xref: /petsc/src/tao/leastsquares/impls/pounders/pounders.c (revision 4f02bc6a7df4e4b03c783003a8e0899ee35fcb05)
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,*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     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
330     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));
331     ierr = PetscFPTrapPop();CHKERRQ(ierr);
332     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);
333 
334     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
335       /* accept point */
336       mfqP->model_indices[mfqP->nmodelpoints] = point;
337       /* Copy Q_tmp to Q */
338       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
339         mfqP->Q[i] = mfqP->Q_tmp[i];
340       }
341       for (i=0;i<mfqP->npmax;i++){
342         mfqP->tau[i] = mfqP->tau_tmp[i];
343       }
344       mfqP->nmodelpoints++;
345       blasnp = mfqP->nmodelpoints;
346 
347       /* Copy L_save to L */
348       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
349         mfqP->L[i] = mfqP->L_save[i];
350       }
351     }
352     point--;
353   }
354 
355   blasnp = mfqP->nmodelpoints;
356   /* Copy Q(:,n+2:np) to Z */
357   /* First set Q_tmp to I */
358   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
359     mfqP->Q_tmp[i] = 0.0;
360   }
361   for (i=0;i<mfqP->npmax;i++) {
362     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
363   }
364 
365   /* Q_tmp = I * Q */
366   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
367   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
368 
369   /* Copy Q_tmp(:,n+2:np) to Z) */
370   offset = mfqP->npmax * (mfqP->n+1);
371   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
372     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
373   }
374 
375   if (mfqP->nmodelpoints == mfqP->n + 1) {
376     /* Set L to I_{n+1} */
377     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
378       mfqP->L[i] = 0.0;
379     }
380     for (i=0;i<mfqP->n;i++) {
381       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
382     }
383   }
384   PetscFunctionReturn(0);
385 }
386 
387 #undef __FUNCT__
388 #define __FUNCT__ "addpoint"
389 /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
390 PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
391 {
392   PetscErrorCode ierr;
393 
394   PetscFunctionBegin;
395   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
396   ierr = VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
397   ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);CHKERRQ(ierr);
398   ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
399   ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
400   ierr = VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
401 
402   /* Project into feasible region */
403   if (tao->XU && tao->XL) {
404     ierr = VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
405   }
406 
407   /* Compute value of new vector */
408   ierr = VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
409   CHKMEMQ;
410   ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
411   ierr = VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
412   if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
413   mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
414 
415   /* Add new vector to model */
416   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
417   mfqP->nmodelpoints++;
418   mfqP->nHist++;
419   PetscFunctionReturn(0);
420 }
421 
422 #undef __FUNCT__
423 #define __FUNCT__ "modelimprove"
424 PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
425 {
426   /* modeld = Q(:,np+1:n)' */
427   PetscErrorCode ierr;
428   PetscInt       i,j,minindex=0;
429   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
430   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
431   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;
432 
433   blask = mfqP->nmodelpoints;
434   /* Qtmp = I(n x n) */
435   for (i=0;i<mfqP->n;i++) {
436     for (j=0;j<mfqP->n;j++) {
437       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
438     }
439   }
440   for (j=0;j<mfqP->n;j++) {
441     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
442   }
443 
444   /* Qtmp = Q * I */
445   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
446 
447   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
448     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
449     if (dp>0.0) { /* Model says use the other direction! */
450       for (j=0;j<mfqP->n;j++) {
451         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
452       }
453     }
454     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
455     for (j=0;j<mfqP->n;j++) {
456       mfqP->work2[j] = mfqP->Gres[j];
457     }
458     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
459     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
460     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
461       minindex=i;
462       minvalue = mfqP->work[i];
463     }
464     if (addallpoints != 0) {
465       ierr = addpoint(tao,mfqP,i);CHKERRQ(ierr);
466     }
467   }
468   if (!addallpoints) {
469     ierr = addpoint(tao,mfqP,minindex);CHKERRQ(ierr);
470   }
471   PetscFunctionReturn(0);
472 }
473 
474 
475 #undef __FUNCT__
476 #define __FUNCT__ "affpoints"
477 PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
478 {
479   PetscInt        i,j;
480   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
481   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
482   PetscReal       proj,normd;
483   const PetscReal *x;
484   PetscErrorCode  ierr;
485 
486   PetscFunctionBegin;
487   for (i=mfqP->nHist-1;i>=0;i--) {
488     ierr = VecGetArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
489     for (j=0;j<mfqP->n;j++) {
490       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
491     }
492     ierr = VecRestoreArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
493     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
494     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
495     if (normd <= c*c) {
496       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
497       if (!mfqP->q_is_I) {
498         /* project D onto null */
499         blask=(mfqP->nmodelpoints);
500         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
501         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
502       }
503       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);
504 
505       if (proj >= mfqP->theta1) { /* add this index to model */
506         mfqP->model_indices[mfqP->nmodelpoints]=i;
507         mfqP->nmodelpoints++;
508         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
509         blask=mfqP->npmax*(mfqP->nmodelpoints);
510         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
511         blask = mfqP->nmodelpoints;
512         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
513         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
514         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
515         mfqP->q_is_I = 0;
516       }
517       if (mfqP->nmodelpoints == mfqP->n)  {
518         break;
519       }
520     }
521   }
522 
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "TaoSolve_POUNDERS"
528 static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
529 {
530   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
531   PetscInt           i,ii,j,k,l;
532   PetscReal          step=1.0;
533   TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
534   PetscInt           low,high;
535   PetscReal          minnorm;
536   PetscReal          *x,*f;
537   const PetscReal    *xmint,*fmin;
538   PetscReal          cres,deltaold;
539   PetscReal          gnorm;
540   PetscBLASInt       info,ione=1,iblas;
541   PetscBool          valid,same;
542   PetscReal          mdec, rho, normxsp;
543   PetscReal          one=1.0,zero=0.0,ratio;
544   PetscBLASInt       blasm,blasn,blasnpmax,blasn2;
545   PetscErrorCode     ierr;
546   static PetscBool   set = PETSC_FALSE;
547 
548   /* n = # of parameters
549      m = dimension (components) of function  */
550   PetscFunctionBegin;
551   ierr = PetscCitationsRegister("@article{UNEDF0,\n"
552                                 "title = {Nuclear energy density optimization},\n"
553                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
554                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
555                                 "journal = {Phys. Rev. C},\n"
556                                 "volume = {82},\n"
557                                 "number = {2},\n"
558                                 "pages = {024313},\n"
559                                 "numpages = {18},\n"
560                                 "year = {2010},\n"
561                                 "month = {Aug},\n"
562                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);CHKERRQ(ierr);
563   tao->niter=0;
564   if (tao->XL && tao->XU) {
565     /* Check x0 <= XU */
566     PetscReal val;
567     ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
568     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
569     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
570     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");
571 
572     /* Check x0 >= xl */
573     ierr = VecCopy(tao->XL,mfqP->Xhist[0]);CHKERRQ(ierr);
574     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);CHKERRQ(ierr);
575     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
576     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");
577 
578     /* Check x0 + delta < XU  -- should be able to get around this eventually */
579 
580     ierr = VecSet(mfqP->Xhist[0],mfqP->delta);CHKERRQ(ierr);
581     ierr = VecAXPY(mfqP->Xhist[0],1.0,tao->solution);CHKERRQ(ierr);
582     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
583     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
584     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
585   }
586 
587   CHKMEMQ;
588   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
589   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) mfqP->H[i]=0;
590 
591   ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
592   CHKMEMQ;
593   ierr = TaoComputeSeparableObjective(tao,tao->solution,mfqP->Fhist[0]);CHKERRQ(ierr);
594 
595   ierr = VecNorm(mfqP->Fhist[0],NORM_2,&mfqP->Fres[0]);CHKERRQ(ierr);
596   if (PetscIsInfOrNanReal(mfqP->Fres[0])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
597   mfqP->Fres[0]*=mfqP->Fres[0];
598   mfqP->minindex = 0;
599   minnorm = mfqP->Fres[0];
600   ierr = TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);CHKERRQ(ierr);
601   tao->niter++;
602 
603   ierr = VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);CHKERRQ(ierr);
604   for (i=1;i<mfqP->n+1;i++) {
605     ierr = VecCopy(tao->solution,mfqP->Xhist[i]);CHKERRQ(ierr);
606     if (i-1 >= low && i-1 < high) {
607       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
608       x[i-1-low] += mfqP->delta;
609       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
610     }
611     CHKMEMQ;
612     ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[i],mfqP->Fhist[i]);CHKERRQ(ierr);
613     ierr = VecNorm(mfqP->Fhist[i],NORM_2,&mfqP->Fres[i]);CHKERRQ(ierr);
614     if (PetscIsInfOrNanReal(mfqP->Fres[i])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
615     mfqP->Fres[i]*=mfqP->Fres[i];
616     if (mfqP->Fres[i] < minnorm) {
617       mfqP->minindex = i;
618       minnorm = mfqP->Fres[i];
619     }
620   }
621   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
622   ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
623   /* Gather mpi vecs to one big local vec */
624 
625   /* Begin serial code */
626 
627   /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
628   /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
629   /* (Column oriented for blas calls) */
630   ii=0;
631 
632   if (mfqP->size == 1) {
633     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
634     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
635     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
636     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
637     for (i=0;i<mfqP->n+1;i++) {
638       if (i == mfqP->minindex) continue;
639 
640       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
641       for (j=0;j<mfqP->n;j++) {
642         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
643       }
644       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
645 
646       ierr = VecGetArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
647       for (j=0;j<mfqP->m;j++) {
648         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
649       }
650       ierr = VecRestoreArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
651       mfqP->model_indices[ii++] = i;
652 
653     }
654     for (j=0;j<mfqP->m;j++) {
655       mfqP->C[j] = fmin[j];
656     }
657     ierr = VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
658   } else {
659     ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
660     ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
661     ierr = VecGetArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
662     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
663     ierr = VecRestoreArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
664 
665     ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
666     ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
667     ierr = VecGetArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
668     for (i=0;i<mfqP->n+1;i++) {
669       if (i == mfqP->minindex) continue;
670 
671       mfqP->model_indices[ii++] = i;
672       ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
673       ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
674       ierr = VecGetArray(mfqP->localx,&x);CHKERRQ(ierr);
675       for (j=0;j<mfqP->n;j++) {
676         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
677       }
678       ierr = VecRestoreArray(mfqP->localx,&x);CHKERRQ(ierr);
679 
680       ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
681       ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
682       ierr = VecGetArray(mfqP->localf,&f);CHKERRQ(ierr);
683       for (j=0;j<mfqP->m;j++) {
684         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
685       }
686       ierr = VecRestoreArray(mfqP->localf,&f);CHKERRQ(ierr);
687     }
688     for (j=0;j<mfqP->m;j++) {
689       mfqP->C[j] = fmin[j];
690     }
691     ierr = VecRestoreArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
692   }
693 
694   /* Determine the initial quadratic models */
695   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
696   /* D (nxn) Fdiff (nxm)  => G (nxm) */
697   blasn2 = blasn;
698   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasn2,&info));
699   ierr = PetscInfo1(tao,"gesv returned %d\n",info);CHKERRQ(ierr);
700 
701   cres = minnorm;
702   /* Gres = G*F(xkin,1:m)'  G (nxm)   Fk (m)   */
703   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
704 
705   /*  Hres = G*G'  */
706   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));
707 
708   valid = PETSC_TRUE;
709 
710   ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
711   ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
712   ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
713   ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
714   gnorm *= mfqP->delta;
715   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
716   ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
717   mfqP->nHist = mfqP->n+1;
718   mfqP->nmodelpoints = mfqP->n+1;
719 
720   while (reason == TAO_CONTINUE_ITERATING) {
721     PetscReal gnm = 1e-4;
722     tao->niter++;
723     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
724     ierr = gqtwrap(tao,&gnm,&mdec);CHKERRQ(ierr);
725     /* Evaluate the function at the new point */
726 
727     for (i=0;i<mfqP->n;i++) {
728         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
729     }
730     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
731     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
732     ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);CHKERRQ(ierr);
733     ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
734     ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
735 
736     ierr = TaoComputeSeparableObjective(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
737     ierr = VecNorm(mfqP->Fhist[mfqP->nHist],NORM_2,&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
738     if (PetscIsInfOrNanReal(mfqP->Fres[mfqP->nHist])) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
739     mfqP->Fres[mfqP->nHist]*=mfqP->Fres[mfqP->nHist];
740     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
741     mfqP->nHist++;
742 
743     /* Update the center */
744     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
745       /* Update model to reflect new base point */
746       for (i=0;i<mfqP->n;i++) {
747         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
748       }
749       for (j=0;j<mfqP->m;j++) {
750         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
751          G(:,j) = G(:,j) + H(:,:,j)*work' */
752         for (k=0;k<mfqP->n;k++) {
753           mfqP->work2[k]=0.0;
754           for (l=0;l<mfqP->n;l++) {
755             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
756           }
757         }
758         for (i=0;i<mfqP->n;i++) {
759           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
760           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
761         }
762       }
763       /* Cres += work*Gres + .5*work*Hres*work';
764        Gres += Hres*work'; */
765 
766       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
767       for (i=0;i<mfqP->n;i++) {
768         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
769         mfqP->Gres[i] += mfqP->work2[i];
770       }
771       mfqP->minindex = mfqP->nHist-1;
772       minnorm = mfqP->Fres[mfqP->minindex];
773       ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
774       /* Change current center */
775       ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
776       for (i=0;i<mfqP->n;i++) {
777         mfqP->xmin[i] = xmint[i];
778       }
779       ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
780     }
781 
782     /* Evaluate at a model-improving point if necessary */
783     if (valid == PETSC_FALSE) {
784       mfqP->q_is_I = 1;
785       mfqP->nmodelpoints = 0;
786       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
787       if (mfqP->nmodelpoints < mfqP->n) {
788         ierr = PetscInfo(tao,"Model not valid -- model-improving\n");CHKERRQ(ierr);
789         ierr = modelimprove(tao,mfqP,1);CHKERRQ(ierr);
790       }
791     }
792 
793     /* Update the trust region radius */
794     deltaold = mfqP->delta;
795     normxsp = 0;
796     for (i=0;i<mfqP->n;i++) {
797       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
798     }
799     normxsp = PetscSqrtReal(normxsp);
800     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
801       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
802     } else if (valid == PETSC_TRUE) {
803       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
804     }
805 
806     /* Compute the next interpolation set */
807     mfqP->q_is_I = 1;
808     mfqP->nmodelpoints=0;
809     ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
810     if (mfqP->nmodelpoints == mfqP->n) {
811       valid = PETSC_TRUE;
812     } else {
813       valid = PETSC_FALSE;
814       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c2);CHKERRQ(ierr);
815       if (mfqP->n > mfqP->nmodelpoints) {
816         ierr = PetscInfo(tao,"Model not valid -- adding geometry points\n");CHKERRQ(ierr);
817         ierr = modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);CHKERRQ(ierr);
818       }
819     }
820     for (i=mfqP->nmodelpoints;i>0;i--) {
821       mfqP->model_indices[i] = mfqP->model_indices[i-1];
822     }
823     mfqP->nmodelpoints++;
824     mfqP->model_indices[0] = mfqP->minindex;
825     ierr = morepoints(mfqP);CHKERRQ(ierr);
826     for (i=0;i<mfqP->nmodelpoints;i++) {
827       ierr = VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
828       for (j=0;j<mfqP->n;j++) {
829         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
830       }
831       ierr = VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
832       ierr = VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
833       for (j=0;j<mfqP->m;j++) {
834         for (k=0;k<mfqP->n;k++)  {
835           mfqP->work[k]=0.0;
836           for (l=0;l<mfqP->n;l++) {
837             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
838           }
839         }
840         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];
841       }
842       ierr = VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
843     }
844 
845     /* Update the quadratic model */
846     ierr = getquadpounders(mfqP);CHKERRQ(ierr);
847     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
848     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
849     /* G = G*(delta/deltaold) + Gdel */
850     ratio = mfqP->delta/deltaold;
851     iblas = blasm*blasn;
852     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
853     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
854     /* H = H*(delta/deltaold) + Hdel */
855     iblas = blasm*blasn*blasn;
856     ratio *= ratio;
857     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
858     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));
859 
860     /* Get residuals */
861     cres = mfqP->Fres[mfqP->minindex];
862     /* Gres = G*F(xkin,1:m)' */
863     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
864     /* Hres = sum i=1..m {F(xkin,i)*H(:,:,i)}   + G*G' */
865     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->Fdiff,&blasn,&zero,mfqP->Hres,&blasn));
866 
867     iblas = mfqP->n*mfqP->n;
868 
869     for (j=0;j<mfqP->m;j++) {
870       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&fmin[j],&mfqP->H[j],&blasm,mfqP->Hres,&ione));
871     }
872 
873     /* Export solution and gradient residual to TAO */
874     ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
875     ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
876     ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
877     ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
878     ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
879     gnorm *= mfqP->delta;
880     /*  final criticality test */
881     ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
882     /* test for repeated model */
883     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
884       same = PETSC_TRUE;
885     } else {
886       same = PETSC_FALSE;
887     }
888     for (i=0;i<mfqP->nmodelpoints;i++) {
889       if (same) {
890         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
891           same = PETSC_TRUE;
892         } else {
893           same = PETSC_FALSE;
894         }
895       }
896       mfqP->last_model_indices[i] = mfqP->model_indices[i];
897     }
898     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
899     if (same && mfqP->delta == deltaold) {
900       ierr = PetscInfo(tao,"Identical model used in successive iterations\n");CHKERRQ(ierr);
901       reason = TAO_CONVERGED_STEPTOL;
902       tao->reason = TAO_CONVERGED_STEPTOL;
903     }
904   }
905   PetscFunctionReturn(0);
906 }
907 
908 #undef __FUNCT__
909 #define __FUNCT__ "TaoSetUp_POUNDERS"
910 static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
911 {
912   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
913   PetscInt       i;
914   IS             isfloc,isfglob,isxloc,isxglob;
915   PetscErrorCode ierr;
916 
917   PetscFunctionBegin;
918   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);  }
919   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);  }
920   ierr = VecGetSize(tao->solution,&mfqP->n);CHKERRQ(ierr);
921   ierr = VecGetSize(tao->sep_objective,&mfqP->m);CHKERRQ(ierr);
922   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
923   if (mfqP->npmax == PETSC_DEFAULT) {
924     mfqP->npmax = 2*mfqP->n + 1;
925   }
926   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
927   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);
928 
929   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);CHKERRQ(ierr);
930   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);CHKERRQ(ierr);
931   for (i=0;i<mfqP->n +1;i++) {
932     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[i]);CHKERRQ(ierr);
933     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);CHKERRQ(ierr);
934   }
935   ierr = VecDuplicate(tao->solution,&mfqP->workxvec);CHKERRQ(ierr);
936   mfqP->nHist = 0;
937 
938   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);CHKERRQ(ierr);
939   ierr = PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);CHKERRQ(ierr);
940   ierr = PetscMalloc1(mfqP->n,&mfqP->work);CHKERRQ(ierr);
941   ierr = PetscMalloc1(mfqP->n,&mfqP->work2);CHKERRQ(ierr);
942   ierr = PetscMalloc1(mfqP->n,&mfqP->work3);CHKERRQ(ierr);
943   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);CHKERRQ(ierr);
944   ierr = PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);CHKERRQ(ierr);
945   ierr = PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);CHKERRQ(ierr);
946   ierr = PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);CHKERRQ(ierr);
947 
948   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);CHKERRQ(ierr);
949   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);CHKERRQ(ierr);
950   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);CHKERRQ(ierr);
951   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);CHKERRQ(ierr);
952   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);CHKERRQ(ierr);
953   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);CHKERRQ(ierr);
954   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);CHKERRQ(ierr);
955   ierr = PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);CHKERRQ(ierr);
956   ierr = PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);CHKERRQ(ierr);
957   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau);CHKERRQ(ierr);
958   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);CHKERRQ(ierr);
959   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
960   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);CHKERRQ(ierr);
961   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);CHKERRQ(ierr);
962   ierr = PetscMalloc1(mfqP->n,&mfqP->xmin);CHKERRQ(ierr);
963   ierr = PetscMalloc1(mfqP->m,&mfqP->C);CHKERRQ(ierr);
964   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);CHKERRQ(ierr);
965   ierr = PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);CHKERRQ(ierr);
966   ierr = PetscMalloc1(mfqP->n,&mfqP->Gres);CHKERRQ(ierr);
967   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);CHKERRQ(ierr);
968   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);CHKERRQ(ierr);
969   ierr = PetscMalloc1(mfqP->npmax,&mfqP->model_indices);CHKERRQ(ierr);
970   ierr = PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);CHKERRQ(ierr);
971   ierr = PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);CHKERRQ(ierr);
972   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);CHKERRQ(ierr);
973   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);CHKERRQ(ierr);
974   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);CHKERRQ(ierr);
975   ierr = PetscMalloc1(mfqP->n,&mfqP->iwork);CHKERRQ(ierr);
976   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
977     mfqP->indices[i] = i;
978   }
979   ierr = MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);CHKERRQ(ierr);
980   if (mfqP->size > 1) {
981     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);CHKERRQ(ierr);
982     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);CHKERRQ(ierr);
983     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);CHKERRQ(ierr);
984     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);CHKERRQ(ierr);
985     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);CHKERRQ(ierr);
986     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);CHKERRQ(ierr);
987     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);CHKERRQ(ierr);
988     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);CHKERRQ(ierr);
989 
990 
991     ierr = VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);CHKERRQ(ierr);
992     ierr = VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);CHKERRQ(ierr);
993 
994     ierr = ISDestroy(&isxloc);CHKERRQ(ierr);
995     ierr = ISDestroy(&isxglob);CHKERRQ(ierr);
996     ierr = ISDestroy(&isfloc);CHKERRQ(ierr);
997     ierr = ISDestroy(&isfglob);CHKERRQ(ierr);
998   }
999 
1000   if (!mfqP->usegqt) {
1001     KSP       ksp;
1002     PC        pc;
1003     ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);CHKERRQ(ierr);
1004     ierr = VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);CHKERRQ(ierr);
1005     ierr = VecDuplicate(mfqP->subxl,&mfqP->subb);CHKERRQ(ierr);
1006     ierr = VecDuplicate(mfqP->subxl,&mfqP->subxu);CHKERRQ(ierr);
1007     ierr = VecDuplicate(mfqP->subxl,&mfqP->subpdel);CHKERRQ(ierr);
1008     ierr = VecDuplicate(mfqP->subxl,&mfqP->subndel);CHKERRQ(ierr);
1009     ierr = TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);CHKERRQ(ierr);
1010     ierr = TaoSetType(mfqP->subtao,TAOTRON);CHKERRQ(ierr);
1011     ierr = TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");CHKERRQ(ierr);
1012     ierr = TaoSetInitialVector(mfqP->subtao,mfqP->subx);CHKERRQ(ierr);
1013     ierr = TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);CHKERRQ(ierr);
1014     ierr = TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);CHKERRQ(ierr);
1015     ierr = TaoSetFromOptions(mfqP->subtao);CHKERRQ(ierr);
1016     ierr = TaoGetKSP(mfqP->subtao,&ksp);CHKERRQ(ierr);
1017     if (ksp) {
1018       ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
1019       ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
1020     }
1021     ierr = TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);CHKERRQ(ierr);
1022     ierr = MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);CHKERRQ(ierr);
1023     ierr = TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);CHKERRQ(ierr);
1024   }
1025   PetscFunctionReturn(0);
1026 }
1027 
1028 #undef __FUNCT__
1029 #define __FUNCT__ "TaoDestroy_POUNDERS"
1030 static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1031 {
1032   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1033   PetscInt       i;
1034   PetscErrorCode ierr;
1035 
1036   PetscFunctionBegin;
1037   if (!mfqP->usegqt) {
1038     ierr = TaoDestroy(&mfqP->subtao);CHKERRQ(ierr);
1039     ierr = VecDestroy(&mfqP->subx);CHKERRQ(ierr);
1040     ierr = VecDestroy(&mfqP->subxl);CHKERRQ(ierr);
1041     ierr = VecDestroy(&mfqP->subxu);CHKERRQ(ierr);
1042     ierr = VecDestroy(&mfqP->subb);CHKERRQ(ierr);
1043     ierr = VecDestroy(&mfqP->subpdel);CHKERRQ(ierr);
1044     ierr = VecDestroy(&mfqP->subndel);CHKERRQ(ierr);
1045     ierr = MatDestroy(&mfqP->subH);CHKERRQ(ierr);
1046   }
1047   ierr = PetscFree(mfqP->Fres);CHKERRQ(ierr);
1048   ierr = PetscFree(mfqP->RES);CHKERRQ(ierr);
1049   ierr = PetscFree(mfqP->work);CHKERRQ(ierr);
1050   ierr = PetscFree(mfqP->work2);CHKERRQ(ierr);
1051   ierr = PetscFree(mfqP->work3);CHKERRQ(ierr);
1052   ierr = PetscFree(mfqP->mwork);CHKERRQ(ierr);
1053   ierr = PetscFree(mfqP->omega);CHKERRQ(ierr);
1054   ierr = PetscFree(mfqP->beta);CHKERRQ(ierr);
1055   ierr = PetscFree(mfqP->alpha);CHKERRQ(ierr);
1056   ierr = PetscFree(mfqP->H);CHKERRQ(ierr);
1057   ierr = PetscFree(mfqP->Q);CHKERRQ(ierr);
1058   ierr = PetscFree(mfqP->Q_tmp);CHKERRQ(ierr);
1059   ierr = PetscFree(mfqP->L);CHKERRQ(ierr);
1060   ierr = PetscFree(mfqP->L_tmp);CHKERRQ(ierr);
1061   ierr = PetscFree(mfqP->L_save);CHKERRQ(ierr);
1062   ierr = PetscFree(mfqP->N);CHKERRQ(ierr);
1063   ierr = PetscFree(mfqP->M);CHKERRQ(ierr);
1064   ierr = PetscFree(mfqP->Z);CHKERRQ(ierr);
1065   ierr = PetscFree(mfqP->tau);CHKERRQ(ierr);
1066   ierr = PetscFree(mfqP->tau_tmp);CHKERRQ(ierr);
1067   ierr = PetscFree(mfqP->npmaxwork);CHKERRQ(ierr);
1068   ierr = PetscFree(mfqP->npmaxiwork);CHKERRQ(ierr);
1069   ierr = PetscFree(mfqP->xmin);CHKERRQ(ierr);
1070   ierr = PetscFree(mfqP->C);CHKERRQ(ierr);
1071   ierr = PetscFree(mfqP->Fdiff);CHKERRQ(ierr);
1072   ierr = PetscFree(mfqP->Disp);CHKERRQ(ierr);
1073   ierr = PetscFree(mfqP->Gres);CHKERRQ(ierr);
1074   ierr = PetscFree(mfqP->Hres);CHKERRQ(ierr);
1075   ierr = PetscFree(mfqP->Gpoints);CHKERRQ(ierr);
1076   ierr = PetscFree(mfqP->model_indices);CHKERRQ(ierr);
1077   ierr = PetscFree(mfqP->last_model_indices);CHKERRQ(ierr);
1078   ierr = PetscFree(mfqP->Xsubproblem);CHKERRQ(ierr);
1079   ierr = PetscFree(mfqP->Gdel);CHKERRQ(ierr);
1080   ierr = PetscFree(mfqP->Hdel);CHKERRQ(ierr);
1081   ierr = PetscFree(mfqP->indices);CHKERRQ(ierr);
1082   ierr = PetscFree(mfqP->iwork);CHKERRQ(ierr);
1083 
1084   for (i=0;i<mfqP->nHist;i++) {
1085     ierr = VecDestroy(&mfqP->Xhist[i]);CHKERRQ(ierr);
1086     ierr = VecDestroy(&mfqP->Fhist[i]);CHKERRQ(ierr);
1087   }
1088   if (mfqP->workxvec) {
1089     ierr = VecDestroy(&mfqP->workxvec);CHKERRQ(ierr);
1090   }
1091   ierr = PetscFree(mfqP->Xhist);CHKERRQ(ierr);
1092   ierr = PetscFree(mfqP->Fhist);CHKERRQ(ierr);
1093 
1094   if (mfqP->size > 1) {
1095     ierr = VecDestroy(&mfqP->localx);CHKERRQ(ierr);
1096     ierr = VecDestroy(&mfqP->localxmin);CHKERRQ(ierr);
1097     ierr = VecDestroy(&mfqP->localf);CHKERRQ(ierr);
1098     ierr = VecDestroy(&mfqP->localfmin);CHKERRQ(ierr);
1099   }
1100   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 
1104 #undef __FUNCT__
1105 #define __FUNCT__ "TaoSetFromOptions_POUNDERS"
1106 static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1107 {
1108   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1109   PetscErrorCode ierr;
1110 
1111   PetscFunctionBegin;
1112   ierr = PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");CHKERRQ(ierr);
1113   ierr = PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);CHKERRQ(ierr);
1114   mfqP->delta = mfqP->delta0;
1115   mfqP->npmax = PETSC_DEFAULT;
1116   ierr = PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);CHKERRQ(ierr);
1117   mfqP->usegqt = PETSC_FALSE;
1118   ierr = PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);CHKERRQ(ierr);
1119   ierr = PetscOptionsTail();CHKERRQ(ierr);
1120   PetscFunctionReturn(0);
1121 }
1122 
1123 #undef __FUNCT__
1124 #define __FUNCT__ "TaoView_POUNDERS"
1125 static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1126 {
1127   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1128   PetscBool      isascii;
1129   PetscInt       nits;
1130   PetscErrorCode ierr;
1131 
1132   PetscFunctionBegin;
1133   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1134   if (isascii) {
1135     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1136     ierr = PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);CHKERRQ(ierr);
1137     ierr = PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);CHKERRQ(ierr);
1138     ierr = PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);CHKERRQ(ierr);
1139     if (mfqP->usegqt) {
1140       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");CHKERRQ(ierr);
1141     } else {
1142       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);CHKERRQ(ierr);
1143       ierr = TaoGetTotalIterationNumber(mfqP->subtao,&nits);CHKERRQ(ierr);
1144       ierr = PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);CHKERRQ(ierr);
1145     }
1146     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1147   }
1148   PetscFunctionReturn(0);
1149 }
1150 /*MC
1151   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares
1152 
1153   Options Database Keys:
1154 + -tao_pounders_delta - initial step length
1155 . -tao_pounders_npmax - maximum number of points in model
1156 - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON
1157 
1158   Level: beginner
1159 
1160 M*/
1161 
1162 #undef __FUNCT__
1163 #define __FUNCT__ "TaoCreate_POUNDERS"
1164 PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1165 {
1166   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1167   PetscErrorCode ierr;
1168 
1169   PetscFunctionBegin;
1170   tao->ops->setup = TaoSetUp_POUNDERS;
1171   tao->ops->solve = TaoSolve_POUNDERS;
1172   tao->ops->view = TaoView_POUNDERS;
1173   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1174   tao->ops->destroy = TaoDestroy_POUNDERS;
1175 
1176   ierr = PetscNewLog(tao,&mfqP);CHKERRQ(ierr);
1177   tao->data = (void*)mfqP;
1178   /* Override default settings (unless already changed) */
1179   if (!tao->max_it_changed) tao->max_it = 2000;
1180   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1181   mfqP->delta0 = 0.1;
1182   mfqP->delta = 0.1;
1183   mfqP->deltamax=1e3;
1184   mfqP->c2 = 100.0;
1185   mfqP->theta1=1e-5;
1186   mfqP->theta2=1e-4;
1187   mfqP->gamma0=0.5;
1188   mfqP->gamma1=2.0;
1189   mfqP->eta0 = 0.0;
1190   mfqP->eta1 = 0.1;
1191   mfqP->gqt_rtol = 0.001;
1192   mfqP->gqt_maxits = 50;
1193   mfqP->workxvec = 0;
1194   PetscFunctionReturn(0);
1195 }
1196 
1197 
1198