xref: /petsc/src/tao/leastsquares/impls/pounders/pounders.c (revision ce90246748e1468ca04fa75c8ef0ad10c20cbbf8)
1 #include <../src/tao/leastsquares/impls/pounders/pounders.h>
2 
3 static PetscErrorCode pounders_h(Tao subtao, Vec v, Mat H, Mat Hpre, void *ctx)
4 {
5   PetscFunctionBegin;
6   PetscFunctionReturn(0);
7 }
8 
9 static PetscErrorCode  pounders_fg(Tao subtao, Vec x, PetscReal *f, Vec g, void *ctx)
10 {
11   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)ctx;
12   PetscReal      d1,d2;
13   PetscErrorCode ierr;
14 
15   PetscFunctionBegin;
16   /* g = A*x  (add b later)*/
17   ierr = MatMult(mfqP->subH,x,g);CHKERRQ(ierr);
18 
19   /* f = 1/2 * x'*(Ax) + b'*x  */
20   ierr = VecDot(x,g,&d1);CHKERRQ(ierr);
21   ierr = VecDot(mfqP->subb,x,&d2);CHKERRQ(ierr);
22   *f = 0.5 *d1 + d2;
23 
24   /* now  g = g + b */
25   ierr = VecAXPY(g, 1.0, mfqP->subb);CHKERRQ(ierr);
26   PetscFunctionReturn(0);
27 }
28 
29 static PetscErrorCode pounders_feval(Tao tao, Vec x, Vec F, PetscReal *fsum)
30 {
31   PetscErrorCode ierr;
32   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
33   PetscInt i,row,col;
34   PetscReal fr,fc;
35   PetscFunctionBegin;
36   ierr = TaoComputeSeparableObjective(tao,x,F);CHKERRQ(ierr);
37   if (tao->sep_weights_v) {
38     ierr = VecPointwiseMult(mfqP->workfvec,tao->sep_weights_v,F);CHKERRQ(ierr);
39     ierr = VecDot(mfqP->workfvec,mfqP->workfvec,fsum);CHKERRQ(ierr);
40   } else if (tao->sep_weights_w) {
41     *fsum=0;
42     for (i=0;i<tao->sep_weights_n;i++) {
43       row=tao->sep_weights_rows[i];
44       col=tao->sep_weights_cols[i];
45       ierr = VecGetValues(F,1,&row,&fr);CHKERRQ(ierr);
46       ierr = VecGetValues(F,1,&col,&fc);CHKERRQ(ierr);
47       *fsum += tao->sep_weights_w[i]*fc*fr;
48     }
49   } else {
50     ierr = VecDot(F,F,fsum);CHKERRQ(ierr);
51   }
52   if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
53   PetscFunctionReturn(0);
54 }
55 
56 PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
57 {
58   PetscErrorCode ierr;
59 #if defined(PETSC_USE_REAL_SINGLE)
60   PetscReal      atol=1.0e-5;
61 #else
62   PetscReal      atol=1.0e-10;
63 #endif
64   PetscInt       info,its;
65   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
66 
67   PetscFunctionBegin;
68   if (!mfqP->usegqt) {
69     PetscReal maxval;
70     PetscInt  i,j;
71 
72     ierr = VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
73     ierr = VecAssemblyBegin(mfqP->subb);CHKERRQ(ierr);
74     ierr = VecAssemblyEnd(mfqP->subb);CHKERRQ(ierr);
75 
76     ierr = VecSet(mfqP->subx,0.0);CHKERRQ(ierr);
77 
78     ierr = VecSet(mfqP->subndel,-1.0);CHKERRQ(ierr);
79     ierr = VecSet(mfqP->subpdel,+1.0);CHKERRQ(ierr);
80 
81     /* Complete the lower triangle of the Hessian matrix */
82     for (i=0;i<mfqP->n;i++) {
83       for (j=i+1;j<mfqP->n;j++) {
84         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
85       }
86     }
87     ierr = MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);CHKERRQ(ierr);
88     ierr = MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
89     ierr = MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
90 
91     ierr = TaoResetStatistics(mfqP->subtao);CHKERRQ(ierr);
92     /* ierr = TaoSetTolerances(mfqP->subtao,*gnorm,*gnorm,PETSC_DEFAULT);CHKERRQ(ierr); */
93     /* enforce bound constraints -- experimental */
94     if (tao->XU && tao->XL) {
95       ierr = VecCopy(tao->XU,mfqP->subxu);CHKERRQ(ierr);
96       ierr = VecAXPY(mfqP->subxu,-1.0,tao->solution);CHKERRQ(ierr);
97       ierr = VecScale(mfqP->subxu,1.0/mfqP->delta);CHKERRQ(ierr);
98       ierr = VecCopy(tao->XL,mfqP->subxl);CHKERRQ(ierr);
99       ierr = VecAXPY(mfqP->subxl,-1.0,tao->solution);CHKERRQ(ierr);
100       ierr = VecScale(mfqP->subxl,1.0/mfqP->delta);CHKERRQ(ierr);
101 
102       ierr = VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);CHKERRQ(ierr);
103       ierr = VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);CHKERRQ(ierr);
104     } else {
105       ierr = VecCopy(mfqP->subpdel,mfqP->subxu);CHKERRQ(ierr);
106       ierr = VecCopy(mfqP->subndel,mfqP->subxl);CHKERRQ(ierr);
107     }
108     /* Make sure xu > xl */
109     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
110     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
111     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
112     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
113     /* Make sure xu > tao->solution > xl */
114     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
115     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
116     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
117     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");
118 
119     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
120     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
121     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
122     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");
123 
124     ierr = TaoSolve(mfqP->subtao);CHKERRQ(ierr);
125     ierr = TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
126 
127     /* test bounds post-solution*/
128     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
129     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
130     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
131     if (maxval > 1e-5) {
132       ierr = PetscInfo(tao,"subproblem solution < lower bound\n");CHKERRQ(ierr);
133       tao->reason = TAO_DIVERGED_TR_REDUCTION;
134     }
135 
136     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
137     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
138     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
139     if (maxval > 1e-5) {
140       ierr = PetscInfo(tao,"subproblem solution > upper bound\n");CHKERRQ(ierr);
141       tao->reason = TAO_DIVERGED_TR_REDUCTION;
142     }
143   } else {
144     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);
145   }
146   *qmin *= -1;
147   PetscFunctionReturn(0);
148 }
149 
150 static PetscErrorCode pounders_update_res(Tao tao)
151 {
152   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
153   PetscInt i,row,col;
154   PetscBLASInt blasn=mfqP->n,blasn2=blasn*blasn,blasm=mfqP->m,ione=1;
155   PetscReal zero=0.0,one=1.0,wii,factor;
156   PetscErrorCode ierr;
157   PetscFunctionBegin;
158 
159   for (i=0;i<mfqP->n;i++) {
160     mfqP->Gres[i]=0;
161   }
162   for (i=0;i<mfqP->n*mfqP->n;i++) {
163     mfqP->Hres[i]=0;
164   }
165 
166   /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
167   if (tao->sep_weights_v) {
168     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
169     for (i=0;i<mfqP->m;i++) {
170       ierr = VecGetValues(tao->sep_weights_v,1,&i,&factor);CHKERRQ(ierr);
171       factor=factor*mfqP->C[i];
172       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
173     }
174 
175     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
176     /* vector(diagonal weights) Hres = sum_i(wii*(ci*Hi + gi * gi' )*/
177     for (i=0;i<mfqP->m;i++) {
178       ierr = VecGetValues(tao->sep_weights_v,1,&i,&wii);CHKERRQ(ierr);
179       if (tao->niter>1) {
180         factor=wii*mfqP->C[i];
181         /* add wii * ci * Hi */
182         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
183       }
184       /* add wii * gi * gi' */
185       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&wii,&mfqP->Fdiff[blasn*i],&blasn,&mfqP->Fdiff[blasn*i],&blasn,&one,mfqP->Hres,&blasn));
186     }
187   } else if (tao->sep_weights_w) {
188     /* General case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
189     for (i=0;i<tao->sep_weights_n;i++) {
190       row=tao->sep_weights_rows[i];
191       col=tao->sep_weights_cols[i];
192 
193       factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
194       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
195       factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
196       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
197     }
198 
199     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
200     /* .5 * sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
201     for (i=0;i<tao->sep_weights_n;i++) {
202       row=tao->sep_weights_rows[i];
203       col=tao->sep_weights_cols[i];
204       factor=tao->sep_weights_w[i]/2.0;
205       /* add wij * gi gj' + wij * gj gi' */
206       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*row],&blasn,&mfqP->Fdiff[blasn*col],&blasn,&one,mfqP->Hres,&blasn));
207       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*col],&blasn,&mfqP->Fdiff[blasn*row],&blasn,&one,mfqP->Hres,&blasn));
208     }
209     if (tao->niter > 1) {
210       for (i=0;i<tao->sep_weights_n;i++) {
211         row=tao->sep_weights_rows[i];
212         col=tao->sep_weights_cols[i];
213 
214         /* add  wij*cj*Hi */
215         factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
216         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[row],&blasn2,mfqP->Hres,&ione));
217 
218         /* add wij*ci*Hj */
219         factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
220         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasn2,mfqP->Hres,&ione));
221       }
222     }
223   } else {
224     /* Default: Gres= sum_i[cigi] = G*c' */
225     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
226 
227     /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
228     /*  Hres = G*G' + 0.5 sum {F(xkin,i)*H(:,:,i)}  */
229     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff, &blasn,&zero,mfqP->Hres,&blasn));
230 
231     /* sum(F(xkin,i)*H(:,:,i)) */
232     if (tao->niter>1) {
233       for (i=0;i<mfqP->m;i++) {
234         factor = mfqP->C[i];
235         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
236       }
237     }
238   }
239   PetscFunctionReturn(0);
240 }
241 
242 PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
243 {
244 /* 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] */
245   PetscInt  i,j,k;
246   PetscReal sqrt2 = PetscSqrtReal(2.0);
247 
248   PetscFunctionBegin;
249   j=0;
250   for (i=0;i<n;i++) {
251     phi[j] = 0.5 * x[i]*x[i];
252     j++;
253     for (k=i+1;k<n;k++) {
254       phi[j]  = x[i]*x[k]/sqrt2;
255       j++;
256     }
257   }
258   PetscFunctionReturn(0);
259 }
260 
261 PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
262 {
263 /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
264    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
265    for j=1,...,m and with a Hessian matrix of least Frobenius norm */
266 
267     /* NB --we are ignoring c */
268   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
269   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
270   PetscBLASInt blasnpmax = mfqP->npmax;
271   PetscBLASInt blasnplus1 = mfqP->n+1;
272   PetscBLASInt blasnp = np;
273   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
274   PetscBLASInt blasint2 = np - mfqP->n-1;
275   PetscBLASInt info,ione=1;
276   PetscReal    sqrt2 = PetscSqrtReal(2.0);
277 
278   PetscFunctionBegin;
279   for (i=0;i<mfqP->n*mfqP->m;i++) {
280     mfqP->Gdel[i] = 0;
281   }
282   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
283     mfqP->Hdel[i] = 0;
284   }
285 
286     /* factor M */
287   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&blasnplus1,&blasnp,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&info));
288   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrf returned with value %d\n",info);
289 
290   if (np == mfqP->n+1) {
291     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
292       mfqP->omega[i]=0.0;
293     }
294     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
295       mfqP->beta[i]=0.0;
296     }
297   } else {
298     /* Let Ltmp = (L'*L) */
299     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));
300 
301     /* factor Ltmp */
302     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
303     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
304   }
305 
306   for (k=0;k<mfqP->m;k++) {
307     if (np != mfqP->n+1) {
308       /* Solve L'*L*Omega = Z' * RESk*/
309       PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasnp,&blasint2,&one,mfqP->Z,&blasnpmax,&mfqP->RES[mfqP->npmax*k],&ione,&zero,mfqP->omega,&ione));
310       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&blasint2,&ione,mfqP->L_tmp,&blasint,mfqP->omega,&blasint2,&info));
311       if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrs returned with value %d\n",info);
312 
313       /* Beta = L*Omega */
314       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
315     }
316 
317     /* solve M'*Alpha = RESk - N'*Beta */
318     PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasint,&blasnp,&negone,mfqP->N,&blasint,mfqP->beta,&ione,&one,&mfqP->RES[mfqP->npmax*k],&ione));
319     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&blasnplus1,&ione,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&mfqP->RES[mfqP->npmax*k],&blasnplus1,&info));
320     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrs returned with value %d\n",info);
321 
322     /* Gdel(:,k) = Alpha(2:n+1) */
323     for (i=0;i<mfqP->n;i++) {
324       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
325     }
326 
327     /* Set Hdels */
328     num=0;
329     for (i=0;i<mfqP->n;i++) {
330       /* H[i,i,k] = Beta(num) */
331       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
332       num++;
333       for (j=i+1;j<mfqP->n;j++) {
334         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
335         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
336         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
337         num++;
338       }
339     }
340   }
341   PetscFunctionReturn(0);
342 }
343 
344 PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
345 {
346   /* Assumes mfqP->model_indices[0]  is minimum index
347    Finishes adding points to mfqP->model_indices (up to npmax)
348    Computes L,Z,M,N
349    np is actual number of points in model (should equal npmax?) */
350   PetscInt        point,i,j,offset;
351   PetscInt        reject;
352   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
353   const PetscReal *x;
354   PetscReal       normd;
355   PetscErrorCode  ierr;
356 
357   PetscFunctionBegin;
358   /* Initialize M,N */
359   for (i=0;i<mfqP->n+1;i++) {
360     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
361     mfqP->M[(mfqP->n+1)*i] = 1.0;
362     for (j=0;j<mfqP->n;j++) {
363       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
364     }
365     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
366     ierr = phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);CHKERRQ(ierr);
367   }
368 
369   /* Now we add points until we have npmax starting with the most recent ones */
370   point = mfqP->nHist-1;
371   mfqP->nmodelpoints = mfqP->n+1;
372   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
373     /* Reject any points already in the model */
374     reject = 0;
375     for (j=0;j<mfqP->n+1;j++) {
376       if (point == mfqP->model_indices[j]) {
377         reject = 1;
378         break;
379       }
380     }
381 
382     /* Reject if norm(d) >c2 */
383     if (!reject) {
384       ierr = VecCopy(mfqP->Xhist[point],mfqP->workxvec);CHKERRQ(ierr);
385       ierr = VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
386       ierr = VecNorm(mfqP->workxvec,NORM_2,&normd);CHKERRQ(ierr);
387       normd /= mfqP->delta;
388       if (normd > mfqP->c2) {
389         reject =1;
390       }
391     }
392     if (reject){
393       point--;
394       continue;
395     }
396 
397     ierr = VecGetArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
398     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
399     for (j=0;j<mfqP->n;j++) {
400       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
401     }
402     ierr = VecRestoreArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
403     ierr = phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);CHKERRQ(ierr);
404 
405     /* Update QR factorization */
406     /* Copy M' to Q_tmp */
407     for (i=0;i<mfqP->n+1;i++) {
408       for (j=0;j<mfqP->npmax;j++) {
409         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
410       }
411     }
412     blasnp = mfqP->nmodelpoints+1;
413     /* Q_tmp,R = qr(M') */
414     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
415     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
416     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);
417 
418     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
419     /* L = N*Qtmp */
420     blasint2 = mfqP->n * (mfqP->n+1) / 2;
421     /* Copy N to L_tmp */
422     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
423       mfqP->L_tmp[i]= mfqP->N[i];
424     }
425     /* Copy L_save to L_tmp */
426 
427     /* L_tmp = N*Qtmp' */
428     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
429     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
430 
431     /* Copy L_tmp to L_save */
432     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
433       mfqP->L_save[i] = mfqP->L_tmp[i];
434     }
435 
436     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
437     blasint = mfqP->nmodelpoints - mfqP->n;
438     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
439     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));
440     ierr = PetscFPTrapPop();CHKERRQ(ierr);
441     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);
442 
443     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
444       /* accept point */
445       mfqP->model_indices[mfqP->nmodelpoints] = point;
446       /* Copy Q_tmp to Q */
447       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
448         mfqP->Q[i] = mfqP->Q_tmp[i];
449       }
450       for (i=0;i<mfqP->npmax;i++){
451         mfqP->tau[i] = mfqP->tau_tmp[i];
452       }
453       mfqP->nmodelpoints++;
454       blasnp = mfqP->nmodelpoints;
455 
456       /* Copy L_save to L */
457       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
458         mfqP->L[i] = mfqP->L_save[i];
459       }
460     }
461     point--;
462   }
463 
464   blasnp = mfqP->nmodelpoints;
465   /* Copy Q(:,n+2:np) to Z */
466   /* First set Q_tmp to I */
467   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
468     mfqP->Q_tmp[i] = 0.0;
469   }
470   for (i=0;i<mfqP->npmax;i++) {
471     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
472   }
473 
474   /* Q_tmp = I * Q */
475   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
476   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
477 
478   /* Copy Q_tmp(:,n+2:np) to Z) */
479   offset = mfqP->npmax * (mfqP->n+1);
480   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
481     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
482   }
483 
484   if (mfqP->nmodelpoints == mfqP->n + 1) {
485     /* Set L to I_{n+1} */
486     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
487       mfqP->L[i] = 0.0;
488     }
489     for (i=0;i<mfqP->n;i++) {
490       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
491     }
492   }
493   PetscFunctionReturn(0);
494 }
495 
496 /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
497 PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
498 {
499   PetscErrorCode ierr;
500 
501   PetscFunctionBegin;
502   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
503   ierr = VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
504   ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);CHKERRQ(ierr);
505   ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
506   ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
507   ierr = VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
508 
509   /* Project into feasible region */
510   if (tao->XU && tao->XL) {
511     ierr = VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
512   }
513 
514   /* Compute value of new vector */
515   ierr = VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
516   CHKMEMQ;
517   ierr = pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
518 
519   /* Add new vector to model */
520   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
521   mfqP->nmodelpoints++;
522   mfqP->nHist++;
523   PetscFunctionReturn(0);
524 }
525 
526 PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
527 {
528   /* modeld = Q(:,np+1:n)' */
529   PetscErrorCode ierr;
530   PetscInt       i,j,minindex=0;
531   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
532   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
533   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;
534 
535   blask = mfqP->nmodelpoints;
536   /* Qtmp = I(n x n) */
537   for (i=0;i<mfqP->n;i++) {
538     for (j=0;j<mfqP->n;j++) {
539       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
540     }
541   }
542   for (j=0;j<mfqP->n;j++) {
543     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
544   }
545 
546   /* Qtmp = Q * I */
547   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
548 
549   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
550     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
551     if (dp>0.0) { /* Model says use the other direction! */
552       for (j=0;j<mfqP->n;j++) {
553         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
554       }
555     }
556     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
557     for (j=0;j<mfqP->n;j++) {
558       mfqP->work2[j] = mfqP->Gres[j];
559     }
560     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
561     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
562     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
563       minindex=i;
564       minvalue = mfqP->work[i];
565     }
566     if (addallpoints != 0) {
567       ierr = addpoint(tao,mfqP,i);CHKERRQ(ierr);
568     }
569   }
570   if (!addallpoints) {
571     ierr = addpoint(tao,mfqP,minindex);CHKERRQ(ierr);
572   }
573   PetscFunctionReturn(0);
574 }
575 
576 
577 PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
578 {
579   PetscInt        i,j;
580   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
581   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
582   PetscReal       proj,normd;
583   const PetscReal *x;
584   PetscErrorCode  ierr;
585 
586   PetscFunctionBegin;
587   for (i=mfqP->nHist-1;i>=0;i--) {
588     ierr = VecGetArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
589     for (j=0;j<mfqP->n;j++) {
590       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
591     }
592     ierr = VecRestoreArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
593     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
594     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
595     if (normd <= c*c) {
596       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
597       if (!mfqP->q_is_I) {
598         /* project D onto null */
599         blask=(mfqP->nmodelpoints);
600         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
601         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
602       }
603       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);
604 
605       if (proj >= mfqP->theta1) { /* add this index to model */
606         mfqP->model_indices[mfqP->nmodelpoints]=i;
607         mfqP->nmodelpoints++;
608         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
609         blask=mfqP->npmax*(mfqP->nmodelpoints);
610         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
611         blask = mfqP->nmodelpoints;
612         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
613         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
614         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
615         mfqP->q_is_I = 0;
616       }
617       if (mfqP->nmodelpoints == mfqP->n)  {
618         break;
619       }
620     }
621   }
622 
623   PetscFunctionReturn(0);
624 }
625 
626 static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
627 {
628   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
629   PetscInt           i,ii,j,k,l;
630   PetscReal          step=1.0;
631   TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
632   PetscInt           low,high;
633   PetscReal          minnorm;
634   PetscReal          *x,*f;
635   const PetscReal    *xmint,*fmin;
636   PetscReal          cres,deltaold;
637   PetscReal          gnorm;
638   PetscBLASInt       info,ione=1,iblas;
639   PetscBool          valid,same;
640   PetscReal          mdec, rho, normxsp;
641   PetscReal          one=1.0,zero=0.0,ratio;
642   PetscBLASInt       blasm,blasn,blasncopy,blasnpmax;
643   PetscErrorCode     ierr;
644   static PetscBool   set = PETSC_FALSE;
645 
646   /* n = # of parameters
647      m = dimension (components) of function  */
648   PetscFunctionBegin;
649   ierr = PetscCitationsRegister("@article{UNEDF0,\n"
650                                 "title = {Nuclear energy density optimization},\n"
651                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
652                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
653                                 "journal = {Phys. Rev. C},\n"
654                                 "volume = {82},\n"
655                                 "number = {2},\n"
656                                 "pages = {024313},\n"
657                                 "numpages = {18},\n"
658                                 "year = {2010},\n"
659                                 "month = {Aug},\n"
660                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);CHKERRQ(ierr);
661   tao->niter=0;
662   if (tao->XL && tao->XU) {
663     /* Check x0 <= XU */
664     PetscReal val;
665 
666     ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
667     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
668     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
669     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 > upper bound");
670 
671     /* Check x0 >= xl */
672     ierr = VecCopy(tao->XL,mfqP->Xhist[0]);CHKERRQ(ierr);
673     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->solution);CHKERRQ(ierr);
674     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
675     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 < lower bound");
676 
677     /* Check x0 + delta < XU  -- should be able to get around this eventually */
678 
679     ierr = VecSet(mfqP->Xhist[0],mfqP->delta);CHKERRQ(ierr);
680     ierr = VecAXPY(mfqP->Xhist[0],1.0,tao->solution);CHKERRQ(ierr);
681     ierr = VecAXPY(mfqP->Xhist[0],-1.0,tao->XU);CHKERRQ(ierr);
682     ierr = VecMax(mfqP->Xhist[0],NULL,&val);CHKERRQ(ierr);
683     if (val > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"X0 + delta > upper bound");
684   }
685 
686   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
687   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;++i) mfqP->H[i]=0;
688 
689   ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
690 
691   /* This provides enough information to approximate the gradient of the objective */
692   /* using a forward difference scheme. */
693 
694   i = 0;
695   ierr = pounders_feval(tao,mfqP->Xhist[0],mfqP->Fhist[0],&mfqP->Fres[0]);CHKERRQ(ierr);
696   mfqP->minindex = 0;
697   minnorm = mfqP->Fres[0];
698 
699   ierr = VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);CHKERRQ(ierr);
700   for (i=1;i<mfqP->n+1;i++) {
701     ierr = VecCopy(mfqP->Xhist[0],mfqP->Xhist[i]);CHKERRQ(ierr);
702 
703     if (i-1 >= low && i-1 < high) {
704       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
705       x[i-1-low] += mfqP->delta;
706       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
707     }
708     CHKMEMQ;
709     ierr = pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);CHKERRQ(ierr);
710     if (mfqP->Fres[i] < minnorm) {
711       mfqP->minindex = i;
712       minnorm = mfqP->Fres[i];
713     }
714   }
715   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
716   ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
717 
718   /* Gather mpi vecs to one big local vec */
719 
720   /* Begin serial code */
721 
722   /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
723   /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
724   /* (Column oriented for blas calls) */
725   ii=0;
726 
727   if (mfqP->size == 1) {
728     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
729     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
730     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
731     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
732     for (i=0;i<mfqP->n+1;i++) {
733       if (i == mfqP->minindex) continue;
734 
735       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
736       for (j=0;j<mfqP->n;j++) {
737         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
738       }
739       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
740 
741       ierr = VecGetArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
742       for (j=0;j<mfqP->m;j++) {
743         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
744       }
745       ierr = VecRestoreArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
746       mfqP->model_indices[ii++] = i;
747 
748     }
749     for (j=0;j<mfqP->m;j++) {
750       mfqP->C[j] = fmin[j];
751     }
752     ierr = VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
753   } else {
754     ierr = VecSet(mfqP->localxmin,0);CHKERRQ(ierr);
755     ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
756     ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
757     ierr = VecGetArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
758 
759     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
760     ierr = VecRestoreArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
761 
762     ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
763     ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
764     ierr = VecGetArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
765     for (i=0;i<mfqP->n+1;i++) {
766       if (i == mfqP->minindex) continue;
767 
768       mfqP->model_indices[ii++] = i;
769       ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
770       ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
771       ierr = VecGetArray(mfqP->localx,&x);CHKERRQ(ierr);
772       for (j=0;j<mfqP->n;j++) {
773         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
774       }
775       ierr = VecRestoreArray(mfqP->localx,&x);CHKERRQ(ierr);
776 
777       ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
778       ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
779       ierr = VecGetArray(mfqP->localf,&f);CHKERRQ(ierr);
780       for (j=0;j<mfqP->m;j++) {
781         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
782       }
783       ierr = VecRestoreArray(mfqP->localf,&f);CHKERRQ(ierr);
784     }
785     for (j=0;j<mfqP->m;j++) {
786       mfqP->C[j] = fmin[j];
787     }
788     ierr = VecRestoreArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
789   }
790 
791   /* Determine the initial quadratic models */
792   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
793   /* D (nxn) Fdiff (nxm)  => G (nxm) */
794   blasncopy = blasn;
795   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasncopy,&info));
796 
797   cres = minnorm;
798   ierr = pounders_update_res(tao);CHKERRQ(ierr);
799 
800   valid = PETSC_TRUE;
801 
802   ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
803   ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
804   ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
805   ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
806   gnorm *= mfqP->delta;
807   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
808   ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
809   mfqP->nHist = mfqP->n+1;
810   mfqP->nmodelpoints = mfqP->n+1;
811 
812   while (reason == TAO_CONTINUE_ITERATING) {
813     PetscReal gnm = 1e-4;
814     tao->niter++;
815     /* Solve the subproblem min{Q(s): ||s|| <= 1.0} */
816     ierr = gqtwrap(tao,&gnm,&mdec);CHKERRQ(ierr);
817     /* Evaluate the function at the new point */
818 
819     for (i=0;i<mfqP->n;i++) {
820         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
821     }
822     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
823     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
824     ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);CHKERRQ(ierr);
825     ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
826     ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
827 
828     ierr = pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
829 
830     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
831     mfqP->nHist++;
832 
833     /* Update the center */
834     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
835       /* Update model to reflect new base point */
836       for (i=0;i<mfqP->n;i++) {
837         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
838       }
839       for (j=0;j<mfqP->m;j++) {
840         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
841          G(:,j) = G(:,j) + H(:,:,j)*work' */
842         for (k=0;k<mfqP->n;k++) {
843           mfqP->work2[k]=0.0;
844           for (l=0;l<mfqP->n;l++) {
845             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
846           }
847         }
848         for (i=0;i<mfqP->n;i++) {
849           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
850           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
851         }
852       }
853       /* Cres += work*Gres + .5*work*Hres*work';
854        Gres += Hres*work'; */
855 
856       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
857       for (i=0;i<mfqP->n;i++) {
858         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
859         mfqP->Gres[i] += mfqP->work2[i];
860       }
861       mfqP->minindex = mfqP->nHist-1;
862       minnorm = mfqP->Fres[mfqP->minindex];
863       ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
864       /* Change current center */
865       ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
866       for (i=0;i<mfqP->n;i++) {
867         mfqP->xmin[i] = xmint[i];
868       }
869       ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
870     }
871 
872     /* Evaluate at a model-improving point if necessary */
873     if (valid == PETSC_FALSE) {
874       mfqP->q_is_I = 1;
875       mfqP->nmodelpoints = 0;
876       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
877       if (mfqP->nmodelpoints < mfqP->n) {
878         ierr = PetscInfo(tao,"Model not valid -- model-improving\n");CHKERRQ(ierr);
879         ierr = modelimprove(tao,mfqP,1);CHKERRQ(ierr);
880       }
881     }
882 
883     /* Update the trust region radius */
884     deltaold = mfqP->delta;
885     normxsp = 0;
886     for (i=0;i<mfqP->n;i++) {
887       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
888     }
889     normxsp = PetscSqrtReal(normxsp);
890     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
891       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
892     } else if (valid == PETSC_TRUE) {
893       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
894     }
895 
896     /* Compute the next interpolation set */
897     mfqP->q_is_I = 1;
898     mfqP->nmodelpoints=0;
899     ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
900     if (mfqP->nmodelpoints == mfqP->n) {
901       valid = PETSC_TRUE;
902     } else {
903       valid = PETSC_FALSE;
904       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c2);CHKERRQ(ierr);
905       if (mfqP->n > mfqP->nmodelpoints) {
906         ierr = PetscInfo(tao,"Model not valid -- adding geometry points\n");CHKERRQ(ierr);
907         ierr = modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);CHKERRQ(ierr);
908       }
909     }
910     for (i=mfqP->nmodelpoints;i>0;i--) {
911       mfqP->model_indices[i] = mfqP->model_indices[i-1];
912     }
913     mfqP->nmodelpoints++;
914     mfqP->model_indices[0] = mfqP->minindex;
915     ierr = morepoints(mfqP);CHKERRQ(ierr);
916     for (i=0;i<mfqP->nmodelpoints;i++) {
917       ierr = VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
918       for (j=0;j<mfqP->n;j++) {
919         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
920       }
921       ierr = VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
922       ierr = VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
923       for (j=0;j<mfqP->m;j++) {
924         for (k=0;k<mfqP->n;k++)  {
925           mfqP->work[k]=0.0;
926           for (l=0;l<mfqP->n;l++) {
927             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
928           }
929         }
930         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];
931       }
932       ierr = VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
933     }
934 
935     /* Update the quadratic model */
936     ierr = getquadpounders(mfqP);CHKERRQ(ierr);
937     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
938     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
939     /* G = G*(delta/deltaold) + Gdel */
940     ratio = mfqP->delta/deltaold;
941     iblas = blasm*blasn;
942     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
943     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
944     /* H = H*(delta/deltaold)^2 + Hdel */
945     iblas = blasm*blasn*blasn;
946     ratio *= ratio;
947     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
948     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));
949 
950     /* Get residuals */
951     cres = mfqP->Fres[mfqP->minindex];
952     ierr = pounders_update_res(tao);CHKERRQ(ierr);
953 
954     /* Export solution and gradient residual to TAO */
955     ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
956     ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
957     ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
958     ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
959     ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
960     gnorm *= mfqP->delta;
961     /*  final criticality test */
962     ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
963     /* test for repeated model */
964     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
965       same = PETSC_TRUE;
966     } else {
967       same = PETSC_FALSE;
968     }
969     for (i=0;i<mfqP->nmodelpoints;i++) {
970       if (same) {
971         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
972           same = PETSC_TRUE;
973         } else {
974           same = PETSC_FALSE;
975         }
976       }
977       mfqP->last_model_indices[i] = mfqP->model_indices[i];
978     }
979     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
980     if (same && mfqP->delta == deltaold) {
981       ierr = PetscInfo(tao,"Identical model used in successive iterations\n");CHKERRQ(ierr);
982       reason = TAO_CONVERGED_STEPTOL;
983       tao->reason = TAO_CONVERGED_STEPTOL;
984     }
985   }
986   PetscFunctionReturn(0);
987 }
988 
989 static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
990 {
991   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
992   PetscInt       i,j;
993   IS             isfloc,isfglob,isxloc,isxglob;
994   PetscErrorCode ierr;
995 
996   PetscFunctionBegin;
997   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);  }
998   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);  }
999   ierr = VecGetSize(tao->solution,&mfqP->n);CHKERRQ(ierr);
1000   ierr = VecGetSize(tao->sep_objective,&mfqP->m);CHKERRQ(ierr);
1001   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
1002   if (mfqP->npmax == PETSC_DEFAULT) {
1003     mfqP->npmax = 2*mfqP->n + 1;
1004   }
1005   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1006   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);
1007 
1008   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);CHKERRQ(ierr);
1009   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);CHKERRQ(ierr);
1010   for (i=0;i<mfqP->n+1;i++) {
1011     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[i]);CHKERRQ(ierr);
1012     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);CHKERRQ(ierr);
1013   }
1014   ierr = VecDuplicate(tao->solution,&mfqP->workxvec);CHKERRQ(ierr);
1015   ierr = VecDuplicate(tao->sep_objective,&mfqP->workfvec);CHKERRQ(ierr);
1016   mfqP->nHist = 0;
1017 
1018   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);CHKERRQ(ierr);
1019   ierr = PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);CHKERRQ(ierr);
1020   ierr = PetscMalloc1(mfqP->n,&mfqP->work);CHKERRQ(ierr);
1021   ierr = PetscMalloc1(mfqP->n,&mfqP->work2);CHKERRQ(ierr);
1022   ierr = PetscMalloc1(mfqP->n,&mfqP->work3);CHKERRQ(ierr);
1023   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);CHKERRQ(ierr);
1024   ierr = PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);CHKERRQ(ierr);
1025   ierr = PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);CHKERRQ(ierr);
1026   ierr = PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);CHKERRQ(ierr);
1027 
1028   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);CHKERRQ(ierr);
1029   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);CHKERRQ(ierr);
1030   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);CHKERRQ(ierr);
1031   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);CHKERRQ(ierr);
1032   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);CHKERRQ(ierr);
1033   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);CHKERRQ(ierr);
1034   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);CHKERRQ(ierr);
1035   ierr = PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);CHKERRQ(ierr);
1036   ierr = PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);CHKERRQ(ierr);
1037   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau);CHKERRQ(ierr);
1038   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);CHKERRQ(ierr);
1039   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1040   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);CHKERRQ(ierr);
1041   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);CHKERRQ(ierr);
1042   ierr = PetscMalloc1(mfqP->n,&mfqP->xmin);CHKERRQ(ierr);
1043   ierr = PetscMalloc1(mfqP->m,&mfqP->C);CHKERRQ(ierr);
1044   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);CHKERRQ(ierr);
1045   ierr = PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);CHKERRQ(ierr);
1046   ierr = PetscMalloc1(mfqP->n,&mfqP->Gres);CHKERRQ(ierr);
1047   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);CHKERRQ(ierr);
1048   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);CHKERRQ(ierr);
1049   ierr = PetscMalloc1(mfqP->npmax,&mfqP->model_indices);CHKERRQ(ierr);
1050   ierr = PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);CHKERRQ(ierr);
1051   ierr = PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);CHKERRQ(ierr);
1052   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);CHKERRQ(ierr);
1053   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);CHKERRQ(ierr);
1054   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);CHKERRQ(ierr);
1055   ierr = PetscMalloc1(mfqP->n,&mfqP->iwork);CHKERRQ(ierr);
1056   ierr = PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);CHKERRQ(ierr);
1057   for (i=0;i<mfqP->m;i++) {
1058     for (j=0;j<mfqP->m;j++) {
1059       if (i==j) {
1060         mfqP->w[i+mfqP->m*j]=1.0;
1061       } else {
1062         mfqP->w[i+mfqP->m*j]=0.0;
1063       }
1064     }
1065   }
1066   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1067     mfqP->indices[i] = i;
1068   }
1069   ierr = MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);CHKERRQ(ierr);
1070   if (mfqP->size > 1) {
1071     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);CHKERRQ(ierr);
1072     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);CHKERRQ(ierr);
1073     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);CHKERRQ(ierr);
1074     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);CHKERRQ(ierr);
1075     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);CHKERRQ(ierr);
1076     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);CHKERRQ(ierr);
1077     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);CHKERRQ(ierr);
1078     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);CHKERRQ(ierr);
1079 
1080 
1081     ierr = VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);CHKERRQ(ierr);
1082     ierr = VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);CHKERRQ(ierr);
1083 
1084     ierr = ISDestroy(&isxloc);CHKERRQ(ierr);
1085     ierr = ISDestroy(&isxglob);CHKERRQ(ierr);
1086     ierr = ISDestroy(&isfloc);CHKERRQ(ierr);
1087     ierr = ISDestroy(&isfglob);CHKERRQ(ierr);
1088   }
1089 
1090   if (!mfqP->usegqt) {
1091     KSP       ksp;
1092     PC        pc;
1093     ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);CHKERRQ(ierr);
1094     ierr = VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);CHKERRQ(ierr);
1095     ierr = VecDuplicate(mfqP->subxl,&mfqP->subb);CHKERRQ(ierr);
1096     ierr = VecDuplicate(mfqP->subxl,&mfqP->subxu);CHKERRQ(ierr);
1097     ierr = VecDuplicate(mfqP->subxl,&mfqP->subpdel);CHKERRQ(ierr);
1098     ierr = VecDuplicate(mfqP->subxl,&mfqP->subndel);CHKERRQ(ierr);
1099     ierr = TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);CHKERRQ(ierr);
1100     ierr = TaoSetType(mfqP->subtao,TAOTRON);CHKERRQ(ierr);
1101     ierr = TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");CHKERRQ(ierr);
1102     ierr = TaoSetInitialVector(mfqP->subtao,mfqP->subx);CHKERRQ(ierr);
1103     ierr = TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);CHKERRQ(ierr);
1104     ierr = TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);CHKERRQ(ierr);
1105     ierr = TaoSetFromOptions(mfqP->subtao);CHKERRQ(ierr);
1106     ierr = TaoGetKSP(mfqP->subtao,&ksp);CHKERRQ(ierr);
1107     if (ksp) {
1108       ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
1109       ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
1110     }
1111     ierr = TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);CHKERRQ(ierr);
1112     ierr = MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);CHKERRQ(ierr);
1113     ierr = TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);CHKERRQ(ierr);
1114   }
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1119 {
1120   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1121   PetscInt       i;
1122   PetscErrorCode ierr;
1123 
1124   PetscFunctionBegin;
1125   if (!mfqP->usegqt) {
1126     ierr = TaoDestroy(&mfqP->subtao);CHKERRQ(ierr);
1127     ierr = VecDestroy(&mfqP->subx);CHKERRQ(ierr);
1128     ierr = VecDestroy(&mfqP->subxl);CHKERRQ(ierr);
1129     ierr = VecDestroy(&mfqP->subxu);CHKERRQ(ierr);
1130     ierr = VecDestroy(&mfqP->subb);CHKERRQ(ierr);
1131     ierr = VecDestroy(&mfqP->subpdel);CHKERRQ(ierr);
1132     ierr = VecDestroy(&mfqP->subndel);CHKERRQ(ierr);
1133     ierr = MatDestroy(&mfqP->subH);CHKERRQ(ierr);
1134   }
1135   ierr = PetscFree(mfqP->Fres);CHKERRQ(ierr);
1136   ierr = PetscFree(mfqP->RES);CHKERRQ(ierr);
1137   ierr = PetscFree(mfqP->work);CHKERRQ(ierr);
1138   ierr = PetscFree(mfqP->work2);CHKERRQ(ierr);
1139   ierr = PetscFree(mfqP->work3);CHKERRQ(ierr);
1140   ierr = PetscFree(mfqP->mwork);CHKERRQ(ierr);
1141   ierr = PetscFree(mfqP->omega);CHKERRQ(ierr);
1142   ierr = PetscFree(mfqP->beta);CHKERRQ(ierr);
1143   ierr = PetscFree(mfqP->alpha);CHKERRQ(ierr);
1144   ierr = PetscFree(mfqP->H);CHKERRQ(ierr);
1145   ierr = PetscFree(mfqP->Q);CHKERRQ(ierr);
1146   ierr = PetscFree(mfqP->Q_tmp);CHKERRQ(ierr);
1147   ierr = PetscFree(mfqP->L);CHKERRQ(ierr);
1148   ierr = PetscFree(mfqP->L_tmp);CHKERRQ(ierr);
1149   ierr = PetscFree(mfqP->L_save);CHKERRQ(ierr);
1150   ierr = PetscFree(mfqP->N);CHKERRQ(ierr);
1151   ierr = PetscFree(mfqP->M);CHKERRQ(ierr);
1152   ierr = PetscFree(mfqP->Z);CHKERRQ(ierr);
1153   ierr = PetscFree(mfqP->tau);CHKERRQ(ierr);
1154   ierr = PetscFree(mfqP->tau_tmp);CHKERRQ(ierr);
1155   ierr = PetscFree(mfqP->npmaxwork);CHKERRQ(ierr);
1156   ierr = PetscFree(mfqP->npmaxiwork);CHKERRQ(ierr);
1157   ierr = PetscFree(mfqP->xmin);CHKERRQ(ierr);
1158   ierr = PetscFree(mfqP->C);CHKERRQ(ierr);
1159   ierr = PetscFree(mfqP->Fdiff);CHKERRQ(ierr);
1160   ierr = PetscFree(mfqP->Disp);CHKERRQ(ierr);
1161   ierr = PetscFree(mfqP->Gres);CHKERRQ(ierr);
1162   ierr = PetscFree(mfqP->Hres);CHKERRQ(ierr);
1163   ierr = PetscFree(mfqP->Gpoints);CHKERRQ(ierr);
1164   ierr = PetscFree(mfqP->model_indices);CHKERRQ(ierr);
1165   ierr = PetscFree(mfqP->last_model_indices);CHKERRQ(ierr);
1166   ierr = PetscFree(mfqP->Xsubproblem);CHKERRQ(ierr);
1167   ierr = PetscFree(mfqP->Gdel);CHKERRQ(ierr);
1168   ierr = PetscFree(mfqP->Hdel);CHKERRQ(ierr);
1169   ierr = PetscFree(mfqP->indices);CHKERRQ(ierr);
1170   ierr = PetscFree(mfqP->iwork);CHKERRQ(ierr);
1171   ierr = PetscFree(mfqP->w);CHKERRQ(ierr);
1172   for (i=0;i<mfqP->nHist;i++) {
1173     ierr = VecDestroy(&mfqP->Xhist[i]);CHKERRQ(ierr);
1174     ierr = VecDestroy(&mfqP->Fhist[i]);CHKERRQ(ierr);
1175   }
1176   ierr = VecDestroy(&mfqP->workxvec);CHKERRQ(ierr);
1177   ierr = VecDestroy(&mfqP->workfvec);CHKERRQ(ierr);
1178   ierr = PetscFree(mfqP->Xhist);CHKERRQ(ierr);
1179   ierr = PetscFree(mfqP->Fhist);CHKERRQ(ierr);
1180 
1181   if (mfqP->size > 1) {
1182     ierr = VecDestroy(&mfqP->localx);CHKERRQ(ierr);
1183     ierr = VecDestroy(&mfqP->localxmin);CHKERRQ(ierr);
1184     ierr = VecDestroy(&mfqP->localf);CHKERRQ(ierr);
1185     ierr = VecDestroy(&mfqP->localfmin);CHKERRQ(ierr);
1186   }
1187   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1192 {
1193   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1194   PetscErrorCode ierr;
1195 
1196   PetscFunctionBegin;
1197   ierr = PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");CHKERRQ(ierr);
1198   ierr = PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);CHKERRQ(ierr);
1199   mfqP->delta = mfqP->delta0;
1200   mfqP->npmax = PETSC_DEFAULT;
1201   ierr = PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);CHKERRQ(ierr);
1202   mfqP->usegqt = PETSC_FALSE;
1203   ierr = PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);CHKERRQ(ierr);
1204   ierr = PetscOptionsTail();CHKERRQ(ierr);
1205   PetscFunctionReturn(0);
1206 }
1207 
1208 static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1209 {
1210   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1211   PetscBool      isascii;
1212   PetscInt       nits;
1213   PetscErrorCode ierr;
1214 
1215   PetscFunctionBegin;
1216   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1217   if (isascii) {
1218     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1219     ierr = PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);CHKERRQ(ierr);
1220     ierr = PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);CHKERRQ(ierr);
1221     ierr = PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);CHKERRQ(ierr);
1222     if (mfqP->usegqt) {
1223       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");CHKERRQ(ierr);
1224     } else {
1225       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);CHKERRQ(ierr);
1226       ierr = TaoGetTotalIterationNumber(mfqP->subtao,&nits);CHKERRQ(ierr);
1227       ierr = PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);CHKERRQ(ierr);
1228     }
1229     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1230   }
1231   PetscFunctionReturn(0);
1232 }
1233 /*MC
1234   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares
1235 
1236   Options Database Keys:
1237 + -tao_pounders_delta - initial step length
1238 . -tao_pounders_npmax - maximum number of points in model
1239 - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON
1240 
1241   Level: beginner
1242 
1243 M*/
1244 
1245 PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1246 {
1247   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1248   PetscErrorCode ierr;
1249 
1250   PetscFunctionBegin;
1251   tao->ops->setup = TaoSetUp_POUNDERS;
1252   tao->ops->solve = TaoSolve_POUNDERS;
1253   tao->ops->view = TaoView_POUNDERS;
1254   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1255   tao->ops->destroy = TaoDestroy_POUNDERS;
1256 
1257   ierr = PetscNewLog(tao,&mfqP);CHKERRQ(ierr);
1258   tao->data = (void*)mfqP;
1259   /* Override default settings (unless already changed) */
1260   if (!tao->max_it_changed) tao->max_it = 2000;
1261   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1262   mfqP->delta0 = 0.1;
1263   mfqP->delta = 0.1;
1264   mfqP->deltamax=1e3;
1265   mfqP->deltamin=1e-6;
1266   mfqP->c2 = 100.0;
1267   mfqP->theta1=1e-5;
1268   mfqP->theta2=1e-4;
1269   mfqP->gamma0=0.5;
1270   mfqP->gamma1=2.0;
1271   mfqP->eta0 = 0.0;
1272   mfqP->eta1 = 0.1;
1273   mfqP->gqt_rtol = 0.001;
1274   mfqP->gqt_maxits = 50;
1275   mfqP->workxvec = 0;
1276   PetscFunctionReturn(0);
1277 }
1278 
1279 
1280