Actual source code: qcg.c
1: #include <../src/ksp/ksp/impls/qcg/qcgimpl.h>
3: /*
4: KSPQCGQuadraticRoots - Computes the roots of the quadratic,
5: ||s + step*p|| - delta = 0
6: such that step1 >= 0 >= step2.
7: where
8: delta:
9: On entry delta must contain scalar delta.
10: On exit delta is unchanged.
11: step1:
12: On entry step1 need not be specified.
13: On exit step1 contains the non-negative root.
14: step2:
15: On entry step2 need not be specified.
16: On exit step2 contains the non-positive root.
17: C code is translated from the Fortran version of the MINPACK-2 Project,
18: Argonne National Laboratory, Brett M. Averick and Richard G. Carter.
19: */
20: static PetscErrorCode KSPQCGQuadraticRoots(Vec s, Vec p, PetscReal delta, PetscReal *step1, PetscReal *step2)
21: {
22: PetscReal dsq, ptp, pts, rad, sts;
24: PetscFunctionBegin;
25: PetscCall(VecDotRealPart(p, s, &pts));
26: PetscCall(VecDotRealPart(p, p, &ptp));
27: PetscCall(VecDotRealPart(s, s, &sts));
28: dsq = delta * delta;
29: rad = PetscSqrtReal((pts * pts) - ptp * (sts - dsq));
30: if (pts > 0.0) {
31: *step2 = -(pts + rad) / ptp;
32: *step1 = (sts - dsq) / (ptp * *step2);
33: } else {
34: *step1 = -(pts - rad) / ptp;
35: *step2 = (sts - dsq) / (ptp * *step1);
36: }
37: PetscFunctionReturn(PETSC_SUCCESS);
38: }
40: /*@
41: KSPQCGSetTrustRegionRadius - Sets the radius of the trust region for `KSPQCG`
43: Logically Collective
45: Input Parameters:
46: + ksp - the iterative context
47: - delta - the trust region radius (Infinity is the default)
49: Options Database Key:
50: . -ksp_qcg_trustregionradius <delta> - trust region radius
52: Level: advanced
54: Developer Note:
55: `KSPMINRESSetRadius()`, for example, does not have TrustRegion in the name
57: .seealso: [](ch_ksp), `KSPQCG`, `KSPQCGGetTrialStepNorm()`
58: @*/
59: PetscErrorCode KSPQCGSetTrustRegionRadius(KSP ksp, PetscReal delta)
60: {
61: PetscFunctionBegin;
63: PetscCheck(delta >= 0.0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Tolerance must be non-negative");
64: PetscTryMethod(ksp, "KSPQCGSetTrustRegionRadius_C", (KSP, PetscReal), (ksp, delta));
65: PetscFunctionReturn(PETSC_SUCCESS);
66: }
68: /*@
69: KSPQCGGetTrialStepNorm - Gets the norm of a trial step vector in `KSPQCG`. The WCG step may be
70: constrained, so this is not necessarily the length of the ultimate step taken in `KSPQCG`.
72: Not Collective
74: Input Parameter:
75: . ksp - the iterative context
77: Output Parameter:
78: . tsnorm - the norm
80: Level: advanced
82: .seealso: [](ch_ksp), `KSPQCG`, `KSPQCGSetTrustRegionRadius()`
83: @*/
84: PetscErrorCode KSPQCGGetTrialStepNorm(KSP ksp, PetscReal *tsnorm)
85: {
86: PetscFunctionBegin;
88: PetscUseMethod(ksp, "KSPQCGGetTrialStepNorm_C", (KSP, PetscReal *), (ksp, tsnorm));
89: PetscFunctionReturn(PETSC_SUCCESS);
90: }
92: /*@
93: KSPQCGGetQuadratic - Gets the value of the quadratic function, evaluated at the new iterate
95: Collective
97: Input Parameter:
98: . ksp - the iterative context
100: Output Parameter:
101: . quadratic - the quadratic function evaluated at the new iterate
103: Level: advanced
105: Note:
106: The quadratic function is
108: $$
109: q(s) = g^T * s + 0.5 * s^T * H * s
110: $$
112: which satisfies the Euclidean Norm trust region constraint
114: $$
115: || D * s || \le delta,
116: $$
118: where
119: .vb
120: delta is the trust region radius,
121: g is the gradient vector, and
122: H is Hessian matrix,
123: D is a scaling matrix.
124: .ve
126: .seealso: [](ch_ksp), `KSPQCG`
127: @*/
128: PetscErrorCode KSPQCGGetQuadratic(KSP ksp, PetscReal *quadratic)
129: {
130: PetscFunctionBegin;
132: PetscUseMethod(ksp, "KSPQCGGetQuadratic_C", (KSP, PetscReal *), (ksp, quadratic));
133: PetscFunctionReturn(PETSC_SUCCESS);
134: }
136: static PetscErrorCode KSPSolve_QCG(KSP ksp)
137: {
138: /*
139: Correspondence with documentation above:
140: B = g = gradient,
141: X = s = step
142: Note: This is not coded correctly for complex arithmetic!
143: */
145: KSP_QCG *pcgP = (KSP_QCG *)ksp->data;
146: Mat Amat, Pmat;
147: Vec W, WA, WA2, R, P, ASP, BS, X, B;
148: PetscScalar scal, beta, rntrn, step;
149: PetscReal q1, q2, xnorm, step1, step2, rnrm = 0.0, btx, xtax;
150: PetscReal ptasp, rtr, wtasp, bstp;
151: PetscReal dzero = 0.0, bsnrm = 0.0;
152: PetscInt i, maxit;
153: PC pc = ksp->pc;
154: PetscBool diagonalscale;
156: PetscFunctionBegin;
157: PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
158: PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
159: PetscCheck(!ksp->transpose_solve, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Currently does not support transpose solve");
161: ksp->its = 0;
162: maxit = ksp->max_it;
163: WA = ksp->work[0];
164: R = ksp->work[1];
165: P = ksp->work[2];
166: ASP = ksp->work[3];
167: BS = ksp->work[4];
168: W = ksp->work[5];
169: WA2 = ksp->work[6];
170: X = ksp->vec_sol;
171: B = ksp->vec_rhs;
173: PetscCheck(pcgP->delta > dzero, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Input error: delta <= 0");
175: /* Initialize variables */
176: PetscCall(VecSet(W, 0.0)); /* W = 0 */
177: PetscCall(VecSet(X, 0.0)); /* X = 0 */
178: PetscCall(PCGetOperators(pc, &Amat, &Pmat));
180: /* Compute: BS = D^{-1} B */
181: PetscCall(PCApplySymmetricLeft(pc, B, BS));
183: if (ksp->normtype != KSP_NORM_NONE) {
184: PetscCall(VecNorm(BS, NORM_2, &bsnrm));
185: KSPCheckNorm(ksp, bsnrm);
186: }
187: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
188: ksp->its = 0;
189: ksp->rnorm = bsnrm;
190: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
191: PetscCall(KSPLogResidualHistory(ksp, bsnrm));
192: PetscCall(KSPMonitor(ksp, 0, bsnrm));
193: PetscCall((*ksp->converged)(ksp, 0, bsnrm, &ksp->reason, ksp->cnvP));
194: if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);
196: /* Compute the initial scaled direction and scaled residual */
197: PetscCall(VecCopy(BS, R));
198: PetscCall(VecScale(R, -1.0));
199: PetscCall(VecCopy(R, P));
200: PetscCall(VecDotRealPart(R, R, &rtr));
202: for (i = 0; i <= maxit; i++) {
203: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
204: ksp->its++;
205: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
207: /* Compute: asp = D^{-T}*A*D^{-1}*p */
208: PetscCall(PCApplySymmetricRight(pc, P, WA));
209: PetscCall(KSP_MatMult(ksp, Amat, WA, WA2));
210: PetscCall(PCApplySymmetricLeft(pc, WA2, ASP));
212: /* Check for negative curvature */
213: PetscCall(VecDotRealPart(P, ASP, &ptasp));
214: if (ptasp <= dzero) {
215: /* Scaled negative curvature direction: Compute a step so that
216: ||w + step*p|| = delta and QS(w + step*p) is least */
218: if (!i) {
219: PetscCall(VecCopy(P, X));
220: PetscCall(VecNorm(X, NORM_2, &xnorm));
221: KSPCheckNorm(ksp, xnorm);
222: scal = pcgP->delta / xnorm;
223: PetscCall(VecScale(X, scal));
224: } else {
225: /* Compute roots of quadratic */
226: PetscCall(KSPQCGQuadraticRoots(W, P, pcgP->delta, &step1, &step2));
227: PetscCall(VecDotRealPart(W, ASP, &wtasp));
228: PetscCall(VecDotRealPart(BS, P, &bstp));
229: PetscCall(VecCopy(W, X));
230: q1 = step1 * (bstp + wtasp + .5 * step1 * ptasp);
231: q2 = step2 * (bstp + wtasp + .5 * step2 * ptasp);
232: if (q1 <= q2) {
233: PetscCall(VecAXPY(X, step1, P));
234: } else {
235: PetscCall(VecAXPY(X, step2, P));
236: }
237: }
238: pcgP->ltsnrm = pcgP->delta; /* convergence in direction of */
239: ksp->reason = ksp->converged_neg_curve ? KSP_CONVERGED_NEG_CURVE : KSP_DIVERGED_INDEFINITE_MAT;
240: if (!i) {
241: PetscCall(PetscInfo(ksp, "negative curvature: delta=%g\n", (double)pcgP->delta));
242: } else {
243: PetscCall(PetscInfo(ksp, "negative curvature: step1=%g, step2=%g, delta=%g\n", (double)step1, (double)step2, (double)pcgP->delta));
244: }
246: } else {
247: /* Compute step along p */
248: step = rtr / ptasp;
249: PetscCall(VecCopy(W, X)); /* x = w */
250: PetscCall(VecAXPY(X, step, P)); /* x <- step*p + x */
251: PetscCall(VecNorm(X, NORM_2, &pcgP->ltsnrm));
252: KSPCheckNorm(ksp, pcgP->ltsnrm);
254: if (pcgP->ltsnrm > pcgP->delta) {
255: /* Since the trial iterate is outside the trust region,
256: evaluate a constrained step along p so that
257: ||w + step*p|| = delta
258: The positive step is always better in this case. */
259: if (!i) {
260: scal = pcgP->delta / pcgP->ltsnrm;
261: PetscCall(VecScale(X, scal));
262: } else {
263: /* Compute roots of quadratic */
264: PetscCall(KSPQCGQuadraticRoots(W, P, pcgP->delta, &step1, &step2));
265: PetscCall(VecCopy(W, X));
266: PetscCall(VecAXPY(X, step1, P)); /* x <- step1*p + x */
267: }
268: pcgP->ltsnrm = pcgP->delta;
269: ksp->reason = KSP_CONVERGED_STEP_LENGTH; /* convergence along constrained step */
270: if (!i) {
271: PetscCall(PetscInfo(ksp, "constrained step: delta=%g\n", (double)pcgP->delta));
272: } else {
273: PetscCall(PetscInfo(ksp, "constrained step: step1=%g, step2=%g, delta=%g\n", (double)step1, (double)step2, (double)pcgP->delta));
274: }
276: } else {
277: /* Evaluate the current step */
278: PetscCall(VecCopy(X, W)); /* update interior iterate */
279: PetscCall(VecAXPY(R, -step, ASP)); /* r <- -step*asp + r */
280: if (ksp->normtype != KSP_NORM_NONE) {
281: PetscCall(VecNorm(R, NORM_2, &rnrm));
282: KSPCheckNorm(ksp, rnrm);
283: }
284: PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
285: ksp->rnorm = rnrm;
286: PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
287: PetscCall(KSPLogResidualHistory(ksp, rnrm));
288: PetscCall(KSPMonitor(ksp, i + 1, rnrm));
289: PetscCall((*ksp->converged)(ksp, i + 1, rnrm, &ksp->reason, ksp->cnvP));
290: if (ksp->reason) { /* convergence for */
291: PetscCall(PetscInfo(ksp, "truncated step: step=%g, rnrm=%g, delta=%g\n", (double)PetscRealPart(step), (double)rnrm, (double)pcgP->delta));
292: }
293: }
294: }
295: if (ksp->reason) break; /* Convergence has been attained */
296: else { /* Compute a new AS-orthogonal direction */ PetscCall(VecDot(R, R, &rntrn));
297: beta = rntrn / rtr;
298: PetscCall(VecAYPX(P, beta, R)); /* p <- r + beta*p */
299: rtr = PetscRealPart(rntrn);
300: }
301: }
302: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
304: /* Unscale x */
305: PetscCall(VecCopy(X, WA2));
306: PetscCall(PCApplySymmetricRight(pc, WA2, X));
308: PetscCall(KSP_MatMult(ksp, Amat, X, WA));
309: PetscCall(VecDotRealPart(B, X, &btx));
310: PetscCall(VecDotRealPart(X, WA, &xtax));
312: pcgP->quadratic = btx + .5 * xtax;
313: PetscFunctionReturn(PETSC_SUCCESS);
314: }
316: static PetscErrorCode KSPSetUp_QCG(KSP ksp)
317: {
318: PetscFunctionBegin;
319: /* Get work vectors from user code */
320: PetscCall(KSPSetWorkVecs(ksp, 7));
321: PetscFunctionReturn(PETSC_SUCCESS);
322: }
324: static PetscErrorCode KSPDestroy_QCG(KSP ksp)
325: {
326: PetscFunctionBegin;
327: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGGetQuadratic_C", NULL));
328: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGGetTrialStepNorm_C", NULL));
329: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGSetTrustRegionRadius_C", NULL));
330: PetscCall(KSPDestroyDefault(ksp));
331: PetscFunctionReturn(PETSC_SUCCESS);
332: }
334: static PetscErrorCode KSPQCGSetTrustRegionRadius_QCG(KSP ksp, PetscReal delta)
335: {
336: KSP_QCG *cgP = (KSP_QCG *)ksp->data;
338: PetscFunctionBegin;
339: cgP->delta = delta;
340: PetscFunctionReturn(PETSC_SUCCESS);
341: }
343: static PetscErrorCode KSPQCGGetTrialStepNorm_QCG(KSP ksp, PetscReal *ltsnrm)
344: {
345: KSP_QCG *cgP = (KSP_QCG *)ksp->data;
347: PetscFunctionBegin;
348: *ltsnrm = cgP->ltsnrm;
349: PetscFunctionReturn(PETSC_SUCCESS);
350: }
352: static PetscErrorCode KSPQCGGetQuadratic_QCG(KSP ksp, PetscReal *quadratic)
353: {
354: KSP_QCG *cgP = (KSP_QCG *)ksp->data;
356: PetscFunctionBegin;
357: *quadratic = cgP->quadratic;
358: PetscFunctionReturn(PETSC_SUCCESS);
359: }
361: static PetscErrorCode KSPSetFromOptions_QCG(KSP ksp, PetscOptionItems PetscOptionsObject)
362: {
363: PetscReal delta;
364: KSP_QCG *cgP = (KSP_QCG *)ksp->data;
365: PetscBool flg;
367: PetscFunctionBegin;
368: PetscOptionsHeadBegin(PetscOptionsObject, "KSP QCG Options");
369: PetscCall(PetscOptionsReal("-ksp_qcg_trustregionradius", "Trust Region Radius", "KSPQCGSetTrustRegionRadius", cgP->delta, &delta, &flg));
370: if (flg) PetscCall(KSPQCGSetTrustRegionRadius(ksp, delta));
371: PetscOptionsHeadEnd();
372: PetscFunctionReturn(PETSC_SUCCESS);
373: }
375: /*MC
376: KSPQCG - Code to run conjugate gradient method subject to a constraint on the solution norm {cite}`steihaug:83`.
378: Options Database Key:
379: . -ksp_qcg_trustregionradius <r> - Trust Region Radius
381: Level: developer
383: Notes:
384: This is rarely used directly, ir is used in Trust Region methods for nonlinear equations, `SNESNEWTONTR`
386: Uses preconditioned conjugate gradient to compute
387: an approximate minimizer of the quadratic function $ q(s) = g^T * s + .5 * s^T * H * s $ subject to the Euclidean norm trust region constraint
388: $ || D * s || \le delta$, where
389: .vb
390: delta is the trust region radius,
391: g is the gradient vector, and
392: H is Hessian matrix,
393: D is a scaling matrix.
394: .ve
396: `KSPConvergedReason` may include
397: + `KSP_CONVERGED_NEG_CURVE` - if convergence is reached along a negative curvature direction,
398: - `KSP_CONVERGED_STEP_LENGTH` - if convergence is reached along a constrained step,
400: Note:
401: Allows symmetric preconditioning with the following scaling matrices:
402: .vb
403: `PCNONE`: D = Identity matrix
404: `PCJACOBI`: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i])
405: `PCICC`: D = L^T, implemented with forward and backward solves. Here L is an incomplete Cholesky factor of H.
406: .ve
408: .seealso: [](ch_ksp), `KSPNASH`, `KSPGLTR`, `KSPSTCG`, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPQCGSetTrustRegionRadius()`
409: `KSPQCGGetTrialStepNorm()`, `KSPQCGGetQuadratic()`
410: M*/
412: PETSC_EXTERN PetscErrorCode KSPCreate_QCG(KSP ksp)
413: {
414: KSP_QCG *cgP;
416: PetscFunctionBegin;
417: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_SYMMETRIC, 3));
418: PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_SYMMETRIC, 1));
419: PetscCall(KSPSetConvergedNegativeCurvature(ksp, PETSC_TRUE));
420: PetscCall(PetscNew(&cgP));
422: ksp->data = (void *)cgP;
423: ksp->ops->setup = KSPSetUp_QCG;
424: ksp->ops->setfromoptions = KSPSetFromOptions_QCG;
425: ksp->ops->solve = KSPSolve_QCG;
426: ksp->ops->destroy = KSPDestroy_QCG;
427: ksp->ops->buildsolution = KSPBuildSolutionDefault;
428: ksp->ops->buildresidual = KSPBuildResidualDefault;
429: ksp->ops->view = NULL;
431: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGGetQuadratic_C", KSPQCGGetQuadratic_QCG));
432: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGGetTrialStepNorm_C", KSPQCGGetTrialStepNorm_QCG));
433: PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPQCGSetTrustRegionRadius_C", KSPQCGSetTrustRegionRadius_QCG));
434: cgP->delta = PETSC_MAX_REAL; /* default trust region radius is infinite */
435: PetscFunctionReturn(PETSC_SUCCESS);
436: }