpha <= 0.0) {
132:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
133:       PetscFunctionReturn(PETSC_SUCCESS);
134:     }
135:     alpha = PetscSqrtReal(alpha);
136:     PetscCall(VecScale(Z, 1.0 / alpha));
137:   }
138:   PetscCall(VecScale(V, 1.0 / alpha));

140:   if (nopreconditioner) {
141:     PetscCall(VecCopy(V, W));
142:   } else {
143:     PetscCall(VecCopy(Z, W));
144:   }

146:   if (lsqr->exact_norm) {
147:     PetscCall(MatNorm(Amat, NORM_FROBENIUS, &lsqr->anorm));
148:   } else lsqr->anorm = 0.0;

150:   lsqr->arnorm = alpha * beta;
151:   phibar       = beta;
152:   rhobar       = alpha;
153:   i            = 0;
154:   do {
155:     if (nopreconditioner) {
156:       PetscCall(KSP_MatMult(ksp, Amat, V, U1));
157:     } else {
158:       PetscCall(KSP_MatMult(ksp, Amat, Z, U1));
159:     }
160:     PetscCall(VecAXPY(U1, -alpha, U));
161:     PetscCall(VecNorm(U1, NORM_2, &beta));
162:     KSPCheckNorm(ksp, beta);
163:     if (beta > 0.0) {
164:       PetscCall(VecScale(U1, 1.0 / beta)); /* beta*U1 = Amat*V - alpha*U */
165:       if (!lsqr->exact_norm) lsqr->anorm = PetscSqrtReal(PetscSqr(lsqr->anorm) + PetscSqr(alpha) + PetscSqr(beta));
166:     }

168:     PetscCall(KSP_MatMultHermitianTranspose(ksp, Amat, U1, V1));
169:     PetscCall(VecAXPY(V1, -beta, V));
170:     if (nopreconditioner) {
171:       PetscCall(VecNorm(V1, NORM_2, &alpha));
172:       KSPCheckNorm(ksp, alpha);
173:     } else {
174:       PetscCall(PCApply(ksp->pc, V1, Z));
175:       PetscCall(VecDotRealPart(V1, Z, &alpha));
176:       if (alpha <= 0.0) {
177:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
178:         break;
179:       }
180:       alpha = PetscSqrtReal(alpha);
181:       PetscCall(VecScale(Z, 1.0 / alpha));
182:     }
183:     PetscCall(VecScale(V1, 1.0 / alpha)); /* alpha*V1 = Amat^T*U1 - beta*V */
184:     rho    = PetscSqrtScalar(rhobar * rhobar + beta * beta);
185:     c      = rhobar / rho;
186:     s      = beta / rho;
187:     theta  = s * alpha;
188:     rhobar = -c * alpha;
189:     phi    = c * phibar;
190:     phibar = s * phibar;
191:     tau    = s * phi;

193:     PetscCall(VecAXPY(X, phi / rho, W)); /*    x <- x + (phi/rho) w   */

195:     if (lsqr->se) {
196:       PetscCall(VecCopy(W, W2));
197:       PetscCall(VecSquare(W2));
198:       PetscCall(VecScale(W2, 1.0 / (rho * rho)));
199:       PetscCall(VecAXPY(lsqr->se, 1.0, W2)); /* lsqr->se <- lsqr->se + (w^2/rho^2) */
200:     }
201:     if (nopreconditioner) {
202:       PetscCall(VecAYPX(W, -theta / rho, V1)); /* w <- v - (theta/rho) w */
203:     } else {
204:       PetscCall(VecAYPX(W, -theta / rho, Z)); /* w <- z - (theta/rho) w */
205:     }

207:     lsqr->arnorm = alpha * PetscAbsScalar(tau);
208:     rnorm        = PetscRealPart(phibar);

210:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
211:     ksp->its++;
212:     ksp->rnorm = rnorm;
213:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
214:     PetscCall(KSPLogResidualHistory(ksp, rnorm));
215:     PetscCall(KSPMonitor(ksp, i + 1, rnorm));
216:     PetscCall((*ksp->converged)(ksp, i + 1, rnorm, &ksp->reason, ksp->cnvP));
217:     if (ksp->reason) break;
218:     SWAP(U1, U, TMP);
219:     SWAP(V1, V, TMP);

221:     i++;
222:   } while (i < ksp->max_it);
223:   if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

225:   /* Finish off the standard error estimates */
226:   if (lsqr->se) {
227:     tmp = 1.0;
228:     PetscCall(MatGetSize(Amat, &size1, &size2));
229:     if (size1 > size2) tmp = size1 - size2;
230:     tmp = rnorm / PetscSqrtScalar(tmp);
231:     PetscCall(VecSqrtAbs(lsqr->se));
232:     PetscCall(VecScale(lsqr->se, tmp));
233:   }
234:   PetscFunctionReturn(PETSC_SUCCESS);
235: }

237: static PetscErrorCode KSPDestroy_LSQR(KSP ksp)
238: {
239:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

241:   PetscFunctionBegin;
242:   /* Free work vectors */
243:   if (lsqr->vwork_n) PetscCall(VecDestroyVecs(lsqr->nwork_n, &lsqr->vwork_n));
244:   if (lsqr->vwork_m) PetscCall(VecDestroyVecs(lsqr->nwork_m, &lsqr->vwork_m));
245:   PetscCall(VecDestroy(&lsqr->se));
246:   /* Revert convergence test */
247:   PetscCall(KSPSetConvergenceTest(ksp, lsqr->converged, lsqr->cnvP, lsqr->convergeddestroy));
248:   /* Free the KSP_LSQR context */
249:   PetscCall(PetscFree(ksp->data));
250:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLSQRMonitorResidual_C", NULL));
251:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLSQRMonitorResidualDrawLG_C", NULL));
252:   PetscFunctionReturn(PETSC_SUCCESS);
253: }

255: /*@
256:   KSPLSQRSetComputeStandardErrorVec - Compute a vector of standard error estimates during `KSPSolve()` for  `KSPLSQR`.

258:   Logically Collective

260:   Input Parameters:
261: + ksp - iterative context
262: - flg - compute the vector of standard estimates or not

264:   Level: intermediate

266:   Developer Notes:
267:   Vaclav: I'm not sure whether this vector is useful for anything.

269: .seealso: [](ch_ksp), `KSPSolve()`, `KSPLSQR`, `KSPLSQRGetStandardErrorVec()`
270: @*/
271: PetscErrorCode KSPLSQRSetComputeStandardErrorVec(KSP ksp, PetscBool flg)
272: {
273:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

275:   PetscFunctionBegin;
276:   lsqr->se_flg = flg;
277:   PetscFunctionReturn(PETSC_SUCCESS);
278: }

280: /*@
281:   KSPLSQRSetExactMatNorm - Compute exact matrix norm instead of iteratively refined estimate.

283:   Not Collective

285:   Input Parameters:
286: + ksp - iterative context
287: - flg - compute exact matrix norm or not

289:   Level: intermediate

291:   Notes:
292:   By default, `flg` = `PETSC_FALSE`. This is usually preferred to avoid possibly expensive computation of the norm.
293:   For `flg` = `PETSC_TRUE`, we call `MatNorm`(Amat,`NORM_FROBENIUS`,&lsqr->anorm) which will work only for some types of explicitly assembled matrices.
294:   This can affect convergence rate as `KSPLSQRConvergedDefault()` assumes different value of ||A|| used in normal equation stopping criterion.

296: .seealso: [](ch_ksp), `KSPSolve()`, `KSPLSQR`, `KSPLSQRGetNorms()`, `KSPLSQRConvergedDefault()`
297: @*/
298: PetscErrorCode KSPLSQRSetExactMatNorm(KSP ksp, PetscBool flg)
299: {
300:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

302:   PetscFunctionBegin;
303:   lsqr->exact_norm = flg;
304:   PetscFunctionReturn(PETSC_SUCCESS);
305: }

307: /*@
308:   KSPLSQRGetStandardErrorVec - Get vector of standard error estimates.
309:   Only available if -ksp_lsqr_set_standard_error was set to true
310:   or `KSPLSQRSetComputeStandardErrorVec`(ksp, `PETSC_TRUE`) was called.
311:   Otherwise returns `NULL`.

313:   Not Collective

315:   Input Parameter:
316: . ksp - iterative context

318:   Output Parameter:
319: . se - vector of standard estimates

321:   Level: intermediate

323:   Developer Notes:
324:   Vaclav: I'm not sure whether this vector is useful for anything.

326: .seealso: [](ch_ksp), `KSPSolve()`, `KSPLSQR`, `KSPLSQRSetComputeStandardErrorVec()`
327: @*/
328: PetscErrorCode KSPLSQRGetStandardErrorVec(KSP ksp, Vec *se)
329: {
330:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

332:   PetscFunctionBegin;
333:   *se = lsqr->se;
334:   PetscFunctionReturn(PETSC_SUCCESS);
335: }

337: /*@
338:   KSPLSQRGetNorms - Get the norm estimates that `KSPLSQR` computes internally during `KSPSolve()`.

340:   Not Collective

342:   Input Parameter:
343: . ksp - iterative context

345:   Output Parameters:
346: + arnorm - good estimate of $\|(A*Pmat^{-T})*r\|$, where $r = A*x - b$, used in specific stopping criterion
347: - anorm  - poor estimate of $\|A*Pmat^{-T}\|_{frobenius}$ used in specific stopping criterion

349:   Level: intermediate

351:   Notes:
352:   Output parameters are meaningful only after `KSPSolve()`.

354:   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.

356:   If -ksp_lsqr_exact_mat_norm is set or `KSPLSQRSetExactMatNorm`(ksp, `PETSC_TRUE`) called, then anorm is the exact Frobenius norm.

358: .seealso: [](ch_ksp), `KSPSolve()`, `KSPLSQR`, `KSPLSQRSetExactMatNorm()`
359: @*/
360: PetscErrorCode KSPLSQRGetNorms(KSP ksp, PetscReal *arnorm, PetscReal *anorm)
361: {
362:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

364:   PetscFunctionBegin;
365:   if (arnorm) *arnorm = lsqr->arnorm;
366:   if (anorm) *anorm = lsqr->anorm;
367:   PetscFunctionReturn(PETSC_SUCCESS);
368: }

370: static PetscErrorCode KSPLSQRMonitorResidual_LSQR(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
371: {
372:   KSP_LSQR         *lsqr   = (KSP_LSQR *)ksp->data;
373:   PetscViewer       viewer = vf->viewer;
374:   PetscViewerFormat format = vf->format;
375:   char              normtype[256];
376:   PetscInt          tablevel;
377:   const char       *prefix;

379:   PetscFunctionBegin;
380:   PetscCall(PetscObjectGetTabLevel((PetscObject)ksp, &tablevel));
381:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ksp, &prefix));
382:   PetscCall(PetscStrncpy(normtype, KSPNormTypes[ksp->normtype], sizeof(normtype)));
383:   PetscCall(PetscStrtolower(normtype));
384:   PetscCall(PetscViewerPushFormat(viewer, format));
385:   PetscCall(PetscViewerASCIIAddTab(viewer, tablevel));
386:   if (n == 0 && prefix) PetscCall(PetscViewerASCIIPrintf(viewer, "  Residual norm, norm of normal equations, and matrix norm for %s solve.\n", prefix));
387:   if (!n) {
388:     PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " KSP resid norm %14.12e\n", n, (double)rnorm));
389:   } else {
390:     PetscCall(PetscViewerASCIIPrintf(viewer, "%3" PetscInt_FMT " 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));
391:   }
392:   PetscCall(PetscViewerASCIISubtractTab(viewer, tablevel));
393:   PetscCall(PetscViewerPopFormat(viewer));
394:   PetscFunctionReturn(PETSC_SUCCESS);
395: }

397: /*@C
398:   KSPLSQRMonitorResidual - Prints the residual norm, as well as the normal equation residual norm, at each iteration of an iterative solver for the `KSPLSQR` solver

400:   Collective

402:   Input Parameters:
403: + ksp   - iterative context
404: . n     - iteration number
405: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
406: - vf    - The viewer context

408:   Options Database Key:
409: . -ksp_lsqr_monitor - Activates `KSPLSQRMonitorResidual()`

411:   Level: intermediate

413: .seealso: [](ch_ksp), `KSPLSQR`, `KSPMonitorSet()`, `KSPMonitorResidual()`, `KSPMonitorTrueResidualMaxNorm()`, `KSPLSQRMonitorResidualDrawLG()`
414: @*/
415: PetscErrorCode KSPLSQRMonitorResidual(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
416: {
417:   PetscFunctionBegin;
419:   PetscAssertPointer(vf, 4);
421:   PetscTryMethod(ksp, "KSPLSQRMonitorResidual_C", (KSP, PetscInt, PetscReal, PetscViewerAndFormat *), (ksp, n, rnorm, vf));
422:   PetscFunctionReturn(PETSC_SUCCESS);
423: }

425: static PetscErrorCode KSPLSQRMonitorResidualDrawLG_LSQR(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
426: {
427:   KSP_LSQR          *lsqr   = (KSP_LSQR *)ksp->data;
428:   PetscViewer        viewer = vf->viewer;
429:   PetscViewerFormat  format = vf->format;
430:   PetscDrawLG        lg     = vf->lg;
431:   KSPConvergedReason reason;
432:   PetscReal          x[2], y[2];

434:   PetscFunctionBegin;
435:   PetscCall(PetscViewerPushFormat(viewer, format));
436:   if (!n) PetscCall(PetscDrawLGReset(lg));
437:   x[0] = (PetscReal)n;
438:   if (rnorm > 0.0) y[0] = PetscLog10Real(rnorm);
439:   else y[0] = -15.0;
440:   x[1] = (PetscReal)n;
441:   if (lsqr->arnorm > 0.0) y[1] = PetscLog10Real(lsqr->arnorm);
442:   else y[1] = -15.0;
443:   PetscCall(PetscDrawLGAddPoint(lg, x, y));
444:   PetscCall(KSPGetConvergedReason(ksp, &reason));
445:   if (n <= 20 || !(n % 5) || reason) {
446:     PetscCall(PetscDrawLGDraw(lg));
447:     PetscCall(PetscDrawLGSave(lg));
448:   }
449:   PetscCall(PetscViewerPopFormat(viewer));
450:   PetscFunctionReturn(PETSC_SUCCESS);
451: }

453: /*@C
454:   KSPLSQRMonitorResidualDrawLG - Plots the true residual norm at each iteration of an iterative solver for the `KSPLSQR` solver

456:   Collective

458:   Input Parameters:
459: + ksp   - iterative context
460: . n     - iteration number
461: . rnorm - 2-norm (preconditioned) residual value (may be estimated).
462: - vf    - The viewer context

464:   Options Database Key:
465: . -ksp_lsqr_monitor draw::draw_lg - Activates `KSPMonitorTrueResidualDrawLG()`

467:   Level: intermediate

469: .seealso: [](ch_ksp), `KSPLSQR`, `KSPMonitorSet()`, `KSPMonitorTrueResidual()`, `KSPLSQRMonitorResidual()`, `KSPLSQRMonitorResidualDrawLGCreate()`
470: @*/
471: PetscErrorCode KSPLSQRMonitorResidualDrawLG(KSP ksp, PetscInt n, PetscReal rnorm, PetscViewerAndFormat *vf)
472: {
473:   PetscFunctionBegin;
475:   PetscAssertPointer(vf, 4);
478:   PetscTryMethod(ksp, "KSPLSQRMonitorResidualDrawLG_C", (KSP, PetscInt, PetscReal, PetscViewerAndFormat *), (ksp, n, rnorm, vf));
479:   PetscFunctionReturn(PETSC_SUCCESS);
480: }

482: /*@C
483:   KSPLSQRMonitorResidualDrawLGCreate - Creates the line graph object for the `KSPLSQR` residual and normal equation residual norm

485:   Collective

487:   Input Parameters:
488: + viewer - The `PetscViewer`
489: . format - The viewer format
490: - ctx    - An optional user context

492:   Output Parameter:
493: . vf - The `PetscViewerAndFormat`

495:   Level: intermediate

497: .seealso: [](ch_ksp), `KSPLSQR`, `KSPMonitorSet()`, `KSPLSQRMonitorResidual()`, `KSPLSQRMonitorResidualDrawLG()`
498: @*/
499: PetscErrorCode KSPLSQRMonitorResidualDrawLGCreate(PetscViewer viewer, PetscViewerFormat format, void *ctx, PetscViewerAndFormat **vf)
500: {
501:   const char *names[] = {"residual", "normal eqn residual"};

503:   PetscFunctionBegin;
504:   PetscCall(PetscViewerAndFormatCreate(viewer, format, vf));
505:   (*vf)->data = ctx;
506:   PetscCall(KSPMonitorLGCreate(PetscObjectComm((PetscObject)viewer), NULL, NULL, "Log Residual Norm", 2, names, PETSC_DECIDE, PETSC_DECIDE, 400, 300, &(*vf)->lg));
507:   PetscFunctionReturn(PETSC_SUCCESS);
508: }

510: static PetscErrorCode KSPSetFromOptions_LSQR(KSP ksp, PetscOptionItems *PetscOptionsObject)
511: {
512:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

514:   PetscFunctionBegin;
515:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP LSQR Options");
516:   PetscCall(PetscOptionsBool("-ksp_lsqr_compute_standard_error", "Set Standard Error Estimates of Solution", "KSPLSQRSetComputeStandardErrorVec", lsqr->se_flg, &lsqr->se_flg, NULL));
517:   PetscCall(PetscOptionsBool("-ksp_lsqr_exact_mat_norm", "Compute exact matrix norm instead of iteratively refined estimate", "KSPLSQRSetExactMatNorm", lsqr->exact_norm, &lsqr->exact_norm, NULL));
518:   PetscCall(KSPMonitorSetFromOptions(ksp, "-ksp_lsqr_monitor", "lsqr_residual", NULL));
519:   PetscOptionsHeadEnd();
520:   PetscFunctionReturn(PETSC_SUCCESS);
521: }

523: static PetscErrorCode KSPView_LSQR(KSP ksp, PetscViewer viewer)
524: {
525:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;
526:   PetscBool iascii;

528:   PetscFunctionBegin;
529:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
530:   if (iascii) {
531:     if (lsqr->se) {
532:       PetscReal rnorm;
533:       PetscCall(VecNorm(lsqr->se, NORM_2, &rnorm));
534:       PetscCall(PetscViewerASCIIPrintf(viewer, "  norm of standard error %g, iterations %" PetscInt_FMT "\n", (double)rnorm, ksp->its));
535:     } else {
536:       PetscCall(PetscViewerASCIIPrintf(viewer, "  standard error not computed\n"));
537:     }
538:     if (lsqr->exact_norm) {
539:       PetscCall(PetscViewerASCIIPrintf(viewer, "  using exact matrix norm\n"));
540:     } else {
541:       PetscCall(PetscViewerASCIIPrintf(viewer, "  using inexact matrix norm\n"));
542:     }
543:   }
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

547: /*@C
548:   KSPLSQRConvergedDefault - Determines convergence of the `KSPLSQR` Krylov method.

550:   Collective

552:   Input Parameters:
553: + ksp   - iterative context
554: . n     - iteration number
555: . rnorm - 2-norm residual value (may be estimated)
556: - ctx   - convergence context which must have been created by `KSPConvergedDefaultCreate()`

558:   Output Parameter:
559: . reason - the convergence reason

561:   Level: advanced

563:   Notes:
564:   This is not called directly but rather is passed to `KSPSetConvergenceTest()`. It is used automatically by `KSPLSQR`

566:   `KSPConvergedDefault()` is called first to check for convergence in $A*x=b$.
567:   If that does not determine convergence then checks convergence for the least squares problem, i.e. in min{|b-A*x|}.
568:   Possible convergence for the least squares problem (which is based on the residual of the normal equations) are `KSP_CONVERGED_RTOL_NORMAL` norm
569:   and `KSP_CONVERGED_ATOL_NORMAL`.

571:   `KSP_CONVERGED_RTOL_NORMAL` is returned if $||A^T*r|| < rtol * ||A|| * ||r||$.
572:   Matrix norm $||A||$ is iteratively refined estimate, see `KSPLSQRGetNorms()`.
573:   This criterion is largely compatible with that in MATLAB `lsqr()`.

575: .seealso: [](ch_ksp), `KSPLSQR`, `KSPSetConvergenceTest()`, `KSPSetTolerances()`, `KSPConvergedSkip()`, `KSPConvergedReason`, `KSPGetConvergedReason()`,
576:           `KSPConvergedDefaultSetUIRNorm()`, `KSPConvergedDefaultSetUMIRNorm()`, `KSPConvergedDefaultCreate()`, `KSPConvergedDefaultDestroy()`, `KSPConvergedDefault()`, `KSPLSQRGetNorms()`, `KSPLSQRSetExactMatNorm()`
577: @*/
578: PetscErrorCode KSPLSQRConvergedDefault(KSP ksp, PetscInt n, PetscReal rnorm, KSPConvergedReason *reason, void *ctx)
579: {
580:   KSP_LSQR *lsqr = (KSP_LSQR *)ksp->data;

582:   PetscFunctionBegin;
583:   /* check for convergence in A*x=b */
584:   PetscCall(KSPConvergedDefault(ksp, n, rnorm, reason, ctx));
585:   if (!n || *reason) PetscFunctionReturn(PETSC_SUCCESS);

587:   /* check for convergence in min{|b-A*x|} */
588:   if (lsqr->arnorm < ksp->abstol) {
589:     PetscCall(PetscInfo(ksp, "LSQR solver has converged. Normal equation residual %14.12e is less than absolute tolerance %14.12e at iteration %" PetscInt_FMT "\n", (double)lsqr->arnorm, (double)ksp->abstol, n));
590:     *reason = KSP_CONVERGED_ATOL_NORMAL;
591:   } else if (lsqr->arnorm < ksp->rtol * lsqr->anorm * rnorm) {
592:     PetscCall(PetscInfo(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 %" PetscInt_FMT "\n", (double)lsqr->arnorm,
593:                         (double)ksp->rtol, lsqr->exact_norm ? "exact" : "approx.", (double)lsqr->anorm, (double)rnorm, n));
594:     *reason = KSP_CONVERGED_RTOL_NORMAL;
595:   }
596:   PetscFunctionReturn(PETSC_SUCCESS);
597: }

599: /*MC
600:    KSPLSQR - Implements LSQR  {cite}`paige.saunders:lsqr`

602:    Options Database Keys:
603: +   -ksp_lsqr_set_standard_error  - set standard error estimates of solution, see `KSPLSQRSetComputeStandardErrorVec()` and `KSPLSQRGetStandardErrorVec()`
604: .   -ksp_lsqr_exact_mat_norm - compute exact matrix norm instead of iteratively refined estimate, see `KSPLSQRSetExactMatNorm()`
605: -   -ksp_lsqr_monitor - monitor residual norm, norm of residual of normal equations A'*A x = A' b, and estimate of matrix norm ||A||

607:    Level: beginner

609:    Notes:
610:    Supports non-square (rectangular) matrices.

612:    This variant, when applied with no preconditioning is identical to the original algorithm in exact arithmetic; however, in practice, with no preconditioning
613:    due to inexact arithmetic, it can converge differently. Hence when no preconditioner is used (`PCType` `PCNONE`) it automatically reverts to the original algorithm.

615:    With the PETSc built-in preconditioners, such as `PCICC`, one should call `KSPSetOperators`(ksp,A,A'*A)) since the preconditioner needs to work
616:    for the normal equations A'*A.

618:    Supports only left preconditioning.

620:    For least squares problems with nonzero residual $A*x - b$, there are additional convergence tests for the residual of the normal equations, $A^T*(b - Ax)$, see `KSPLSQRConvergedDefault()`.

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.
624:    It appears the implementation with preconditioning tracks the true norm of the residual and uses that in the convergence test.

626:    Developer Note:
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 $A^T*A$ as the third argument to `KSPSetOperators()`.

630: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPSolve()`, `KSPLSQRConvergedDefault()`, `KSPLSQRSetComputeStandardErrorVec()`, `KSPLSQRGetStandardErrorVec()`, `KSPLSQRSetExactMatNorm()`, `KSPLSQRMonitorResidualDrawLGCreate()`, `KSPLSQRMonitorResidualDrawLG()`, `KSPLSQRMonitorResidual()`
631: M*/
632: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
633: {
634:   KSP_LSQR *lsqr;
635:   void     *ctx;

637:   PetscFunctionBegin;
638:   PetscCall(PetscNew(&lsqr));
639:   lsqr->se         = NULL;
640:   lsqr->se_flg     = PETSC_FALSE;
641:   lsqr->exact_norm = PETSC_FALSE;
642:   lsqr->anorm      = -1.0;
643:   lsqr->arnorm     = -1.0;
644:   ksp->data        = (void *)lsqr;
645:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 3));

647:   ksp->ops->setup          = KSPSetUp_LSQR;
648:   ksp->ops->solve          = KSPSolve_LSQR;
649:   ksp->ops->destroy        = KSPDestroy_LSQR;
650:   ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
651:   ksp->ops->view           = KSPView_LSQR;

653:   /* Backup current convergence test; remove destroy routine from KSP to prevent destroying the convergence context in KSPSetConvergenceTest() */
654:   PetscCall(KSPGetAndClearConvergenceTest(ksp, &lsqr->converged, &lsqr->cnvP, &lsqr->convergeddestroy));
655:   /* Override current convergence test */
656:   PetscCall(KSPConvergedDefaultCreate(&ctx));
657:   PetscCall(KSPSetConvergenceTest(ksp, KSPLSQRConvergedDefault, ctx, KSPConvergedDefaultDestroy));
658:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLSQRMonitorResidual_C", KSPLSQRMonitorResidual_LSQR));
659:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLSQRMonitorResidualDrawLG_C", KSPLSQRMonitorResidualDrawLG_LSQR));
660:   PetscFunctionReturn(PETSC_SUCCESS);
661: }