Actual source code: pounders.c
petsc-3.7.5 2017-01-01
1: #include <../src/tao/leastsquares/impls/pounders/pounders.h>
5: static PetscErrorCode pounders_h(Tao subtao, Vec v, Mat H, Mat Hpre, void *ctx)
6: {
8: return(0);
9: }
12: static PetscErrorCode pounders_fg(Tao subtao, Vec x, PetscReal *f, Vec g, void *ctx)
13: {
14: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)ctx;
15: PetscReal d1,d2;
19: /* g = A*x (add b later)*/
20: MatMult(mfqP->subH,x,g);
22: /* f = 1/2 * x'*(Ax) + b'*x */
23: VecDot(x,g,&d1);
24: VecDot(mfqP->subb,x,&d2);
25: *f = 0.5 *d1 + d2;
27: /* now g = g + b */
28: VecAXPY(g, 1.0, mfqP->subb);
29: return(0);
30: }
33: static PetscErrorCode pounders_feval(Tao tao, Vec x, Vec F, PetscReal *fsum)
34: {
36: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
37: PetscInt i,row,col;
38: PetscReal fr,fc;
40: TaoComputeSeparableObjective(tao,x,F);
41: if (tao->sep_weights_v) {
42: VecPointwiseMult(mfqP->workfvec,tao->sep_weights_v,F);
43: VecNorm(mfqP->workfvec,NORM_2,fsum);
44: *fsum*=(*fsum);
45: } else if (tao->sep_weights_w) {
46: *fsum=0;
47: for (i=0;i<tao->sep_weights_n;i++) {
48: row=tao->sep_weights_rows[i];
49: col=tao->sep_weights_cols[i];
50: VecGetValues(F,1,&row,&fr);
51: VecGetValues(F,1,&col,&fc);
52: *fsum += tao->sep_weights_w[i]*fc*fr;
53: }
54: } else {
55: VecNorm(F,NORM_2,fsum);
56: *fsum*=(*fsum);
57: }
58: if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
59: return(0);
60: }
64: PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
65: {
67: #if defined(PETSC_USE_REAL_SINGLE)
68: PetscReal atol=1.0e-5;
69: #else
70: PetscReal atol=1.0e-10;
71: #endif
72: PetscInt info,its;
73: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
76: if (! mfqP->usegqt) {
77: PetscReal maxval;
78: PetscInt i,j;
80: VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
81: VecAssemblyBegin(mfqP->subb);
82: VecAssemblyEnd(mfqP->subb);
84: VecSet(mfqP->subx,0.0);
86: VecSet(mfqP->subndel,-mfqP->delta);
87: VecSet(mfqP->subpdel,mfqP->delta);
89: for (i=0;i<mfqP->n;i++) {
90: for (j=i;j<mfqP->n;j++) {
91: mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
92: }
93: }
94: MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);
95: MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);
96: MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);
98: TaoResetStatistics(mfqP->subtao);
99: TaoSetTolerances(mfqP->subtao,*gnorm,*gnorm,PETSC_DEFAULT);
100: /* enforce bound constraints -- experimental */
101: if (tao->XU && tao->XL) {
102: VecCopy(tao->XU,mfqP->subxu);
103: VecAXPY(mfqP->subxu,-1.0,tao->solution);
104: VecScale(mfqP->subxu,1.0/mfqP->delta);
105: VecCopy(tao->XL,mfqP->subxl);
106: VecAXPY(mfqP->subxl,-1.0,tao->solution);
107: VecScale(mfqP->subxl,1.0/mfqP->delta);
109: VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);
110: VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);
111: } else {
112: VecCopy(mfqP->subpdel,mfqP->subxu);
113: VecCopy(mfqP->subndel,mfqP->subxl);
114: }
115: /* Make sure xu > xl */
116: VecCopy(mfqP->subxl,mfqP->subpdel);
117: VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
118: VecMax(mfqP->subpdel,NULL,&maxval);
119: if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
120: /* Make sure xu > tao->solution > xl */
121: VecCopy(mfqP->subxl,mfqP->subpdel);
122: VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
123: VecMax(mfqP->subpdel,NULL,&maxval);
124: if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");
126: VecCopy(mfqP->subx,mfqP->subpdel);
127: VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
128: VecMax(mfqP->subpdel,NULL,&maxval);
129: if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");
131: TaoSolve(mfqP->subtao);
132: TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);
134: /* test bounds post-solution*/
135: VecCopy(mfqP->subxl,mfqP->subpdel);
136: VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);
137: VecMax(mfqP->subpdel,NULL,&maxval);
138: if (maxval > 1e-5) {
139: PetscInfo(tao,"subproblem solution < lower bound\n");
140: tao->reason = TAO_DIVERGED_TR_REDUCTION;
141: }
143: VecCopy(mfqP->subx,mfqP->subpdel);
144: VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);
145: VecMax(mfqP->subpdel,NULL,&maxval);
146: if (maxval > 1e-5) {
147: PetscInfo(tao,"subproblem solution > upper bound\n");
148: tao->reason = TAO_DIVERGED_TR_REDUCTION;
149: }
150: } else {
151: gqt(mfqP->n,mfqP->Hres,mfqP->n,mfqP->Gres,1.0,mfqP->gqt_rtol,atol,mfqP->gqt_maxits,gnorm,qmin,mfqP->Xsubproblem,&info,&its,mfqP->work,mfqP->work2, mfqP->work3);
152: }
153: *qmin *= -1;
154: return(0);
155: }
159: static PetscErrorCode pounders_update_res(Tao tao)
160: {
161: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
162: PetscInt i,row,col;
163: PetscBLASInt blasn=mfqP->n,blasn2=blasn*blasn,blasm=mfqP->m,ione=1;
164: PetscReal zero=0.0,one=1.0,wii,factor;
168: for (i=0;i<mfqP->n;i++) {
169: mfqP->Gres[i]=0;
170: }
171: for (i=0;i<mfqP->n*mfqP->n;i++) {
172: mfqP->Hres[i]=0;
173: }
175: /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
176: if (tao->sep_weights_v) {
177: /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
178: for (i=0;i<mfqP->m;i++) {
179: VecGetValues(tao->sep_weights_v,1,&i,&factor);
180: factor=factor*mfqP->C[i];
181: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
182: }
183: } else if (tao->sep_weights_n) {
184: /* general case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
185: for (i=0;i<tao->sep_weights_n;i++) {
186: row=tao->sep_weights_rows[i];
187: col=tao->sep_weights_cols[i];
189: factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
190: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
191: factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
192: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
193: }
194: } else {
195: /* default: Gres= sum_i[cigi] = G*c' */
196: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
197: }
199: /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
200: if (tao->sep_weights_v) {
201: /* vector(diagonal weights) Hres = sum_i(wii*(ci*Hi + gi * gi' )*/
202: for (i=0;i<mfqP->m;i++) {
203: VecGetValues(tao->sep_weights_v,1,&i,&wii);
204: if (tao->niter>1) {
205: factor=wii*mfqP->C[i];
206: /* add wii * ci * Hi */
207: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
208: }
209: /* add wii * gi * gi' */
210: PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&wii,&mfqP->Fdiff[blasn*i],&blasn,&mfqP->Fdiff[blasn*i],&blasn,&one,mfqP->Hres,&blasn));
211: }
212: } else if (tao->sep_weights_w) {
213: /* .5 * sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
214: for (i=0;i<tao->sep_weights_n;i++) {
215: row=tao->sep_weights_rows[i];
216: col=tao->sep_weights_cols[i];
217: factor=tao->sep_weights_w[i]/2.0;
218: /* add wij * gi gj' + wij * gj gi' */
219: PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*row],&blasn,&mfqP->Fdiff[blasn*col],&blasn,&one,mfqP->Hres,&blasn));
220: PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*col],&blasn,&mfqP->Fdiff[blasn*row],&blasn,&one,mfqP->Hres,&blasn));
221: }
222: if (tao->niter > 1) {
223: for (i=0;i<tao->sep_weights_n;i++) {
224: row=tao->sep_weights_rows[i];
225: col=tao->sep_weights_cols[i];
227: /* add wij*cj*Hi */
228: factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
229: PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[row],&blasn2,mfqP->Hres,&ione));
231: /* add wij*ci*Hj */
232: factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
233: PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasn2,mfqP->Hres,&ione));
234: }
235: }
236: } else {
237: /* Hres = G*G' + 0.5 sum {F(xkin,i)*H(:,:,i)} */
238: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff, &blasn,&zero,mfqP->Hres,&blasn));
240: /* sum(F(xkin,i)*H(:,:,i)) */
241: if (tao->niter>1) {
242: for (i=0;i<mfqP->m;i++) {
243: factor = mfqP->C[i];
244: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
245: }
246: }
247: }
249: return(0);
250: }
253: PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
254: {
255: /* Phi = .5*[x(1)^2 sqrt(2)*x(1)*x(2) ... sqrt(2)*x(1)*x(n) ... x(2)^2 sqrt(2)*x(2)*x(3) .. x(n)^2] */
256: PetscInt i,j,k;
257: PetscReal sqrt2 = PetscSqrtReal(2.0);
260: j=0;
261: for (i=0;i<n;i++) {
262: phi[j] = 0.5 * x[i]*x[i];
263: j++;
264: for (k=i+1;k<n;k++) {
265: phi[j] = x[i]*x[k]/sqrt2;
266: j++;
267: }
268: }
269: return(0);
270: }
274: PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
275: {
276: /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
277: that satisfies the interpolation conditions Q(X[:,j]) = f(j)
278: for j=1,...,m and with a Hessian matrix of least Frobenius norm */
280: /* NB --we are ignoring c */
281: PetscInt i,j,k,num,np = mfqP->nmodelpoints;
282: PetscReal one = 1.0,zero=0.0,negone=-1.0;
283: PetscBLASInt blasnpmax = mfqP->npmax;
284: PetscBLASInt blasnplus1 = mfqP->n+1;
285: PetscBLASInt blasnp = np;
286: PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
287: PetscBLASInt blasint2 = np - mfqP->n-1;
288: PetscBLASInt info,ione=1;
289: PetscReal sqrt2 = PetscSqrtReal(2.0);
292: for (i=0;i<mfqP->n*mfqP->m;i++) {
293: mfqP->Gdel[i] = 0;
294: }
295: for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
296: mfqP->Hdel[i] = 0;
297: }
299: /* factor M */
300: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&blasnplus1,&blasnp,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&info));
301: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrf returned with value %d\n",info);
303: if (np == mfqP->n+1) {
304: for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
305: mfqP->omega[i]=0.0;
306: }
307: for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
308: mfqP->beta[i]=0.0;
309: }
310: } else {
311: /* Let Ltmp = (L'*L) */
312: PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&blasint2,&blasint2,&blasint,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&mfqP->L[(mfqP->n+1)*blasint],&blasint,&zero,mfqP->L_tmp,&blasint));
314: /* factor Ltmp */
315: PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
316: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
317: }
319: for (k=0;k<mfqP->m;k++) {
320: if (np != mfqP->n+1) {
321: /* Solve L'*L*Omega = Z' * RESk*/
322: PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasnp,&blasint2,&one,mfqP->Z,&blasnpmax,&mfqP->RES[mfqP->npmax*k],&ione,&zero,mfqP->omega,&ione));
323: PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&blasint2,&ione,mfqP->L_tmp,&blasint,mfqP->omega,&blasint2,&info));
324: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrs returned with value %d\n",info);
326: /* Beta = L*Omega */
327: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
328: }
330: /* solve M'*Alpha = RESk - N'*Beta */
331: PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasint,&blasnp,&negone,mfqP->N,&blasint,mfqP->beta,&ione,&one,&mfqP->RES[mfqP->npmax*k],&ione));
332: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&blasnplus1,&ione,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&mfqP->RES[mfqP->npmax*k],&blasnplus1,&info));
333: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrs returned with value %d\n",info);
335: /* Gdel(:,k) = Alpha(2:n+1) */
336: for (i=0;i<mfqP->n;i++) {
337: mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
338: }
340: /* Set Hdels */
341: num=0;
342: for (i=0;i<mfqP->n;i++) {
343: /* H[i,i,k] = Beta(num) */
344: mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
345: num++;
346: for (j=i+1;j<mfqP->n;j++) {
347: /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
348: mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
349: mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
350: num++;
351: }
352: }
353: }
354: return(0);
355: }
359: PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
360: {
361: /* Assumes mfqP->model_indices[0] is minimum index
362: Finishes adding points to mfqP->model_indices (up to npmax)
363: Computes L,Z,M,N
364: np is actual number of points in model (should equal npmax?) */
365: PetscInt point,i,j,offset;
366: PetscInt reject;
367: PetscBLASInt blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
368: const PetscReal *x;
369: PetscReal normd;
370: PetscErrorCode ierr;
373: /* Initialize M,N */
374: for (i=0;i<mfqP->n+1;i++) {
375: VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
376: mfqP->M[(mfqP->n+1)*i] = 1.0;
377: for (j=0;j<mfqP->n;j++) {
378: mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j] - mfqP->xmin[j]) / mfqP->delta;
379: }
380: VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);
381: phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);
382: }
384: /* Now we add points until we have npmax starting with the most recent ones */
385: point = mfqP->nHist-1;
386: mfqP->nmodelpoints = mfqP->n+1;
387: while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
388: /* Reject any points already in the model */
389: reject = 0;
390: for (j=0;j<mfqP->n+1;j++) {
391: if (point == mfqP->model_indices[j]) {
392: reject = 1;
393: break;
394: }
395: }
397: /* Reject if norm(d) >c2 */
398: if (!reject) {
399: VecCopy(mfqP->Xhist[point],mfqP->workxvec);
400: VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);
401: VecNorm(mfqP->workxvec,NORM_2,&normd);
402: normd /= mfqP->delta;
403: if (normd > mfqP->c2) {
404: reject =1;
405: }
406: }
407: if (reject){
408: point--;
409: continue;
410: }
412: VecGetArrayRead(mfqP->Xhist[point],&x);
413: mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
414: for (j=0;j<mfqP->n;j++) {
415: mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j] - mfqP->xmin[j]) / mfqP->delta;
416: }
417: VecRestoreArrayRead(mfqP->Xhist[point],&x);
418: phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);
420: /* Update QR factorization */
421: /* Copy M' to Q_tmp */
422: for (i=0;i<mfqP->n+1;i++) {
423: for (j=0;j<mfqP->npmax;j++) {
424: mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
425: }
426: }
427: blasnp = mfqP->nmodelpoints+1;
428: /* Q_tmp,R = qr(M') */
429: blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
430: PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
431: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);
433: /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
434: /* L = N*Qtmp */
435: blasint2 = mfqP->n * (mfqP->n+1) / 2;
436: /* Copy N to L_tmp */
437: for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
438: mfqP->L_tmp[i]= mfqP->N[i];
439: }
440: /* Copy L_save to L_tmp */
442: /* L_tmp = N*Qtmp' */
443: PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
444: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
446: /* Copy L_tmp to L_save */
447: for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
448: mfqP->L_save[i] = mfqP->L_tmp[i];
449: }
451: /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
452: blasint = mfqP->nmodelpoints - mfqP->n;
453: PetscFPTrapPush(PETSC_FP_TRAP_OFF);
454: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&blasint2,&blasint,&mfqP->L_tmp[(mfqP->n+1)*blasint2],&blasint2,mfqP->beta,mfqP->work,&blasn,mfqP->work,&blasn,mfqP->npmaxwork,&blasnmax,&info));
455: PetscFPTrapPop();
456: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);
458: if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
459: /* accept point */
460: mfqP->model_indices[mfqP->nmodelpoints] = point;
461: /* Copy Q_tmp to Q */
462: for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
463: mfqP->Q[i] = mfqP->Q_tmp[i];
464: }
465: for (i=0;i<mfqP->npmax;i++){
466: mfqP->tau[i] = mfqP->tau_tmp[i];
467: }
468: mfqP->nmodelpoints++;
469: blasnp = mfqP->nmodelpoints;
471: /* Copy L_save to L */
472: for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
473: mfqP->L[i] = mfqP->L_save[i];
474: }
475: }
476: point--;
477: }
479: blasnp = mfqP->nmodelpoints;
480: /* Copy Q(:,n+2:np) to Z */
481: /* First set Q_tmp to I */
482: for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
483: mfqP->Q_tmp[i] = 0.0;
484: }
485: for (i=0;i<mfqP->npmax;i++) {
486: mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
487: }
489: /* Q_tmp = I * Q */
490: PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
491: if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
493: /* Copy Q_tmp(:,n+2:np) to Z) */
494: offset = mfqP->npmax * (mfqP->n+1);
495: for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
496: mfqP->Z[i-offset] = mfqP->Q_tmp[i];
497: }
499: if (mfqP->nmodelpoints == mfqP->n + 1) {
500: /* Set L to I_{n+1} */
501: for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
502: mfqP->L[i] = 0.0;
503: }
504: for (i=0;i<mfqP->n;i++) {
505: mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
506: }
507: }
508: return(0);
509: }
513: /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
514: PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
515: {
519: /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
520: VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);
521: VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);
522: VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
523: VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
524: VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);
526: /* Project into feasible region */
527: if (tao->XU && tao->XL) {
528: VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);
529: }
531: /* Compute value of new vector */
532: VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);
533: CHKMEMQ;
534: pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);
536: /* Add new vector to model */
537: mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
538: mfqP->nmodelpoints++;
539: mfqP->nHist++;
540: return(0);
541: }
545: PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
546: {
547: /* modeld = Q(:,np+1:n)' */
549: PetscInt i,j,minindex=0;
550: PetscReal dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
551: PetscBLASInt blasn=mfqP->n, blasnpmax = mfqP->npmax, blask,info;
552: PetscBLASInt blas1=1,blasnmax = mfqP->nmax;
554: blask = mfqP->nmodelpoints;
555: /* Qtmp = I(n x n) */
556: for (i=0;i<mfqP->n;i++) {
557: for (j=0;j<mfqP->n;j++) {
558: mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
559: }
560: }
561: for (j=0;j<mfqP->n;j++) {
562: mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
563: }
565: /* Qtmp = Q * I */
566: PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
568: for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
569: dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
570: if (dp>0.0) { /* Model says use the other direction! */
571: for (j=0;j<mfqP->n;j++) {
572: mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
573: }
574: }
575: /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
576: for (j=0;j<mfqP->n;j++) {
577: mfqP->work2[j] = mfqP->Gres[j];
578: }
579: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
580: mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
581: if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
582: minindex=i;
583: minvalue = mfqP->work[i];
584: }
585: if (addallpoints != 0) {
586: addpoint(tao,mfqP,i);
587: }
588: }
589: if (!addallpoints) {
590: addpoint(tao,mfqP,minindex);
591: }
592: return(0);
593: }
598: PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
599: {
600: PetscInt i,j;
601: PetscBLASInt blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
602: PetscBLASInt blasnpmax = mfqP->npmax,blasmaxmn;
603: PetscReal proj,normd;
604: const PetscReal *x;
605: PetscErrorCode ierr;
608: for (i=mfqP->nHist-1;i>=0;i--) {
609: VecGetArrayRead(mfqP->Xhist[i],&x);
610: for (j=0;j<mfqP->n;j++) {
611: mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
612: }
613: VecRestoreArrayRead(mfqP->Xhist[i],&x);
614: PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
615: normd = BLASnrm2_(&blasn,mfqP->work,&ione);
616: if (normd <= c*c) {
617: blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
618: if (!mfqP->q_is_I) {
619: /* project D onto null */
620: blask=(mfqP->nmodelpoints);
621: PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
622: if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
623: }
624: proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);
626: if (proj >= mfqP->theta1) { /* add this index to model */
627: mfqP->model_indices[mfqP->nmodelpoints]=i;
628: mfqP->nmodelpoints++;
629: PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
630: blask=mfqP->npmax*(mfqP->nmodelpoints);
631: PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
632: blask = mfqP->nmodelpoints;
633: blasmaxmn = PetscMax(mfqP->m,mfqP->n);
634: PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
635: if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
636: mfqP->q_is_I = 0;
637: }
638: if (mfqP->nmodelpoints == mfqP->n) {
639: break;
640: }
641: }
642: }
644: return(0);
645: }
649: static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
650: {
651: TAO_POUNDERS *mfqP = (TAO_POUNDERS *)tao->data;
652: PetscInt i,ii,j,k,l;
653: PetscReal step=1.0;
654: TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
655: PetscInt low,high;
656: PetscReal minnorm;
657: PetscReal *x,*f;
658: const PetscReal *xmint,*fmin;
659: PetscReal cres,deltaold;
660: PetscReal gnorm;
661: PetscBLASInt info,ione=1,iblas;
662: PetscBool valid,same;
663: PetscReal mdec, rho, normxsp;
664: PetscReal one=1.0,zero=0.0,ratio;
665: PetscBLASInt blasm,blasn,blasncopy,blasnpmax;
666: PetscErrorCode ierr;
667: static PetscBool set = PETSC_FALSE;
669: /* n = # of parameters
670: m = dimension (components) of function */
672: PetscCitationsRegister("@article{UNEDF0,\n"
673: "title = {Nuclear energy density optimization},\n"
674: "author = {Kortelainen, M. and Lesinski, T. and Mor\'e, J. and Nazarewicz, W.\n"
675: " and Sarich, J. and Schunck, N. and Stoitsov, M. V. and Wild, S. },\n"
676: "journal = {Phys. Rev. C},\n"
677: "volume = {82},\n"
678: "number = {2},\n"
679: "pages = {024313},\n"
680: "numpages = {18},\n"
681: "year = {2010},\n"
682: "month = {Aug},\n"
683: "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);
684: tao->niter=0;
685: if (tao->XL && tao->XU) {
686: /* Check x0 <= XU */
687: PetscReal val;
688: VecCopy(tao->solution,mfqP->Xhist[0]);
689: VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
690: VecMax(mfqP->Xhist[0],NULL,&val);
691: if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");
693: /* Check x0 >= xl */
694: VecCopy(tao->XL,mfqP->Xhist[0]);
695: VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);
696: VecMax(mfqP->Xhist[0],NULL,&val);
697: if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");
699: /* Check x0 + delta < XU -- should be able to get around this eventually */
701: VecSet(mfqP->Xhist[0],mfqP->delta);
702: VecAXPY(mfqP->Xhist[0],1.0,tao->solution);
703: VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);
704: VecMax(mfqP->Xhist[0],NULL,&val);
705: if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
706: }
708: CHKMEMQ;
709: blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
710: for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) mfqP->H[i]=0;
712: VecCopy(tao->solution,mfqP->Xhist[0]);
713: CHKMEMQ;
714: pounders_feval(tao,tao->solution,mfqP->Fhist[0],&mfqP->Fres[0]);
715: mfqP->minindex = 0;
716: minnorm = mfqP->Fres[0];
717: TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);
718: tao->niter++;
720: VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);
721: for (i=1;i<mfqP->n+1;i++) {
722: VecCopy(tao->solution,mfqP->Xhist[i]);
723: if (i-1 >= low && i-1 < high) {
724: VecGetArray(mfqP->Xhist[i],&x);
725: x[i-1-low] += mfqP->delta;
726: VecRestoreArray(mfqP->Xhist[i],&x);
727: }
728: CHKMEMQ;
729: pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);
730: if (mfqP->Fres[i] < minnorm) {
731: mfqP->minindex = i;
732: minnorm = mfqP->Fres[i];
733: }
734: }
735: VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
736: VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
737: /* Gather mpi vecs to one big local vec */
739: /* Begin serial code */
741: /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
742: /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
743: /* (Column oriented for blas calls) */
744: ii=0;
746: if (mfqP->size == 1) {
747: VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
748: for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
749: VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
750: VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
751: for (i=0;i<mfqP->n+1;i++) {
752: if (i == mfqP->minindex) continue;
754: VecGetArray(mfqP->Xhist[i],&x);
755: for (j=0;j<mfqP->n;j++) {
756: mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
757: }
758: VecRestoreArray(mfqP->Xhist[i],&x);
760: VecGetArray(mfqP->Fhist[i],&f);
761: for (j=0;j<mfqP->m;j++) {
762: mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
763: }
764: VecRestoreArray(mfqP->Fhist[i],&f);
765: mfqP->model_indices[ii++] = i;
767: }
768: for (j=0;j<mfqP->m;j++) {
769: mfqP->C[j] = fmin[j];
770: }
771: VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
772: } else {
773: VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
774: VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);
775: VecGetArrayRead(mfqP->localxmin,&xmint);
776: for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
777: VecRestoreArrayRead(mfqP->localxmin,&xmint);
779: VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
780: VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);
781: VecGetArrayRead(mfqP->localfmin,&fmin);
782: for (i=0;i<mfqP->n+1;i++) {
783: if (i == mfqP->minindex) continue;
785: mfqP->model_indices[ii++] = i;
786: VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
787: VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);
788: VecGetArray(mfqP->localx,&x);
789: for (j=0;j<mfqP->n;j++) {
790: mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
791: }
792: VecRestoreArray(mfqP->localx,&x);
794: VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
795: VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);
796: VecGetArray(mfqP->localf,&f);
797: for (j=0;j<mfqP->m;j++) {
798: mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
799: }
800: VecRestoreArray(mfqP->localf,&f);
801: }
802: for (j=0;j<mfqP->m;j++) {
803: mfqP->C[j] = fmin[j];
804: }
805: VecRestoreArrayRead(mfqP->localfmin,&fmin);
806: }
808: /* Determine the initial quadratic models */
809: /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
810: /* D (nxn) Fdiff (nxm) => G (nxm) */
811: blasncopy = blasn;
812: PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasncopy,&info));
813: PetscInfo1(tao,"gesv returned %d\n",info);
815: cres = minnorm;
816: pounders_update_res(tao);
818: valid = PETSC_TRUE;
820: VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
821: VecAssemblyBegin(tao->gradient);
822: VecAssemblyEnd(tao->gradient);
823: VecNorm(tao->gradient,NORM_2,&gnorm);
824: gnorm *= mfqP->delta;
825: VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
826: TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
827: mfqP->nHist = mfqP->n+1;
828: mfqP->nmodelpoints = mfqP->n+1;
830: while (reason == TAO_CONTINUE_ITERATING) {
831: PetscReal gnm = 1e-4;
832: tao->niter++;
833: /* Solve the subproblem min{Q(s): ||s|| <= delta} */
834: gqtwrap(tao,&gnm,&mdec);
835: /* Evaluate the function at the new point */
837: for (i=0;i<mfqP->n;i++) {
838: mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
839: }
840: VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);
841: VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);
842: VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);
843: VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);
844: VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);
846: pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);
848: rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
849: mfqP->nHist++;
851: /* Update the center */
852: if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
853: /* Update model to reflect new base point */
854: for (i=0;i<mfqP->n;i++) {
855: mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
856: }
857: for (j=0;j<mfqP->m;j++) {
858: /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
859: G(:,j) = G(:,j) + H(:,:,j)*work' */
860: for (k=0;k<mfqP->n;k++) {
861: mfqP->work2[k]=0.0;
862: for (l=0;l<mfqP->n;l++) {
863: mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
864: }
865: }
866: for (i=0;i<mfqP->n;i++) {
867: mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
868: mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
869: }
870: }
871: /* Cres += work*Gres + .5*work*Hres*work';
872: Gres += Hres*work'; */
874: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
875: for (i=0;i<mfqP->n;i++) {
876: cres += mfqP->work[i]*(mfqP->Gres[i] + 0.5*mfqP->work2[i]);
877: mfqP->Gres[i] += mfqP->work2[i];
878: }
879: mfqP->minindex = mfqP->nHist-1;
880: minnorm = mfqP->Fres[mfqP->minindex];
881: VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);
882: /* Change current center */
883: VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
884: for (i=0;i<mfqP->n;i++) {
885: mfqP->xmin[i] = xmint[i];
886: }
887: VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);
888: }
890: /* Evaluate at a model-improving point if necessary */
891: if (valid == PETSC_FALSE) {
892: mfqP->q_is_I = 1;
893: mfqP->nmodelpoints = 0;
894: affpoints(mfqP,mfqP->xmin,mfqP->c1);
895: if (mfqP->nmodelpoints < mfqP->n) {
896: PetscInfo(tao,"Model not valid -- model-improving\n");
897: modelimprove(tao,mfqP,1);
898: }
899: }
901: /* Update the trust region radius */
902: deltaold = mfqP->delta;
903: normxsp = 0;
904: for (i=0;i<mfqP->n;i++) {
905: normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
906: }
907: normxsp = PetscSqrtReal(normxsp);
908: if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
909: mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
910: } else if (valid == PETSC_TRUE) {
911: mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
912: }
914: /* Compute the next interpolation set */
915: mfqP->q_is_I = 1;
916: mfqP->nmodelpoints=0;
917: affpoints(mfqP,mfqP->xmin,mfqP->c1);
918: if (mfqP->nmodelpoints == mfqP->n) {
919: valid = PETSC_TRUE;
920: } else {
921: valid = PETSC_FALSE;
922: affpoints(mfqP,mfqP->xmin,mfqP->c2);
923: if (mfqP->n > mfqP->nmodelpoints) {
924: PetscInfo(tao,"Model not valid -- adding geometry points\n");
925: modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);
926: }
927: }
928: for (i=mfqP->nmodelpoints;i>0;i--) {
929: mfqP->model_indices[i] = mfqP->model_indices[i-1];
930: }
931: mfqP->nmodelpoints++;
932: mfqP->model_indices[0] = mfqP->minindex;
933: morepoints(mfqP);
934: for (i=0;i<mfqP->nmodelpoints;i++) {
935: VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
936: for (j=0;j<mfqP->n;j++) {
937: mfqP->Disp[i + mfqP->npmax*j] = (x[j] - mfqP->xmin[j]) / deltaold;
938: }
939: VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);
940: VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
941: for (j=0;j<mfqP->m;j++) {
942: for (k=0;k<mfqP->n;k++) {
943: mfqP->work[k]=0.0;
944: for (l=0;l<mfqP->n;l++) {
945: mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
946: }
947: }
948: mfqP->RES[j*mfqP->npmax + i] = -mfqP->C[j] - BLASdot_(&blasn,&mfqP->Fdiff[j*mfqP->n],&ione,&mfqP->Disp[i],&blasnpmax) - 0.5*BLASdot_(&blasn,mfqP->work,&ione,&mfqP->Disp[i],&blasnpmax) + f[j];
949: }
950: VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);
951: }
953: /* Update the quadratic model */
954: getquadpounders(mfqP);
955: VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);
956: PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
957: /* G = G*(delta/deltaold) + Gdel */
958: ratio = mfqP->delta/deltaold;
959: iblas = blasm*blasn;
960: PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
961: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
962: /* H = H*(delta/deltaold)^2 + Hdel */
963: iblas = blasm*blasn*blasn;
964: ratio *= ratio;
965: PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
966: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));
968: /* Get residuals */
969: cres = mfqP->Fres[mfqP->minindex];
970: pounders_update_res(tao);
972: /* Export solution and gradient residual to TAO */
973: VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);
974: VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);
975: VecAssemblyBegin(tao->gradient);
976: VecAssemblyEnd(tao->gradient);
977: VecNorm(tao->gradient,NORM_2,&gnorm);
978: gnorm *= mfqP->delta;
979: /* final criticality test */
980: TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);
981: /* test for repeated model */
982: if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
983: same = PETSC_TRUE;
984: } else {
985: same = PETSC_FALSE;
986: }
987: for (i=0;i<mfqP->nmodelpoints;i++) {
988: if (same) {
989: if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
990: same = PETSC_TRUE;
991: } else {
992: same = PETSC_FALSE;
993: }
994: }
995: mfqP->last_model_indices[i] = mfqP->model_indices[i];
996: }
997: mfqP->last_nmodelpoints = mfqP->nmodelpoints;
998: if (same && mfqP->delta == deltaold) {
999: PetscInfo(tao,"Identical model used in successive iterations\n");
1000: reason = TAO_CONVERGED_STEPTOL;
1001: tao->reason = TAO_CONVERGED_STEPTOL;
1002: }
1003: }
1004: return(0);
1005: }
1009: static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
1010: {
1011: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
1012: PetscInt i,j;
1013: IS isfloc,isfglob,isxloc,isxglob;
1017: if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient); }
1018: if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection); }
1019: VecGetSize(tao->solution,&mfqP->n);
1020: VecGetSize(tao->sep_objective,&mfqP->m);
1021: mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
1022: if (mfqP->npmax == PETSC_DEFAULT) {
1023: mfqP->npmax = 2*mfqP->n + 1;
1024: }
1025: mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1026: mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);
1028: PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);
1029: PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);
1030: for (i=0;i<mfqP->n +1;i++) {
1031: VecDuplicate(tao->solution,&mfqP->Xhist[i]);
1032: VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);
1033: }
1034: VecDuplicate(tao->solution,&mfqP->workxvec);
1035: VecDuplicate(tao->sep_objective,&mfqP->workfvec);
1036: mfqP->nHist = 0;
1038: PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);
1039: PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);
1040: PetscMalloc1(mfqP->n,&mfqP->work);
1041: PetscMalloc1(mfqP->n,&mfqP->work2);
1042: PetscMalloc1(mfqP->n,&mfqP->work3);
1043: PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);
1044: PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);
1045: PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);
1046: PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);
1048: PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);
1049: PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);
1050: PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);
1051: PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);
1052: PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);
1053: PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);
1054: PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);
1055: PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);
1056: PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);
1057: PetscMalloc1(mfqP->npmax,&mfqP->tau);
1058: PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);
1059: mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1060: PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);
1061: PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);
1062: PetscMalloc1(mfqP->n,&mfqP->xmin);
1063: PetscMalloc1(mfqP->m,&mfqP->C);
1064: PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);
1065: PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);
1066: PetscMalloc1(mfqP->n,&mfqP->Gres);
1067: PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);
1068: PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);
1069: PetscMalloc1(mfqP->npmax,&mfqP->model_indices);
1070: PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);
1071: PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);
1072: PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);
1073: PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);
1074: PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);
1075: PetscMalloc1(mfqP->n,&mfqP->iwork);
1076: PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);
1077: for (i=0;i<mfqP->m;i++) {
1078: for (j=0;j<mfqP->m;j++) {
1079: if (i==j) {
1080: mfqP->w[i+mfqP->m*j]=1.0;
1081: } else {
1082: mfqP->w[i+mfqP->m*j]=0.0;
1083: }
1084: }
1085: }
1086: for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1087: mfqP->indices[i] = i;
1088: }
1089: MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);
1090: if (mfqP->size > 1) {
1091: VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);
1092: VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);
1093: VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);
1094: VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);
1095: ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);
1096: ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);
1097: ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);
1098: ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);
1101: VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);
1102: VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);
1104: ISDestroy(&isxloc);
1105: ISDestroy(&isxglob);
1106: ISDestroy(&isfloc);
1107: ISDestroy(&isfglob);
1108: }
1110: if (!mfqP->usegqt) {
1111: KSP ksp;
1112: PC pc;
1113: VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);
1114: VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);
1115: VecDuplicate(mfqP->subxl,&mfqP->subb);
1116: VecDuplicate(mfqP->subxl,&mfqP->subxu);
1117: VecDuplicate(mfqP->subxl,&mfqP->subpdel);
1118: VecDuplicate(mfqP->subxl,&mfqP->subndel);
1119: TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);
1120: TaoSetType(mfqP->subtao,TAOTRON);
1121: TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");
1122: TaoSetInitialVector(mfqP->subtao,mfqP->subx);
1123: TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);
1124: TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);
1125: TaoSetFromOptions(mfqP->subtao);
1126: TaoGetKSP(mfqP->subtao,&ksp);
1127: if (ksp) {
1128: KSPGetPC(ksp,&pc);
1129: PCSetType(pc,PCNONE);
1130: }
1131: TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);
1132: MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);
1133: TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);
1134: }
1135: return(0);
1136: }
1140: static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1141: {
1142: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
1143: PetscInt i;
1147: if (!mfqP->usegqt) {
1148: TaoDestroy(&mfqP->subtao);
1149: VecDestroy(&mfqP->subx);
1150: VecDestroy(&mfqP->subxl);
1151: VecDestroy(&mfqP->subxu);
1152: VecDestroy(&mfqP->subb);
1153: VecDestroy(&mfqP->subpdel);
1154: VecDestroy(&mfqP->subndel);
1155: MatDestroy(&mfqP->subH);
1156: }
1157: PetscFree(mfqP->Fres);
1158: PetscFree(mfqP->RES);
1159: PetscFree(mfqP->work);
1160: PetscFree(mfqP->work2);
1161: PetscFree(mfqP->work3);
1162: PetscFree(mfqP->mwork);
1163: PetscFree(mfqP->omega);
1164: PetscFree(mfqP->beta);
1165: PetscFree(mfqP->alpha);
1166: PetscFree(mfqP->H);
1167: PetscFree(mfqP->Q);
1168: PetscFree(mfqP->Q_tmp);
1169: PetscFree(mfqP->L);
1170: PetscFree(mfqP->L_tmp);
1171: PetscFree(mfqP->L_save);
1172: PetscFree(mfqP->N);
1173: PetscFree(mfqP->M);
1174: PetscFree(mfqP->Z);
1175: PetscFree(mfqP->tau);
1176: PetscFree(mfqP->tau_tmp);
1177: PetscFree(mfqP->npmaxwork);
1178: PetscFree(mfqP->npmaxiwork);
1179: PetscFree(mfqP->xmin);
1180: PetscFree(mfqP->C);
1181: PetscFree(mfqP->Fdiff);
1182: PetscFree(mfqP->Disp);
1183: PetscFree(mfqP->Gres);
1184: PetscFree(mfqP->Hres);
1185: PetscFree(mfqP->Gpoints);
1186: PetscFree(mfqP->model_indices);
1187: PetscFree(mfqP->last_model_indices);
1188: PetscFree(mfqP->Xsubproblem);
1189: PetscFree(mfqP->Gdel);
1190: PetscFree(mfqP->Hdel);
1191: PetscFree(mfqP->indices);
1192: PetscFree(mfqP->iwork);
1193: PetscFree(mfqP->w);
1194: for (i=0;i<mfqP->nHist;i++) {
1195: VecDestroy(&mfqP->Xhist[i]);
1196: VecDestroy(&mfqP->Fhist[i]);
1197: }
1198: VecDestroy(&mfqP->workxvec);
1199: VecDestroy(&mfqP->workfvec);
1200: PetscFree(mfqP->Xhist);
1201: PetscFree(mfqP->Fhist);
1203: if (mfqP->size > 1) {
1204: VecDestroy(&mfqP->localx);
1205: VecDestroy(&mfqP->localxmin);
1206: VecDestroy(&mfqP->localf);
1207: VecDestroy(&mfqP->localfmin);
1208: }
1209: PetscFree(tao->data);
1210: return(0);
1211: }
1215: static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1216: {
1217: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
1221: PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");
1222: PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);
1223: mfqP->delta = mfqP->delta0;
1224: mfqP->npmax = PETSC_DEFAULT;
1225: PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);
1226: mfqP->usegqt = PETSC_FALSE;
1227: PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);
1228: PetscOptionsTail();
1229: return(0);
1230: }
1234: static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1235: {
1236: TAO_POUNDERS *mfqP = (TAO_POUNDERS *)tao->data;
1237: PetscBool isascii;
1238: PetscInt nits;
1242: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1243: if (isascii) {
1244: PetscViewerASCIIPushTab(viewer);
1245: PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);
1246: PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);
1247: PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);
1248: if (mfqP->usegqt) {
1249: PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");
1250: } else {
1251: PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);
1252: TaoGetTotalIterationNumber(mfqP->subtao,&nits);
1253: PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);
1254: }
1255: PetscViewerASCIIPopTab(viewer);
1256: }
1257: return(0);
1258: }
1259: /*MC
1260: TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares
1262: Options Database Keys:
1263: + -tao_pounders_delta - initial step length
1264: . -tao_pounders_npmax - maximum number of points in model
1265: - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON
1267: Level: beginner
1268:
1269: M*/
1273: PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1274: {
1275: TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
1279: tao->ops->setup = TaoSetUp_POUNDERS;
1280: tao->ops->solve = TaoSolve_POUNDERS;
1281: tao->ops->view = TaoView_POUNDERS;
1282: tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1283: tao->ops->destroy = TaoDestroy_POUNDERS;
1285: PetscNewLog(tao,&mfqP);
1286: tao->data = (void*)mfqP;
1287: /* Override default settings (unless already changed) */
1288: if (!tao->max_it_changed) tao->max_it = 2000;
1289: if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1290: mfqP->delta0 = 0.1;
1291: mfqP->delta = 0.1;
1292: mfqP->deltamax=1e3;
1293: mfqP->deltamin=1e-6;
1294: mfqP->c2 = 100.0;
1295: mfqP->theta1=1e-5;
1296: mfqP->theta2=1e-4;
1297: mfqP->gamma0=0.5;
1298: mfqP->gamma1=2.0;
1299: mfqP->eta0 = 0.0;
1300: mfqP->eta1 = 0.1;
1301: mfqP->gqt_rtol = 0.001;
1302: mfqP->gqt_maxits = 50;
1303: mfqP->workxvec = 0;
1304: return(0);
1305: }