Actual source code: pdipm.c
petsc-3.14.6 2021-03-30
1: #include <petsctaolinesearch.h>
2: #include <../src/tao/constrained/impls/ipm/pdipm.h>
3: #include <petscsnes.h>
5: /*
6: TaoPDIPMEvaluateFunctionsAndJacobians - Evaluate the objective function f, gradient fx, constraints, and all the Jacobians at current vector
8: Collective on tao
10: Input Parameter:
11: + tao - solver context
12: - x - vector at which all objects to be evaluated
14: Level: beginner
16: .seealso: TaoPDIPMUpdateConstraints(), TaoPDIPMSetUpBounds()
17: */
18: PetscErrorCode TaoPDIPMEvaluateFunctionsAndJacobians(Tao tao,Vec x)
19: {
21: TAO_PDIPM *pdipm=(TAO_PDIPM*)tao->data;
24: /* Compute user objective function and gradient */
25: TaoComputeObjectiveAndGradient(tao,x,&pdipm->obj,tao->gradient);
27: /* Equality constraints and Jacobian */
28: if (pdipm->Ng) {
29: TaoComputeEqualityConstraints(tao,x,tao->constraints_equality);
30: TaoComputeJacobianEquality(tao,x,tao->jacobian_equality,tao->jacobian_equality_pre);
31: }
33: /* Inequality constraints and Jacobian */
34: if (pdipm->Nh) {
35: TaoComputeInequalityConstraints(tao,x,tao->constraints_inequality);
36: TaoComputeJacobianInequality(tao,x,tao->jacobian_inequality,tao->jacobian_inequality_pre);
37: }
38: return(0);
39: }
41: /*
42: TaoPDIPMUpdateConstraints - Update the vectors ce and ci at x
44: Collective
46: Input Parameter:
47: + tao - Tao context
48: - x - vector at which constraints to be evaluted
50: Level: beginner
52: .seealso: TaoPDIPMEvaluateFunctionsAndJacobians()
53: */
54: PetscErrorCode TaoPDIPMUpdateConstraints(Tao tao,Vec x)
55: {
56: PetscErrorCode ierr;
57: TAO_PDIPM *pdipm=(TAO_PDIPM*)tao->data;
58: PetscInt i,offset,offset1,k,xstart;
59: PetscScalar *carr;
60: const PetscInt *ubptr,*lbptr,*bxptr,*fxptr;
61: const PetscScalar *xarr,*xuarr,*xlarr,*garr,*harr;
64: VecGetOwnershipRange(x,&xstart,NULL);
66: VecGetArrayRead(x,&xarr);
67: VecGetArrayRead(tao->XU,&xuarr);
68: VecGetArrayRead(tao->XL,&xlarr);
70: /* (1) Update ce vector */
71: VecGetArray(pdipm->ce,&carr);
73: if (pdipm->Ng) {
74: /* (1.a) Inserting updated g(x) */
75: VecGetArrayRead(tao->constraints_equality,&garr);
76: PetscMemcpy(carr,garr,pdipm->ng*sizeof(PetscScalar));
77: VecRestoreArrayRead(tao->constraints_equality,&garr);
78: }
80: /* (1.b) Update xfixed */
81: if (pdipm->Nxfixed) {
82: offset = pdipm->ng;
83: ISGetIndices(pdipm->isxfixed,&fxptr); /* global indices in x */
84: for (k=0;k < pdipm->nxfixed;k++){
85: i = fxptr[k]-xstart;
86: carr[offset + k] = xarr[i] - xuarr[i];
87: }
88: }
89: VecRestoreArray(pdipm->ce,&carr);
91: /* (2) Update ci vector */
92: VecGetArray(pdipm->ci,&carr);
94: if (pdipm->Nh) {
95: /* (2.a) Inserting updated h(x) */
96: VecGetArrayRead(tao->constraints_inequality,&harr);
97: PetscMemcpy(carr,harr,pdipm->nh*sizeof(PetscScalar));
98: VecRestoreArrayRead(tao->constraints_inequality,&harr);
99: }
101: /* (2.b) Update xub */
102: offset = pdipm->nh;
103: if (pdipm->Nxub) {
104: ISGetIndices(pdipm->isxub,&ubptr);
105: for (k=0; k<pdipm->nxub; k++){
106: i = ubptr[k]-xstart;
107: carr[offset + k] = xuarr[i] - xarr[i];
108: }
109: }
111: if (pdipm->Nxlb) {
112: /* (2.c) Update xlb */
113: offset += pdipm->nxub;
114: ISGetIndices(pdipm->isxlb,&lbptr); /* global indices in x */
115: for (k=0; k<pdipm->nxlb; k++){
116: i = lbptr[k]-xstart;
117: carr[offset + k] = xarr[i] - xlarr[i];
118: }
119: }
121: if (pdipm->Nxbox) {
122: /* (2.d) Update xbox */
123: offset += pdipm->nxlb;
124: offset1 = offset + pdipm->nxbox;
125: ISGetIndices(pdipm->isxbox,&bxptr); /* global indices in x */
126: for (k=0; k<pdipm->nxbox; k++){
127: i = bxptr[k]-xstart; /* local indices in x */
128: carr[offset+k] = xuarr[i] - xarr[i];
129: carr[offset1+k] = xarr[i] - xlarr[i];
130: }
131: }
132: VecRestoreArray(pdipm->ci,&carr);
134: /* Restoring Vectors */
135: VecRestoreArrayRead(x,&xarr);
136: VecRestoreArrayRead(tao->XU,&xuarr);
137: VecRestoreArrayRead(tao->XL,&xlarr);
138: return(0);
139: }
141: /*
142: TaoPDIPMSetUpBounds - Create upper and lower bound vectors of x
144: Collective
146: Input Parameter:
147: . tao - holds pdipm and XL & XU
149: Level: beginner
151: .seealso: TaoPDIPMUpdateConstraints
152: */
153: PetscErrorCode TaoPDIPMSetUpBounds(Tao tao)
154: {
155: PetscErrorCode ierr;
156: TAO_PDIPM *pdipm=(TAO_PDIPM*)tao->data;
157: const PetscScalar *xl,*xu;
158: PetscInt n,*ixlb,*ixub,*ixfixed,*ixfree,*ixbox,i,low,high,idx;
159: MPI_Comm comm;
160: PetscInt sendbuf[5],recvbuf[5];
163: /* Creates upper and lower bounds vectors on x, if not created already */
164: TaoComputeVariableBounds(tao);
166: VecGetLocalSize(tao->XL,&n);
167: PetscMalloc5(n,&ixlb,n,&ixub,n,&ixfree,n,&ixfixed,n,&ixbox);
169: VecGetOwnershipRange(tao->XL,&low,&high);
170: VecGetArrayRead(tao->XL,&xl);
171: VecGetArrayRead(tao->XU,&xu);
172: for (i=0; i<n; i++) {
173: idx = low + i;
174: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
175: if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
176: ixfixed[pdipm->nxfixed++] = idx;
177: } else ixbox[pdipm->nxbox++] = idx;
178: } else {
179: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
180: ixlb[pdipm->nxlb++] = idx;
181: } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
182: ixub[pdipm->nxlb++] = idx;
183: } else ixfree[pdipm->nxfree++] = idx;
184: }
185: }
186: VecRestoreArrayRead(tao->XL,&xl);
187: VecRestoreArrayRead(tao->XU,&xu);
189: PetscObjectGetComm((PetscObject)tao,&comm);
190: sendbuf[0] = pdipm->nxlb;
191: sendbuf[1] = pdipm->nxub;
192: sendbuf[2] = pdipm->nxfixed;
193: sendbuf[3] = pdipm->nxbox;
194: sendbuf[4] = pdipm->nxfree;
196: MPI_Allreduce(sendbuf,recvbuf,5,MPIU_INT,MPI_SUM,comm);
197: pdipm->Nxlb = recvbuf[0];
198: pdipm->Nxub = recvbuf[1];
199: pdipm->Nxfixed = recvbuf[2];
200: pdipm->Nxbox = recvbuf[3];
201: pdipm->Nxfree = recvbuf[4];
203: if (pdipm->Nxlb) {
204: ISCreateGeneral(comm,pdipm->nxlb,ixlb,PETSC_COPY_VALUES,&pdipm->isxlb);
205: }
206: if (pdipm->Nxub) {
207: ISCreateGeneral(comm,pdipm->nxub,ixub,PETSC_COPY_VALUES,&pdipm->isxub);
208: }
209: if (pdipm->Nxfixed) {
210: ISCreateGeneral(comm,pdipm->nxfixed,ixfixed,PETSC_COPY_VALUES,&pdipm->isxfixed);
211: }
212: if (pdipm->Nxbox) {
213: ISCreateGeneral(comm,pdipm->nxbox,ixbox,PETSC_COPY_VALUES,&pdipm->isxbox);
214: }
215: if (pdipm->Nxfree) {
216: ISCreateGeneral(comm,pdipm->nxfree,ixfree,PETSC_COPY_VALUES,&pdipm->isxfree);
217: }
218: PetscFree5(ixlb,ixub,ixfixed,ixbox,ixfree);
219: return(0);
220: }
222: /*
223: TaoPDIPMInitializeSolution - Initialize PDIPM solution X = [x; lambdae; lambdai; z].
224: X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
225: four subvectors need to be initialized and its values copied over to X. Instead
226: of copying, we use VecPlace/ResetArray functions to share the memory locations for
227: X and the subvectors
229: Collective
231: Input Parameter:
232: . tao - Tao context
234: Level: beginner
235: */
236: PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
237: {
239: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
240: PetscScalar *Xarr,*z,*lambdai;
241: PetscInt i;
242: const PetscScalar *xarr,*h;
245: VecGetArray(pdipm->X,&Xarr);
247: /* Set Initialize X.x = tao->solution */
248: VecGetArrayRead(tao->solution,&xarr);
249: PetscMemcpy(Xarr,xarr,pdipm->nx*sizeof(PetscScalar));
250: VecRestoreArrayRead(tao->solution,&xarr);
252: /* Initialize X.lambdae = 0.0 */
253: if (pdipm->lambdae) {
254: VecSet(pdipm->lambdae,0.0);
255: }
256: /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
257: if (pdipm->lambdai) {
258: VecSet(pdipm->lambdai,pdipm->push_init_lambdai);
259: }
260: if (pdipm->z) {
261: VecSet(pdipm->z,pdipm->push_init_slack);
262: }
264: /* Additional modification for X.lambdai and X.z */
265: if (pdipm->lambdai) {
266: VecGetArray(pdipm->lambdai,&lambdai);
267: }
268: if (pdipm->z) {
269: VecGetArray(pdipm->z,&z);
270: }
271: if (pdipm->Nh) {
272: VecGetArrayRead(tao->constraints_inequality,&h);
273: for (i=0; i < pdipm->nh; i++) {
274: if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
275: if (pdipm->mu/z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu/z[i];
276: }
277: VecRestoreArrayRead(tao->constraints_inequality,&h);
278: }
279: if (pdipm->lambdai) {
280: VecRestoreArray(pdipm->lambdai,&lambdai);
281: }
282: if (pdipm->z) {
283: VecRestoreArray(pdipm->z,&z);
284: }
286: VecRestoreArray(pdipm->X,&Xarr);
287: return(0);
288: }
290: /*
291: TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X
293: Input Parameter:
294: snes - SNES context
295: X - KKT Vector
296: *ctx - pdipm context
298: Output Parameter:
299: J - Hessian matrix
300: Jpre - Preconditioner
301: */
302: PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes,Vec X, Mat J, Mat Jpre, void *ctx)
303: {
304: PetscErrorCode ierr;
305: Tao tao=(Tao)ctx;
306: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
307: PetscInt i,row,cols[2],Jrstart,rjstart,nc,j;
308: const PetscInt *aj,*ranges,*Jranges,*rranges,*cranges;
309: const PetscScalar *Xarr,*aa;
310: PetscScalar vals[2];
311: PetscInt proc,nx_all,*nce_all=pdipm->nce_all;
312: MPI_Comm comm;
313: PetscMPIInt rank,size;
314: Mat jac_equality_trans=pdipm->jac_equality_trans,jac_inequality_trans=pdipm->jac_inequality_trans;
317: PetscObjectGetComm((PetscObject)snes,&comm);
318: MPI_Comm_rank(comm,&rank);
319: MPI_Comm_rank(comm,&size);
321: MatGetOwnershipRanges(Jpre,&Jranges);
322: MatGetOwnershipRange(Jpre,&Jrstart,NULL);
323: MatGetOwnershipRangesColumn(tao->hessian,&rranges);
324: MatGetOwnershipRangesColumn(tao->hessian,&cranges);
326: VecGetArrayRead(X,&Xarr);
328: /* (2) insert Z and Ci to Jpre -- overwrite existing values */
329: for (i=0; i < pdipm->nci; i++) {
330: row = Jrstart + pdipm->off_z + i;
331: cols[0] = Jrstart + pdipm->off_lambdai + i;
332: cols[1] = row;
333: vals[0] = Xarr[pdipm->off_z + i];
334: vals[1] = Xarr[pdipm->off_lambdai + i];
335: MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
336: }
338: /* (3) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
339: if (pdipm->Ng) {
340: MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
341: for (i=0; i<pdipm->ng; i++){
342: row = Jrstart + pdipm->off_lambdae + i;
344: MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
345: proc = 0;
346: for (j=0; j < nc; j++) {
347: while (aj[j] >= cranges[proc+1]) proc++;
348: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
349: MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
350: }
351: MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
352: }
353: }
355: if (pdipm->Nh) {
356: /* (4) insert 3nd row block of Jpre: [ grad h, 0, 0, 0] */
357: MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
358: for (i=0; i < pdipm->nh; i++){
359: row = Jrstart + pdipm->off_lambdai + i;
361: MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
362: proc = 0;
363: for (j=0; j < nc; j++) {
364: while (aj[j] >= cranges[proc+1]) proc++;
365: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
366: MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
367: }
368: MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
369: }
370: }
372: /* (5) insert Wxx, grad g' and -grad h' to Jpre */
373: if (pdipm->Ng) {
374: MatTranspose(tao->jacobian_equality,MAT_REUSE_MATRIX,&jac_equality_trans);
375: }
376: if (pdipm->Nh) {
377: MatTranspose(tao->jacobian_inequality,MAT_REUSE_MATRIX,&jac_inequality_trans);
378: }
380: VecPlaceArray(pdipm->x,Xarr);
381: TaoComputeHessian(tao,pdipm->x,tao->hessian,tao->hessian_pre);
382: VecResetArray(pdipm->x);
384: MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
385: for (i=0; i<pdipm->nx; i++){
386: row = Jrstart + i;
388: /* insert Wxx */
389: MatGetRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
390: proc = 0;
391: for (j=0; j < nc; j++) {
392: while (aj[j] >= cranges[proc+1]) proc++;
393: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
394: MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
395: }
396: MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
398: if (pdipm->ng) {
399: /* insert grad g' */
400: MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
401: MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
402: proc = 0;
403: for (j=0; j < nc; j++) {
404: /* find row ownership of */
405: while (aj[j] >= ranges[proc+1]) proc++;
406: nx_all = rranges[proc+1] - rranges[proc];
407: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
408: MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
409: }
410: MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
411: }
413: if (pdipm->nh) {
414: /* insert -grad h' */
415: MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
416: MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
417: proc = 0;
418: for (j=0; j < nc; j++) {
419: /* find row ownership of */
420: while (aj[j] >= ranges[proc+1]) proc++;
421: nx_all = rranges[proc+1] - rranges[proc];
422: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
423: MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
424: }
425: MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
426: }
427: }
428: VecRestoreArrayRead(X,&Xarr);
430: /* (6) assemble Jpre and J */
431: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
432: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
434: if (J != Jpre) {
435: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
436: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
437: }
438: return(0);
439: }
441: /*
442: TaoSnesFunction_PDIPM - Evaluate KKT function at X
444: Input Parameter:
445: snes - SNES context
446: X - KKT Vector
447: *ctx - pdipm
449: Output Parameter:
450: F - Updated Lagrangian vector
451: */
452: PetscErrorCode TaoSNESFunction_PDIPM(SNES snes,Vec X,Vec F,void *ctx)
453: {
455: Tao tao=(Tao)ctx;
456: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
457: PetscScalar *Farr;
458: Vec x,L1;
459: PetscInt i;
460: PetscReal res[2],cnorm[2];
461: const PetscScalar *Xarr,*carr,*zarr,*larr;
464: VecSet(F,0.0);
466: VecGetArrayRead(X,&Xarr);
467: VecGetArray(F,&Farr);
469: /* (0) Evaluate f, fx, Gx, Hx at X.x Note: pdipm->x is not changed below */
470: x = pdipm->x;
471: VecPlaceArray(x,Xarr);
472: TaoPDIPMEvaluateFunctionsAndJacobians(tao,x);
474: /* Update ce, ci, and Jci at X.x */
475: TaoPDIPMUpdateConstraints(tao,x);
476: VecResetArray(x);
478: /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
479: L1 = pdipm->x;
480: VecPlaceArray(L1,Farr);
481: if (pdipm->Nci) {
482: if (pdipm->Nh) {
483: /* L1 += gradH'*DI. Note: tao->DI is not changed below */
484: VecPlaceArray(tao->DI,Xarr+pdipm->off_lambdai);
485: MatMultTransposeAdd(tao->jacobian_inequality,tao->DI,L1,L1);
486: VecResetArray(tao->DI);
487: }
489: /* L1 += Jci_xb'*lambdai_xb */
490: VecPlaceArray(pdipm->lambdai_xb,Xarr+pdipm->off_lambdai+pdipm->nh);
491: MatMultTransposeAdd(pdipm->Jci_xb,pdipm->lambdai_xb,L1,L1);
492: VecResetArray(pdipm->lambdai_xb);
494: /* (1.4) L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
495: VecScale(L1,-1.0);
496: }
498: /* L1 += fx */
499: VecAXPY(L1,1.0,tao->gradient);
501: if (pdipm->Nce) {
502: if (pdipm->Ng) {
503: /* L1 += gradG'*DE. Note: tao->DE is not changed below */
504: VecPlaceArray(tao->DE,Xarr+pdipm->off_lambdae);
505: MatMultTransposeAdd(tao->jacobian_equality,tao->DE,L1,L1);
506: VecResetArray(tao->DE);
507: }
508: if (pdipm->Nxfixed) {
509: /* L1 += Jce_xfixed'*lambdae_xfixed */
510: VecPlaceArray(pdipm->lambdae_xfixed,Xarr+pdipm->off_lambdae+pdipm->ng);
511: MatMultTransposeAdd(pdipm->Jce_xfixed,pdipm->lambdae_xfixed,L1,L1);
512: VecResetArray(pdipm->lambdae_xfixed);
513: }
514: }
515: VecNorm(L1,NORM_2,&res[0]);
516: VecResetArray(L1);
518: /* (2) L2 = ce(x) */
519: if (pdipm->Nce) {
520: VecGetArrayRead(pdipm->ce,&carr);
521: for (i=0; i<pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
522: VecRestoreArrayRead(pdipm->ce,&carr);
523: }
524: VecNorm(pdipm->ce,NORM_2,&cnorm[0]);
526: if (pdipm->Nci) {
527: /* (3) L3 = ci(x) - z;
528: (4) L4 = Z * Lambdai * e - mu * e
529: */
530: VecGetArrayRead(pdipm->ci,&carr);
531: larr = Xarr+pdipm->off_lambdai;
532: zarr = Xarr+pdipm->off_z;
533: for (i=0; i<pdipm->nci; i++) {
534: Farr[pdipm->off_lambdai + i] = carr[i] - zarr[i];
535: Farr[pdipm->off_z + i] = zarr[i]*larr[i] - pdipm->mu;
536: }
537: VecRestoreArrayRead(pdipm->ci,&carr);
538: }
540: VecPlaceArray(pdipm->ci,Farr+pdipm->off_lambdai);
541: VecNorm(pdipm->ci,NORM_2,&cnorm[1]);
542: VecResetArray(pdipm->ci);
544: /* note: pdipm->z is not changed below */
545: if (pdipm->z) {
546: VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
547: VecNorm(pdipm->z,NORM_2,&res[1]);
548: VecResetArray(pdipm->z);
549: } else res[1] = 0.0;
551: tao->residual = PetscSqrtReal(res[0]*res[0] + res[1]*res[1]);
552: tao->cnorm = PetscSqrtReal(cnorm[0]*cnorm[0] + cnorm[1]*cnorm[1]);
554: VecRestoreArrayRead(X,&Xarr);
555: VecRestoreArray(F,&Farr);
556: return(0);
557: }
559: /*
560: PDIPMLineSearch - Custom line search used with PDIPM.
562: Collective on TAO
564: Notes:
565: PDIPMLineSearch employs a simple backtracking line-search to keep
566: the slack variables (z) and inequality constraints lagrange multipliers
567: (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
568: alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
569: slack variables are updated as X = X + alpha_d*dx. The constraint multipliers
570: are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
571: is also updated as mu = mu + z'lambdai/Nci
572: */
573: PetscErrorCode PDIPMLineSearch(SNESLineSearch linesearch,void *ctx)
574: {
576: Tao tao=(Tao)ctx;
577: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
578: SNES snes;
579: Vec X,F,Y,W,G;
580: PetscInt i,iter;
581: PetscReal alpha_p=1.0,alpha_d=1.0,alpha[4];
582: PetscScalar *Xarr,*z,*lambdai,dot;
583: const PetscScalar *dXarr,*dz,*dlambdai;
584: PetscScalar *taosolarr;
587: SNESLineSearchGetSNES(linesearch,&snes);
588: SNESGetIterationNumber(snes,&iter);
590: SNESLineSearchSetReason(linesearch,SNES_LINESEARCH_SUCCEEDED);
591: SNESLineSearchGetVecs(linesearch,&X,&F,&Y,&W,&G);
593: VecGetArray(X,&Xarr);
594: VecGetArrayRead(Y,&dXarr);
595: z = Xarr + pdipm->off_z;
596: dz = dXarr + pdipm->off_z;
597: for (i=0; i < pdipm->nci; i++) {
598: if (z[i] - dz[i] < 0.0) {
599: alpha_p = PetscMin(alpha_p,0.9999*z[i]/dz[i]);
600: }
601: }
603: lambdai = Xarr + pdipm->off_lambdai;
604: dlambdai = dXarr + pdipm->off_lambdai;
606: for (i=0; i<pdipm->nci; i++) {
607: if (lambdai[i] - dlambdai[i] < 0.0) {
608: alpha_d = PetscMin(0.9999*lambdai[i]/dlambdai[i],alpha_d);
609: }
610: }
612: alpha[0] = alpha_p;
613: alpha[1] = alpha_d;
614: VecRestoreArrayRead(Y,&dXarr);
615: VecRestoreArray(X,&Xarr);
617: /* alpha = min(alpha) over all processes */
618: MPI_Allreduce(alpha,alpha+2,2,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)tao));
620: alpha_p = alpha[2];
621: alpha_d = alpha[3];
623: VecGetArray(X,&Xarr);
624: VecGetArrayRead(Y,&dXarr);
625: for (i=0; i<pdipm->nx; i++) {
626: Xarr[i] = Xarr[i] - alpha_p * dXarr[i];
627: }
629: for (i=0; i<pdipm->nce; i++) {
630: Xarr[i+pdipm->off_lambdae] = Xarr[i+pdipm->off_lambdae] - alpha_d * dXarr[i+pdipm->off_lambdae];
631: }
633: for (i=0; i<pdipm->nci; i++) {
634: Xarr[i+pdipm->off_lambdai] = Xarr[i+pdipm->off_lambdai] - alpha_d * dXarr[i+pdipm->off_lambdai];
635: }
637: for (i=0; i<pdipm->nci; i++) {
638: Xarr[i+pdipm->off_z] = Xarr[i+pdipm->off_z] - alpha_p * dXarr[i+pdipm->off_z];
639: }
641: VecGetArray(tao->solution,&taosolarr);
642: PetscMemcpy(taosolarr,Xarr,pdipm->nx*sizeof(PetscScalar));
643: VecRestoreArray(tao->solution,&taosolarr);
646: VecRestoreArray(X,&Xarr);
647: VecRestoreArrayRead(Y,&dXarr);
649: /* Evaluate F at X */
650: SNESComputeFunction(snes,X,F);
651: SNESLineSearchComputeNorms(linesearch); /* must call this func, do not know why */
653: /* update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
654: if (pdipm->z) {
655: VecDot(pdipm->z,pdipm->lambdai,&dot);
656: } else dot = 0.0;
658: /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu) */
659: pdipm->mu = pdipm->mu_update_factor * dot/pdipm->Nci;
661: /* Update F; get tao->residual and tao->cnorm */
662: TaoSNESFunction_PDIPM(snes,X,F,(void*)tao);
664: tao->niter++;
665: TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
666: TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
668: (*tao->ops->convergencetest)(tao,tao->cnvP);
669: if (tao->reason) {
670: SNESSetConvergedReason(snes,SNES_CONVERGED_FNORM_ABS);
671: }
672: return(0);
673: }
675: /*
676: TaoSolve_PDIPM
678: Input Parameter:
679: tao - TAO context
681: Output Parameter:
682: tao - TAO context
683: */
684: PetscErrorCode TaoSolve_PDIPM(Tao tao)
685: {
686: PetscErrorCode ierr;
687: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
688: SNESLineSearch linesearch; /* SNESLineSearch context */
689: Vec dummy;
692: if (!tao->constraints_equality && !tao->constraints_inequality) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_NULL,"Equality and inequality constraints are not set. Either set them or switch to a different algorithm");
694: /* Initialize all variables */
695: TaoPDIPMInitializeSolution(tao);
697: /* Set linesearch */
698: SNESGetLineSearch(pdipm->snes,&linesearch);
699: SNESLineSearchSetType(linesearch,SNESLINESEARCHSHELL);
700: SNESLineSearchShellSetUserFunc(linesearch,PDIPMLineSearch,tao);
701: SNESLineSearchSetFromOptions(linesearch);
703: tao->reason = TAO_CONTINUE_ITERATING;
705: /* -tao_monitor for iteration 0 and check convergence */
706: VecDuplicate(pdipm->X,&dummy);
707: TaoSNESFunction_PDIPM(pdipm->snes,pdipm->X,dummy,(void*)tao);
709: TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
710: TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
711: VecDestroy(&dummy);
712: (*tao->ops->convergencetest)(tao,tao->cnvP);
713: if (tao->reason) {
714: SNESSetConvergedReason(pdipm->snes,SNES_CONVERGED_FNORM_ABS);
715: }
717: while (tao->reason == TAO_CONTINUE_ITERATING) {
718: SNESConvergedReason reason;
719: SNESSolve(pdipm->snes,NULL,pdipm->X);
721: /* Check SNES convergence */
722: SNESGetConvergedReason(pdipm->snes,&reason);
723: if (reason < 0) {
724: PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes),"SNES solve did not converged due to reason %D\n",reason);
725: }
727: /* Check TAO convergence */
728: if (PetscIsInfOrNanReal(pdipm->obj)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"User-provided compute function generated Inf or NaN");
729: }
730: return(0);
731: }
733: /*
734: TaoSetup_PDIPM - Sets up tao and pdipm
736: Input Parameter:
737: tao - TAO object
739: Output: pdipm - initialized object
740: */
741: PetscErrorCode TaoSetup_PDIPM(Tao tao)
742: {
743: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
745: MPI_Comm comm;
746: PetscMPIInt rank,size;
747: PetscInt row,col,Jcrstart,Jcrend,k,tmp,nc,proc,*nh_all,*ng_all;
748: PetscInt offset,*xa,*xb,i,j,rstart,rend;
749: PetscScalar one=1.0,neg_one=-1.0,*Xarr;
750: const PetscInt *cols,*rranges,*cranges,*aj,*ranges;
751: const PetscScalar *aa;
752: Mat J,jac_equality_trans,jac_inequality_trans;
753: Mat Jce_xfixed_trans,Jci_xb_trans;
754: PetscInt *dnz,*onz,rjstart,nx_all,*nce_all,*Jranges,cols1[2];
757: PetscObjectGetComm((PetscObject)tao,&comm);
758: MPI_Comm_rank(comm,&rank);
759: MPI_Comm_size(comm,&size);
761: /* (1) Setup Bounds and create Tao vectors */
762: TaoPDIPMSetUpBounds(tao);
764: if (!tao->gradient) {
765: VecDuplicate(tao->solution,&tao->gradient);
766: VecDuplicate(tao->solution,&tao->stepdirection);
767: }
769: /* (2) Get sizes */
770: /* Size of vector x - This is set by TaoSetInitialVector */
771: VecGetSize(tao->solution,&pdipm->Nx);
772: VecGetLocalSize(tao->solution,&pdipm->nx);
774: /* Size of equality constraints and vectors */
775: if (tao->constraints_equality) {
776: VecGetSize(tao->constraints_equality,&pdipm->Ng);
777: VecGetLocalSize(tao->constraints_equality,&pdipm->ng);
778: } else {
779: pdipm->ng = pdipm->Ng = 0;
780: }
782: pdipm->nce = pdipm->ng + pdipm->nxfixed;
783: pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;
785: /* Size of inequality constraints and vectors */
786: if (tao->constraints_inequality) {
787: VecGetSize(tao->constraints_inequality,&pdipm->Nh);
788: VecGetLocalSize(tao->constraints_inequality,&pdipm->nh);
789: } else {
790: pdipm->nh = pdipm->Nh = 0;
791: }
793: pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2*pdipm->nxbox;
794: pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2*pdipm->Nxbox;
796: /* Full size of the KKT system to be solved */
797: pdipm->n = pdipm->nx + pdipm->nce + 2*pdipm->nci;
798: pdipm->N = pdipm->Nx + pdipm->Nce + 2*pdipm->Nci;
800: /* list below to TaoView_PDIPM()? */
801: /* PetscPrintf(PETSC_COMM_SELF,"[%d] nce %d = ng %d + nxfixed %d\n",rank,pdipm->nce,pdipm->ng,pdipm->nxfixed); */
802: /* PetscPrintf(PETSC_COMM_SELF,"[%d] nci %d = nh %d + nxlb %d + nxub %d + 2*nxbox %d\n",rank,pdipm->nci,pdipm->nh,pdipm->nxlb,pdipm->nxub,pdipm->nxbox); */
803: /* PetscPrintf(PETSC_COMM_SELF,"[%d] n %d = nx %d + nce %d + 2*nci %d\n",rank,pdipm->n,pdipm->nx,pdipm->nce,pdipm->nci); */
805: /* (3) Offsets for subvectors */
806: pdipm->off_lambdae = pdipm->nx;
807: pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
808: pdipm->off_z = pdipm->off_lambdai + pdipm->nci;
810: /* (4) Create vectors and subvectors */
811: /* Ce and Ci vectors */
812: VecCreate(comm,&pdipm->ce);
813: VecSetSizes(pdipm->ce,pdipm->nce,pdipm->Nce);
814: VecSetFromOptions(pdipm->ce);
816: VecCreate(comm,&pdipm->ci);
817: VecSetSizes(pdipm->ci,pdipm->nci,pdipm->Nci);
818: VecSetFromOptions(pdipm->ci);
820: /* X=[x; lambdae; lambdai; z] for the big KKT system */
821: VecCreate(comm,&pdipm->X);
822: VecSetSizes(pdipm->X,pdipm->n,pdipm->N);
823: VecSetFromOptions(pdipm->X);
825: /* Subvectors; they share local arrays with X */
826: VecGetArray(pdipm->X,&Xarr);
827: /* x shares local array with X.x */
828: if (pdipm->Nx) {
829: VecCreateMPIWithArray(comm,1,pdipm->nx,pdipm->Nx,Xarr,&pdipm->x);
830: }
832: /* lambdae shares local array with X.lambdae */
833: if (pdipm->Nce) {
834: VecCreateMPIWithArray(comm,1,pdipm->nce,pdipm->Nce,Xarr+pdipm->off_lambdae,&pdipm->lambdae);
835: }
837: /* tao->DE shares local array with X.lambdae_g */
838: if (pdipm->Ng) {
839: VecCreateMPIWithArray(comm,1,pdipm->ng,pdipm->Ng,Xarr+pdipm->off_lambdae,&tao->DE);
841: VecCreate(comm,&pdipm->lambdae_xfixed);
842: VecSetSizes(pdipm->lambdae_xfixed,pdipm->nxfixed,PETSC_DECIDE);
843: VecSetFromOptions(pdipm->lambdae_xfixed);
844: }
846: if (pdipm->Nci) {
847: /* lambdai shares local array with X.lambdai */
848: VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_lambdai,&pdipm->lambdai);
850: /* z for slack variables; it shares local array with X.z */
851: VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_z,&pdipm->z);
852: }
854: /* tao->DI which shares local array with X.lambdai_h */
855: if (pdipm->Nh) {
856: VecCreateMPIWithArray(comm,1,pdipm->nh,pdipm->Nh,Xarr+pdipm->off_lambdai,&tao->DI);
857: }
859: VecCreate(comm,&pdipm->lambdai_xb);
860: VecSetSizes(pdipm->lambdai_xb,(pdipm->nci - pdipm->nh),PETSC_DECIDE);
861: VecSetFromOptions(pdipm->lambdai_xb);
863: VecRestoreArray(pdipm->X,&Xarr);
865: /* (5) Create Jacobians Jce_xfixed and Jci */
866: /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
867: if (pdipm->Nxfixed) {
868: /* Create Jce_xfixed */
869: MatCreate(comm,&pdipm->Jce_xfixed);
870: MatSetSizes(pdipm->Jce_xfixed,pdipm->nxfixed,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
871: MatSetFromOptions(pdipm->Jce_xfixed);
872: MatSeqAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL);
873: MatMPIAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL,1,NULL);
875: MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,&Jcrend);
876: ISGetIndices(pdipm->isxfixed,&cols);
877: k = 0;
878: for (row = Jcrstart; row < Jcrend; row++) {
879: MatSetValues(pdipm->Jce_xfixed,1,&row,1,cols+k,&one,INSERT_VALUES);
880: k++;
881: }
882: ISRestoreIndices(pdipm->isxfixed, &cols);
883: MatAssemblyBegin(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
884: MatAssemblyEnd(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
885: }
887: /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
888: MatCreate(comm,&pdipm->Jci_xb);
889: MatSetSizes(pdipm->Jci_xb,pdipm->nci-pdipm->nh,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
890: MatSetFromOptions(pdipm->Jci_xb);
891: MatSeqAIJSetPreallocation(pdipm->Jci_xb,1,NULL);
892: MatMPIAIJSetPreallocation(pdipm->Jci_xb,1,NULL,1,NULL);
894: MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,&Jcrend);
895: offset = Jcrstart;
896: if (pdipm->Nxub) {
897: /* Add xub to Jci_xb */
898: ISGetIndices(pdipm->isxub,&cols);
899: k = 0;
900: for (row = offset; row < offset + pdipm->nxub; row++) {
901: MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
902: k++;
903: }
904: ISRestoreIndices(pdipm->isxub, &cols);
905: }
907: if (pdipm->Nxlb) {
908: /* Add xlb to Jci_xb */
909: ISGetIndices(pdipm->isxlb,&cols);
910: k = 0;
911: offset += pdipm->nxub;
912: for (row = offset; row < offset + pdipm->nxlb; row++) {
913: MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&one,INSERT_VALUES);
914: k++;
915: }
916: ISRestoreIndices(pdipm->isxlb, &cols);
917: }
919: /* Add xbox to Jci_xb */
920: if (pdipm->Nxbox) {
921: ISGetIndices(pdipm->isxbox,&cols);
922: k = 0;
923: offset += pdipm->nxlb;
924: for (row = offset; row < offset + pdipm->nxbox; row++) {
925: MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
926: tmp = row + pdipm->nxbox;
927: MatSetValues(pdipm->Jci_xb,1,&tmp,1,cols+k,&one,INSERT_VALUES);
928: k++;
929: }
930: ISRestoreIndices(pdipm->isxbox, &cols);
931: }
933: MatAssemblyBegin(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
934: MatAssemblyEnd(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
935: /* MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD); */
937: /* (6) Set up ISs for PC Fieldsplit */
938: if (pdipm->solve_reduced_kkt) {
939: PetscMalloc2(pdipm->nx+pdipm->nce,&xa,2*pdipm->nci,&xb);
940: for (i=0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
941: for (i=0; i < 2*pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;
943: ISCreateGeneral(comm,pdipm->nx+pdipm->nce,xa,PETSC_OWN_POINTER,&pdipm->is1);
944: ISCreateGeneral(comm,2*pdipm->nci,xb,PETSC_OWN_POINTER,&pdipm->is2);
945: }
947: /* (7) Gather offsets from all processes */
948: PetscMalloc1(size,&pdipm->nce_all);
950: /* Get rstart of KKT matrix */
951: MPI_Scan(&pdipm->n,&rstart,1,MPIU_INT,MPI_SUM,comm);
952: rstart -= pdipm->n;
954: MPI_Allgather(&pdipm->nce,1,MPIU_INT,pdipm->nce_all,1,MPIU_INT,comm);
956: PetscMalloc3(size,&ng_all,size,&nh_all,size,&Jranges);
957: MPI_Allgather(&rstart,1,MPIU_INT,Jranges,1,MPIU_INT,comm);
958: MPI_Allgather(&pdipm->nh,1,MPIU_INT,nh_all,1,MPIU_INT,comm);
959: MPI_Allgather(&pdipm->ng,1,MPIU_INT,ng_all,1,MPIU_INT,comm);
961: MatGetOwnershipRanges(tao->hessian,&rranges);
962: MatGetOwnershipRangesColumn(tao->hessian,&cranges);
964: if (pdipm->Ng) {
965: TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);
966: MatTranspose(tao->jacobian_equality,MAT_INITIAL_MATRIX,&pdipm->jac_equality_trans);
967: }
968: if (pdipm->Nh) {
969: TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);
970: MatTranspose(tao->jacobian_inequality,MAT_INITIAL_MATRIX,&pdipm->jac_inequality_trans);
971: }
973: /* Count dnz,onz for preallocation of KKT matrix */
974: jac_equality_trans = pdipm->jac_equality_trans;
975: jac_inequality_trans = pdipm->jac_inequality_trans;
976: nce_all = pdipm->nce_all;
978: if (pdipm->Nxfixed) {
979: MatTranspose(pdipm->Jce_xfixed,MAT_INITIAL_MATRIX,&Jce_xfixed_trans);
980: }
981: MatTranspose(pdipm->Jci_xb,MAT_INITIAL_MATRIX,&Jci_xb_trans);
983: MatPreallocateInitialize(comm,pdipm->n,pdipm->n,dnz,onz);
985: /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
986: TaoPDIPMEvaluateFunctionsAndJacobians(tao,pdipm->x);
987: TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
989: /* Insert tao->hessian */
990: MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
991: for (i=0; i<pdipm->nx; i++){
992: row = rstart + i;
994: MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
995: proc = 0;
996: for (j=0; j < nc; j++) {
997: while (aj[j] >= cranges[proc+1]) proc++;
998: col = aj[j] - cranges[proc] + Jranges[proc];
999: MatPreallocateSet(row,1,&col,dnz,onz);
1000: }
1001: MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
1003: if (pdipm->ng) {
1004: /* Insert grad g' */
1005: MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
1006: MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
1007: proc = 0;
1008: for (j=0; j < nc; j++) {
1009: /* find row ownership of */
1010: while (aj[j] >= ranges[proc+1]) proc++;
1011: nx_all = rranges[proc+1] - rranges[proc];
1012: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
1013: MatPreallocateSet(row,1,&col,dnz,onz);
1014: }
1015: MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
1016: }
1018: /* Insert Jce_xfixed^T' */
1019: if (pdipm->nxfixed) {
1020: MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
1021: MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);
1022: proc = 0;
1023: for (j=0; j < nc; j++) {
1024: /* find row ownership of */
1025: while (aj[j] >= ranges[proc+1]) proc++;
1026: nx_all = rranges[proc+1] - rranges[proc];
1027: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
1028: MatPreallocateSet(row,1,&col,dnz,onz);
1029: }
1030: MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
1031: }
1033: if (pdipm->nh) {
1034: /* Insert -grad h' */
1035: MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
1036: MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
1037: proc = 0;
1038: for (j=0; j < nc; j++) {
1039: /* find row ownership of */
1040: while (aj[j] >= ranges[proc+1]) proc++;
1041: nx_all = rranges[proc+1] - rranges[proc];
1042: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
1043: MatPreallocateSet(row,1,&col,dnz,onz);
1044: }
1045: MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
1046: }
1048: /* Insert Jci_xb^T' */
1049: MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
1050: MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);
1051: proc = 0;
1052: for (j=0; j < nc; j++) {
1053: /* find row ownership of */
1054: while (aj[j] >= ranges[proc+1]) proc++;
1055: nx_all = rranges[proc+1] - rranges[proc];
1056: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
1057: MatPreallocateSet(row,1,&col,dnz,onz);
1058: }
1059: MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
1060: }
1062: /* 2nd Row block of KKT matrix: [grad Ce, 0, 0, 0] */
1063: if (pdipm->Ng) {
1064: MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
1065: for (i=0; i < pdipm->ng; i++){
1066: row = rstart + pdipm->off_lambdae + i;
1068: MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
1069: proc = 0;
1070: for (j=0; j < nc; j++) {
1071: while (aj[j] >= cranges[proc+1]) proc++;
1072: col = aj[j] - cranges[proc] + Jranges[proc];
1073: MatPreallocateSet(row,1,&col,dnz,onz); /* grad g */
1074: }
1075: MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
1076: }
1077: }
1078: /* Jce_xfixed */
1079: if (pdipm->Nxfixed) {
1080: MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
1081: for (i=0; i < (pdipm->nce - pdipm->ng); i++){
1082: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1084: MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
1085: if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
1087: proc = 0;
1088: j = 0;
1089: while (cols[j] >= cranges[proc+1]) proc++;
1090: col = cols[j] - cranges[proc] + Jranges[proc];
1091: MatPreallocateSet(row,1,&col,dnz,onz);
1092: MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
1093: }
1094: }
1096: /* 3rd Row block of KKT matrix: [ gradCi, 0, 0, -I] */
1097: if (pdipm->Nh) {
1098: MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
1099: for (i=0; i < pdipm->nh; i++){
1100: row = rstart + pdipm->off_lambdai + i;
1102: MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
1103: proc = 0;
1104: for (j=0; j < nc; j++) {
1105: while (aj[j] >= cranges[proc+1]) proc++;
1106: col = aj[j] - cranges[proc] + Jranges[proc];
1107: MatPreallocateSet(row,1,&col,dnz,onz); /* grad h */
1108: }
1109: MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
1110: }
1111: /* -I */
1112: for (i=0; i < pdipm->nh; i++){
1113: row = rstart + pdipm->off_lambdai + i;
1114: col = rstart + pdipm->off_z + i;
1115: MatPreallocateSet(row,1,&col,dnz,onz);
1116: }
1117: }
1119: /* Jci_xb */
1120: MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
1121: for (i=0; i < (pdipm->nci - pdipm->nh); i++){
1122: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1124: MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
1125: if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
1126: proc = 0;
1127: for (j=0; j < nc; j++) {
1128: while (cols[j] >= cranges[proc+1]) proc++;
1129: col = cols[j] - cranges[proc] + Jranges[proc];
1130: MatPreallocateSet(row,1,&col,dnz,onz);
1131: }
1132: MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
1133: /* -I */
1134: col = rstart + pdipm->off_z + pdipm->nh + i;
1135: MatPreallocateSet(row,1,&col,dnz,onz);
1136: }
1138: /* 4-th Row block of KKT matrix: Z and Ci */
1139: for (i=0; i < pdipm->nci; i++) {
1140: row = rstart + pdipm->off_z + i;
1141: cols1[0] = rstart + pdipm->off_lambdai + i;
1142: cols1[1] = row;
1143: MatPreallocateSet(row,2,cols1,dnz,onz);
1144: }
1146: /* diagonal entry */
1147: for (i=0; i<pdipm->n; i++) dnz[i]++; /* diagonal entry */
1149: /* Create KKT matrix */
1150: MatCreate(comm,&J);
1151: MatSetSizes(J,pdipm->n,pdipm->n,PETSC_DECIDE,PETSC_DECIDE);
1152: MatSetFromOptions(J);
1153: MatSeqAIJSetPreallocation(J,0,dnz);
1154: MatMPIAIJSetPreallocation(J,0,dnz,0,onz);
1155: /* MatSetOption(J,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE); */
1156: MatPreallocateFinalize(dnz,onz);
1157: pdipm->K = J;
1159: /* (8) Set up nonlinear solver SNES */
1160: SNESSetFunction(pdipm->snes,NULL,TaoSNESFunction_PDIPM,(void*)tao);
1161: SNESSetJacobian(pdipm->snes,J,J,TaoSNESJacobian_PDIPM,(void*)tao);
1163: if (pdipm->solve_reduced_kkt) {
1164: PC pc;
1165: KSPGetPC(tao->ksp,&pc);
1166: PCSetType(pc,PCFIELDSPLIT);
1167: PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);
1168: PCFieldSplitSetIS(pc,"2",pdipm->is2);
1169: PCFieldSplitSetIS(pc,"1",pdipm->is1);
1170: }
1171: SNESSetFromOptions(pdipm->snes);
1173: /* (9) Insert constant entries to K */
1174: /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
1175: MatGetOwnershipRange(J,&rstart,&rend);
1176: for (i=rstart; i<rend; i++){
1177: MatSetValue(J,i,i,0.0,INSERT_VALUES);
1178: }
1180: /* Row block of K: [ grad Ce, 0, 0, 0] */
1181: if (pdipm->Nxfixed) {
1182: MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
1183: for (i=0; i < (pdipm->nce - pdipm->ng); i++){
1184: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1186: MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
1187: proc = 0;
1188: for (j=0; j < nc; j++) {
1189: while (cols[j] >= cranges[proc+1]) proc++;
1190: col = cols[j] - cranges[proc] + Jranges[proc];
1191: MatSetValue(J,row,col,aa[j],INSERT_VALUES); /* grad Ce */
1192: MatSetValue(J,col,row,aa[j],INSERT_VALUES); /* grad Ce' */
1193: }
1194: MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
1195: }
1196: }
1198: /* Row block of K: [ grad Ci, 0, 0, -I] */
1199: MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
1200: for (i=0; i < pdipm->nci - pdipm->nh; i++){
1201: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1203: MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
1204: proc = 0;
1205: for (j=0; j < nc; j++) {
1206: while (cols[j] >= cranges[proc+1]) proc++;
1207: col = cols[j] - cranges[proc] + Jranges[proc];
1208: MatSetValue(J,col,row,-aa[j],INSERT_VALUES);
1209: MatSetValue(J,row,col,aa[j],INSERT_VALUES);
1210: }
1211: MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
1213: col = rstart + pdipm->off_z + pdipm->nh + i;
1214: MatSetValue(J,row,col,-1,INSERT_VALUES);
1215: }
1217: for (i=0; i < pdipm->nh; i++){
1218: row = rstart + pdipm->off_lambdai + i;
1219: col = rstart + pdipm->off_z + i;
1220: MatSetValue(J,row,col,-1,INSERT_VALUES);
1221: }
1223: if (pdipm->Nxfixed) {
1224: MatDestroy(&Jce_xfixed_trans);
1225: }
1226: MatDestroy(&Jci_xb_trans);
1227: PetscFree3(ng_all,nh_all,Jranges);
1228: return(0);
1229: }
1231: /*
1232: TaoDestroy_PDIPM - Destroys the pdipm object
1234: Input:
1235: full pdipm
1237: Output:
1238: Destroyed pdipm
1239: */
1240: PetscErrorCode TaoDestroy_PDIPM(Tao tao)
1241: {
1242: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
1246: /* Freeing Vectors assocaiated with KKT (X) */
1247: VecDestroy(&pdipm->x); /* Solution x */
1248: VecDestroy(&pdipm->lambdae); /* Equality constraints lagrangian multiplier*/
1249: VecDestroy(&pdipm->lambdai); /* Inequality constraints lagrangian multiplier*/
1250: VecDestroy(&pdipm->z); /* Slack variables */
1251: VecDestroy(&pdipm->X); /* Big KKT system vector [x; lambdae; lambdai; z] */
1253: /* work vectors */
1254: VecDestroy(&pdipm->lambdae_xfixed);
1255: VecDestroy(&pdipm->lambdai_xb);
1257: /* Legrangian equality and inequality Vec */
1258: VecDestroy(&pdipm->ce); /* Vec of equality constraints */
1259: VecDestroy(&pdipm->ci); /* Vec of inequality constraints */
1261: /* Matrices */
1262: MatDestroy(&pdipm->Jce_xfixed);
1263: MatDestroy(&pdipm->Jci_xb); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
1264: MatDestroy(&pdipm->K);
1266: /* Index Sets */
1267: if (pdipm->Nxub) {
1268: ISDestroy(&pdipm->isxub); /* Finite upper bound only -inf < x < ub */
1269: }
1271: if (pdipm->Nxlb) {
1272: ISDestroy(&pdipm->isxlb); /* Finite lower bound only lb <= x < inf */
1273: }
1275: if (pdipm->Nxfixed) {
1276: ISDestroy(&pdipm->isxfixed); /* Fixed variables lb = x = ub */
1277: }
1279: if (pdipm->Nxbox) {
1280: ISDestroy(&pdipm->isxbox); /* Boxed variables lb <= x <= ub */
1281: }
1283: if (pdipm->Nxfree) {
1284: ISDestroy(&pdipm->isxfree); /* Free variables -inf <= x <= inf */
1285: }
1287: if (pdipm->solve_reduced_kkt) {
1288: ISDestroy(&pdipm->is1);
1289: ISDestroy(&pdipm->is2);
1290: }
1292: /* SNES */
1293: SNESDestroy(&pdipm->snes); /* Nonlinear solver */
1294: PetscFree(pdipm->nce_all);
1295: MatDestroy(&pdipm->jac_equality_trans);
1296: MatDestroy(&pdipm->jac_inequality_trans);
1298: /* Destroy pdipm */
1299: PetscFree(tao->data); /* Holding locations of pdipm */
1301: /* Destroy Dual */
1302: VecDestroy(&tao->DE); /* equality dual */
1303: VecDestroy(&tao->DI); /* dinequality dual */
1304: return(0);
1305: }
1307: PetscErrorCode TaoSetFromOptions_PDIPM(PetscOptionItems *PetscOptionsObject,Tao tao)
1308: {
1309: TAO_PDIPM *pdipm = (TAO_PDIPM*)tao->data;
1313: PetscOptionsHead(PetscOptionsObject,"PDIPM method for constrained optimization");
1314: PetscOptionsReal("-tao_pdipm_push_init_slack","parameter to push initial slack variables away from bounds",NULL,pdipm->push_init_slack,&pdipm->push_init_slack,NULL);
1315: PetscOptionsReal("-tao_pdipm_push_init_lambdai","parameter to push initial (inequality) dual variables away from bounds",NULL,pdipm->push_init_lambdai,&pdipm->push_init_lambdai,NULL);
1316: PetscOptionsBool("-tao_pdipm_solve_reduced_kkt","Solve reduced KKT system using Schur-complement",NULL,pdipm->solve_reduced_kkt,&pdipm->solve_reduced_kkt,NULL);
1317: PetscOptionsReal("-tao_pdipm_mu_update_factor","Update scalar for barrier parameter (mu) update",NULL,pdipm->mu_update_factor,&pdipm->mu_update_factor,NULL);
1318: PetscOptionsTail();
1319: return(0);
1320: }
1322: /*MC
1323: TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.
1325: Option Database Keys:
1326: + -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
1327: . -tao_pdipm_push_init_slack - parameter to push initial slack variables away from bounds (> 0)
1328: - -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)
1330: Level: beginner
1331: M*/
1332: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
1333: {
1334: TAO_PDIPM *pdipm;
1338: tao->ops->setup = TaoSetup_PDIPM;
1339: tao->ops->solve = TaoSolve_PDIPM;
1340: tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
1341: tao->ops->destroy = TaoDestroy_PDIPM;
1343: PetscNewLog(tao,&pdipm);
1344: tao->data = (void*)pdipm;
1346: pdipm->nx = pdipm->Nx = 0;
1347: pdipm->nxfixed = pdipm->Nxfixed = 0;
1348: pdipm->nxlb = pdipm->Nxlb = 0;
1349: pdipm->nxub = pdipm->Nxub = 0;
1350: pdipm->nxbox = pdipm->Nxbox = 0;
1351: pdipm->nxfree = pdipm->Nxfree = 0;
1353: pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
1354: pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
1355: pdipm->n = pdipm->N = 0;
1356: pdipm->mu = 1.0;
1357: pdipm->mu_update_factor = 0.1;
1359: pdipm->push_init_slack = 1.0;
1360: pdipm->push_init_lambdai = 1.0;
1361: pdipm->solve_reduced_kkt = PETSC_FALSE;
1363: /* Override default settings (unless already changed) */
1364: if (!tao->max_it_changed) tao->max_it = 200;
1365: if (!tao->max_funcs_changed) tao->max_funcs = 500;
1367: SNESCreate(((PetscObject)tao)->comm,&pdipm->snes);
1368: SNESSetOptionsPrefix(pdipm->snes,tao->hdr.prefix);
1369: SNESGetKSP(pdipm->snes,&tao->ksp);
1370: PetscObjectReference((PetscObject)tao->ksp);
1371: return(0);
1372: }