xref: /petsc/src/tao/leastsquares/impls/pounders/pounders.c (revision 5e71baeff2f3138f93cd4f5927dfd596eb8325cc)
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 = VecNorm(mfqP->workfvec,NORM_2,fsum);CHKERRQ(ierr);
40     *fsum*=(*fsum);
41   } else if (tao->sep_weights_w) {
42     *fsum=0;
43     for (i=0;i<tao->sep_weights_n;i++) {
44       row=tao->sep_weights_rows[i];
45       col=tao->sep_weights_cols[i];
46       ierr = VecGetValues(F,1,&row,&fr);CHKERRQ(ierr);
47       ierr = VecGetValues(F,1,&col,&fc);CHKERRQ(ierr);
48       *fsum += tao->sep_weights_w[i]*fc*fr;
49     }
50   } else {
51     ierr = VecNorm(F,NORM_2,fsum);CHKERRQ(ierr);
52     *fsum*=(*fsum);
53   }
54   if (PetscIsInfOrNanReal(*fsum)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
55   PetscFunctionReturn(0);
56 }
57 
58 PetscErrorCode gqtwrap(Tao tao,PetscReal *gnorm, PetscReal *qmin)
59 {
60   PetscErrorCode ierr;
61 #if defined(PETSC_USE_REAL_SINGLE)
62   PetscReal      atol=1.0e-5;
63 #else
64   PetscReal      atol=1.0e-10;
65 #endif
66   PetscInt       info,its;
67   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
68 
69   PetscFunctionBegin;
70   if (!mfqP->usegqt) {
71     PetscReal maxval;
72     PetscInt  i,j;
73 
74     ierr = VecSetValues(mfqP->subb,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
75     ierr = VecAssemblyBegin(mfqP->subb);CHKERRQ(ierr);
76     ierr = VecAssemblyEnd(mfqP->subb);CHKERRQ(ierr);
77 
78     ierr = VecSet(mfqP->subx,0.0);CHKERRQ(ierr);
79 
80     ierr = VecSet(mfqP->subndel,-mfqP->delta);CHKERRQ(ierr);
81     ierr = VecSet(mfqP->subpdel,mfqP->delta);CHKERRQ(ierr);
82 
83     for (i=0;i<mfqP->n;i++) {
84       for (j=i;j<mfqP->n;j++) {
85         mfqP->Hres[j+mfqP->n*i] = mfqP->Hres[mfqP->n*j+i];
86       }
87     }
88     ierr = MatSetValues(mfqP->subH,mfqP->n,mfqP->indices,mfqP->n,mfqP->indices,mfqP->Hres,INSERT_VALUES);CHKERRQ(ierr);
89     ierr = MatAssemblyBegin(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
90     ierr = MatAssemblyEnd(mfqP->subH,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
91 
92     ierr = TaoResetStatistics(mfqP->subtao);CHKERRQ(ierr);
93     /* ierr = TaoSetTolerances(mfqP->subtao,*gnorm,*gnorm,PETSC_DEFAULT);CHKERRQ(ierr); */
94     /* enforce bound constraints -- experimental */
95     if (tao->XU && tao->XL) {
96       ierr = VecCopy(tao->XU,mfqP->subxu);CHKERRQ(ierr);
97       ierr = VecAXPY(mfqP->subxu,-1.0,tao->solution);CHKERRQ(ierr);
98       ierr = VecScale(mfqP->subxu,1.0/mfqP->delta);CHKERRQ(ierr);
99       ierr = VecCopy(tao->XL,mfqP->subxl);CHKERRQ(ierr);
100       ierr = VecAXPY(mfqP->subxl,-1.0,tao->solution);CHKERRQ(ierr);
101       ierr = VecScale(mfqP->subxl,1.0/mfqP->delta);CHKERRQ(ierr);
102 
103       ierr = VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);CHKERRQ(ierr);
104       ierr = VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);CHKERRQ(ierr);
105     } else {
106       ierr = VecCopy(mfqP->subpdel,mfqP->subxu);CHKERRQ(ierr);
107       ierr = VecCopy(mfqP->subndel,mfqP->subxl);CHKERRQ(ierr);
108     }
109     /* Make sure xu > xl */
110     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
111     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
112     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
113     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
114     /* Make sure xu > tao->solution > xl */
115     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
116     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
117     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
118     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");
119 
120     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
121     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
122     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
123     if (maxval > 1e-10) SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");
124 
125     ierr = TaoSolve(mfqP->subtao);CHKERRQ(ierr);
126     ierr = TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
127 
128     /* test bounds post-solution*/
129     ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
130     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx);CHKERRQ(ierr);
131     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
132     if (maxval > 1e-5) {
133       ierr = PetscInfo(tao,"subproblem solution < lower bound\n");CHKERRQ(ierr);
134       tao->reason = TAO_DIVERGED_TR_REDUCTION;
135     }
136 
137     ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
138     ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu);CHKERRQ(ierr);
139     ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
140     if (maxval > 1e-5) {
141       ierr = PetscInfo(tao,"subproblem solution > upper bound\n");CHKERRQ(ierr);
142       tao->reason = TAO_DIVERGED_TR_REDUCTION;
143     }
144   } else {
145     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);
146   }
147   *qmin *= -1;
148   PetscFunctionReturn(0);
149 }
150 
151 static PetscErrorCode pounders_update_res(Tao tao)
152 {
153   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
154   PetscInt i,row,col;
155   PetscBLASInt blasn=mfqP->n,blasn2=blasn*blasn,blasm=mfqP->m,ione=1;
156   PetscReal zero=0.0,one=1.0,wii,factor;
157   PetscErrorCode ierr;
158   PetscFunctionBegin;
159 
160   for (i=0;i<mfqP->n;i++) {
161     mfqP->Gres[i]=0;
162   }
163   for (i=0;i<mfqP->n*mfqP->n;i++) {
164     mfqP->Hres[i]=0;
165   }
166 
167   /* Compute Gres= sum_ij[wij * (cjgi + cigj)] */
168   if (tao->sep_weights_v) {
169     /* Vector(diagonal) weights: gres = sum_i(wii*ci*gi) */
170     for (i=0;i<mfqP->m;i++) {
171       ierr = VecGetValues(tao->sep_weights_v,1,&i,&factor);CHKERRQ(ierr);
172       factor=factor*mfqP->C[i];
173       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*i],&ione,mfqP->Gres,&ione));
174     }
175   } else if (tao->sep_weights_n) {
176     /* general case: .5 * Gres= sum_ij[wij * (cjgi + cigj)] */
177     for (i=0;i<tao->sep_weights_n;i++) {
178       row=tao->sep_weights_rows[i];
179       col=tao->sep_weights_cols[i];
180 
181       factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
182       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*row],&ione,mfqP->Gres,&ione));
183       factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
184       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn,&factor,&mfqP->Fdiff[blasn*col],&ione,mfqP->Gres,&ione));
185     }
186   } else {
187     /* default: Gres= sum_i[cigi] = G*c' */
188     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasm,&one,mfqP->Fdiff,&blasn,mfqP->C,&ione,&zero,mfqP->Gres,&ione));
189   }
190 
191   /* compute Hres = sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
192   if (tao->sep_weights_v) {
193     /* vector(diagonal weights) Hres = sum_i(wii*(ci*Hi + gi * gi' )*/
194     for (i=0;i<mfqP->m;i++) {
195       ierr = VecGetValues(tao->sep_weights_v,1,&i,&wii);CHKERRQ(ierr);
196       if (tao->niter>1) {
197         factor=wii*mfqP->C[i];
198         /* add wii * ci * Hi */
199         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
200       }
201       /* add wii * gi * gi' */
202       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&wii,&mfqP->Fdiff[blasn*i],&blasn,&mfqP->Fdiff[blasn*i],&blasn,&one,mfqP->Hres,&blasn));
203     }
204   } else if (tao->sep_weights_w) {
205     /* .5 * sum_ij [wij * (*ci*Hj + cj*Hi + gi gj' + gj gi') ] */
206     for (i=0;i<tao->sep_weights_n;i++) {
207       row=tao->sep_weights_rows[i];
208       col=tao->sep_weights_cols[i];
209       factor=tao->sep_weights_w[i]/2.0;
210       /* add wij * gi gj' + wij * gj gi' */
211       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*row],&blasn,&mfqP->Fdiff[blasn*col],&blasn,&one,mfqP->Hres,&blasn));
212       PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","T",&blasn,&blasn,&ione,&factor,&mfqP->Fdiff[blasn*col],&blasn,&mfqP->Fdiff[blasn*row],&blasn,&one,mfqP->Hres,&blasn));
213     }
214     if (tao->niter > 1) {
215       for (i=0;i<tao->sep_weights_n;i++) {
216         row=tao->sep_weights_rows[i];
217         col=tao->sep_weights_cols[i];
218 
219         /* add  wij*cj*Hi */
220         factor = tao->sep_weights_w[i]*mfqP->C[col]/2.0;
221         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[row],&blasn2,mfqP->Hres,&ione));
222 
223         /* add wij*ci*Hj */
224         factor = tao->sep_weights_w[i]*mfqP->C[row]/2.0;
225         PetscStackCallBLAS("BLASaxpy_",BLASaxpy_(&blasn2,&factor,&mfqP->H[col],&blasn2,mfqP->Hres,&ione));
226       }
227     }
228   } else {
229     /*  Hres = G*G' + 0.5 sum {F(xkin,i)*H(:,:,i)}  */
230     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&blasn,&blasn,&blasm,&one,mfqP->Fdiff, &blasn,mfqP->Fdiff, &blasn,&zero,mfqP->Hres,&blasn));
231 
232     /* sum(F(xkin,i)*H(:,:,i)) */
233     if (tao->niter>1) {
234       for (i=0;i<mfqP->m;i++) {
235         factor = mfqP->C[i];
236         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&blasn2,&factor,&mfqP->H[i],&blasn2,mfqP->Hres,&ione));
237       }
238     }
239   }
240   PetscFunctionReturn(0);
241 }
242 
243 PetscErrorCode phi2eval(PetscReal *x, PetscInt n, PetscReal *phi)
244 {
245 /* 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] */
246   PetscInt  i,j,k;
247   PetscReal sqrt2 = PetscSqrtReal(2.0);
248 
249   PetscFunctionBegin;
250   j=0;
251   for (i=0;i<n;i++) {
252     phi[j] = 0.5 * x[i]*x[i];
253     j++;
254     for (k=i+1;k<n;k++) {
255       phi[j]  = x[i]*x[k]/sqrt2;
256       j++;
257     }
258   }
259   PetscFunctionReturn(0);
260 }
261 
262 PetscErrorCode getquadpounders(TAO_POUNDERS *mfqP)
263 {
264 /* Computes the parameters of the quadratic Q(x) = c + g'*x + 0.5*x*G*x'
265    that satisfies the interpolation conditions Q(X[:,j]) = f(j)
266    for j=1,...,m and with a Hessian matrix of least Frobenius norm */
267 
268     /* NB --we are ignoring c */
269   PetscInt     i,j,k,num,np = mfqP->nmodelpoints;
270   PetscReal    one = 1.0,zero=0.0,negone=-1.0;
271   PetscBLASInt blasnpmax = mfqP->npmax;
272   PetscBLASInt blasnplus1 = mfqP->n+1;
273   PetscBLASInt blasnp = np;
274   PetscBLASInt blasint = mfqP->n*(mfqP->n+1) / 2;
275   PetscBLASInt blasint2 = np - mfqP->n-1;
276   PetscBLASInt info,ione=1;
277   PetscReal    sqrt2 = PetscSqrtReal(2.0);
278 
279   PetscFunctionBegin;
280   for (i=0;i<mfqP->n*mfqP->m;i++) {
281     mfqP->Gdel[i] = 0;
282   }
283   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) {
284     mfqP->Hdel[i] = 0;
285   }
286 
287     /* factor M */
288   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&blasnplus1,&blasnp,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&info));
289   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrf returned with value %d\n",info);
290 
291   if (np == mfqP->n+1) {
292     for (i=0;i<mfqP->npmax-mfqP->n-1;i++) {
293       mfqP->omega[i]=0.0;
294     }
295     for (i=0;i<mfqP->n*(mfqP->n+1)/2;i++) {
296       mfqP->beta[i]=0.0;
297     }
298   } else {
299     /* Let Ltmp = (L'*L) */
300     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));
301 
302     /* factor Ltmp */
303     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&blasint2,mfqP->L_tmp,&blasint,&info));
304     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrf returned with value %d\n",info);
305   }
306 
307   for (k=0;k<mfqP->m;k++) {
308     if (np != mfqP->n+1) {
309       /* Solve L'*L*Omega = Z' * RESk*/
310       PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasnp,&blasint2,&one,mfqP->Z,&blasnpmax,&mfqP->RES[mfqP->npmax*k],&ione,&zero,mfqP->omega,&ione));
311       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&blasint2,&ione,mfqP->L_tmp,&blasint,mfqP->omega,&blasint2,&info));
312       if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine potrs returned with value %d\n",info);
313 
314       /* Beta = L*Omega */
315       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasint,&blasint2,&one,&mfqP->L[(mfqP->n+1)*blasint],&blasint,mfqP->omega,&ione,&zero,mfqP->beta,&ione));
316     }
317 
318     /* solve M'*Alpha = RESk - N'*Beta */
319     PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&blasint,&blasnp,&negone,mfqP->N,&blasint,mfqP->beta,&ione,&one,&mfqP->RES[mfqP->npmax*k],&ione));
320     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&blasnplus1,&ione,mfqP->M,&blasnplus1,mfqP->npmaxiwork,&mfqP->RES[mfqP->npmax*k],&blasnplus1,&info));
321     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine getrs returned with value %d\n",info);
322 
323     /* Gdel(:,k) = Alpha(2:n+1) */
324     for (i=0;i<mfqP->n;i++) {
325       mfqP->Gdel[i + mfqP->n*k] = mfqP->RES[mfqP->npmax*k + i+1];
326     }
327 
328     /* Set Hdels */
329     num=0;
330     for (i=0;i<mfqP->n;i++) {
331       /* H[i,i,k] = Beta(num) */
332       mfqP->Hdel[(i*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num];
333       num++;
334       for (j=i+1;j<mfqP->n;j++) {
335         /* H[i,j,k] = H[j,i,k] = Beta(num)/sqrt(2) */
336         mfqP->Hdel[(j*mfqP->n + i)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
337         mfqP->Hdel[(i*mfqP->n + j)*mfqP->m + k] = mfqP->beta[num]/sqrt2;
338         num++;
339       }
340     }
341   }
342   PetscFunctionReturn(0);
343 }
344 
345 PetscErrorCode morepoints(TAO_POUNDERS *mfqP)
346 {
347   /* Assumes mfqP->model_indices[0]  is minimum index
348    Finishes adding points to mfqP->model_indices (up to npmax)
349    Computes L,Z,M,N
350    np is actual number of points in model (should equal npmax?) */
351   PetscInt        point,i,j,offset;
352   PetscInt        reject;
353   PetscBLASInt    blasn=mfqP->n,blasnpmax=mfqP->npmax,blasnplus1=mfqP->n+1,info,blasnmax=mfqP->nmax,blasint,blasint2,blasnp,blasmaxmn;
354   const PetscReal *x;
355   PetscReal       normd;
356   PetscErrorCode  ierr;
357 
358   PetscFunctionBegin;
359   /* Initialize M,N */
360   for (i=0;i<mfqP->n+1;i++) {
361     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
362     mfqP->M[(mfqP->n+1)*i] = 1.0;
363     for (j=0;j<mfqP->n;j++) {
364       mfqP->M[j+1+((mfqP->n+1)*i)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
365     }
366     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
367     ierr = phi2eval(&mfqP->M[1+((mfqP->n+1)*i)],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * i]);CHKERRQ(ierr);
368   }
369 
370   /* Now we add points until we have npmax starting with the most recent ones */
371   point = mfqP->nHist-1;
372   mfqP->nmodelpoints = mfqP->n+1;
373   while (mfqP->nmodelpoints < mfqP->npmax && point>=0) {
374     /* Reject any points already in the model */
375     reject = 0;
376     for (j=0;j<mfqP->n+1;j++) {
377       if (point == mfqP->model_indices[j]) {
378         reject = 1;
379         break;
380       }
381     }
382 
383     /* Reject if norm(d) >c2 */
384     if (!reject) {
385       ierr = VecCopy(mfqP->Xhist[point],mfqP->workxvec);CHKERRQ(ierr);
386       ierr = VecAXPY(mfqP->workxvec,-1.0,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
387       ierr = VecNorm(mfqP->workxvec,NORM_2,&normd);CHKERRQ(ierr);
388       normd /= mfqP->delta;
389       if (normd > mfqP->c2) {
390         reject =1;
391       }
392     }
393     if (reject){
394       point--;
395       continue;
396     }
397 
398     ierr = VecGetArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
399     mfqP->M[(mfqP->n+1)*mfqP->nmodelpoints] = 1.0;
400     for (j=0;j<mfqP->n;j++) {
401       mfqP->M[j+1+((mfqP->n+1)*mfqP->nmodelpoints)] = (x[j]  - mfqP->xmin[j]) / mfqP->delta;
402     }
403     ierr = VecRestoreArrayRead(mfqP->Xhist[point],&x);CHKERRQ(ierr);
404     ierr = phi2eval(&mfqP->M[1+(mfqP->n+1)*mfqP->nmodelpoints],mfqP->n,&mfqP->N[mfqP->n*(mfqP->n+1)/2 * (mfqP->nmodelpoints)]);CHKERRQ(ierr);
405 
406     /* Update QR factorization */
407     /* Copy M' to Q_tmp */
408     for (i=0;i<mfqP->n+1;i++) {
409       for (j=0;j<mfqP->npmax;j++) {
410         mfqP->Q_tmp[j+mfqP->npmax*i] = mfqP->M[i+(mfqP->n+1)*j];
411       }
412     }
413     blasnp = mfqP->nmodelpoints+1;
414     /* Q_tmp,R = qr(M') */
415     blasmaxmn=PetscMax(mfqP->m,mfqP->n+1);
416     PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
417     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine geqrf returned with value %d\n",info);
418 
419     /* Reject if min(svd(N*Q(:,n+2:np+1)) <= theta2 */
420     /* L = N*Qtmp */
421     blasint2 = mfqP->n * (mfqP->n+1) / 2;
422     /* Copy N to L_tmp */
423     for (i=0;i<mfqP->n*(mfqP->n+1)/2 * mfqP->npmax;i++) {
424       mfqP->L_tmp[i]= mfqP->N[i];
425     }
426     /* Copy L_save to L_tmp */
427 
428     /* L_tmp = N*Qtmp' */
429     PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasint2,&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->L_tmp,&blasint2,mfqP->npmaxwork,&blasnmax,&info));
430     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
431 
432     /* Copy L_tmp to L_save */
433     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
434       mfqP->L_save[i] = mfqP->L_tmp[i];
435     }
436 
437     /* Get svd for L_tmp(:,n+2:np+1) (L_tmp is modified in process) */
438     blasint = mfqP->nmodelpoints - mfqP->n;
439     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
440     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));
441     ierr = PetscFPTrapPop();CHKERRQ(ierr);
442     if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine gesvd returned with value %d\n",info);
443 
444     if (mfqP->beta[PetscMin(blasint,blasint2)-1] > mfqP->theta2) {
445       /* accept point */
446       mfqP->model_indices[mfqP->nmodelpoints] = point;
447       /* Copy Q_tmp to Q */
448       for (i=0;i<mfqP->npmax* mfqP->npmax;i++) {
449         mfqP->Q[i] = mfqP->Q_tmp[i];
450       }
451       for (i=0;i<mfqP->npmax;i++){
452         mfqP->tau[i] = mfqP->tau_tmp[i];
453       }
454       mfqP->nmodelpoints++;
455       blasnp = mfqP->nmodelpoints;
456 
457       /* Copy L_save to L */
458       for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
459         mfqP->L[i] = mfqP->L_save[i];
460       }
461     }
462     point--;
463   }
464 
465   blasnp = mfqP->nmodelpoints;
466   /* Copy Q(:,n+2:np) to Z */
467   /* First set Q_tmp to I */
468   for (i=0;i<mfqP->npmax*mfqP->npmax;i++) {
469     mfqP->Q_tmp[i] = 0.0;
470   }
471   for (i=0;i<mfqP->npmax;i++) {
472     mfqP->Q_tmp[i + mfqP->npmax*i] = 1.0;
473   }
474 
475   /* Q_tmp = I * Q */
476   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasnp,&blasnp,&blasnplus1,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->Q_tmp,&blasnpmax,mfqP->npmaxwork,&blasnmax,&info));
477   if (info != 0) SETERRQ1(PETSC_COMM_SELF,1,"LAPACK routine ormqr returned with value %d\n",info);
478 
479   /* Copy Q_tmp(:,n+2:np) to Z) */
480   offset = mfqP->npmax * (mfqP->n+1);
481   for (i=offset;i<mfqP->npmax*mfqP->npmax;i++) {
482     mfqP->Z[i-offset] = mfqP->Q_tmp[i];
483   }
484 
485   if (mfqP->nmodelpoints == mfqP->n + 1) {
486     /* Set L to I_{n+1} */
487     for (i=0;i<mfqP->npmax * mfqP->n*(mfqP->n+1)/2;i++) {
488       mfqP->L[i] = 0.0;
489     }
490     for (i=0;i<mfqP->n;i++) {
491       mfqP->L[(mfqP->n*(mfqP->n+1)/2)*i + i] = 1.0;
492     }
493   }
494   PetscFunctionReturn(0);
495 }
496 
497 /* Only call from modelimprove, addpoint() needs ->Q_tmp and ->work to be set */
498 PetscErrorCode addpoint(Tao tao, TAO_POUNDERS *mfqP, PetscInt index)
499 {
500   PetscErrorCode ierr;
501 
502   PetscFunctionBegin;
503   /* Create new vector in history: X[newidx] = X[mfqP->index] + delta*X[index]*/
504   ierr = VecDuplicate(mfqP->Xhist[0],&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
505   ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,&mfqP->Q_tmp[index*mfqP->npmax],INSERT_VALUES);CHKERRQ(ierr);
506   ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
507   ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
508   ierr = VecAYPX(mfqP->Xhist[mfqP->nHist],mfqP->delta,mfqP->Xhist[mfqP->minindex]);CHKERRQ(ierr);
509 
510   /* Project into feasible region */
511   if (tao->XU && tao->XL) {
512     ierr = VecMedian(mfqP->Xhist[mfqP->nHist], tao->XL, tao->XU, mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
513   }
514 
515   /* Compute value of new vector */
516   ierr = VecDuplicate(mfqP->Fhist[0],&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
517   CHKMEMQ;
518   ierr = pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
519 
520   /* Add new vector to model */
521   mfqP->model_indices[mfqP->nmodelpoints] = mfqP->nHist;
522   mfqP->nmodelpoints++;
523   mfqP->nHist++;
524   PetscFunctionReturn(0);
525 }
526 
527 PetscErrorCode modelimprove(Tao tao, TAO_POUNDERS *mfqP, PetscInt addallpoints)
528 {
529   /* modeld = Q(:,np+1:n)' */
530   PetscErrorCode ierr;
531   PetscInt       i,j,minindex=0;
532   PetscReal      dp,half=0.5,one=1.0,minvalue=PETSC_INFINITY;
533   PetscBLASInt   blasn=mfqP->n,  blasnpmax = mfqP->npmax, blask,info;
534   PetscBLASInt   blas1=1,blasnmax = mfqP->nmax;
535 
536   blask = mfqP->nmodelpoints;
537   /* Qtmp = I(n x n) */
538   for (i=0;i<mfqP->n;i++) {
539     for (j=0;j<mfqP->n;j++) {
540       mfqP->Q_tmp[i + mfqP->npmax*j] = 0.0;
541     }
542   }
543   for (j=0;j<mfqP->n;j++) {
544     mfqP->Q_tmp[j + mfqP->npmax*j] = 1.0;
545   }
546 
547   /* Qtmp = Q * I */
548   PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&blasn,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau, mfqP->Q_tmp, &blasnpmax, mfqP->npmaxwork,&blasnmax, &info));
549 
550   for (i=mfqP->nmodelpoints;i<mfqP->n;i++) {
551     dp = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->Gres,&blas1);
552     if (dp>0.0) { /* Model says use the other direction! */
553       for (j=0;j<mfqP->n;j++) {
554         mfqP->Q_tmp[i*mfqP->npmax+j] *= -1;
555       }
556     }
557     /* mfqP->work[i] = Cres+Modeld(i,:)*(Gres+.5*Hres*Modeld(i,:)') */
558     for (j=0;j<mfqP->n;j++) {
559       mfqP->work2[j] = mfqP->Gres[j];
560     }
561     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&half,mfqP->Hres,&blasn,&mfqP->Q_tmp[i*mfqP->npmax], &blas1, &one, mfqP->work2,&blas1));
562     mfqP->work[i] = BLASdot_(&blasn,&mfqP->Q_tmp[i*mfqP->npmax],&blas1,mfqP->work2,&blas1);
563     if (i==mfqP->nmodelpoints || mfqP->work[i] < minvalue) {
564       minindex=i;
565       minvalue = mfqP->work[i];
566     }
567     if (addallpoints != 0) {
568       ierr = addpoint(tao,mfqP,i);CHKERRQ(ierr);
569     }
570   }
571   if (!addallpoints) {
572     ierr = addpoint(tao,mfqP,minindex);CHKERRQ(ierr);
573   }
574   PetscFunctionReturn(0);
575 }
576 
577 
578 PetscErrorCode affpoints(TAO_POUNDERS *mfqP, PetscReal *xmin,PetscReal c)
579 {
580   PetscInt        i,j;
581   PetscBLASInt    blasm=mfqP->m,blasj,blask,blasn=mfqP->n,ione=1,info;
582   PetscBLASInt    blasnpmax = mfqP->npmax,blasmaxmn;
583   PetscReal       proj,normd;
584   const PetscReal *x;
585   PetscErrorCode  ierr;
586 
587   PetscFunctionBegin;
588   for (i=mfqP->nHist-1;i>=0;i--) {
589     ierr = VecGetArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
590     for (j=0;j<mfqP->n;j++) {
591       mfqP->work[j] = (x[j] - xmin[j])/mfqP->delta;
592     }
593     ierr = VecRestoreArrayRead(mfqP->Xhist[i],&x);CHKERRQ(ierr);
594     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,mfqP->work2,&ione));
595     normd = BLASnrm2_(&blasn,mfqP->work,&ione);
596     if (normd <= c*c) {
597       blasj=PetscMax((mfqP->n - mfqP->nmodelpoints),0);
598       if (!mfqP->q_is_I) {
599         /* project D onto null */
600         blask=(mfqP->nmodelpoints);
601         PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("R","N",&ione,&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->work2,&ione,mfqP->mwork,&blasm,&info));
602         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"ormqr returned value %d\n",info);
603       }
604       proj = BLASnrm2_(&blasj,&mfqP->work2[mfqP->nmodelpoints],&ione);
605 
606       if (proj >= mfqP->theta1) { /* add this index to model */
607         mfqP->model_indices[mfqP->nmodelpoints]=i;
608         mfqP->nmodelpoints++;
609         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasn,mfqP->work,&ione,&mfqP->Q_tmp[mfqP->npmax*(mfqP->nmodelpoints-1)],&ione));
610         blask=mfqP->npmax*(mfqP->nmodelpoints);
611         PetscStackCallBLAS("BLAScopy",BLAScopy_(&blask,mfqP->Q_tmp,&ione,mfqP->Q,&ione));
612         blask = mfqP->nmodelpoints;
613         blasmaxmn = PetscMax(mfqP->m,mfqP->n);
614         PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));
615         if (info < 0) SETERRQ1(PETSC_COMM_SELF,1,"geqrf returned value %d\n",info);
616         mfqP->q_is_I = 0;
617       }
618       if (mfqP->nmodelpoints == mfqP->n)  {
619         break;
620       }
621     }
622   }
623 
624   PetscFunctionReturn(0);
625 }
626 
627 static PetscErrorCode TaoSolve_POUNDERS(Tao tao)
628 {
629   TAO_POUNDERS       *mfqP = (TAO_POUNDERS *)tao->data;
630   PetscInt           i,ii,j,k,l;
631   PetscReal          step=1.0;
632   TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
633   PetscInt           low,high;
634   PetscReal          minnorm;
635   PetscReal          *x,*f;
636   const PetscReal    *xmint,*fmin;
637   PetscReal          cres,deltaold;
638   PetscReal          gnorm;
639   PetscBLASInt       info,ione=1,iblas;
640   PetscBool          valid,same;
641   PetscReal          mdec, rho, normxsp;
642   PetscReal          one=1.0,zero=0.0,ratio;
643   PetscBLASInt       blasm,blasn,blasncopy,blasnpmax;
644   PetscErrorCode     ierr;
645   static PetscBool   set = PETSC_FALSE;
646 
647   /* n = # of parameters
648      m = dimension (components) of function  */
649   PetscFunctionBegin;
650   ierr = PetscCitationsRegister("@article{UNEDF0,\n"
651                                 "title = {Nuclear energy density optimization},\n"
652                                 "author = {Kortelainen, M.  and Lesinski, T.  and Mor\'e, J.  and Nazarewicz, W.\n"
653                                 "          and Sarich, J.  and Schunck, N.  and Stoitsov, M. V. and Wild, S. },\n"
654                                 "journal = {Phys. Rev. C},\n"
655                                 "volume = {82},\n"
656                                 "number = {2},\n"
657                                 "pages = {024313},\n"
658                                 "numpages = {18},\n"
659                                 "year = {2010},\n"
660                                 "month = {Aug},\n"
661                                 "doi = {10.1103/PhysRevC.82.024313}\n}\n",&set);CHKERRQ(ierr);
662   tao->niter=0;
663   if (tao->XL && tao->XU) {
664     /* Check x0 <= XU */
665     PetscReal val;
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   CHKMEMQ;
687   blasm = mfqP->m; blasn=mfqP->n; blasnpmax = mfqP->npmax;
688   for (i=0;i<mfqP->n*mfqP->n*mfqP->m;i++) mfqP->H[i]=0;
689 
690   ierr = VecCopy(tao->solution,mfqP->Xhist[0]);CHKERRQ(ierr);
691   CHKMEMQ;
692   ierr = pounders_feval(tao,tao->solution,mfqP->Fhist[0],&mfqP->Fres[0]);CHKERRQ(ierr);
693   mfqP->minindex = 0;
694   minnorm = mfqP->Fres[0];
695   ierr = TaoMonitor(tao, tao->niter, minnorm, PETSC_INFINITY, 0.0, step, &reason);CHKERRQ(ierr);
696   tao->niter++;
697 
698   ierr = VecGetOwnershipRange(mfqP->Xhist[0],&low,&high);CHKERRQ(ierr);
699   for (i=1;i<mfqP->n+1;i++) {
700     ierr = VecCopy(tao->solution,mfqP->Xhist[i]);CHKERRQ(ierr);
701     if (i-1 >= low && i-1 < high) {
702       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
703       x[i-1-low] += mfqP->delta;
704       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
705     }
706     CHKMEMQ;
707     ierr = pounders_feval(tao,mfqP->Xhist[i],mfqP->Fhist[i],&mfqP->Fres[i]);CHKERRQ(ierr);
708     if (mfqP->Fres[i] < minnorm) {
709       mfqP->minindex = i;
710       minnorm = mfqP->Fres[i];
711     }
712   }
713   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
714   ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
715   /* Gather mpi vecs to one big local vec */
716 
717   /* Begin serial code */
718 
719   /* Disp[i] = Xi-xmin, i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
720   /* Fdiff[i] = (Fi-Fmin)', i=1,..,mfqP->minindex-1,mfqP->minindex+1,..,n */
721   /* (Column oriented for blas calls) */
722   ii=0;
723 
724   if (mfqP->size == 1) {
725     ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
726     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
727     ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
728     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
729     for (i=0;i<mfqP->n+1;i++) {
730       if (i == mfqP->minindex) continue;
731 
732       ierr = VecGetArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
733       for (j=0;j<mfqP->n;j++) {
734         mfqP->Disp[ii+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
735       }
736       ierr = VecRestoreArray(mfqP->Xhist[i],&x);CHKERRQ(ierr);
737 
738       ierr = VecGetArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
739       for (j=0;j<mfqP->m;j++) {
740         mfqP->Fdiff[ii+mfqP->n*j] = f[j] - fmin[j];
741       }
742       ierr = VecRestoreArray(mfqP->Fhist[i],&f);CHKERRQ(ierr);
743       mfqP->model_indices[ii++] = i;
744 
745     }
746     for (j=0;j<mfqP->m;j++) {
747       mfqP->C[j] = fmin[j];
748     }
749     ierr = VecRestoreArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
750   } else {
751     ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
752     ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[mfqP->minindex],mfqP->localxmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
753     ierr = VecGetArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
754     for (i=0;i<mfqP->n;i++) mfqP->xmin[i] = xmint[i];
755     ierr = VecRestoreArrayRead(mfqP->localxmin,&xmint);CHKERRQ(ierr);
756 
757     ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
758     ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[mfqP->minindex],mfqP->localfmin,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
759     ierr = VecGetArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
760     for (i=0;i<mfqP->n+1;i++) {
761       if (i == mfqP->minindex) continue;
762 
763       mfqP->model_indices[ii++] = i;
764       ierr = VecScatterBegin(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
765       ierr = VecScatterEnd(mfqP->scatterx,mfqP->Xhist[ii],mfqP->localx,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
766       ierr = VecGetArray(mfqP->localx,&x);CHKERRQ(ierr);
767       for (j=0;j<mfqP->n;j++) {
768         mfqP->Disp[i+mfqP->npmax*j] = (x[j] - mfqP->xmin[j])/mfqP->delta;
769       }
770       ierr = VecRestoreArray(mfqP->localx,&x);CHKERRQ(ierr);
771 
772       ierr = VecScatterBegin(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
773       ierr = VecScatterEnd(mfqP->scatterf,mfqP->Fhist[ii],mfqP->localf,INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
774       ierr = VecGetArray(mfqP->localf,&f);CHKERRQ(ierr);
775       for (j=0;j<mfqP->m;j++) {
776         mfqP->Fdiff[i*mfqP->n+j] = f[j] - fmin[j];
777       }
778       ierr = VecRestoreArray(mfqP->localf,&f);CHKERRQ(ierr);
779     }
780     for (j=0;j<mfqP->m;j++) {
781       mfqP->C[j] = fmin[j];
782     }
783     ierr = VecRestoreArrayRead(mfqP->localfmin,&fmin);CHKERRQ(ierr);
784   }
785 
786   /* Determine the initial quadratic models */
787   /* G = D(ModelIn,:) \ (F(ModelIn,1:m)-repmat(F(xkin,1:m),n,1)); */
788   /* D (nxn) Fdiff (nxm)  => G (nxm) */
789   blasncopy = blasn;
790   PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&blasn,&blasm,mfqP->Disp,&blasnpmax,mfqP->iwork,mfqP->Fdiff,&blasncopy,&info));
791   ierr = PetscInfo1(tao,"gesv returned %d\n",info);CHKERRQ(ierr);
792 
793   cres = minnorm;
794   ierr = pounders_update_res(tao);CHKERRQ(ierr);
795 
796   valid = PETSC_TRUE;
797 
798   ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
799   ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
800   ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
801   ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
802   gnorm *= mfqP->delta;
803   ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
804   ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
805   mfqP->nHist = mfqP->n+1;
806   mfqP->nmodelpoints = mfqP->n+1;
807 
808   while (reason == TAO_CONTINUE_ITERATING) {
809     PetscReal gnm = 1e-4;
810     tao->niter++;
811     /* Solve the subproblem min{Q(s): ||s|| <= delta} */
812     ierr = gqtwrap(tao,&gnm,&mdec);CHKERRQ(ierr);
813     /* Evaluate the function at the new point */
814 
815     for (i=0;i<mfqP->n;i++) {
816         mfqP->work[i] = mfqP->Xsubproblem[i]*mfqP->delta + mfqP->xmin[i];
817     }
818     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
819     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[mfqP->nHist]);CHKERRQ(ierr);
820     ierr = VecSetValues(mfqP->Xhist[mfqP->nHist],mfqP->n,mfqP->indices,mfqP->work,INSERT_VALUES);CHKERRQ(ierr);
821     ierr = VecAssemblyBegin(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
822     ierr = VecAssemblyEnd(mfqP->Xhist[mfqP->nHist]);CHKERRQ(ierr);
823 
824     ierr = pounders_feval(tao,mfqP->Xhist[mfqP->nHist],mfqP->Fhist[mfqP->nHist],&mfqP->Fres[mfqP->nHist]);CHKERRQ(ierr);
825 
826     rho = (mfqP->Fres[mfqP->minindex] - mfqP->Fres[mfqP->nHist]) / mdec;
827     mfqP->nHist++;
828 
829     /* Update the center */
830     if ((rho >= mfqP->eta1) || (rho > mfqP->eta0 && valid==PETSC_TRUE)) {
831       /* Update model to reflect new base point */
832       for (i=0;i<mfqP->n;i++) {
833         mfqP->work[i] = (mfqP->work[i] - mfqP->xmin[i])/mfqP->delta;
834       }
835       for (j=0;j<mfqP->m;j++) {
836         /* C(j) = C(j) + work*G(:,j) + .5*work*H(:,:,j)*work';
837          G(:,j) = G(:,j) + H(:,:,j)*work' */
838         for (k=0;k<mfqP->n;k++) {
839           mfqP->work2[k]=0.0;
840           for (l=0;l<mfqP->n;l++) {
841             mfqP->work2[k]+=mfqP->H[j + mfqP->m*(k + l*mfqP->n)]*mfqP->work[l];
842           }
843         }
844         for (i=0;i<mfqP->n;i++) {
845           mfqP->C[j]+=mfqP->work[i]*(mfqP->Fdiff[i + mfqP->n* j] + 0.5*mfqP->work2[i]);
846           mfqP->Fdiff[i+mfqP->n*j] +=mfqP-> work2[i];
847         }
848       }
849       /* Cres += work*Gres + .5*work*Hres*work';
850        Gres += Hres*work'; */
851 
852       PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&blasn,&blasn,&one,mfqP->Hres,&blasn,mfqP->work,&ione,&zero,mfqP->work2,&ione));
853       for (i=0;i<mfqP->n;i++) {
854         cres += mfqP->work[i]*(mfqP->Gres[i]  + 0.5*mfqP->work2[i]);
855         mfqP->Gres[i] += mfqP->work2[i];
856       }
857       mfqP->minindex = mfqP->nHist-1;
858       minnorm = mfqP->Fres[mfqP->minindex];
859       ierr = VecCopy(mfqP->Fhist[mfqP->minindex],tao->sep_objective);CHKERRQ(ierr);
860       /* Change current center */
861       ierr = VecGetArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
862       for (i=0;i<mfqP->n;i++) {
863         mfqP->xmin[i] = xmint[i];
864       }
865       ierr = VecRestoreArrayRead(mfqP->Xhist[mfqP->minindex],&xmint);CHKERRQ(ierr);
866     }
867 
868     /* Evaluate at a model-improving point if necessary */
869     if (valid == PETSC_FALSE) {
870       mfqP->q_is_I = 1;
871       mfqP->nmodelpoints = 0;
872       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
873       if (mfqP->nmodelpoints < mfqP->n) {
874         ierr = PetscInfo(tao,"Model not valid -- model-improving\n");CHKERRQ(ierr);
875         ierr = modelimprove(tao,mfqP,1);CHKERRQ(ierr);
876       }
877     }
878 
879     /* Update the trust region radius */
880     deltaold = mfqP->delta;
881     normxsp = 0;
882     for (i=0;i<mfqP->n;i++) {
883       normxsp += mfqP->Xsubproblem[i]*mfqP->Xsubproblem[i];
884     }
885     normxsp = PetscSqrtReal(normxsp);
886     if (rho >= mfqP->eta1 && normxsp > 0.5*mfqP->delta) {
887       mfqP->delta = PetscMin(mfqP->delta*mfqP->gamma1,mfqP->deltamax);
888     } else if (valid == PETSC_TRUE) {
889       mfqP->delta = PetscMax(mfqP->delta*mfqP->gamma0,mfqP->deltamin);
890     }
891 
892     /* Compute the next interpolation set */
893     mfqP->q_is_I = 1;
894     mfqP->nmodelpoints=0;
895     ierr = affpoints(mfqP,mfqP->xmin,mfqP->c1);CHKERRQ(ierr);
896     if (mfqP->nmodelpoints == mfqP->n) {
897       valid = PETSC_TRUE;
898     } else {
899       valid = PETSC_FALSE;
900       ierr = affpoints(mfqP,mfqP->xmin,mfqP->c2);CHKERRQ(ierr);
901       if (mfqP->n > mfqP->nmodelpoints) {
902         ierr = PetscInfo(tao,"Model not valid -- adding geometry points\n");CHKERRQ(ierr);
903         ierr = modelimprove(tao,mfqP,mfqP->n - mfqP->nmodelpoints);CHKERRQ(ierr);
904       }
905     }
906     for (i=mfqP->nmodelpoints;i>0;i--) {
907       mfqP->model_indices[i] = mfqP->model_indices[i-1];
908     }
909     mfqP->nmodelpoints++;
910     mfqP->model_indices[0] = mfqP->minindex;
911     ierr = morepoints(mfqP);CHKERRQ(ierr);
912     for (i=0;i<mfqP->nmodelpoints;i++) {
913       ierr = VecGetArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
914       for (j=0;j<mfqP->n;j++) {
915         mfqP->Disp[i + mfqP->npmax*j] = (x[j]  - mfqP->xmin[j]) / deltaold;
916       }
917       ierr = VecRestoreArray(mfqP->Xhist[mfqP->model_indices[i]],&x);CHKERRQ(ierr);
918       ierr = VecGetArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
919       for (j=0;j<mfqP->m;j++) {
920         for (k=0;k<mfqP->n;k++)  {
921           mfqP->work[k]=0.0;
922           for (l=0;l<mfqP->n;l++) {
923             mfqP->work[k] += mfqP->H[j + mfqP->m*(k + mfqP->n*l)] * mfqP->Disp[i + mfqP->npmax*l];
924           }
925         }
926         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];
927       }
928       ierr = VecRestoreArray(mfqP->Fhist[mfqP->model_indices[i]],&f);CHKERRQ(ierr);
929     }
930 
931     /* Update the quadratic model */
932     ierr = getquadpounders(mfqP);CHKERRQ(ierr);
933     ierr = VecGetArrayRead(mfqP->Fhist[mfqP->minindex],&fmin);CHKERRQ(ierr);
934     PetscStackCallBLAS("BLAScopy",BLAScopy_(&blasm,fmin,&ione,mfqP->C,&ione));
935     /* G = G*(delta/deltaold) + Gdel */
936     ratio = mfqP->delta/deltaold;
937     iblas = blasm*blasn;
938     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->Fdiff,&ione));
939     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Gdel,&ione,mfqP->Fdiff,&ione));
940     /* H = H*(delta/deltaold)^2 + Hdel */
941     iblas = blasm*blasn*blasn;
942     ratio *= ratio;
943     PetscStackCallBLAS("BLASscal",BLASscal_(&iblas,&ratio,mfqP->H,&ione));
944     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&iblas,&one,mfqP->Hdel,&ione,mfqP->H,&ione));
945 
946     /* Get residuals */
947     cres = mfqP->Fres[mfqP->minindex];
948     ierr = pounders_update_res(tao);CHKERRQ(ierr);
949 
950     /* Export solution and gradient residual to TAO */
951     ierr = VecCopy(mfqP->Xhist[mfqP->minindex],tao->solution);CHKERRQ(ierr);
952     ierr = VecSetValues(tao->gradient,mfqP->n,mfqP->indices,mfqP->Gres,INSERT_VALUES);CHKERRQ(ierr);
953     ierr = VecAssemblyBegin(tao->gradient);CHKERRQ(ierr);
954     ierr = VecAssemblyEnd(tao->gradient);CHKERRQ(ierr);
955     ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
956     gnorm *= mfqP->delta;
957     /*  final criticality test */
958     ierr = TaoMonitor(tao, tao->niter, minnorm, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
959     /* test for repeated model */
960     if (mfqP->nmodelpoints==mfqP->last_nmodelpoints) {
961       same = PETSC_TRUE;
962     } else {
963       same = PETSC_FALSE;
964     }
965     for (i=0;i<mfqP->nmodelpoints;i++) {
966       if (same) {
967         if (mfqP->model_indices[i] == mfqP->last_model_indices[i]) {
968           same = PETSC_TRUE;
969         } else {
970           same = PETSC_FALSE;
971         }
972       }
973       mfqP->last_model_indices[i] = mfqP->model_indices[i];
974     }
975     mfqP->last_nmodelpoints = mfqP->nmodelpoints;
976     if (same && mfqP->delta == deltaold) {
977       ierr = PetscInfo(tao,"Identical model used in successive iterations\n");CHKERRQ(ierr);
978       reason = TAO_CONVERGED_STEPTOL;
979       tao->reason = TAO_CONVERGED_STEPTOL;
980     }
981   }
982   PetscFunctionReturn(0);
983 }
984 
985 static PetscErrorCode TaoSetUp_POUNDERS(Tao tao)
986 {
987   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
988   PetscInt       i,j;
989   IS             isfloc,isfglob,isxloc,isxglob;
990   PetscErrorCode ierr;
991 
992   PetscFunctionBegin;
993   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);  }
994   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);  }
995   ierr = VecGetSize(tao->solution,&mfqP->n);CHKERRQ(ierr);
996   ierr = VecGetSize(tao->sep_objective,&mfqP->m);CHKERRQ(ierr);
997   mfqP->c1 = PetscSqrtReal((PetscReal)mfqP->n);
998   if (mfqP->npmax == PETSC_DEFAULT) {
999     mfqP->npmax = 2*mfqP->n + 1;
1000   }
1001   mfqP->npmax = PetscMin((mfqP->n+1)*(mfqP->n+2)/2,mfqP->npmax);
1002   mfqP->npmax = PetscMax(mfqP->npmax, mfqP->n+2);
1003 
1004   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Xhist);CHKERRQ(ierr);
1005   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fhist);CHKERRQ(ierr);
1006   for (i=0;i<mfqP->n +1;i++) {
1007     ierr = VecDuplicate(tao->solution,&mfqP->Xhist[i]);CHKERRQ(ierr);
1008     ierr = VecDuplicate(tao->sep_objective,&mfqP->Fhist[i]);CHKERRQ(ierr);
1009   }
1010   ierr = VecDuplicate(tao->solution,&mfqP->workxvec);CHKERRQ(ierr);
1011   ierr = VecDuplicate(tao->sep_objective,&mfqP->workfvec);CHKERRQ(ierr);
1012   mfqP->nHist = 0;
1013 
1014   ierr = PetscMalloc1(tao->max_funcs+10,&mfqP->Fres);CHKERRQ(ierr);
1015   ierr = PetscMalloc1(mfqP->npmax*mfqP->m,&mfqP->RES);CHKERRQ(ierr);
1016   ierr = PetscMalloc1(mfqP->n,&mfqP->work);CHKERRQ(ierr);
1017   ierr = PetscMalloc1(mfqP->n,&mfqP->work2);CHKERRQ(ierr);
1018   ierr = PetscMalloc1(mfqP->n,&mfqP->work3);CHKERRQ(ierr);
1019   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n+1),&mfqP->mwork);CHKERRQ(ierr);
1020   ierr = PetscMalloc1(mfqP->npmax - mfqP->n - 1,&mfqP->omega);CHKERRQ(ierr);
1021   ierr = PetscMalloc1(mfqP->n * (mfqP->n+1) / 2,&mfqP->beta);CHKERRQ(ierr);
1022   ierr = PetscMalloc1(mfqP->n + 1 ,&mfqP->alpha);CHKERRQ(ierr);
1023 
1024   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m,&mfqP->H);CHKERRQ(ierr);
1025   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q);CHKERRQ(ierr);
1026   ierr = PetscMalloc1(mfqP->npmax*mfqP->npmax,&mfqP->Q_tmp);CHKERRQ(ierr);
1027   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L);CHKERRQ(ierr);
1028   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_tmp);CHKERRQ(ierr);
1029   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->L_save);CHKERRQ(ierr);
1030   ierr = PetscMalloc1(mfqP->n*(mfqP->n+1)/2*(mfqP->npmax),&mfqP->N);CHKERRQ(ierr);
1031   ierr = PetscMalloc1(mfqP->npmax * (mfqP->n+1) ,&mfqP->M);CHKERRQ(ierr);
1032   ierr = PetscMalloc1(mfqP->npmax * (mfqP->npmax - mfqP->n - 1) , &mfqP->Z);CHKERRQ(ierr);
1033   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau);CHKERRQ(ierr);
1034   ierr = PetscMalloc1(mfqP->npmax,&mfqP->tau_tmp);CHKERRQ(ierr);
1035   mfqP->nmax = PetscMax(5*mfqP->npmax,mfqP->n*(mfqP->n+1)/2);
1036   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxwork);CHKERRQ(ierr);
1037   ierr = PetscMalloc1(mfqP->nmax,&mfqP->npmaxiwork);CHKERRQ(ierr);
1038   ierr = PetscMalloc1(mfqP->n,&mfqP->xmin);CHKERRQ(ierr);
1039   ierr = PetscMalloc1(mfqP->m,&mfqP->C);CHKERRQ(ierr);
1040   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Fdiff);CHKERRQ(ierr);
1041   ierr = PetscMalloc1(mfqP->npmax*mfqP->n,&mfqP->Disp);CHKERRQ(ierr);
1042   ierr = PetscMalloc1(mfqP->n,&mfqP->Gres);CHKERRQ(ierr);
1043   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Hres);CHKERRQ(ierr);
1044   ierr = PetscMalloc1(mfqP->n*mfqP->n,&mfqP->Gpoints);CHKERRQ(ierr);
1045   ierr = PetscMalloc1(mfqP->npmax,&mfqP->model_indices);CHKERRQ(ierr);
1046   ierr = PetscMalloc1(mfqP->npmax,&mfqP->last_model_indices);CHKERRQ(ierr);
1047   ierr = PetscMalloc1(mfqP->n,&mfqP->Xsubproblem);CHKERRQ(ierr);
1048   ierr = PetscMalloc1(mfqP->m*mfqP->n,&mfqP->Gdel);CHKERRQ(ierr);
1049   ierr = PetscMalloc1(mfqP->n*mfqP->n*mfqP->m, &mfqP->Hdel);CHKERRQ(ierr);
1050   ierr = PetscMalloc1(PetscMax(mfqP->m,mfqP->n),&mfqP->indices);CHKERRQ(ierr);
1051   ierr = PetscMalloc1(mfqP->n,&mfqP->iwork);CHKERRQ(ierr);
1052   ierr = PetscMalloc1(mfqP->m*mfqP->m,&mfqP->w);CHKERRQ(ierr);
1053   for (i=0;i<mfqP->m;i++) {
1054     for (j=0;j<mfqP->m;j++) {
1055       if (i==j) {
1056         mfqP->w[i+mfqP->m*j]=1.0;
1057       } else {
1058         mfqP->w[i+mfqP->m*j]=0.0;
1059       }
1060     }
1061   }
1062   for (i=0;i<PetscMax(mfqP->m,mfqP->n);i++) {
1063     mfqP->indices[i] = i;
1064   }
1065   ierr = MPI_Comm_size(((PetscObject)tao)->comm,&mfqP->size);CHKERRQ(ierr);
1066   if (mfqP->size > 1) {
1067     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localx);CHKERRQ(ierr);
1068     VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->localxmin);CHKERRQ(ierr);
1069     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localf);CHKERRQ(ierr);
1070     VecCreateSeq(PETSC_COMM_SELF,mfqP->m,&mfqP->localfmin);CHKERRQ(ierr);
1071     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxloc);CHKERRQ(ierr);
1072     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->n,0,1,&isxglob);CHKERRQ(ierr);
1073     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfloc);CHKERRQ(ierr);
1074     ierr = ISCreateStride(MPI_COMM_SELF,mfqP->m,0,1,&isfglob);CHKERRQ(ierr);
1075 
1076 
1077     ierr = VecScatterCreate(tao->solution,isxglob,mfqP->localx,isxloc,&mfqP->scatterx);CHKERRQ(ierr);
1078     ierr = VecScatterCreate(tao->sep_objective,isfglob,mfqP->localf,isfloc,&mfqP->scatterf);CHKERRQ(ierr);
1079 
1080     ierr = ISDestroy(&isxloc);CHKERRQ(ierr);
1081     ierr = ISDestroy(&isxglob);CHKERRQ(ierr);
1082     ierr = ISDestroy(&isfloc);CHKERRQ(ierr);
1083     ierr = ISDestroy(&isfglob);CHKERRQ(ierr);
1084   }
1085 
1086   if (!mfqP->usegqt) {
1087     KSP       ksp;
1088     PC        pc;
1089     ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Xsubproblem,&mfqP->subx);CHKERRQ(ierr);
1090     ierr = VecCreateSeq(PETSC_COMM_SELF,mfqP->n,&mfqP->subxl);CHKERRQ(ierr);
1091     ierr = VecDuplicate(mfqP->subxl,&mfqP->subb);CHKERRQ(ierr);
1092     ierr = VecDuplicate(mfqP->subxl,&mfqP->subxu);CHKERRQ(ierr);
1093     ierr = VecDuplicate(mfqP->subxl,&mfqP->subpdel);CHKERRQ(ierr);
1094     ierr = VecDuplicate(mfqP->subxl,&mfqP->subndel);CHKERRQ(ierr);
1095     ierr = TaoCreate(PETSC_COMM_SELF,&mfqP->subtao);CHKERRQ(ierr);
1096     ierr = TaoSetType(mfqP->subtao,TAOTRON);CHKERRQ(ierr);
1097     ierr = TaoSetOptionsPrefix(mfqP->subtao,"pounders_subsolver_");CHKERRQ(ierr);
1098     ierr = TaoSetInitialVector(mfqP->subtao,mfqP->subx);CHKERRQ(ierr);
1099     ierr = TaoSetObjectiveAndGradientRoutine(mfqP->subtao,pounders_fg,(void*)mfqP);CHKERRQ(ierr);
1100     ierr = TaoSetMaximumIterations(mfqP->subtao,mfqP->gqt_maxits);CHKERRQ(ierr);
1101     ierr = TaoSetFromOptions(mfqP->subtao);CHKERRQ(ierr);
1102     ierr = TaoGetKSP(mfqP->subtao,&ksp);CHKERRQ(ierr);
1103     if (ksp) {
1104       ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
1105       ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
1106     }
1107     ierr = TaoSetVariableBounds(mfqP->subtao,mfqP->subxl,mfqP->subxu);CHKERRQ(ierr);
1108     ierr = MatCreateSeqDense(PETSC_COMM_SELF,mfqP->n,mfqP->n,mfqP->Hres,&mfqP->subH);CHKERRQ(ierr);
1109     ierr = TaoSetHessianRoutine(mfqP->subtao,mfqP->subH,mfqP->subH,pounders_h,(void*)mfqP);CHKERRQ(ierr);
1110   }
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 static PetscErrorCode TaoDestroy_POUNDERS(Tao tao)
1115 {
1116   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1117   PetscInt       i;
1118   PetscErrorCode ierr;
1119 
1120   PetscFunctionBegin;
1121   if (!mfqP->usegqt) {
1122     ierr = TaoDestroy(&mfqP->subtao);CHKERRQ(ierr);
1123     ierr = VecDestroy(&mfqP->subx);CHKERRQ(ierr);
1124     ierr = VecDestroy(&mfqP->subxl);CHKERRQ(ierr);
1125     ierr = VecDestroy(&mfqP->subxu);CHKERRQ(ierr);
1126     ierr = VecDestroy(&mfqP->subb);CHKERRQ(ierr);
1127     ierr = VecDestroy(&mfqP->subpdel);CHKERRQ(ierr);
1128     ierr = VecDestroy(&mfqP->subndel);CHKERRQ(ierr);
1129     ierr = MatDestroy(&mfqP->subH);CHKERRQ(ierr);
1130   }
1131   ierr = PetscFree(mfqP->Fres);CHKERRQ(ierr);
1132   ierr = PetscFree(mfqP->RES);CHKERRQ(ierr);
1133   ierr = PetscFree(mfqP->work);CHKERRQ(ierr);
1134   ierr = PetscFree(mfqP->work2);CHKERRQ(ierr);
1135   ierr = PetscFree(mfqP->work3);CHKERRQ(ierr);
1136   ierr = PetscFree(mfqP->mwork);CHKERRQ(ierr);
1137   ierr = PetscFree(mfqP->omega);CHKERRQ(ierr);
1138   ierr = PetscFree(mfqP->beta);CHKERRQ(ierr);
1139   ierr = PetscFree(mfqP->alpha);CHKERRQ(ierr);
1140   ierr = PetscFree(mfqP->H);CHKERRQ(ierr);
1141   ierr = PetscFree(mfqP->Q);CHKERRQ(ierr);
1142   ierr = PetscFree(mfqP->Q_tmp);CHKERRQ(ierr);
1143   ierr = PetscFree(mfqP->L);CHKERRQ(ierr);
1144   ierr = PetscFree(mfqP->L_tmp);CHKERRQ(ierr);
1145   ierr = PetscFree(mfqP->L_save);CHKERRQ(ierr);
1146   ierr = PetscFree(mfqP->N);CHKERRQ(ierr);
1147   ierr = PetscFree(mfqP->M);CHKERRQ(ierr);
1148   ierr = PetscFree(mfqP->Z);CHKERRQ(ierr);
1149   ierr = PetscFree(mfqP->tau);CHKERRQ(ierr);
1150   ierr = PetscFree(mfqP->tau_tmp);CHKERRQ(ierr);
1151   ierr = PetscFree(mfqP->npmaxwork);CHKERRQ(ierr);
1152   ierr = PetscFree(mfqP->npmaxiwork);CHKERRQ(ierr);
1153   ierr = PetscFree(mfqP->xmin);CHKERRQ(ierr);
1154   ierr = PetscFree(mfqP->C);CHKERRQ(ierr);
1155   ierr = PetscFree(mfqP->Fdiff);CHKERRQ(ierr);
1156   ierr = PetscFree(mfqP->Disp);CHKERRQ(ierr);
1157   ierr = PetscFree(mfqP->Gres);CHKERRQ(ierr);
1158   ierr = PetscFree(mfqP->Hres);CHKERRQ(ierr);
1159   ierr = PetscFree(mfqP->Gpoints);CHKERRQ(ierr);
1160   ierr = PetscFree(mfqP->model_indices);CHKERRQ(ierr);
1161   ierr = PetscFree(mfqP->last_model_indices);CHKERRQ(ierr);
1162   ierr = PetscFree(mfqP->Xsubproblem);CHKERRQ(ierr);
1163   ierr = PetscFree(mfqP->Gdel);CHKERRQ(ierr);
1164   ierr = PetscFree(mfqP->Hdel);CHKERRQ(ierr);
1165   ierr = PetscFree(mfqP->indices);CHKERRQ(ierr);
1166   ierr = PetscFree(mfqP->iwork);CHKERRQ(ierr);
1167   ierr = PetscFree(mfqP->w);CHKERRQ(ierr);
1168   for (i=0;i<mfqP->nHist;i++) {
1169     ierr = VecDestroy(&mfqP->Xhist[i]);CHKERRQ(ierr);
1170     ierr = VecDestroy(&mfqP->Fhist[i]);CHKERRQ(ierr);
1171   }
1172   ierr = VecDestroy(&mfqP->workxvec);CHKERRQ(ierr);
1173   ierr = VecDestroy(&mfqP->workfvec);CHKERRQ(ierr);
1174   ierr = PetscFree(mfqP->Xhist);CHKERRQ(ierr);
1175   ierr = PetscFree(mfqP->Fhist);CHKERRQ(ierr);
1176 
1177   if (mfqP->size > 1) {
1178     ierr = VecDestroy(&mfqP->localx);CHKERRQ(ierr);
1179     ierr = VecDestroy(&mfqP->localxmin);CHKERRQ(ierr);
1180     ierr = VecDestroy(&mfqP->localf);CHKERRQ(ierr);
1181     ierr = VecDestroy(&mfqP->localfmin);CHKERRQ(ierr);
1182   }
1183   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1184   PetscFunctionReturn(0);
1185 }
1186 
1187 static PetscErrorCode TaoSetFromOptions_POUNDERS(PetscOptionItems *PetscOptionsObject,Tao tao)
1188 {
1189   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1190   PetscErrorCode ierr;
1191 
1192   PetscFunctionBegin;
1193   ierr = PetscOptionsHead(PetscOptionsObject,"POUNDERS method for least-squares optimization");CHKERRQ(ierr);
1194   ierr = PetscOptionsReal("-tao_pounders_delta","initial delta","",mfqP->delta,&mfqP->delta0,NULL);CHKERRQ(ierr);
1195   mfqP->delta = mfqP->delta0;
1196   mfqP->npmax = PETSC_DEFAULT;
1197   ierr = PetscOptionsInt("-tao_pounders_npmax","max number of points in model","",mfqP->npmax,&mfqP->npmax,NULL);CHKERRQ(ierr);
1198   mfqP->usegqt = PETSC_FALSE;
1199   ierr = PetscOptionsBool("-tao_pounders_gqt","use gqt algorithm for subproblem","",mfqP->usegqt,&mfqP->usegqt,NULL);CHKERRQ(ierr);
1200   ierr = PetscOptionsTail();CHKERRQ(ierr);
1201   PetscFunctionReturn(0);
1202 }
1203 
1204 static PetscErrorCode TaoView_POUNDERS(Tao tao, PetscViewer viewer)
1205 {
1206   TAO_POUNDERS   *mfqP = (TAO_POUNDERS *)tao->data;
1207   PetscBool      isascii;
1208   PetscInt       nits;
1209   PetscErrorCode ierr;
1210 
1211   PetscFunctionBegin;
1212   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1213   if (isascii) {
1214     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1215     ierr = PetscViewerASCIIPrintf(viewer, "initial delta: %g\n",(double)mfqP->delta0);CHKERRQ(ierr);
1216     ierr = PetscViewerASCIIPrintf(viewer, "final delta: %g\n",(double)mfqP->delta);CHKERRQ(ierr);
1217     ierr = PetscViewerASCIIPrintf(viewer, "model points: %D\n",mfqP->nmodelpoints);CHKERRQ(ierr);
1218     if (mfqP->usegqt) {
1219       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: gqt\n");CHKERRQ(ierr);
1220     } else {
1221       ierr = PetscViewerASCIIPrintf(viewer, "subproblem solver: %s\n",((PetscObject)mfqP->subtao)->type_name);CHKERRQ(ierr);
1222       ierr = TaoGetTotalIterationNumber(mfqP->subtao,&nits);CHKERRQ(ierr);
1223       ierr = PetscViewerASCIIPrintf(viewer, "total subproblem iterations: %D\n",nits);CHKERRQ(ierr);
1224     }
1225     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1226   }
1227   PetscFunctionReturn(0);
1228 }
1229 /*MC
1230   TAOPOUNDERS - POUNDERS derivate-free model-based algorithm for nonlinear least squares
1231 
1232   Options Database Keys:
1233 + -tao_pounders_delta - initial step length
1234 . -tao_pounders_npmax - maximum number of points in model
1235 - -tao_pounders_gqt - use gqt algorithm for subproblem instead of TRON
1236 
1237   Level: beginner
1238 
1239 M*/
1240 
1241 PETSC_EXTERN PetscErrorCode TaoCreate_POUNDERS(Tao tao)
1242 {
1243   TAO_POUNDERS   *mfqP = (TAO_POUNDERS*)tao->data;
1244   PetscErrorCode ierr;
1245 
1246   PetscFunctionBegin;
1247   tao->ops->setup = TaoSetUp_POUNDERS;
1248   tao->ops->solve = TaoSolve_POUNDERS;
1249   tao->ops->view = TaoView_POUNDERS;
1250   tao->ops->setfromoptions = TaoSetFromOptions_POUNDERS;
1251   tao->ops->destroy = TaoDestroy_POUNDERS;
1252 
1253   ierr = PetscNewLog(tao,&mfqP);CHKERRQ(ierr);
1254   tao->data = (void*)mfqP;
1255   /* Override default settings (unless already changed) */
1256   if (!tao->max_it_changed) tao->max_it = 2000;
1257   if (!tao->max_funcs_changed) tao->max_funcs = 4000;
1258   mfqP->delta0 = 0.1;
1259   mfqP->delta = 0.1;
1260   mfqP->deltamax=1e3;
1261   mfqP->deltamin=1e-6;
1262   mfqP->c2 = 100.0;
1263   mfqP->theta1=1e-5;
1264   mfqP->theta2=1e-4;
1265   mfqP->gamma0=0.5;
1266   mfqP->gamma1=2.0;
1267   mfqP->eta0 = 0.0;
1268   mfqP->eta1 = 0.1;
1269   mfqP->gqt_rtol = 0.001;
1270   mfqP->gqt_maxits = 50;
1271   mfqP->workxvec = 0;
1272   PetscFunctionReturn(0);
1273 }
1274 
1275 
1276