xref: /petsc/src/tao/leastsquares/impls/pounders/pounders.c (revision a7fac7c2b47dbcd8ece0cc2dfdfe0e63be1bb7b5)
1 #include <../src/tao/leastsquares/impls/pounders/pounders.h>
2 
3 #undef __FUNCT__
4 #define __FUNCT__ "pounders_h"
5 static PetscErrorCode pounders_h(Tao subtao, Vec v, Mat H, Mat Hpre, void *ctx)
6 {
7   PetscFunctionBegin;
8   PetscFunctionReturn(0);
9 }
10 #undef __FUNCT__
11 #define __FUNCT__ "pounders_fg"
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;
16   PetscErrorCode ierr;
17 
18   PetscFunctionBegin;
19   /* g = A*x  (add b later)*/
20   ierr = MatMult(mfqP->subH,x,g);CHKERRQ(ierr);
21 
22   /* f = 1/2 * x'*(Ax) + b'*x  */
23   ierr = VecDot(x,g,&d1);CHKERRQ(ierr);
24   ierr = VecDot(mfqP->subb,x,&d2);CHKERRQ(ierr);
25   *f = 0.5 *d1 + d2;
26 
27   /* now  g = g + b */
28   ierr = VecAXPY(g, 1.0, mfqP->subb);CHKERRQ(ierr);
29   PetscFunctionReturn(0);
30 }
31 
32 #undef __FUNCT__
33 #define __FUNCT__ "gqtwrap"
34 PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
35 {
36   PetscErrorCode ierr;
37 #if defined(PETSC_USE_REAL_SINGLE)
38   PetscReal      atol=1.0e-5;
39 #else
40   PetscReal      atol=1.0e-10;
41 #endif
42   PetscInt       info,its;
43   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
44 
45   PetscFunctionBegin;
46   if (! mfqP->usegqt) {
47     PetscReal maxval;
48     PetscInt  i,j;
49 
50     ierr = VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
51     ierr = VecAssemblyBegin(mfqP->subb);CHKERRQ(ierr);
52     ierr = VecAssemblyEnd(mfqP->subb);CHKERRQ(ierr);
53 
54     ierr = VecSet(mfqP->subx,0.0);CHKERRQ(ierr);
55 
56     ierr = VecSet(mfqP->subndel,-mfqP->delta);CHKERRQ(ierr);
57     ierr = VecSet(mfqP->subpdel,mfqP->delta);CHKERRQ(ierr);
58 
59     for (i=0;i<mfqP->n;i++) {
60       for (j=i;j<mfqP->n;j++) {
61         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
62       }
63     }
64     ierr = MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);CHKERRQ(ierr);
65     ierr = MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
66     ierr = MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
67 
68     ierr = TaoResetStatistics(mfqP->subtao);CHKERRQ(ierr);
69     ierr = TaoSetTolerances(mfqP->subtao,PETSC_DEFAULT,PETSC_DEFAULT,*gnorm,*gnorm,PETSC_DEFAULT);CHKERRQ(ierr);
70     /* enforce bound constraints -- experimental */
71     if (tao->XU && tao->XL) {
72       ierr = VecCopy(tao->XU,mfqP->subxu);CHKERRQ(ierr);
73       ierr = VecAXPY(mfqP->subxu,-1.0,tao->solution);CHKERRQ(ierr);
74       ierr = VecScale(mfqP->subxu,1.0/mfqP->delta);CHKERRQ(ierr);
75       ierr = VecCopy(tao->XL,mfqP->subxl);CHKERRQ(ierr);
76       ierr = VecAXPY(mfqP->subxl,-1.0,tao->solution);CHKERRQ(ierr);
77       ierr = VecScale(mfqP->subxl,1.0/mfqP->delta);CHKERRQ(ierr);
78 
79       ierr = VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);CHKERRQ(ierr);
80       ierr = VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);CHKERRQ(ierr);
81     } else {
82       ierr = VecCopy(mfqP->subpdel,mfqP->subxu);CHKERRQ(ierr);
83       ierr = VecCopy(mfqP->subndel,mfqP->subxl);CHKERRQ(ierr);
84     }
85     /* Make sure xu > xl */
86     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
87     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
88     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
89     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
90     /* Make sure xu > tao->solution > xl */
91     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
92     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
93     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
94     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");
95 
96     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
97     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
98     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
99     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");
100 
101     ierr = TaoSolve(mfqP->subtao);CHKERRQ(ierr);
102     ierr = TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
103 
104     /* test bounds post-solution*/
105     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
106     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
107     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
108     if (maxval > 1e-5) {
109       ierr = PetscInfo(tao,"subproblem solution < lower bound\n");CHKERRQ(ierr);
110       tao->reason = TAO_DIVERGED_TR_REDUCTION;
111     }
112 
113     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
114     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
115     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
116     if (maxval > 1e-5) {
117       ierr = PetscInfo(tao,"subproblem solution > upper bound\n");CHKERRQ(ierr);
118       tao->reason = TAO_DIVERGED_TR_REDUCTION;
119     }
120   } else {
121     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);
122   }
123   *qmin *= -1;
124   PetscFunctionReturn(0);
125 }
126 
127 #undef __FUNCT__
128 #define __FUNCT__ "phi2eval"
129 PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
130 {
131 /* 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] */
132   PetscInt  i,j,k;
133   PetscReal sqrt2 = PetscSqrtReal(2.0);
134 
135   PetscFunctionBegin;
136   j=0;
137   for (i=0;i<n;i++) {
138     phi[j] = 0.5 * x[i]*x[i];
139     j++;
140     for (k=i+1;k<n;k++) {
141       phi[j]  = x[i]*x[k]/sqrt2;
142       j++;
143     }
144   }
145   PetscFunctionReturn(0);
146 }
147 
148 #undef __FUNCT__
149 #define __FUNCT__ "getquadpounders"
150 PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
151 {
152 /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
153    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
154    for j=1,...,m and with a Hessian matrix of least Frobenius norm */
155 
156     /* NB --we are ignoring c */
157   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
158   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
159   PetscBLASInt blasnpmax = mfqP->npmax;
160   PetscBLASInt blasnplus1 = mfqP->n+1;
161   PetscBLASInt blasnp = np;
162   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
163   PetscBLASInt blasint2 = np - mfqP->n-1;
164   PetscBLASInt info,ione=1;
165   PetscReal    sqrt2 = PetscSqrtReal(2.0);
166 
167   PetscFunctionBegin;
168   for (i=0;i<mfqP->n*mfqP->m;i++) {
169     mfqP->Gdel[i] = 0;
170   }
171   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
172     mfqP->Hdel[i] = 0;
173   }
174 
175     /* factor M */
176   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&blasnplus1,&blasnp,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&info));
177   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrf returned with value %d\n",info);
178 
179   if (np == mfqP->n+1) {
180     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
181       mfqP->omega[i]=0.0;
182     }
183     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
184       mfqP->beta[i]=0.0;
185     }
186   } else {
187     /* Let Ltmp = (L'*L) */
188     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));
189 
190     /* factor Ltmp */
191     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
192     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
193   }
194 
195   for (k=0;k<mfqP->m;k++) {
196     if (np != mfqP->n+1) {
197       /* Solve L'*L*Omega = Z' * RESk*/
198       PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasnp,&blasint2,&one,mfqP->Z,&blasnpmax,&mfqP->RES[mfqP->npmax*k],&ione,&zero,mfqP->omega,&ione));
199       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&blasint2,&ione,mfqP->L_tmp,&blasint,mfqP->omega,&blasint2,&info));
200       if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrs returned with value %d\n",info);
201 
202       /* Beta = L*Omega */
203       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
204     }
205 
206     /* solve M'*Alpha = RESk - N'*Beta */
207     PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasint,&blasnp,&negone,mfqP->N,&blasint,mfqP->beta,&ione,&one,&mfqP->RES[mfqP->npmax*k],&ione));
208     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&blasnplus1,&ione,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&mfqP->RES[mfqP->npmax*k],&blasnplus1,&info));
209     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrs returned with value %d\n",info);
210 
211     /* Gdel(:,k) = Alpha(2:n+1) */
212     for (i=0;i<mfqP->n;i++) {
213       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
214     }
215 
216     /* Set Hdels */
217     num=0;
218     for (i=0;i<mfqP->n;i++) {
219       /* H[i,i,k] = Beta(num) */
220       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
221       num++;
222       for (j=i+1;j<mfqP->n;j++) {
223         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
224         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
225         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
226         num++;
227       }
228     }
229   }
230   PetscFunctionReturn(0);
231 }
232 
233 #undef __FUNCT__
234 #define __FUNCT__ "morepoints"
235 PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
236 {
237   /* Assumes mfqP->model_indices[0]  is minimum index
238    Finishes adding points to mfqP->model_indices (up to npmax)
239    Computes L,Z,M,N
240    np is actual number of points in model (should equal npmax?) */
241   PetscInt        point,i,j,offset;
242   PetscInt        reject;
243   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
244   const PetscReal *x;
245   PetscReal       normd;
246   PetscErrorCode  ierr;
247 
248   PetscFunctionBegin;
249   /* Initialize M,N */
250   for (i=0;i<mfqP->n+1;i++) {
251     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
252     mfqP->M[(mfqP->n+1)*i] = 1.0;
253     for (j=0;j<mfqP->n;j++) {
254       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
255     }
256     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
257     ierr = phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);CHKERRQ(ierr);
258   }
259 
260   /* Now we add points until we have npmax starting with the most recent ones */
261   point = mfqP->nHist-1;
262   mfqP->nmodelpoints = mfqP->n+1;
263   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
264     /* Reject any points already in the model */
265     reject = 0;
266     for (j=0;j<mfqP->n+1;j++) {
267       if (point == mfqP->model_indices[j]) {
268         reject = 1;
269         break;
270       }
271     }
272 
273     /* Reject if norm(d) >c2 */
274     if (!reject) {
275       ierr = VecCopy(mfqP->Xhist[point],mfqP->workxvec);CHKERRQ(ierr);
276       ierr = VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
277       ierr = VecNorm(mfqP->workxvec,NORM_2,&normd);CHKERRQ(ierr);
278       normd /= mfqP->delta;
279       if (normd > mfqP->c2) {
280         reject =1;
281       }
282     }
283     if (reject){
284       point--;
285       continue;
286     }
287 
288     ierr = VecGetArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
289     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
290     for (j=0;j<mfqP->n;j++) {
291       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
292     }
293     ierr = VecRestoreArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
294     ierr = phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);CHKERRQ(ierr);
295 
296     /* Update QR factorization */
297     /* Copy M' to Q_tmp */
298     for (i=0;i<mfqP->n+1;i++) {
299       for (j=0;j<mfqP->npmax;j++) {
300         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
301       }
302     }
303     blasnp = mfqP->nmodelpoints+1;
304     /* Q_tmp,R = qr(M') */
305     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
306     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
307     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);
308 
309     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
310     /* L = N*Qtmp */
311     blasint2 = mfqP->n * (mfqP->n+1) / 2;
312     /* Copy N to L_tmp */
313     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
314       mfqP->L_tmp[i]= mfqP->N[i];
315     }
316     /* Copy L_save to L_tmp */
317 
318     /* L_tmp = N*Qtmp' */
319     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
320     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
321 
322     /* Copy L_tmp to L_save */
323     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
324       mfqP->L_save[i] = mfqP->L_tmp[i];
325     }
326 
327     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
328     blasint = mfqP->nmodelpoints - mfqP->n;
329     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));
330     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);
331 
332     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
333       /* accept point */
334       mfqP->model_indices[mfqP->nmodelpoints] = point;
335       /* Copy Q_tmp to Q */
336       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
337         mfqP->Q[i] = mfqP->Q_tmp[i];
338       }
339       for (i=0;i<mfqP->npmax;i++){
340         mfqP->tau[i] = mfqP->tau_tmp[i];
341       }
342       mfqP->nmodelpoints++;
343       blasnp = mfqP->nmodelpoints;
344 
345       /* Copy L_save to L */
346       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
347         mfqP->L[i] = mfqP->L_save[i];
348       }
349     }
350     point--;
351   }
352 
353   blasnp = mfqP->nmodelpoints;
354   /* Copy Q(:,n+2:np) to Z */
355   /* First set Q_tmp to I */
356   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
357     mfqP->Q_tmp[i] = 0.0;
358   }
359   for (i=0;i<mfqP->npmax;i++) {
360     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
361   }
362 
363   /* Q_tmp = I * Q */
364   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
365   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
366 
367   /* Copy Q_tmp(:,n+2:np) to Z) */
368   offset = mfqP->npmax * (mfqP->n+1);
369   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
370     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
371   }
372 
373   if (mfqP->nmodelpoints == mfqP->n + 1) {
374     /* Set L to I_{n+1} */
375     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
376       mfqP->L[i] = 0.0;
377     }
378     for (i=0;i<mfqP->n;i++) {
379       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
380     }
381   }
382   PetscFunctionReturn(0);
383 }
384 
385 #undef __FUNCT__
386 #define __FUNCT__ "addpoint"
387 /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
388 PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
389 {
390   PetscErrorCode ierr;
391 
392   PetscFunctionBegin;
393   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
394   ierr = VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
395   ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);CHKERRQ(ierr);
396   ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
397   ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
398   ierr = VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
399 
400   /* Project into feasible region */
401   if (tao->XU && tao->XL) {
402     ierr = VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
403   }
404 
405   /* Compute value of new vector */
406   ierr = VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
407   CHKMEMQ;
408   ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
409   ierr = VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
410   if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
411   mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
412 
413   /* Add new vector to model */
414   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
415   mfqP->nmodelpoints++;
416   mfqP->nHist++;
417   PetscFunctionReturn(0);
418 }
419 
420 #undef __FUNCT__
421 #define __FUNCT__ "modelimprove"
422 PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
423 {
424   /* modeld = Q(:,np+1:n)' */
425   PetscErrorCode ierr;
426   PetscInt       i,j,minindex=0;
427   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
428   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
429   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;
430 
431   blask = mfqP->nmodelpoints;
432   /* Qtmp = I(n x n) */
433   for (i=0;i<mfqP->n;i++) {
434     for (j=0;j<mfqP->n;j++) {
435       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
436     }
437   }
438   for (j=0;j<mfqP->n;j++) {
439     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
440   }
441 
442   /* Qtmp = Q * I */
443   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
444 
445   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
446     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
447     if (dp>0.0) { /* Model says use the other direction! */
448       for (j=0;j<mfqP->n;j++) {
449         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
450       }
451     }
452     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
453     for (j=0;j<mfqP->n;j++) {
454       mfqP->work2[j] = mfqP->Gres[j];
455     }
456     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
457     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
458     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
459       minindex=i;
460       minvalue = mfqP->work[i];
461     }
462     if (addallpoints != 0) {
463       ierr = addpoint(tao,mfqP,i);CHKERRQ(ierr);
464     }
465   }
466   if (!addallpoints) {
467     ierr = addpoint(tao,mfqP,minindex);CHKERRQ(ierr);
468   }
469   PetscFunctionReturn(0);
470 }
471 
472 
473 #undef __FUNCT__
474 #define __FUNCT__ "affpoints"
475 PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
476 {
477   PetscInt        i,j;
478   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
479   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
480   PetscReal       proj,normd;
481   const PetscReal *x;
482   PetscErrorCode  ierr;
483 
484   PetscFunctionBegin;
485   for (i=mfqP->nHist-1;i>=0;i--) {
486     ierr = VecGetArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
487     for (j=0;j<mfqP->n;j++) {
488       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
489     }
490     ierr = VecRestoreArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
491     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
492     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
493     if (normd <= c*c) {
494       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
495       if (!mfqP->q_is_I) {
496         /* project D onto null */
497         blask=(mfqP->nmodelpoints);
498         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
499         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
500       }
501       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);
502 
503       if (proj >= mfqP->theta1) { /* add this index to model */
504         mfqP->model_indices[mfqP->nmodelpoints]=i;
505         mfqP->nmodelpoints++;
506         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
507         blask=mfqP->npmax*(mfqP->nmodelpoints);
508         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
509         blask = mfqP->nmodelpoints;
510         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
511         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
512         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
513         mfqP->q_is_I = 0;
514       }
515       if (mfqP->nmodelpoints == mfqP->n)  {
516         break;
517       }
518     }
519   }
520 
521   PetscFunctionReturn(0);
522 }
523 
524 #undef __FUNCT__
525 #define __FUNCT__ "TaoSolve_POUNDERS"
526 static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
527 {
528   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
529   PetscInt           i,ii,j,k,l;
530   PetscReal          step=1.0;
531   TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
532   PetscInt           low,high;
533   PetscReal          minnorm;
534   PetscReal          *x,*f;
535   const PetscReal    *xmint,*fmin;
536   PetscReal          cres,deltaold;
537   PetscReal          gnorm;
538   PetscBLASInt       info,ione=1,iblas;
539   PetscBool          valid,same;
540   PetscReal          mdec, rho, normxsp;
541   PetscReal          one=1.0,zero=0.0,ratio;
542   PetscBLASInt       blasm,blasn,blasnpmax,blasn2;
543   PetscErrorCode     ierr;
544   static PetscBool   set = PETSC_FALSE;
545 
546   /* n = # of parameters
547      m = dimension (components) of function  */
548   PetscFunctionBegin;
549   ierr = PetscCitationsRegister("@article{UNEDF0,\n"
550                                 "title = {Nuclear energy density optimization},\n"
551                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
552                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
553                                 "journal = {Phys. Rev. C},\n"
554                                 "volume = {82},\n"
555                                 "number = {2},\n"
556                                 "pages = {024313},\n"
557                                 "numpages = {18},\n"
558                                 "year = {2010},\n"
559                                 "month = {Aug},\n"
560                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);CHKERRQ(ierr);
561   tao->niter=0;
562   if (tao->XL && tao->XU) {
563     /* Check x0 <= XU */
564     PetscReal val;
565     ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
566     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
567     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
568     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");
569 
570     /* Check x0 >= xl */
571     ierr = VecCopy(tao->XL,mfqP->Xhist[0]);CHKERRQ(ierr);
572     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);CHKERRQ(ierr);
573     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
574     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");
575 
576     /* Check x0 + delta < XU  -- should be able to get around this eventually */
577 
578     ierr = VecSet(mfqP->Xhist[0],mfqP->delta);CHKERRQ(ierr);
579     ierr = VecAXPY(mfqP->Xhist[0],1.0,tao->solution);CHKERRQ(ierr);
580     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
581     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
582     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
583   }
584 
585   CHKMEMQ;
586   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
587   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) mfqP->H[i]=0;
588 
589   ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
590   CHKMEMQ;
591   ierr = TaoComputeSeparableObjective(tao,tao->solution,mfqP->Fhist[0]);CHKERRQ(ierr);
592 
593   ierr = VecNorm(mfqP->Fhist[0],NORM_2,&mfqP->Fres[0]);CHKERRQ(ierr);
594   if (PetscIsInfOrNanReal(mfqP->Fres[0])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
595   mfqP->Fres[0]*=mfqP->Fres[0];
596   mfqP->minindex = 0;
597   minnorm = mfqP->Fres[0];
598   ierr = TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);CHKERRQ(ierr);
599   tao->niter++;
600 
601   ierr = VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);CHKERRQ(ierr);
602   for (i=1;i<mfqP->n+1;i++) {
603     ierr = VecCopy(tao->solution,mfqP->Xhist[i]);CHKERRQ(ierr);
604     if (i-1 >= low && i-1 < high) {
605       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
606       x[i-1-low] += mfqP->delta;
607       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
608     }
609     CHKMEMQ;
610     ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[i],mfqP->Fhist[i]);CHKERRQ(ierr);
611     ierr = VecNorm(mfqP->Fhist[i],NORM_2,&mfqP->Fres[i]);CHKERRQ(ierr);
612     if (PetscIsInfOrNanReal(mfqP->Fres[i])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
613     mfqP->Fres[i]*=mfqP->Fres[i];
614     if (mfqP->Fres[i] < minnorm) {
615       mfqP->minindex = i;
616       minnorm = mfqP->Fres[i];
617     }
618   }
619   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
620   ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
621   /* Gather mpi vecs to one big local vec */
622 
623   /* Begin serial code */
624 
625   /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
626   /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
627   /* (Column oriented for blas calls) */
628   ii=0;
629 
630   if (mfqP->size == 1) {
631     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
632     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
633     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
634     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
635     for (i=0;i<mfqP->n+1;i++) {
636       if (i == mfqP->minindex) continue;
637 
638       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
639       for (j=0;j<mfqP->n;j++) {
640         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
641       }
642       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
643 
644       ierr = VecGetArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
645       for (j=0;j<mfqP->m;j++) {
646         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
647       }
648       ierr = VecRestoreArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
649       mfqP->model_indices[ii++] = i;
650 
651     }
652     for (j=0;j<mfqP->m;j++) {
653       mfqP->C[j] = fmin[j];
654     }
655     ierr = VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
656   } else {
657     ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
658     ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
659     ierr = VecGetArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
660     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
661     ierr = VecRestoreArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
662 
663     ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
664     ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
665     ierr = VecGetArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
666     for (i=0;i<mfqP->n+1;i++) {
667       if (i == mfqP->minindex) continue;
668 
669       mfqP->model_indices[ii++] = i;
670       ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
671       ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
672       ierr = VecGetArray(mfqP->localx,&x);CHKERRQ(ierr);
673       for (j=0;j<mfqP->n;j++) {
674         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
675       }
676       ierr = VecRestoreArray(mfqP->localx,&x);CHKERRQ(ierr);
677 
678       ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
679       ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
680       ierr = VecGetArray(mfqP->localf,&f);CHKERRQ(ierr);
681       for (j=0;j<mfqP->m;j++) {
682         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
683       }
684       ierr = VecRestoreArray(mfqP->localf,&f);CHKERRQ(ierr);
685     }
686     for (j=0;j<mfqP->m;j++) {
687       mfqP->C[j] = fmin[j];
688     }
689     ierr = VecRestoreArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
690   }
691 
692   /* Determine the initial quadratic models */
693   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
694   /* D (nxn) Fdiff (nxm)  => G (nxm) */
695   blasn2 = blasn;
696   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasn2,&info));
697   ierr = PetscInfo1(tao,"gesv returned %d\n",info);CHKERRQ(ierr);
698 
699   cres = minnorm;
700   /* Gres = G*F(xkin,1:m)'  G (nxm)   Fk (m)   */
701   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
702 
703   /*  Hres = G*G'  */
704   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));
705 
706   valid = PETSC_TRUE;
707 
708   ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
709   ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
710   ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
711   ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
712   gnorm *= mfqP->delta;
713   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
714   ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
715   mfqP->nHist = mfqP->n+1;
716   mfqP->nmodelpoints = mfqP->n+1;
717 
718   while (reason == TAO_CONTINUE_ITERATING) {
719     PetscReal gnm = 1e-4;
720     tao->niter++;
721     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
722     ierr = gqtwrap(tao,&gnm,&mdec);CHKERRQ(ierr);
723     /* Evaluate the function at the new point */
724 
725     for (i=0;i<mfqP->n;i++) {
726         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
727     }
728     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
729     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
730     ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);CHKERRQ(ierr);
731     ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
732     ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
733 
734     ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
735     ierr = VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
736     if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
737     mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
738     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
739     mfqP->nHist++;
740 
741     /* Update the center */
742     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
743       /* Update model to reflect new base point */
744       for (i=0;i<mfqP->n;i++) {
745         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
746       }
747       for (j=0;j<mfqP->m;j++) {
748         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
749          G(:,j) = G(:,j) + H(:,:,j)*work' */
750         for (k=0;k<mfqP->n;k++) {
751           mfqP->work2[k]=0.0;
752           for (l=0;l<mfqP->n;l++) {
753             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
754           }
755         }
756         for (i=0;i<mfqP->n;i++) {
757           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
758           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
759         }
760       }
761       /* Cres += work*Gres + .5*work*Hres*work';
762        Gres += Hres*work'; */
763 
764       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
765       for (i=0;i<mfqP->n;i++) {
766         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
767         mfqP->Gres[i] += mfqP->work2[i];
768       }
769       mfqP->minindex = mfqP->nHist-1;
770       minnorm = mfqP->Fres[mfqP->minindex];
771       ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
772       /* Change current center */
773       ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
774       for (i=0;i<mfqP->n;i++) {
775         mfqP->xmin[i] = xmint[i];
776       }
777       ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
778     }
779 
780     /* Evaluate at a model-improving point if necessary */
781     if (valid == PETSC_FALSE) {
782       mfqP->q_is_I = 1;
783       mfqP->nmodelpoints = 0;
784       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
785       if (mfqP->nmodelpoints < mfqP->n) {
786         ierr = PetscInfo(tao,"Model not valid -- model-improving\n");CHKERRQ(ierr);
787         ierr = modelimprove(tao,mfqP,1);CHKERRQ(ierr);
788       }
789     }
790 
791     /* Update the trust region radius */
792     deltaold = mfqP->delta;
793     normxsp = 0;
794     for (i=0;i<mfqP->n;i++) {
795       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
796     }
797     normxsp = PetscSqrtReal(normxsp);
798     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
799       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
800     } else if (valid == PETSC_TRUE) {
801       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
802     }
803 
804     /* Compute the next interpolation set */
805     mfqP->q_is_I = 1;
806     mfqP->nmodelpoints=0;
807     ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
808     if (mfqP->nmodelpoints == mfqP->n) {
809       valid = PETSC_TRUE;
810     } else {
811       valid = PETSC_FALSE;
812       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c2);CHKERRQ(ierr);
813       if (mfqP->n > mfqP->nmodelpoints) {
814         ierr = PetscInfo(tao,"Model not valid -- adding geometry points\n");CHKERRQ(ierr);
815         ierr = modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);CHKERRQ(ierr);
816       }
817     }
818     for (i=mfqP->nmodelpoints;i>0;i--) {
819       mfqP->model_indices[i] = mfqP->model_indices[i-1];
820     }
821     mfqP->nmodelpoints++;
822     mfqP->model_indices[0] = mfqP->minindex;
823     ierr = morepoints(mfqP);CHKERRQ(ierr);
824     for (i=0;i<mfqP->nmodelpoints;i++) {
825       ierr = VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
826       for (j=0;j<mfqP->n;j++) {
827         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
828       }
829       ierr = VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
830       ierr = VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
831       for (j=0;j<mfqP->m;j++) {
832         for (k=0;k<mfqP->n;k++)  {
833           mfqP->work[k]=0.0;
834           for (l=0;l<mfqP->n;l++) {
835             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
836           }
837         }
838         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];
839       }
840       ierr = VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
841     }
842 
843     /* Update the quadratic model */
844     ierr = getquadpounders(mfqP);CHKERRQ(ierr);
845     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
846     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
847     /* G = G*(delta/deltaold) + Gdel */
848     ratio = mfqP->delta/deltaold;
849     iblas = blasm*blasn;
850     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
851     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
852     /* H = H*(delta/deltaold) + Hdel */
853     iblas = blasm*blasn*blasn;
854     ratio *= ratio;
855     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
856     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));
857 
858     /* Get residuals */
859     cres = mfqP->Fres[mfqP->minindex];
860     /* Gres = G*F(xkin,1:m)' */
861     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
862     /* Hres = sum i=1..m {F(xkin,i)*H(:,:,i)}   + G*G' */
863     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));
864 
865     iblas = mfqP->n*mfqP->n;
866 
867     for (j=0;j<mfqP->m;j++) {
868       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&fmin[j],&mfqP->H[j],&blasm,mfqP->Hres,&ione));
869     }
870 
871     /* Export solution and gradient residual to TAO */
872     ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
873     ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
874     ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
875     ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
876     ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
877     gnorm *= mfqP->delta;
878     /*  final criticality test */
879     ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
880     /* test for repeated model */
881     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
882       same = PETSC_TRUE;
883     } else {
884       same = PETSC_FALSE;
885     }
886     for (i=0;i<mfqP->nmodelpoints;i++) {
887       if (same) {
888         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
889           same = PETSC_TRUE;
890         } else {
891           same = PETSC_FALSE;
892         }
893       }
894       mfqP->last_model_indices[i] = mfqP->model_indices[i];
895     }
896     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
897     if (same && mfqP->delta == deltaold) {
898       ierr = PetscInfo(tao,"Identical model used in successive iterations\n");CHKERRQ(ierr);
899       reason = TAO_CONVERGED_STEPTOL;
900       tao->reason = TAO_CONVERGED_STEPTOL;
901     }
902   }
903   PetscFunctionReturn(0);
904 }
905 
906 #undef __FUNCT__
907 #define __FUNCT__ "TaoSetUp_POUNDERS"
908 static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
909 {
910   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
911   PetscInt       i;
912   IS             isfloc,isfglob,isxloc,isxglob;
913   PetscErrorCode ierr;
914 
915   PetscFunctionBegin;
916   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);  }
917   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);  }
918   ierr = VecGetSize(tao->solution,&mfqP->n);CHKERRQ(ierr);
919   ierr = VecGetSize(tao->sep_objective,&mfqP->m);CHKERRQ(ierr);
920   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
921   if (mfqP->npmax == PETSC_DEFAULT) {
922     mfqP->npmax = 2*mfqP->n + 1;
923   }
924   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
925   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);
926 
927   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);CHKERRQ(ierr);
928   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);CHKERRQ(ierr);
929   for (i=0;i<mfqP->n +1;i++) {
930     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[i]);CHKERRQ(ierr);
931     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);CHKERRQ(ierr);
932   }
933   ierr = VecDuplicate(tao->solution,&mfqP->workxvec);CHKERRQ(ierr);
934   mfqP->nHist = 0;
935 
936   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);CHKERRQ(ierr);
937   ierr = PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);CHKERRQ(ierr);
938   ierr = PetscMalloc1(mfqP->n,&mfqP->work);CHKERRQ(ierr);
939   ierr = PetscMalloc1(mfqP->n,&mfqP->work2);CHKERRQ(ierr);
940   ierr = PetscMalloc1(mfqP->n,&mfqP->work3);CHKERRQ(ierr);
941   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);CHKERRQ(ierr);
942   ierr = PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);CHKERRQ(ierr);
943   ierr = PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);CHKERRQ(ierr);
944   ierr = PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);CHKERRQ(ierr);
945 
946   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);CHKERRQ(ierr);
947   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);CHKERRQ(ierr);
948   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);CHKERRQ(ierr);
949   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);CHKERRQ(ierr);
950   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);CHKERRQ(ierr);
951   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);CHKERRQ(ierr);
952   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);CHKERRQ(ierr);
953   ierr = PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);CHKERRQ(ierr);
954   ierr = PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);CHKERRQ(ierr);
955   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau);CHKERRQ(ierr);
956   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);CHKERRQ(ierr);
957   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
958   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);CHKERRQ(ierr);
959   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);CHKERRQ(ierr);
960   ierr = PetscMalloc1(mfqP->n,&mfqP->xmin);CHKERRQ(ierr);
961   ierr = PetscMalloc1(mfqP->m,&mfqP->C);CHKERRQ(ierr);
962   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);CHKERRQ(ierr);
963   ierr = PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);CHKERRQ(ierr);
964   ierr = PetscMalloc1(mfqP->n,&mfqP->Gres);CHKERRQ(ierr);
965   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);CHKERRQ(ierr);
966   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);CHKERRQ(ierr);
967   ierr = PetscMalloc1(mfqP->npmax,&mfqP->model_indices);CHKERRQ(ierr);
968   ierr = PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);CHKERRQ(ierr);
969   ierr = PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);CHKERRQ(ierr);
970   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);CHKERRQ(ierr);
971   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);CHKERRQ(ierr);
972   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);CHKERRQ(ierr);
973   ierr = PetscMalloc1(mfqP->n,&mfqP->iwork);CHKERRQ(ierr);
974   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
975     mfqP->indices[i] = i;
976   }
977   ierr = MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);CHKERRQ(ierr);
978   if (mfqP->size > 1) {
979     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);CHKERRQ(ierr);
980     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);CHKERRQ(ierr);
981     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);CHKERRQ(ierr);
982     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);CHKERRQ(ierr);
983     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);CHKERRQ(ierr);
984     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);CHKERRQ(ierr);
985     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);CHKERRQ(ierr);
986     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);CHKERRQ(ierr);
987 
988 
989     ierr = VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);CHKERRQ(ierr);
990     ierr = VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);CHKERRQ(ierr);
991 
992     ierr = ISDestroy(&isxloc);CHKERRQ(ierr);
993     ierr = ISDestroy(&isxglob);CHKERRQ(ierr);
994     ierr = ISDestroy(&isfloc);CHKERRQ(ierr);
995     ierr = ISDestroy(&isfglob);CHKERRQ(ierr);
996   }
997 
998   if (!mfqP->usegqt) {
999     KSP       ksp;
1000     PC        pc;
1001     ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);CHKERRQ(ierr);
1002     ierr = VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);CHKERRQ(ierr);
1003     ierr = VecDuplicate(mfqP->subxl,&mfqP->subb);CHKERRQ(ierr);
1004     ierr = VecDuplicate(mfqP->subxl,&mfqP->subxu);CHKERRQ(ierr);
1005     ierr = VecDuplicate(mfqP->subxl,&mfqP->subpdel);CHKERRQ(ierr);
1006     ierr = VecDuplicate(mfqP->subxl,&mfqP->subndel);CHKERRQ(ierr);
1007     ierr = TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);CHKERRQ(ierr);
1008     ierr = TaoSetType(mfqP->subtao,TAOTRON);CHKERRQ(ierr);
1009     ierr = TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");CHKERRQ(ierr);
1010     ierr = TaoSetInitialVector(mfqP->subtao,mfqP->subx);CHKERRQ(ierr);
1011     ierr = TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);CHKERRQ(ierr);
1012     ierr = TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);CHKERRQ(ierr);
1013     ierr = TaoSetFromOptions(mfqP->subtao);CHKERRQ(ierr);
1014     ierr = TaoGetKSP(mfqP->subtao,&ksp);CHKERRQ(ierr);
1015     if (ksp) {
1016       ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
1017       ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
1018     }
1019     ierr = TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);CHKERRQ(ierr);
1020     ierr = MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);CHKERRQ(ierr);
1021     ierr = TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);CHKERRQ(ierr);
1022   }
1023   PetscFunctionReturn(0);
1024 }
1025 
1026 #undef __FUNCT__
1027 #define __FUNCT__ "TaoDestroy_POUNDERS"
1028 static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1029 {
1030   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1031   PetscInt       i;
1032   PetscErrorCode ierr;
1033 
1034   PetscFunctionBegin;
1035   if (!mfqP->usegqt) {
1036     ierr = TaoDestroy(&mfqP->subtao);CHKERRQ(ierr);
1037     ierr = VecDestroy(&mfqP->subx);CHKERRQ(ierr);
1038     ierr = VecDestroy(&mfqP->subxl);CHKERRQ(ierr);
1039     ierr = VecDestroy(&mfqP->subxu);CHKERRQ(ierr);
1040     ierr = VecDestroy(&mfqP->subb);CHKERRQ(ierr);
1041     ierr = VecDestroy(&mfqP->subpdel);CHKERRQ(ierr);
1042     ierr = VecDestroy(&mfqP->subndel);CHKERRQ(ierr);
1043     ierr = MatDestroy(&mfqP->subH);CHKERRQ(ierr);
1044   }
1045   ierr = PetscFree(mfqP->Fres);CHKERRQ(ierr);
1046   ierr = PetscFree(mfqP->RES);CHKERRQ(ierr);
1047   ierr = PetscFree(mfqP->work);CHKERRQ(ierr);
1048   ierr = PetscFree(mfqP->work2);CHKERRQ(ierr);
1049   ierr = PetscFree(mfqP->work3);CHKERRQ(ierr);
1050   ierr = PetscFree(mfqP->mwork);CHKERRQ(ierr);
1051   ierr = PetscFree(mfqP->omega);CHKERRQ(ierr);
1052   ierr = PetscFree(mfqP->beta);CHKERRQ(ierr);
1053   ierr = PetscFree(mfqP->alpha);CHKERRQ(ierr);
1054   ierr = PetscFree(mfqP->H);CHKERRQ(ierr);
1055   ierr = PetscFree(mfqP->Q);CHKERRQ(ierr);
1056   ierr = PetscFree(mfqP->Q_tmp);CHKERRQ(ierr);
1057   ierr = PetscFree(mfqP->L);CHKERRQ(ierr);
1058   ierr = PetscFree(mfqP->L_tmp);CHKERRQ(ierr);
1059   ierr = PetscFree(mfqP->L_save);CHKERRQ(ierr);
1060   ierr = PetscFree(mfqP->N);CHKERRQ(ierr);
1061   ierr = PetscFree(mfqP->M);CHKERRQ(ierr);
1062   ierr = PetscFree(mfqP->Z);CHKERRQ(ierr);
1063   ierr = PetscFree(mfqP->tau);CHKERRQ(ierr);
1064   ierr = PetscFree(mfqP->tau_tmp);CHKERRQ(ierr);
1065   ierr = PetscFree(mfqP->npmaxwork);CHKERRQ(ierr);
1066   ierr = PetscFree(mfqP->npmaxiwork);CHKERRQ(ierr);
1067   ierr = PetscFree(mfqP->xmin);CHKERRQ(ierr);
1068   ierr = PetscFree(mfqP->C);CHKERRQ(ierr);
1069   ierr = PetscFree(mfqP->Fdiff);CHKERRQ(ierr);
1070   ierr = PetscFree(mfqP->Disp);CHKERRQ(ierr);
1071   ierr = PetscFree(mfqP->Gres);CHKERRQ(ierr);
1072   ierr = PetscFree(mfqP->Hres);CHKERRQ(ierr);
1073   ierr = PetscFree(mfqP->Gpoints);CHKERRQ(ierr);
1074   ierr = PetscFree(mfqP->model_indices);CHKERRQ(ierr);
1075   ierr = PetscFree(mfqP->last_model_indices);CHKERRQ(ierr);
1076   ierr = PetscFree(mfqP->Xsubproblem);CHKERRQ(ierr);
1077   ierr = PetscFree(mfqP->Gdel);CHKERRQ(ierr);
1078   ierr = PetscFree(mfqP->Hdel);CHKERRQ(ierr);
1079   ierr = PetscFree(mfqP->indices);CHKERRQ(ierr);
1080   ierr = PetscFree(mfqP->iwork);CHKERRQ(ierr);
1081 
1082   for (i=0;i<mfqP->nHist;i++) {
1083     ierr = VecDestroy(&mfqP->Xhist[i]);CHKERRQ(ierr);
1084     ierr = VecDestroy(&mfqP->Fhist[i]);CHKERRQ(ierr);
1085   }
1086   if (mfqP->workxvec) {
1087     ierr = VecDestroy(&mfqP->workxvec);CHKERRQ(ierr);
1088   }
1089   ierr = PetscFree(mfqP->Xhist);CHKERRQ(ierr);
1090   ierr = PetscFree(mfqP->Fhist);CHKERRQ(ierr);
1091 
1092   if (mfqP->size > 1) {
1093     ierr = VecDestroy(&mfqP->localx);CHKERRQ(ierr);
1094     ierr = VecDestroy(&mfqP->localxmin);CHKERRQ(ierr);
1095     ierr = VecDestroy(&mfqP->localf);CHKERRQ(ierr);
1096     ierr = VecDestroy(&mfqP->localfmin);CHKERRQ(ierr);
1097   }
1098   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1099   PetscFunctionReturn(0);
1100 }
1101 
1102 #undef __FUNCT__
1103 #define __FUNCT__ "TaoSetFromOptions_POUNDERS"
1104 static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptions *PetscOptionsObject,Tao tao)
1105 {
1106   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   ierr = PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");CHKERRQ(ierr);
1111   ierr = PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);CHKERRQ(ierr);
1112   mfqP->delta = mfqP->delta0;
1113   mfqP->npmax = PETSC_DEFAULT;
1114   ierr = PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);CHKERRQ(ierr);
1115   mfqP->usegqt = PETSC_FALSE;
1116   ierr = PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);CHKERRQ(ierr);
1117   ierr = PetscOptionsTail();CHKERRQ(ierr);
1118   PetscFunctionReturn(0);
1119 }
1120 
1121 #undef __FUNCT__
1122 #define __FUNCT__ "TaoView_POUNDERS"
1123 static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1124 {
1125   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1126   PetscBool      isascii;
1127   PetscInt       nits;
1128   PetscErrorCode ierr;
1129 
1130   PetscFunctionBegin;
1131   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1132   if (isascii) {
1133     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1134     ierr = PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);CHKERRQ(ierr);
1135     ierr = PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);CHKERRQ(ierr);
1136     ierr = PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);CHKERRQ(ierr);
1137     if (mfqP->usegqt) {
1138       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");CHKERRQ(ierr);
1139     } else {
1140       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);CHKERRQ(ierr);
1141       ierr = TaoGetTotalIterationNumber(mfqP->subtao,&nits);CHKERRQ(ierr);
1142       ierr = PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);CHKERRQ(ierr);
1143     }
1144     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1145   }
1146   PetscFunctionReturn(0);
1147 }
1148 /*MC
1149   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares
1150 
1151   Options Database Keys:
1152 + -tao_pounders_delta - initial step length
1153 . -tao_pounders_npmax - maximum number of points in model
1154 - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON
1155 
1156   Level: beginner
1157 
1158 M*/
1159 
1160 #undef __FUNCT__
1161 #define __FUNCT__ "TaoCreate_POUNDERS"
1162 PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1163 {
1164   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1165   PetscErrorCode ierr;
1166 
1167   PetscFunctionBegin;
1168   tao->ops->setup = TaoSetUp_POUNDERS;
1169   tao->ops->solve = TaoSolve_POUNDERS;
1170   tao->ops->view = TaoView_POUNDERS;
1171   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1172   tao->ops->destroy = TaoDestroy_POUNDERS;
1173 
1174   ierr = PetscNewLog(tao,&mfqP);CHKERRQ(ierr);
1175   tao->data = (void*)mfqP;
1176   /* Override default settings (unless already changed) */
1177   if (!tao->max_it_changed) tao->max_it = 2000;
1178   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1179 #if defined(PETSC_USE_REAL_SINGLE)
1180   if (!tao->fatol_changed) tao->fatol = 1.0e-4;
1181   if (!tao->frtol_changed) tao->frtol = 1.0e-4;
1182   mfqP->deltamin=1e-3;
1183 #else
1184   if (!tao->fatol_changed) tao->fatol = 1.0e-8;
1185   if (!tao->frtol_changed) tao->frtol = 1.0e-8;
1186   mfqP->deltamin=1e-6;
1187 #endif
1188   mfqP->delta0 = 0.1;
1189   mfqP->delta = 0.1;
1190   mfqP->deltamax=1e3;
1191   mfqP->c2 = 100.0;
1192   mfqP->theta1=1e-5;
1193   mfqP->theta2=1e-4;
1194   mfqP->gamma0=0.5;
1195   mfqP->gamma1=2.0;
1196   mfqP->eta0 = 0.0;
1197   mfqP->eta1 = 0.1;
1198   mfqP->gqt_rtol = 0.001;
1199   mfqP->gqt_maxits = 50;
1200   mfqP->workxvec = 0;
1201   PetscFunctionReturn(0);
1202 }
1203 
1204 
1205