Actual source code: bfgs.c
petsc-3.13.6 2020-09-29
1: #include <../src/ksp/ksp/utils/lmvm/symbrdn/symbrdn.h>
2: #include <../src/ksp/ksp/utils/lmvm/diagbrdn/diagbrdn.h>
4: /*
5: Limited-memory Broyden-Fletcher-Goldfarb-Shano method for approximating both
6: the forward product and inverse Section 1.5 Writing Application Codes with PETSc of a Jacobian.
7: */
9: /*------------------------------------------------------------*/
11: /*
12: The solution method (approximate inverse Jacobian Section 1.5 Writing Application Codes with PETSc) is adapted
13: from Algorithm 7.4 on page 178 of Nocedal and Wright "Numerical Optimization"
14: 2nd edition (https://doi.org/10.1007/978-0-387-40065-5). The initial inverse
15: Jacobian Section 1.5 Writing Application Codes with PETSc falls back onto the gamma scaling recommended in equation
16: (7.20) if the user has not provided any estimation of the initial Jacobian or
17: its inverse.
19: work <- F
21: for i = k,k-1,k-2,...,0
22: rho[i] = 1 / (Y[i]^T S[i])
23: alpha[i] = rho[i] * (S[i]^T work)
24: Fwork <- work - (alpha[i] * Y[i])
25: end
27: dX <- J0^{-1} * work
29: for i = 0,1,2,...,k
30: beta = rho[i] * (Y[i]^T dX)
31: dX <- dX + ((alpha[i] - beta) * S[i])
32: end
33: */
34: PetscErrorCode MatSolve_LMVMBFGS(Mat B, Vec F, Vec dX)
35: {
36: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
37: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
38: PetscErrorCode ierr;
39: PetscInt i;
40: PetscReal *alpha, beta;
41: PetscScalar stf, ytx;
42:
44: VecCheckSameSize(F, 2, dX, 3);
45: VecCheckMatCompatible(B, dX, 3, F, 2);
46:
47: /* Copy the function into the work vector for the first loop */
48: VecCopy(F, lbfgs->work);
49:
50: /* Start the first loop */
51: PetscMalloc1(lmvm->k+1, &alpha);
52: for (i = lmvm->k; i >= 0; --i) {
53: VecDot(lmvm->S[i], lbfgs->work, &stf);
54: alpha[i] = PetscRealPart(stf)/lbfgs->yts[i];
55: VecAXPY(lbfgs->work, -alpha[i], lmvm->Y[i]);
56: }
57:
58: /* Invert the initial Jacobian onto the work vector (or apply scaling) */
59: MatSymBrdnApplyJ0Inv(B, lbfgs->work, dX);
60:
61: /* Start the second loop */
62: for (i = 0; i <= lmvm->k; ++i) {
63: VecDot(lmvm->Y[i], dX, &ytx);
64: beta = PetscRealPart(ytx)/lbfgs->yts[i];
65: VecAXPY(dX, alpha[i]-beta, lmvm->S[i]);
66: }
67: PetscFree(alpha);
68: return(0);
69: }
71: /*------------------------------------------------------------*/
73: /*
74: The forward product for the approximate Jacobian is the matrix-free
75: implementation of Equation (6.19) in Nocedal and Wright "Numerical
76: Optimization" 2nd Edition, pg 140.
77:
78: This forward product has the same structure as the inverse Jacobian
79: Section 1.5 Writing Application Codes with PETSc in the DFP formulation, except with S and Y exchanging
80: roles.
81:
82: Note: P[i] = (B_i)*S[i] terms are computed ahead of time whenever
83: the matrix is updated with a new (S[i], Y[i]) pair. This allows
84: repeated calls of MatMult inside KSP solvers without unnecessarily
85: recomputing P[i] terms in expensive nested-loops.
87: Z <- J0 * X
89: for i = 0,1,2,...,k
90: P[i] <- J0 * S[i]
91: for j = 0,1,2,...,(i-1)
92: gamma = (Y[j]^T S[i]) / (Y[j]^T S[j])
93: zeta = (S[j]^ P[i]) / (S[j]^T P[j])
94: P[i] <- P[i] - (zeta * P[j]) + (gamma * Y[j])
95: end
96: gamma = (Y[i]^T X) / (Y[i]^T S[i])
97: zeta = (S[i]^T Z) / (S[i]^T P[i])
98: Z <- Z - (zeta * P[i]) + (gamma * Y[i])
99: end
100: */
101: PetscErrorCode MatMult_LMVMBFGS(Mat B, Vec X, Vec Z)
102: {
103: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
104: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
105: PetscErrorCode ierr;
106: PetscInt i, j;
107: PetscScalar sjtpi, yjtsi, ytx, stz, stp;
108:
110: VecCheckSameSize(X, 2, Z, 3);
111: VecCheckMatCompatible(B, X, 2, Z, 3);
112:
113: if (lbfgs->needP) {
114: /* Pre-compute (P[i] = B_i * S[i]) */
115: for (i = 0; i <= lmvm->k; ++i) {
116: MatSymBrdnApplyJ0Fwd(B, lmvm->S[i], lbfgs->P[i]);
117: for (j = 0; j <= i-1; ++j) {
118: /* Compute the necessary dot products */
119: VecDotBegin(lmvm->S[j], lbfgs->P[i], &sjtpi);
120: VecDotBegin(lmvm->Y[j], lmvm->S[i], &yjtsi);
121: VecDotEnd(lmvm->S[j], lbfgs->P[i], &sjtpi);
122: VecDotEnd(lmvm->Y[j], lmvm->S[i], &yjtsi);
123: /* Compute the pure BFGS component of the forward product */
124: VecAXPBYPCZ(lbfgs->P[i], -PetscRealPart(sjtpi)/lbfgs->stp[j], PetscRealPart(yjtsi)/lbfgs->yts[j], 1.0, lbfgs->P[j], lmvm->Y[j]);
125: }
126: VecDot(lmvm->S[i], lbfgs->P[i], &stp);
127: lbfgs->stp[i] = PetscRealPart(stp);
128: }
129: lbfgs->needP = PETSC_FALSE;
130: }
131:
132: /* Start the outer loop (i) for the recursive formula */
133: MatSymBrdnApplyJ0Fwd(B, X, Z);
134: for (i = 0; i <= lmvm->k; ++i) {
135: /* Get all the dot products we need */
136: VecDotBegin(lmvm->S[i], Z, &stz);
137: VecDotBegin(lmvm->Y[i], X, &ytx);
138: VecDotEnd(lmvm->S[i], Z, &stz);
139: VecDotEnd(lmvm->Y[i], X, &ytx);
140: /* Update Z_{i+1} = B_{i+1} * X */
141: VecAXPBYPCZ(Z, -PetscRealPart(stz)/lbfgs->stp[i], PetscRealPart(ytx)/lbfgs->yts[i], 1.0, lbfgs->P[i], lmvm->Y[i]);
142: }
143: return(0);
144: }
146: /*------------------------------------------------------------*/
148: static PetscErrorCode MatUpdate_LMVMBFGS(Mat B, Vec X, Vec F)
149: {
150: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
151: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
152: Mat_LMVM *dbase;
153: Mat_DiagBrdn *dctx;
154: PetscErrorCode ierr;
155: PetscInt old_k, i;
156: PetscReal curvtol;
157: PetscScalar curvature, ytytmp, ststmp;
160: if (!lmvm->m) return(0);
161: if (lmvm->prev_set) {
162: /* Compute the new (S = X - Xprev) and (Y = F - Fprev) vectors */
163: VecAYPX(lmvm->Xprev, -1.0, X);
164: VecAYPX(lmvm->Fprev, -1.0, F);
165: /* Test if the updates can be accepted */
166: VecDotBegin(lmvm->Xprev, lmvm->Fprev, &curvature);
167: VecDotBegin(lmvm->Xprev, lmvm->Xprev, &ststmp);
168: VecDotEnd(lmvm->Xprev, lmvm->Fprev, &curvature);
169: VecDotEnd(lmvm->Xprev, lmvm->Xprev, &ststmp);
170: if (PetscRealPart(ststmp) < lmvm->eps) {
171: curvtol = 0.0;
172: } else {
173: curvtol = lmvm->eps * PetscRealPart(ststmp);
174: }
175: if (PetscRealPart(curvature) > curvtol) {
176: /* Update is good, accept it */
177: lbfgs->watchdog = 0;
178: lbfgs->needP = PETSC_TRUE;
179: old_k = lmvm->k;
180: MatUpdateKernel_LMVM(B, lmvm->Xprev, lmvm->Fprev);
181: /* If we hit the memory limit, shift the yts, yty and sts arrays */
182: if (old_k == lmvm->k) {
183: for (i = 0; i <= lmvm->k-1; ++i) {
184: lbfgs->yts[i] = lbfgs->yts[i+1];
185: lbfgs->yty[i] = lbfgs->yty[i+1];
186: lbfgs->sts[i] = lbfgs->sts[i+1];
187: }
188: }
189: /* Update history of useful scalars */
190: VecDot(lmvm->Y[lmvm->k], lmvm->Y[lmvm->k], &ytytmp);
191: lbfgs->yts[lmvm->k] = PetscRealPart(curvature);
192: lbfgs->yty[lmvm->k] = PetscRealPart(ytytmp);
193: lbfgs->sts[lmvm->k] = PetscRealPart(ststmp);
194: /* Compute the scalar scale if necessary */
195: if (lbfgs->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_SCALAR) {
196: MatSymBrdnComputeJ0Scalar(B);
197: }
198: } else {
199: /* Update is bad, skip it */
200: ++lmvm->nrejects;
201: ++lbfgs->watchdog;
202: }
203: } else {
204: switch (lbfgs->scale_type) {
205: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
206: dbase = (Mat_LMVM*)lbfgs->D->data;
207: dctx = (Mat_DiagBrdn*)dbase->ctx;
208: VecSet(dctx->invD, lbfgs->delta);
209: break;
210: case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
211: lbfgs->sigma = lbfgs->delta;
212: break;
213: case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
214: lbfgs->sigma = 1.0;
215: break;
216: default:
217: break;
218: }
219: }
220:
221: /* Update the scaling */
222: if (lbfgs->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
223: MatLMVMUpdate(lbfgs->D, X, F);
224: }
225:
226: if (lbfgs->watchdog > lbfgs->max_seq_rejects) {
227: MatLMVMReset(B, PETSC_FALSE);
228: if (lbfgs->scale_type == MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL) {
229: MatLMVMReset(lbfgs->D, PETSC_FALSE);
230: }
231: }
233: /* Save the solution and function to be used in the next update */
234: VecCopy(X, lmvm->Xprev);
235: VecCopy(F, lmvm->Fprev);
236: lmvm->prev_set = PETSC_TRUE;
237: return(0);
238: }
240: /*------------------------------------------------------------*/
242: static PetscErrorCode MatCopy_LMVMBFGS(Mat B, Mat M, MatStructure str)
243: {
244: Mat_LMVM *bdata = (Mat_LMVM*)B->data;
245: Mat_SymBrdn *bctx = (Mat_SymBrdn*)bdata->ctx;
246: Mat_LMVM *mdata = (Mat_LMVM*)M->data;
247: Mat_SymBrdn *mctx = (Mat_SymBrdn*)mdata->ctx;
248: PetscErrorCode ierr;
249: PetscInt i;
252: mctx->needP = bctx->needP;
253: for (i=0; i<=bdata->k; ++i) {
254: mctx->stp[i] = bctx->stp[i];
255: mctx->yts[i] = bctx->yts[i];
256: VecCopy(bctx->P[i], mctx->P[i]);
257: }
258: mctx->scale_type = bctx->scale_type;
259: mctx->alpha = bctx->alpha;
260: mctx->beta = bctx->beta;
261: mctx->rho = bctx->rho;
262: mctx->delta = bctx->delta;
263: mctx->sigma_hist = bctx->sigma_hist;
264: mctx->watchdog = bctx->watchdog;
265: mctx->max_seq_rejects = bctx->max_seq_rejects;
266: switch (bctx->scale_type) {
267: case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
268: mctx->sigma = bctx->sigma;
269: break;
270: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
271: MatCopy(bctx->D, mctx->D, SAME_NONZERO_PATTERN);
272: break;
273: case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
274: mctx->sigma = 1.0;
275: break;
276: default:
277: break;
278: }
279: return(0);
280: }
282: /*------------------------------------------------------------*/
284: static PetscErrorCode MatReset_LMVMBFGS(Mat B, PetscBool destructive)
285: {
286: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
287: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
288: Mat_LMVM *dbase;
289: Mat_DiagBrdn *dctx;
290: PetscErrorCode ierr;
291:
293: lbfgs->watchdog = 0;
294: lbfgs->needP = PETSC_TRUE;
295: if (lbfgs->allocated) {
296: if (destructive) {
297: VecDestroy(&lbfgs->work);
298: PetscFree4(lbfgs->stp, lbfgs->yts, lbfgs->yty, lbfgs->sts);
299: VecDestroyVecs(lmvm->m, &lbfgs->P);
300: switch (lbfgs->scale_type) {
301: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
302: MatLMVMReset(lbfgs->D, PETSC_TRUE);
303: break;
304: default:
305: break;
306: }
307: lbfgs->allocated = PETSC_FALSE;
308: } else {
309: switch (lbfgs->scale_type) {
310: case MAT_LMVM_SYMBROYDEN_SCALE_SCALAR:
311: lbfgs->sigma = lbfgs->delta;
312: break;
313: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
314: MatLMVMReset(lbfgs->D, PETSC_FALSE);
315: dbase = (Mat_LMVM*)lbfgs->D->data;
316: dctx = (Mat_DiagBrdn*)dbase->ctx;
317: VecSet(dctx->invD, lbfgs->delta);
318: break;
319: case MAT_LMVM_SYMBROYDEN_SCALE_NONE:
320: lbfgs->sigma = 1.0;
321: break;
322: default:
323: break;
324: }
325: }
326: }
327: MatReset_LMVM(B, destructive);
328: return(0);
329: }
331: /*------------------------------------------------------------*/
333: static PetscErrorCode MatAllocate_LMVMBFGS(Mat B, Vec X, Vec F)
334: {
335: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
336: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
337: PetscErrorCode ierr;
338:
340: MatAllocate_LMVM(B, X, F);
341: if (!lbfgs->allocated) {
342: VecDuplicate(X, &lbfgs->work);
343: PetscMalloc4(lmvm->m, &lbfgs->stp, lmvm->m, &lbfgs->yts, lmvm->m, &lbfgs->yty, lmvm->m, &lbfgs->sts);
344: if (lmvm->m > 0) {
345: VecDuplicateVecs(X, lmvm->m, &lbfgs->P);
346: }
347: switch (lbfgs->scale_type) {
348: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
349: MatLMVMAllocate(lbfgs->D, X, F);
350: break;
351: default:
352: break;
353: }
354: lbfgs->allocated = PETSC_TRUE;
355: }
356: return(0);
357: }
359: /*------------------------------------------------------------*/
361: static PetscErrorCode MatDestroy_LMVMBFGS(Mat B)
362: {
363: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
364: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
365: PetscErrorCode ierr;
368: if (lbfgs->allocated) {
369: VecDestroy(&lbfgs->work);
370: PetscFree4(lbfgs->stp, lbfgs->yts, lbfgs->yty, lbfgs->sts);
371: VecDestroyVecs(lmvm->m, &lbfgs->P);
372: lbfgs->allocated = PETSC_FALSE;
373: }
374: MatDestroy(&lbfgs->D);
375: PetscFree(lmvm->ctx);
376: MatDestroy_LMVM(B);
377: return(0);
378: }
380: /*------------------------------------------------------------*/
382: static PetscErrorCode MatSetUp_LMVMBFGS(Mat B)
383: {
384: Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
385: Mat_SymBrdn *lbfgs = (Mat_SymBrdn*)lmvm->ctx;
386: PetscErrorCode ierr;
387: PetscInt n, N;
388:
390: MatSetUp_LMVM(B);
391: lbfgs->max_seq_rejects = lmvm->m/2;
392: if (!lbfgs->allocated) {
393: VecDuplicate(lmvm->Xprev, &lbfgs->work);
394: PetscMalloc4(lmvm->m, &lbfgs->stp, lmvm->m, &lbfgs->yts, lmvm->m, &lbfgs->yty, lmvm->m, &lbfgs->sts);
395: if (lmvm->m > 0) {
396: VecDuplicateVecs(lmvm->Xprev, lmvm->m, &lbfgs->P);
397: }
398: switch (lbfgs->scale_type) {
399: case MAT_LMVM_SYMBROYDEN_SCALE_DIAGONAL:
400: MatGetLocalSize(B, &n, &n);
401: MatGetSize(B, &N, &N);
402: MatSetSizes(lbfgs->D, n, n, N, N);
403: MatSetUp(lbfgs->D);
404: break;
405: default:
406: break;
407: }
408: lbfgs->allocated = PETSC_TRUE;
409: }
410: return(0);
411: }
413: /*------------------------------------------------------------*/
415: static PetscErrorCode MatSetFromOptions_LMVMBFGS(PetscOptionItems *PetscOptionsObject, Mat B)
416: {
417: PetscErrorCode ierr;
420: MatSetFromOptions_LMVM(PetscOptionsObject, B);
421: PetscOptionsHead(PetscOptionsObject,"L-BFGS method for approximating SPD Jacobian actions (MATLMVMBFGS)");
422: MatSetFromOptions_LMVMSymBrdn_Private(PetscOptionsObject, B);
423: PetscOptionsTail();
424: return(0);
425: }
427: /*------------------------------------------------------------*/
429: PetscErrorCode MatCreate_LMVMBFGS(Mat B)
430: {
431: Mat_LMVM *lmvm;
432: Mat_SymBrdn *lbfgs;
433: PetscErrorCode ierr;
436: MatCreate_LMVMSymBrdn(B);
437: PetscObjectChangeTypeName((PetscObject)B, MATLMVMBFGS);
438: B->ops->setup = MatSetUp_LMVMBFGS;
439: B->ops->destroy = MatDestroy_LMVMBFGS;
440: B->ops->setfromoptions = MatSetFromOptions_LMVMBFGS;
441: B->ops->solve = MatSolve_LMVMBFGS;
443: lmvm = (Mat_LMVM*)B->data;
444: lmvm->ops->allocate = MatAllocate_LMVMBFGS;
445: lmvm->ops->reset = MatReset_LMVMBFGS;
446: lmvm->ops->update = MatUpdate_LMVMBFGS;
447: lmvm->ops->mult = MatMult_LMVMBFGS;
448: lmvm->ops->copy = MatCopy_LMVMBFGS;
450: lbfgs = (Mat_SymBrdn*)lmvm->ctx;
451: lbfgs->needQ = PETSC_FALSE;
452: lbfgs->phi = 0.0;
453: return(0);
454: }
456: /*------------------------------------------------------------*/
458: /*@
459: MatCreateLMVMBFGS - Creates a limited-memory Broyden-Fletcher-Goldfarb-Shano (BFGS)
460: matrix used for approximating Jacobians. L-BFGS is symmetric positive-definite by
461: construction, and is commonly used to approximate Hessians in optimization
462: problems.
463:
464: The provided local and global sizes must match the solution and function vectors
465: used with MatLMVMUpdate() and MatSolve(). The resulting L-BFGS matrix will have
466: storage vectors allocated with VecCreateSeq() in serial and VecCreateMPI() in
467: parallel. To use the L-BFGS matrix with other vector types, the matrix must be
468: created using MatCreate() and MatSetType(), followed by MatLMVMAllocate().
469: This ensures that the internal storage and work vectors are duplicated from the
470: correct type of vector.
472: Collective
474: Input Parameters:
475: + comm - MPI communicator, set to PETSC_COMM_SELF
476: . n - number of local rows for storage vectors
477: - N - global size of the storage vectors
479: Output Parameter:
480: . B - the matrix
482: It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions()
483: paradigm instead of this routine directly.
485: Options Database Keys:
486: + -mat_lmvm_num_vecs - maximum number of correction vectors (i.e.: updates) stored
487: . -mat_lmvm_scale_type - (developer) type of scaling applied to J0 (none, scalar, diagonal)
488: . -mat_lmvm_theta - (developer) convex ratio between BFGS and DFP components of the diagonal J0 scaling
489: . -mat_lmvm_rho - (developer) update limiter for the J0 scaling
490: . -mat_lmvm_alpha - (developer) coefficient factor for the quadratic subproblem in J0 scaling
491: . -mat_lmvm_beta - (developer) exponential factor for the diagonal J0 scaling
492: - -mat_lmvm_sigma_hist - (developer) number of past updates to use in J0 scaling
494: Level: intermediate
496: .seealso: MatCreate(), MATLMVM, MATLMVMBFGS, MatCreateLMVMDFP(), MatCreateLMVMSR1(),
497: MatCreateLMVMBrdn(), MatCreateLMVMBadBrdn(), MatCreateLMVMSymBrdn()
498: @*/
499: PetscErrorCode MatCreateLMVMBFGS(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)
500: {
501: PetscErrorCode ierr;
502:
504: MatCreate(comm, B);
505: MatSetSizes(*B, n, n, N, N);
506: MatSetType(*B, MATLMVMBFGS);
507: MatSetUp(*B);
508: return(0);
509: }